CREST vs GOAT: A Comprehensive Comparison of Conformational Search Algorithms for Drug Discovery

Abstract

This article provides a detailed comparative analysis of two prominent conformational search algorithms, CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimization Algorithm), specifically tailored for researchers and professionals in computational chemistry and drug development. We explore the foundational principles underpinning each method, from CREST's reliance on metadynamics and genetic algorithms to GOAT's innovative, molecular dynamics-free approach. The analysis extends to practical application guidelines, troubleshooting common challenges, and a rigorous validation of performance across diverse molecular systems, including organic molecules, metal complexes, and nanoparticles. By synthesizing findings from recent literature, this work aims to serve as a definitive guide for scientists selecting and optimizing conformational search strategies to accelerate robust molecular design and discovery.

Understanding the Core Principles: CREST's Dynamics vs. GOAT's Direct Optimization

Conformational search, the process of identifying the three-dimensional structures a molecule can adopt, is a cornerstone of computational chemistry. It is vital for predicting molecular properties, understanding reaction mechanisms, and designing new drugs and materials. The global minimum energy structure and the ensemble of low-energy conformers directly influence a molecule's behavior, from its biological activity to its function in a material. This guide objectively compares two modern algorithms for conformational searching: the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT). We will examine their underlying methodologies, performance, and optimal applications, supported by experimental data and detailed protocols.

Algorithmic Foundations: A Tale of Two Strategies

CREST and GOAT employ fundamentally different strategies to explore the potential energy surface (PES) of molecules.

CREST: Metadynamics-Driven Exploration

CREST uses an iterative meta-dynamics (iMTD) approach to drive conformational sampling [1]. Its workflow can be summarized as follows:

• Initial Sampling: It performs molecular dynamics simulations with a bias potential that discourages the revisiting of already-sampled regions (Root Mean Square Deviation-bias) [1] [2].
• Genetic Z-Matrix Crossing: A unique "genetic" algorithm is used to combine different conformers, generating new candidate structures [1].
• Multilevel Optimization: The vast number of generated structures undergo a multi-step optimization and filtering process, first with crude thresholds and then with increasingly tighter ones, to produce a final ensemble of unique conformers within a specified energy window (default: 6 kcal/mol) [1].

GOAT: Basin-Hopping and Simulated Annealing

GOAT is a global optimizer inspired by basin-hopping and minima hopping algorithms [3] [4] [5]. Its core process is:

• Local Minimization: It starts by optimizing an initial guess to the nearest local minimum [3].
• Uphill Push and Barrier Crossing: From a minimum, it applies a "push" in a random direction, effectively moving uphill on the PES until a barrier is crossed [3] [6].
• Descent to New Minimum: The structure is then optimized to a new local minimum [3].
• Monte Carlo Selection: New conformers are accepted or rejected based on a Monte Carlo criterion with simulated annealing, efficiently exploring the low-energy landscape [3] [6]. This cycle repeats until no new low-energy conformers are found.

The diagram below illustrates the core logical workflow of the GOAT algorithm.

GOAT Algorithm Core Workflow

Performance Comparison: CREST vs. GOAT

Direct benchmarks provide critical insights into the relative strengths of these algorithms.

Performance Metrics and Benchmarking Data

The following table summarizes key performance characteristics based on published benchmarks [7] [6] [8].

Table 1: Comparative performance of CREST and GOAT.

Metric	CREST	GOAT
Sampling Exhaustiveness	Excellent coverage of conformer space [7]	Slightly more comprehensive coverage; better at finding global minima for complex systems [7] [6]
Computational Cost	High, requires many gradient calculations [7]	Generally lower, especially for large molecules; avoids long MD simulations [7] [4] [6]
Typical Speed	Baseline	~36x faster than CREST in one TS study; usually faster for large molecules [7] [6]
Strength: Organic Molecules	Excellent performance [6]	Better or very similar to CREST [6]
Strength: Organometallics/Clusters	Can fail for some complexes [6]	Superior performance; succeeds where others fail [4] [5] [6]
Underlying Method	GFN2-xTB (can be refined with DFT) [1] [8]	Any method in ORCA (XTB, DFT, etc.) [3] [4]

A benchmark study focusing on transition state conformer ensembles highlighted dramatic efficiency differences. racerTS was ~36x faster than CREST, which was in turn ~36x faster than GOAT, making CREST ~4100x faster than GOAT in this specific task [7]. However, this does not necessarily reflect performance for ground-state searches, where GOAT is often more efficient [6].

Validity and Low-Energy Accuracy

The ultimate test of a conformational search is the quality of its low-energy structures. When conformers generated by CREST and GOAT are refined with higher-level theories like Density Functional Theory (DFT), the results are telling.

• GOAT demonstrates high validity and very low median error (0.17 kcal/mol) in the low-energy region after DFT optimization [7].
• CREST ensembles, while extensive, often require DFT refinement. Studies note that many GFN2-xTB minima are "spurious" and coalesce upon DFT re-optimization, and the GFN2-xTB ranking of conformers can differ significantly from the DFT ranking [8]. A robust workflow is to use CREST for initial sampling, then re-optimize and re-rank the entire ensemble with a cost-effective DFT method like B97-3c before final refinement [8].

Practical Protocols and Workflows

Example Experiment: Generating a Conformer Ensemble

Objective: To find the low-energy conformational ensemble of a flexible drug-like molecule (e.g., the amino acid histidine) and calculate their Boltzmann-weighted properties.

Protocol 1: Using CREST

• Input: Prepare an initial 3D coordinate file (e.g., histidine.xyz).
• Command: Execute CREST from the command line. A typical command for a GFN2-xTB calculation with implicit solvation (water) using 4 CPU threads is: crest histidine.xyz --gfn2 --gbsa h2o -T 4 [1].
• Process: CREST runs its iMTD-GC workflow, which includes meta-dynamics runs, genetic crossing, and multi-level optimizations [1].
• Output: The main output file (crest_ensemble.xyz) contains all unique conformers within the energy window. The file crest_conformers.csv provides their relative energies and populations [1].

Protocol 2: Using GOAT

• Input: Prepare an ORCA input file (histidine_goat.inp) with the initial geometry in a * xyz block.
• Calculation Setup: The input file specifies the method and the GOAT task.
  [3]
• Process: GOAT performs a series of global iterations, where multiple workers run in parallel, each performing a series of local optimizations interspersed with random pushes [3].
• Output: GOAT prints the conformational ensemble with relative energies and a file containing all final structures [3].

Integrated Workflow for DFT-Quality Ensembles

For high-accuracy studies, a multi-step workflow that leverages the sampling power of these tools with the accuracy of DFT is recommended. The following diagram outlines a robust protocol based on a published tutorial review [8].

Workflow for DFT-Quality Conformer Ensembles

This workflow efficiently produces a high-quality, Boltzmann-weighted conformational ensemble suitable for predicting spectroscopic properties and accurate thermodynamic data [8].

The Scientist's Toolkit: Essential Research Reagents

This table details the key software and computational methods referenced in this guide and their functions.

Table 2: Essential computational tools for conformational search.

Tool / Method	Type	Primary Function	URL / Reference
CREST	Software Program	Conformational ensemble generation using iMTD-GC and GFN-xTB methods.	https://crest-lab.github.io/crest-docs/ [1]
ORCA	Software Program	Quantum chemistry package containing the GOAT algorithm and various DFT methods.	https://www.faccts.de/software/orca/ [3]
xTB (GFN2-xTB)	Semi-empirical QM Method	Fast, approximate quantum mechanical method used for sampling in CREST and GOAT.	https://xtb-docs.readthedocs.io/ [1]
B97-3c	Composite DFT Method	Cost-effective density functional theory method for re-optimizing and re-ranking large ensembles.	[8]
ωB97X-D4	Density Functional Method	High-accuracy DFT functional for final optimization and property calculation.	[8]
libpvol	Software Library	Calculates solvent-accessible volume for conformational sampling at high pressures in CREST.	[2]
IMD-0354	IMD-0354, CAS:978-62-1, MF:C15H8ClF6NO2, MW:383.67 g/mol	Chemical Reagent	Bench Chemicals
FR-188582	FR-188582, CAS:189699-82-9, MF:C16H13ClN2O2S, MW:332.8 g/mol	Chemical Reagent	Bench Chemicals

CREST and GOAT are powerful tools that have modernized conformational search. The choice between them depends on the specific research problem.

• CREST is a highly established and robust tool, particularly excellent for organic molecules and when a comprehensive, metadynamics-driven scan of the PES is desired. Its integration with the xTB suite makes it very accessible.
• GOAT generally offers greater efficiency, particularly for larger molecules and systems containing metals. Its ability to work with various quantum chemical methods within ORCA, including costlier DFT functionals, provides flexibility and can be a decisive advantage for challenging organometallic complexes and clusters [4] [5] [6].

For the highest accuracy, the output from either sampler should be considered a starting point for refinement with higher-level quantum chemical methods. The integrated workflow presented herein provides a path to generating conformational ensembles of DFT quality, which are essential for reliable predictions in drug design and materials science. As both algorithms continue to develop, they will further unlock the ability to model complex, flexible systems with high precision.

In computational chemistry and drug development, predicting the most stable three-dimensional structure of a molecule—its global minimum—is a fundamental challenge with significant implications for understanding molecular properties, reactivity, and biological activity. The potential energy surface (PES) of a flexible, drug-like molecule is extraordinarily complex, characterized by numerous local minima corresponding to different conformers. Traditional approaches to exploring this surface, often reliant on Molecular Dynamics (MD) and metadynamics, require millions of time-consuming gradient calculations, creating a computational bottleneck, especially when using accurate but costly quantum chemical methods like hybrid Density Functional Theory (DFT) [5] [6]. This guide objectively compares two modern algorithms for this task: the established CREST (Conformer-Rotamer Ensemble Sampling Tool) and the novel GOAT (Global Optimization Algorithm), which promises to find global minima without resorting to MD, thereby offering a new level of efficiency and compatibility with high-level theory [5] [3].

CREST (Conformer-Rotamer Ensemble Sampling Tool)

CREST, developed by the Grimme group, is a widely used state-of-the-art tool for conformational sampling. Its workflow leverages the GFN-xTB semi-empirical method for its speed, enabling extensive exploration [9] [10].

• Primary Workflow: CREST employs an iterative metadynamics approach. This method adds a repulsive bias potential to the PES, effectively "filling up" already-visited energy basins and pushing the simulation to explore new regions [3].
• Conformer Generation: It generates a vast ensemble of structures, which are then clustered and optimized. A key subsequent step is the use of CREGEN, a standalone program, to analyze the ensemble, remove duplicate structures, and identify unique conformers based on Root-Mean-Square Deviation (RMSD) and rotational constants [11].

GOAT (Global Optimization Algorithm)

GOAT, integrated into the ORCA software suite, introduces a different philosophy focused on avoiding MD and its associated computational cost [5] [3].

• Core Philosophy: GOAT is designed to work with any quantum chemical method, from fast semi-empirical approaches to costlier hybrid DFT, by reducing the number of required gradient calculations [5] [3].
• Primary Workflow: The algorithm is inspired by basin-hopping and minima hopping. It starts from an initial structure, optimizes it to the nearest local minimum, and then stochastically "pushes" the geometry uphill in a random direction until a barrier is crossed. After the barrier crossing, it performs a new geometry optimization to find a new minimum. This process is repeated, with new conformers accepted based on a Monte Carlo criterion with simulated annealing [6] [3].

The fundamental difference in their search logic is visualized in the following workflow diagrams.

Diagram Title: CREST Metadynamics Workflow

Diagram Title: GOAT Stochastic Basin-Hopping Workflow

Performance Comparison: Experimental Data and Benchmarks

The following tables summarize experimental data and benchmarks comparing GOAT and CREST across various molecular systems, as reported in the literature [5] [6].

Table 1: Performance Comparison on Organic Molecules and Metal Complexes

Molecular System	Performance of GOAT	Performance of CREST	Key Findings
Organic Molecules	Better or very similar in all but one case [6].	Outperformed by GOAT in most cases [6].	GOAT demonstrates high reliability for organic systems.
Organometallic Complexes	Better or similar in most cases [6].	Failed for three tested cases [6].	GOAT shows robustness for complex metal-containing systems.
Metal Complexes & Nanoparticles	Showcased accuracy [5].	Used as a benchmark for comparison [5].	GOAT succeeds in challenging cases where others cannot.

Table 2: Computational Efficiency and Method Flexibility

Aspect	GOAT	CREST
Underlying Method	Avoids Molecular Dynamics (MD) [5].	Relies on metadynamics/MD [3].
Gradient Calculations	Fewer required; avoids "millions of time-consuming" calculations [5].	Requires many gradient evaluations during MD sampling [5].
Speed (Small Molecules)	Slower than CREST [6].	Faster [6].
Speed (Large Molecules)	Usually considerably faster [6].	Slower due to extensive sampling [6].
Method Flexibility	Can be used with any quantum chemical method in ORCA, including hybrid DFT [5] [3].	Typically used with fast GFN-xTB methods for sampling [9] [10].

Detailed Experimental Protocols

Protocol for a GOAT Conformational Search

The following methodology is adapted from the ORCA documentation and relevant publications [5] [3].

• Input Preparation: A reasonable guess geometry of the molecule is required, provided in an XYZ coordinate format.
• ORCA Input Block: The calculation is set up using the !GOAT keyword, combined with a chosen electronic structure method (e.g., !XTB for GFN2-xTB, or !PBE0 for hybrid DFT). The %GOAT block can be used to fine-tune parameters.

• Parallelization: To speed up the calculation, the %PAL block is used to specify the number of parallel processes. GOAT uses a "worker" system where each worker runs independent optimizations.

• Output Analysis: Upon completion, GOAT outputs a file containing all unique conformers and their relative energies. The global minimum is the structure with the lowest energy, and the ensemble can be used to calculate Boltzmann-averaged properties.

Protocol for a CREST Conformational Search

This protocol is based on standard CREST usage, as described in datasets like GEOM and AQM [9] [12].

• Input Preparation: A 3D structure file (e.g., XYZ) of the molecule is needed.
• Command Line Execution: CREST is typically run from the command line, using the GFN2-xTB Hamiltonian as the default. An implicit solvent model can be added if needed.

• Sampling and Clustering: CREST performs its metadynamics-based sampling, generating thousands of structures. It then optimizes and clusters them.
• Post-Processing with CREGEN: The resulting conformational ensemble is analyzed using the cregen utility to remove duplicates and produce the final list of conformers based on RMSD and rotational constant criteria [11].

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key Software and Computational Tools for Conformational Search

Tool Name	Function/Brief Explanation	Relevant Algorithm
ORCA	A quantum chemistry package that integrates the GOAT algorithm for geometry optimization and ensemble generation [3].	GOAT
xTB (GFN1/2-xTB)	Fast semi-empirical quantum methods used for rapid geometry optimizations and preliminary sampling in both GOAT and CREST workflows [3] [10].	Both
CREST	A standalone program for conformational sampling and analysis based on metadynamics and GFN-xTB [9].	CREST
CREGEN	A Fortran program for sorting conformational ensembles and removing duplicates based on RMSD and rotational constants [11].	CREST
PRISM Pruner	A Python-based tool for screening and pruning conformer ensembles, offering an alternative to CREGEN with a rotamer-corrected RMSD metric [11].	Post-Processing
Hybrid DFT (e.g., PBE0)	Higher-accuracy quantum chemical methods used for final energy evaluation and refinement; more feasible with GOAT due to reduced optimization count [5] [9].	GOAT
ICG-001	ICG-001, CAS:780757-88-2, MF:C33H32N4O4, MW:548.6 g/mol	Chemical Reagent
lacto-N-fucopentaose II	lacto-N-fucopentaose II, CAS:21973-23-9, MF:C32H55NO25, MW:853.8 g/mol	Chemical Reagent

Discussion and Outlook

The comparative analysis reveals a clear trade-off. CREST is a mature, highly robust tool that excels at exhaustively mapping conformational landscapes, making it ideal for generating large ensembles for property calculation. However, its reliance on MD can be computationally prohibitive for large systems or when using high-level theory [5] [6].

GOAT presents a paradigm shift by eliminating the MD step. Its key advantage is computational efficiency for larger molecules and methodological flexibility, allowing researchers to use accurate DFT methods like PBE0 from the outset of a search [5]. While it may be slower for small molecules, its superior scaling and success in challenging cases involving metal complexes and nanoparticles make it a valuable addition to the computational chemist's toolbox [5] [6]. The choice between them depends on the research goal: CREST for comprehensive ensemble generation, and GOAT for a more direct and potentially cheaper path to the global minimum with high-level electronic structure theory.

The accurate and efficient identification of low-energy molecular conformations is a cornerstone of computational chemistry, with profound implications for drug design, material science, and catalyst development. This guide provides a comparative analysis of two prominent algorithms for this task: the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT). While both aim to explore molecular chemical space, their underlying philosophies and theoretical frameworks differ significantly. CREST, a well-established tool, leverages molecular dynamics and system-specific parameterization to navigate the potential energy surface (PES). In contrast, GOAT, a newer algorithm, employs a direct, meta-dynamics-free approach that offers greater flexibility in the choice of the underlying quantum chemical method. This article objectively compares their performance, methodologies, and ideal applications to guide researchers in selecting the appropriate tool for their conformational search challenges.

Theoretical Foundations and Algorithmic Philosophies

The core philosophies of CREST and GOAT lead to distinct algorithmic structures and exploration mechanisms.

CREST: Dynamics-Based Ensemble Sampling

CREST is an open-source program designed for the efficient and automated exploration of molecular chemical space. Its primary workflow, iMTD-GC, is based on meta-dynamics (MTD) and a genetic algorithm (GC) for structure crossing [1] [13]. The algorithm uses system-specific parameters derived from the initial structure to conduct a series of meta-dynamics simulations, which bias the exploration by adding repulsive potentials to previously visited regions on the PES. This helps the system escape local minima and explore new conformational states. The structures generated from these simulations are then optimized through a multi-level process (crude pre-optimization followed by optimization with tight thresholds) and subjected to a genetic-z algorithm (or structure crossing) that generates new candidate structures through combinatorial crossing of existing low-energy conformers [1]. CREST is intricately linked with the semi-empirical GFNn-xTB Hamiltonians and the GFN-FF force-field for the energy evaluations during the sampling process, although interfaces to other quantum chemistry software can be created [13].

GOAT: A Direct Global Optimization Approach

GOAT represents a different philosophical approach by entirely avoiding molecular dynamics simulations for its core search functionality [5] [4]. The algorithm operates by walking up the potential energy surface in random directions, detecting when a conformational barrier has been crossed, and then minimizing the energy of the new structure [6]. Newly found conformers are incorporated into an ensemble using a Monte-Carlo criteria with simulated annealing, and the process repeats until no new low-energy conformers are discovered [6]. A key theoretical advantage of this method is its decoupling from any specific quantum chemical method. Because it avoids the millions of gradient calculations typically required by long MD runs, GOAT can be practically used not only with fast semi-empirical methods but also with more costly electronic structure methods like hybrid Density Functional Theory (DFT) without becoming computationally prohibitive [5] [4]. This provides significant flexibility in the choice of the Potential Energy Surface (PES) for the search.

Table 1: Core Philosophical and Methodological Differences Between CREST and GOAT.

Feature	CREST	GOAT
Core Search Engine	Meta-Molecular Dynamics (MTD)	Direct PES walking and barrier detection
System-Dependent Parameters	Yes (e.g., MTD length from flexibility measure) [1]	Not specified in search results
Genetic Algorithm (Crossing)	Yes (Structure Crossing - GC) [1]	Not specified in search results
Primary Energy Method for Sampling	GFN-xTB methods (semi-empirical) [13]	Any QM method (e.g., GFN-xTB, hybrid DFT) [5]
Handling of Solvation	Implicit solvation models (e.g., GBSA) [1] [9]	Not specified in search results

Workflow Visualization

The following diagram illustrates the high-level logical workflows of both algorithms, highlighting their distinct exploration strategies.

Performance and Experimental Data

Comparative studies and benchmark tests indicate distinct performance profiles for CREST and GOAT across different molecular systems.

Accuracy and Efficiency Across Molecular Systems

Independent evaluations highlight that GOAT is generally "more efficient and accurate than previous algorithms in finding global minima" and succeeds in cases where others fail [5] [6]. A detailed comparison shows that for organic molecules, GOAT performs "better or very similar to CREST for all but one," and for organometallic complexes, it is "better or similar to CREST, except for three cases where CREST fails in some way" [6]. From an efficiency standpoint, the performance is size-dependent; for small molecules, GOAT is "a bit slower than CREST, but for large molecules GOAT is usually considerably faster" [6]. This suggests that GOAT's avoidance of long MD runs, which require millions of energy and gradient calculations, provides a scalability advantage for larger, more complex systems [5].

Case Study: Conformational Search for Diclofenac

A practical example of a GOAT calculation is provided in the ORCA documentation, where it was used to find the global minimum conformation of the drug molecule Diclofenac starting from its PubChem structure [14]. Using the GFN2-xTB method, GOAT identified 17 unique conformers. The output showed that the conformational space was dominated by two low-energy conformers, which together accounted for 90.1% of the total population at 298.15 K. The calculation also provided the conformational entropy (Sconf) and free energy (Gconf), demonstrating the algorithm's capability to generate thermochemical data for the ensemble [14]. This example illustrates a typical protocol for a GOAT calculation: start with an initial structure, specify the desired quantum chemical method (e.g., !GOAT XTB), and the algorithm returns the global minimum structure and the full ensemble with relative energies and weights.

Table 2: Comparative Performance Summary of CREST and GOAT.

System Type	CREST Performance	GOAT Performance	Key Evidence
Organic Molecules	State-of-the-art	Better or very similar in all but one case [6]	Comparative benchmark study [6]
Organometallic Complexes	Can fail in certain cases [6]	Better or similar; succeeds where CREST fails [5] [6]	Comparative benchmark study [5] [6]
Computational Speed (Small Molecules)	Faster [6]	A bit slower [6]	Runtime comparison [6]
Computational Speed (Large Molecules)	Slower for large systems	Considerably faster [6]	Runtime comparison [6]
Method Flexibility	Tied to GFN-xTB for sampling [13]	Works with any QM method (e.g., hybrid DFT) [5]	Algorithm design principle [5] [4]

Detailed Experimental Protocols

To ensure reproducibility and provide a clear guide for researchers, this section outlines standard protocols for running conformational searches with both CREST and GOAT.

Protocol for a Standard CREST Conformational Search

The following protocol describes a standard production run using the iMTD-GC workflow in CREST, as exemplified for the alanine-glycine dipeptide [1].

• Initial Preparation: Obtain an initial guess for the molecular structure and save it in XYZ format (e.g., struc.xyz).
• Command Execution: Execute CREST from the command line. A typical command includes the input structure, the Hamiltonian for the calculation, solvation model (if needed), and computational resources.

• Algorithm Execution: The run proceeds automatically through these stages:
  • Initial Optimization: The input geometry is first optimized.
  • Flexibility Assessment: CREST calculates flexibility measures to determine the length of the subsequent meta-dynamics runs [1].
  • Meta-Dynamics Sampling: Multiple MTD simulations with different bias potentials are performed to explore conformational space.
  • Geometry Optimization and Clustering: Structures from the MTDs are collected and optimized through a multi-level process (crude then tight thresholds), followed by clustering based on RMSD.
  • Structure Crossing (GC): A genetic algorithm is used to generate new structures by combining parts of different low-energy conformers.
  • Final Ensemble Optimization: All unique structures are optimized with very tight thresholds to produce the final conformer ensemble.
• Output Analysis: The primary results are found in files like crest_rotamers.xyz (the ensemble) and the detailed output file, which lists relative energies, populations, and the origin of each conformer (e.g., from MTD or GC) [1].

Protocol for a GOAT Conformational Search in ORCA

This protocol is based on the example of finding the global minimum of Diclofenac using GOAT within the ORCA program suite [14].

• Initial Preparation: Obtain an initial guess for the molecular structure in XYZ format (e.g., diclofenac.xyz).
• Input File Creation: Create an ORCA input file (*.inp) with the following simple syntax:
  • !GOAT XTB invokes the GOAT algorithm using the GFN2-xTB method.
  • !PAL4 requests 4 processors for parallelization, recommended to speed up the numerous geometry optimizations.
• Calculation Execution: Run the calculation using the ORCA executable (e.g., orca diclofenac.inp > diclofenac.out).
• Output Analysis: Upon successful completion, GOAT generates:
  • diclofenac.globalminimum.xyz: The structure of the identified global minimum.
  • diclofenac.finalensemble.xyz: A file containing all unique conformers in the final ensemble.
  • The main output file contains a table with the relative energies (in kcal/mol), degeneracies, and Boltzmann populations for each conformer at a specified temperature, as well as the conformational entropy and free energy [14].

This section details the key software tools and computational methods that form the essential "reagents" for conducting conformational searches with CREST and GOAT.

Table 3: Essential Software and Methods for Conformational Searching.

Tool / Method	Function	Role in CREST/GOAT
GFN2-xTB	A semi-empirical quantum chemical method that provides a fast and reasonably accurate approximation of the PES.	Default energy method in CREST sampling [1]; A common, fast option for GOAT [14].
Hybrid DFT (e.g., PBE0)	A more accurate but computationally costlier quantum chemical method.	Not typically used in CREST's sampling phase due to cost [5]; Viable option for GOAT due to its efficient search [5] [4].
Implicit Solvation Models (GBSA/MPB)	Approximate the effect of a solvent environment without explicit solvent molecules.	Commonly used in CREST via --gbsa [1] [9]; Applicable in GOAT depending on the chosen QM method's capabilities.
CREST Program	The standalone program that implements the iMTD-GC workflow for conformational ensemble generation.	The main executable for running CREST searches [1] [13].
ORCA Program	An ab initio quantum chemistry package that contains a variety of modern electronic structure methods.	The main executable that houses the GOAT algorithm [14].
XYZ Coordinate File	A simple, plain-text format for specifying molecular structures by atomic symbols and Cartesian coordinates.	Standard input format for both CREST and GOAT [1] [14].

CREST and GOAT represent two powerful but philosophically divergent approaches to the global optimization problem in computational chemistry. CREST's strength lies in its sophisticated, dynamics-based sampling and structure-crossing, making it a robust and widely-tested tool, particularly when used with its native GFN-xTB methods. GOAT's innovative, direct search strategy offers a compelling advantage in terms of methodological flexibility, allowing researchers to use highly accurate quantum chemical methods like hybrid DFT from the outset. Performance benchmarks suggest that GOAT is particularly advantageous for larger molecules and challenging systems like organometallic complexes, where it can outperform CREST in both efficiency and success rate. The choice between them ultimately depends on the specific research problem: CREST remains an excellent tool for high-throughput screening with semi-empirical methods, while GOAT is a valuable addition for studies requiring high-level theory or dealing with complex systems where other algorithms struggle.

The Critical Role of the Potential Energy Surface (PES) in Both Algorithms

For researchers in computational chemistry and drug development, predicting the stable three-dimensional structures of a molecule is a fundamental challenge. The relationship between a molecule's structure and its energy is described by the Potential Energy Surface (PES), a multidimensional landscape where each point represents the energy of a specific atomic configuration. The low-energy minima on this surface correspond to the molecule's stable conformers, with the very lowest being the global minimum. The efficiency and accuracy of any conformational search algorithm are determined by its strategy for navigating this complex landscape. This guide objectively compares two modern algorithms, CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimization Algorithm), focusing on their distinct approaches to PES exploration, supported by experimental data and benchmarking studies.

Algorithmic Fundamentals and PES Exploration Strategies

The core task of a conformational search algorithm is to efficiently locate the low-energy minima on a molecule's PES. CREST and GOAT are both designed to solve this global optimization problem, but they employ fundamentally different strategies to accomplish it.

CREST: Metadynamics and Genetic Crossing

CREST (Conformer-Rotamer Ensemble Sampling Tool) utilizes a workflow known as iMTD-GC (iterative Meta-Molecular Dynamics with Genetic Crossing) [1]. Its methodology can be broken down as follows:

• Meta-Dynamics (MTD): CREST uses metadynamics to drive the molecule away from local energy minima. It adds a repulsive bias potential to the PES, effectively "filling up" visited minima and pushing the exploration into new, unexplored regions of the conformational space [1].
• Genetic Crossing (GC): After the MTD phase, CREST takes the collected structures and performs a "genetic crossing" step. This operation combines different structures to generate new candidate conformers, which are then optimized [1].
• Underlying Method: CREST is intrinsically linked to the semi-empirical GFNn-xTB methods, which provide the necessary speed for the extensive sampling required by the MTD approach [1].

GOAT: Basin-Hopping and Directed Uphill Moves

The GOAT algorithm, implemented in the ORCA software suite, is inspired by a combination of basin-hopping, minima hopping, simulated annealing, and taboo search algorithms [3] [6]. Its core strategy is distinct from metadynamics:

• Basin-Hopping and Uphill Moves: GOAT starts by optimizing an initial geometry to the nearest local minimum. From there, it does not rely on a bias potential. Instead, it directly perturbs the structure, making a random "uphill" move on the PES until a barrier is crossed. It then locates and optimizes the new minimum on the other side of that barrier [3].
• Stochastic Selection: Newly found conformers are accepted into the ensemble based on a Monte Carlo criterion with simulated annealing, which helps the search escape local funnels and progressively focus on the lowest-energy regions [6].
• Method Agnosticism: A key feature of GOAT is its independence from molecular dynamics (MD). This design allows it to be used with a wider range of underlying quantum chemical methods, from fast semi-empirical approaches like GFN2-xTB to more costly density functional theory (DFT) [5] [4].

The following diagram illustrates the core workflow differences between the two algorithms in their approach to navigating the PES.

Performance Comparison and Benchmarking Data

Independent benchmarking and the authors' own tests provide quantitative data on how these different strategies translate to performance in real-world scenarios. The following table summarizes key comparative findings.

Table 1: Performance Comparison of CREST vs. GOAT

Metric	CREST	GOAT	Experimental Context
Global Minima Finding (Organic Molecules)	Strong performance	Better or very similar in all but one case [6]	Benchmarking on various organic molecules [6]
Global Minima Finding (Organometallics)	Fails in some cases [6]	Better or similar; succeeds where CREST fails [6]	Testing on metal complexes and nanoparticles [6]
Computational Speed (Small Molecules)	Faster [6]	A bit slower [6]	Comparative benchmarking studies [6]
Computational Speed (Large Molecules)	Slower [6]	Usually considerably faster [6]	Comparative benchmarking studies [6]
Underlying PES Method	Tied to GFNn-xTB	Agnostic; works with XTB, DFT, etc. [3] [5]	Algorithm design specification [3] [5]
Core PES Exploration Mechanism	Metadynamics (iMTD) [1]	Basin-Hopping & Uphill Moves [3]	Algorithm design specification [3] [1]

Analysis of Comparative Data

The data indicates a nuanced performance landscape. For organic molecules, both algorithms are highly capable, with GOAT holding a slight edge in reliability. The most significant difference appears in the treatment of organometallic systems and metal clusters, where GOAT's method-agnostic nature allows it to succeed with systems where CREST may fail [6]. The speed comparison is size-dependent; while CREST is optimized for small molecules, GOAT's efficiency becomes more apparent as molecular size and flexibility increase [6].

Detailed Experimental Protocols

To ensure reproducibility and provide a clear understanding of how the benchmarking data is generated, this section outlines standard protocols for running and testing these algorithms.

Typical CREST Workflow Protocol

A standard CREST conformational search, as documented in its official examples, follows this protocol [1]:

• Input Preparation: An initial coordinate file (e.g., struc.xyz) is prepared.

• Command Execution: A typical command for a solvated calculation using 4 CPU threads is:

  Here, --gfn2 specifies the GFN2-xTB Hamiltonian, --gbsa h2o enables an implicit water solvation model, and -T 4 sets the number of threads.

• Algorithm Execution:
  • The initial structure is first optimized.
  • The flexibility is assessed to determine MTD parameters.
  • Multiple iterative MTD runs are performed to sample the PES.
  • Sampled structures are collected and optimized in a multi-level process.
  • A final genetic crossing (GC) step generates and optimizes new structures from the ensemble.
• Output: The primary output is a file (e.g., crest_conformers.xyz) containing the conformer ensemble within a specified energy window (default: 6 kcal/mol) [1].

Typical GOAT Workflow Protocol

A standard GOAT calculation within ORCA involves a different setup [3]:

• Input Preparation: The input is an ORCA block format, starting with a xyz block for molecular coordinates.
• Command Execution: A simple input file to run GOAT with GFN2-xTB would be:
  Options for the GOAT algorithm are controlled within a %GOAT block.
• Algorithm Execution:
  • A regular geometry optimization finds the nearest local minimum.
  • The number of GOAT iterations is computed and divided among parallel workers.
  • Each worker performs a series of geometry optimizations, each starting from a random uphill push from a known minimum.
  • Data is collected after each global cycle, and the process repeats until no new global minimum is found.
• Output: The output includes the global minimum geometry and a file with all unique conformer structures and their relative energies [3].

The Scientist's Toolkit: Essential Research Reagents

Successfully implementing these computational workflows requires a suite of software tools and resources. The following table lists key "research reagents" for scientists in this field.

Table 2: Essential Computational Tools for Conformational Sampling Research

Tool / Resource	Function	Role in CREST/GOAT Workflows
CREST	Conformer-Rotamer Ensemble Sampling Tool	The main executable for running the CREST algorithm [1].
ORCA	An ab initio quantum chemistry program	The software environment in which the GOAT algorithm is implemented [3].
xTB	Semi-empirical quantum chemistry program	Provides the fast GFNn-xTB methods that are central to CREST and commonly used with GOAT [3] [1].
DFT Codes (e.g., Gaussian)	Higher-accuracy electronic structure calculation	Used for final re-optimization and energy refinement of conformers identified by CREST or GOAT [15].
CONFPASS	Conformer prioritization for DFT re-optimization	A tool that post-processes a large conformer ensemble (e.g., from CREST) and prioritizes a subset for costly DFT calculations [15].
FlexiSol / AQM Dataset	Benchmark sets of flexible molecules with conformer ensembles	Used for validating and benchmarking the performance of conformational search algorithms against reliable data [16] [9].
Lamellarin E	Lamellarin E, CAS:115982-19-9, MF:C29H25NO9, MW:531.5 g/mol	Chemical Reagent
Galanthamine	Galanthamine Reagent	High-purity Galanthamine, a potent acetylcholinesterase (AChE) inhibitor and nAChR allosteric modulator. For research applications only. Not for human or veterinary use.

The critical role of the Potential Energy Surface is the common thread linking the CREST and GOAT algorithms, yet their navigation strategies define their respective strengths. CREST's metadynamics-based approach is a robust and highly efficient tool, particularly for organic molecules when used with its native GFN-xTB methods. GOAT's basin-hopping strategy offers distinct advantages in challenging use cases, including organometallic complexes and larger, flexible drug-like molecules, while its method agnosticism provides flexibility in selecting the appropriate level of theory for the PES.

For researchers, the choice is not necessarily about which algorithm is universally superior, but which is most appropriate for their specific system and research question. CREST remains a powerful default for organic systems, while GOAT presents itself as a compelling alternative for metalloenzymes, metal-based catalysts, and large-scale virtual screening where computational efficiency and reliability are paramount. The ongoing development of benchmark sets like FlexiSol and AQM will continue to drive improvements in both algorithms, further refining our ability to map the complex energy landscapes of molecular systems.

Practical Implementation: Applying CREST and GOAT to Real-World Molecular Systems

Step-by-Step Workflow for a Standard CREST Calculation

Conformational ensemble sampling is a cornerstone of computational chemistry, essential for accurately predicting molecular properties, reactivity, and spectroscopic behavior. Two prominent automated tools for this task are CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimizer Algorithm), which employ fundamentally different strategies to explore molecular chemical space [17] [3]. CREST, developed by the Grimme group, utilizes metadynamics simulations biased with quantum chemically derived forces to drive conformational crossing, efficiently probing the potential energy surface [17] [18]. In contrast, GOAT, integrated within the ORCA package, uses a stochastic basin-hopping approach that combines random "uphill" moves to cross barriers followed by geometry optimizations to find new minima, without requiring metadynamics [3]. This guide provides a detailed, step-by-step workflow for performing a standard CREST calculation, objectively compares its performance and methodology against GOAT, and presents experimental data to inform researchers and drug development professionals in their selection of conformational search tools.

CREST Workflow: A Step-by-Step Protocol

Preparation and Input

A standard CREST calculation requires only a reasonable starting geometry for the molecule of interest. The primary input file is a coordinate file in the XYZ format.

Step 1: Obtain a Starting Structure This can come from a database (e.g., PubChem), a previous quantum chemical optimization, or a hand-drawn model. CREST is robust to the initial structure, but a reasonable guess can speed up convergence.

Step 2: Run the Standard Command The most basic command to execute CREST with its default iMTD-GC (iterative Metadynamics with Genetic Cross-over) workflow is:

Here, input.xyz is your input coordinate file. CREST will automatically determine resource allocation, but for larger systems, you can specify the number of parallel processes with the -T flag (e.g., crest input.xyz -T 8) [18].

The Core iMTD-GC Algorithm in Detail

The default CREST workflow unfolds through several automated stages [17]:

• Initial Geometry Optimization: The input structure is first optimized using the GFNn-xTB semiempirical method.

• Iterative Metadynamics (iMTD): Multiple metadynamics simulations are launched from the current lowest-energy conformer. In these simulations, a history-dependent biasing potential (V\text{bias}) is applied: (V\text{bias} = \sum^ni ki \exp ( -\alpha \Deltai^2)) where the collective variables ((\Deltai)) are the Root-Mean-Square Deviations (RMSD) to previously visited minimum structures [17]. This potential penalizes the system for revisiting known regions of the PES, effectively pushing it over high energy barriers to discover new conformers. The simulation length is automatically determined by molecular flexibility.

• Multi-Level Geometry Filtering: Snapshots from the metadynamics trajectories are optimized through a three-step filtering process with progressively tighter convergence criteria and energy windows (15, 10, and 6 kcal/mol, respectively) to select low-energy structures.

• Genetic Z-Matrix Crossing (GC): To comprehensively sample rotamers, structural elements from different conformers are combined in internal coordinate (Z-matrix) space. A new structure is generated as: (R\text{new} = R\text{ref} + R{i} - R{j}) where (R{i}) and (R{j}) are parent structures [17]. The resulting structures are optimized and added to the ensemble.

• Iteration and Convergence: The algorithm is iterative. If a new conformer lower in energy than the initial one is found at any stage, the entire procedure restarts using this new global minimum. The calculation concludes when no new unique, low-energy conformers are discovered.

The following diagram illustrates this integrated workflow.

Output and Analysis

Upon successful completion, CREST generates several key output files:

• crest_conformers.xyz: The main output containing the entire sorted ensemble of non-identical conformers and rotamers.
• crest_best.xyz: The coordinates of the global minimum conformer.
• crest_energies: A file listing the relative energies of all conformers.

The ensemble can be analyzed with the built-in crest utility or the standalone CREGEN program to remove duplicate structures and rank conformers by energy [17] [19]. For integration into Python workflows, the PRISM Pruner tool offers an alternative for screening and pruning conformer ensembles, effectively removing redundant rotamers [19].

Comparative Analysis: CREST vs. GOAT

Methodological Comparison

Table 1: Fundamental methodological differences between CREST and GOAT.

Feature	CREST	GOAT (in ORCA)
Core Algorithm	Iterative Metadynamics (MTD) + Genetic Crossing (GC) [17]	Basin-hopping / Minima hopping [3]
Sampling Driver	History-dependent bias potential (RMSD-based) [17]	Random "uphill" displacements followed by optimization [3]
Key Innovation	Efficient crossing of high barriers via collective variable bias [17]	No metadynamics required; direct PES exploration [3]
Primary Input	XYZ coordinate file [18]	ORCA input block with XYZ coordinates [14]
Typical Resource Use	High (many short MD simulations) [17]	Lower number of gradient calculations [3]

Performance and Application Benchmarking

The theoretical differences translate into distinct practical performance profiles. CREST's iMTD-GC is designed for robust and comprehensive sampling, particularly for flexible molecules with complex energy landscapes, by using metadynamics to drive collective motions [17]. GOAT's strength lies in its directness and transferability; because it is not reliant on pre-defined collective variables and can use any quantum chemical method in ORCA, it is suitable for a wider range of theory levels, including DFT, not just fast semiempirical methods [3].

Table 2: Experimental performance and output comparison for a model system (Diclofenac).

Parameter	CREST (Documented Workflow)	GOAT (Documented Example [14])
System Studied	Flexible drug-like molecule (implicit)	Diclofenac (16 heavy atoms)
Theory Level	GFN2-xTB [17]	GFN2-xTB [14]
Conformers Found	Varies with system & settings	17 unique conformers
Dominant Conformer Population	Varies with system & settings	75.5%
Conformational Entropy (Sconf)	Calculated via iMTD-sMTD [17]	1.83 cal/(mol·K)
Conformational Free Energy (Gconf)	N/A	-0.17 kcal/mol
Key Output	Sorted ensemble, global minimum, protonation sites [17]	Sorted ensemble, global minimum, thermodynamic data [14]

A critical consideration is computational cost. CREST typically requires a large number of single-point energy and gradient calculations due to the nature of MD sampling, but these are very fast with the integrated GFN-xTB methods [17]. GOAT, in contrast, relies on a series of full geometry optimizations. While the number of these optimizations is generally lower than the number of CREST's MD steps, each one is more computationally intensive [3]. The total wall time is highly system-dependent, but GOAT's ability to be efficiently parallelized across many CPUs can significantly accelerate the process [3] [14].

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key software tools and resources for conformational ensemble studies.

Tool / Resource	Function	Role in Workflow
CREST	Primary conformer search engine	Generates initial ensembles using the iMTD-GC algorithm [17] [18].
xTB/tblite	Semiempirical quantum chemistry	Provides fast, accurate potentials for energy/force calculations in CREST [17] [18].
GOAT (ORCA)	Alternative search algorithm	Performs global optimization and ensemble generation using basin-hopping [3] [14].
CREGEN	Ensemble analysis & sorting	Filters, compares, and ranks conformers from CREST output based on RMSD and rot. constants [17] [19].
PRISM Pruner	Conformer ensemble screening	Prunes duplicate structures and redundant rotamers, useful for Python pipelines [19].
IKK 16	IKK 16, CAS:873225-46-8, MF:C28H29N5OS, MW:483.6 g/mol	Chemical Reagent
Deoxylapachol

Both CREST and GOAT represent state-of-the-art approaches to the conformational search problem, yet they cater to slightly different needs within the researcher's toolkit. CREST's iMTD-GC workflow offers a robust, highly automated, and systematically thorough sampling method, making it an excellent choice for standard applications, especially when using its native GFN-xTB methods. Its ability to find low-lying conformers "more efficiently and more safely" is well-documented [17]. GOAT provides a compelling alternative with a simpler algorithmic foundation, potentially lower computational cost in terms of the number of optimizations, and unique compatibility with high-level ab initio methods available in ORCA [3].

The choice between them should be guided by the specific research problem. For high-throughput screening of drug-sized molecules where comprehensive sampling at a fast semiempirical level is key, CREST is a powerful default. For studies requiring conformational ensembles at higher levels of theory (e.g., DFT) or for integration into existing ORCA-based workflows, GOAT presents a streamlined and efficient path. Ultimately, this comparison underscores that the field of automated chemical space exploration is advancing on multiple fronts, providing scientists with multiple validated tools to tackle the complexity of molecular conformations.

Table of Contents

• Introduction
• Methodological Comparison
• Performance Benchmarks
• Computational Protocols
• Research Toolkit
• Workflow Diagrams
• Conclusion

The accurate identification of global minimum energy conformations and comprehensive conformational ensembles is a cornerstone of computational chemistry, with direct implications for drug design, material science, and catalyst development. Two advanced algorithms have emerged as powerful tools for this task: the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT). CREST, developed by Grimme's group, employs a multi-level approach combining metadynamics, molecular dynamics (MD), and genetic algorithms for conformational sampling. In contrast, GOAT represents a paradigm shift by achieving global optimization without relying on molecular dynamics, instead utilizing a sophisticated search methodology that directly navigates the potential energy surface (PES). This comparative analysis examines the fundamental methodologies, performance characteristics, and practical implementation parameters of both algorithms to guide researchers in selecting and configuring the appropriate tool for their computational chemistry workflows.

Methodological Comparison

Fundamental Approaches and Underlying Theories

• CREST Methodology: CREST operates through a multi-algorithmic framework that integrates root-mean-square deviation (RMSD) based metadynamics, short regular MD simulations, and Genetic Z-matrix crossing (GC) algorithms [20]. This combined approach enables thorough exploration of conformational space by systematically breaking and reforming bonds, rotating dihedral angles, and perturbing molecular geometries. The tool can utilize various levels of theory including molecular mechanics and semiempirical methods (particularly GFNn-xTB methods) in both gas phase and implicit solvent environments, providing flexibility for different research applications and computational budgets.

• GOAT Methodology: GOAT implements a distinct global optimization strategy that completely avoids molecular dynamics simulations, thereby circumventing the need for millions of time-consuming gradient calculations typically required by lengthy MD runs [5] [4]. This fundamental architectural difference allows GOAT to function efficiently with any quantum chemical method, including computationally expensive hybrid Density Functional Theory (DFT) functionals. The algorithm's sophisticated search mechanism enables precise navigation of complex potential energy surfaces, making it particularly effective for challenging systems where traditional methods might struggle with kinetic traps or local minima convergence.

Key Differentiating Factors

The core distinction between these algorithms lies in their fundamental approach to conformational space exploration. CREST's MD-based approach provides extensive sampling through simulated thermodynamic processes, while GOAT's direct optimization strategy offers a more targeted search of the energy landscape. This methodological divergence leads to significant differences in computational requirements, performance characteristics, and optimal application domains. CREST has established itself as a versatile tool for various conformational analysis tasks, including protonation state sampling, tautomerism studies, and non-covalent complex modeling [20]. GOAT demonstrates particular strength in locating global minima with high precision across diverse molecular systems, from organic molecules to metal clusters and nanoparticles [5].

Performance Benchmarks

Computational Efficiency and Accuracy

Table 1: Performance Comparison of Conformer Generator Tools

Metric	CREST	GOAT	racerTS
Relative Speed	1x (baseline)	~114x slower	36x faster
Low-energy Region Accuracy	Comprehensive	Most comprehensive	Sufficient (median error 0.17 kcal/mol)
Sampling Exhaustiveness	High	Slightly higher than CREST	Similar to CREST
DFT-optimized TS Validity	Good	Not specified	Better

Recent benchmarking studies against 20 diverse reaction systems reveal striking differences in computational efficiency between these algorithms [7]. The data demonstrates that while GOAT provides slightly more comprehensive conformational space coverage compared to CREST, this comes at a substantial computational cost—approximately 114 times slower than CREST in direct comparisons. This efficiency differential becomes particularly pronounced for larger molecular systems or when using higher levels of electronic structure theory.

Application-Specific Performance

Table 2: Algorithm Performance Across Different Molecular Systems

System Type	CREST Performance	GOAT Performance
Organic Molecules	Reliable	Excellent
Water Clusters	Effective	Accurate
Metal Complexes	Good	Superior
Metal Nanoparticles	Challenging	Successful
Challenging PES	May struggle	Succeeds where others fail

Both algorithms demonstrate robust performance across diverse molecular systems, but with notable differences in specific domains [5]. CREST reliably handles organic molecules and water clusters with established accuracy, while GOAT shows particular strength in more challenging systems including metal complexes and nanoparticles. The free choice of potential energy surface in GOAT contributes to its success in cases where other algorithms encounter difficulties, particularly for systems with complex, multi-modal energy landscapes or subtle conformational preferences.

Computational Protocols

CREST Configuration Parameters

Basic Single-Point Energy Calculation:

This command executes CREST using GFN2-xTB Hamiltonian on 24 processor cores, directing output to struc.out [20]. The -gfn2 flag specifies the semiempirical method, while -T controls parallel processing.

Solvated System Configuration:

This implementation adds implicit solvation using the GBSA model for water via the -g h2o parameter [20]. CREST supports various implicit solvent models for different research applications.

RMSD Calculation Protocol:

This utility command calculates Cartesian RMSD between two structures, printing only the numerical result for scripting purposes [21]. The RMSD is always returned in Ångströms regardless of input file format.

GOAT Implementation Framework

GOAT operates without molecular dynamics, eliminating the need for numerous gradient calculations [5]. This architectural advantage permits compatibility with any quantum chemical method, including hybrid DFT functionals that would be prohibitively expensive for MD-based approaches. While specific command-line implementations for GOAT are not detailed in the available literature, its theoretical framework emphasizes:

• Method Agnosticism: Compatibility with various quantum chemical methods without algorithmic modifications
• Direct Optimization: Targeted search of the potential energy surface without MD preconditioning
• Flexible Initialization: Capacity to start from diverse initial structures without trajectory-dependent biases

Research Toolkit

Table 3: Essential Research Reagents and Computational Solutions

Resource	Function	Application Context
GFNn-xTB Methods	Semiempirical electronic structure	CREST default PES evaluation
Hybrid DFT	High-accuracy energy calculations	GOAT-compatible quantum chemistry
GBSA Models	Implicit solvation treatment	Solvated system simulations
DFT Optimization	Structure refinement	Post-processing of CREST/GOAT outputs
RMSD Analysis	Structural similarity quantification	Conformer ensemble comparison
GANT 61	GANT 61, CAS:500579-04-4, MF:C27H35N5, MW:429.6 g/mol	Chemical Reagent
Lentinan	Lentinan, CAS:37339-90-5, MF:C42H72O36, MW:1153.0 g/mol	Chemical Reagent

Post-Processing Workflows

For both CREST and GOAT, computational protocols strongly recommend further optimization of obtained geometries using more accurate methods [20]. A typical workflow involves:

• Ensemble Generation: Producing conformational ensembles with CREST or GOAT
• Structure Separation: Splitting ensemble outputs into individual geometries
• Higher-Level Optimization: Refining structures with advanced DFT methods
• Ensemble Recombination: Merging optimized structures for analysis
• Duplicate Removal: Eliminating redundant conformers using RMSD criteria
• Energy Ranking: Sorting structures by energy for property analysis

This multi-level approach leverages the sampling efficiency of semiempirical methods with the accuracy of higher-level theory, providing reliable conformational ensembles for research applications.

Workflow Diagrams

The diagram illustrates the fundamental methodological differences between CREST and GOAT. CREST employs a multi-algorithm approach combining molecular dynamics, metadynamics, and genetic algorithms for conformational sampling [20]. In contrast, GOAT utilizes a direct potential energy surface search strategy that completely avoids molecular dynamics simulations [5]. This core architectural difference enables GOAT to function with any quantum chemical method but results in significantly different computational performance characteristics.

This decision tree provides guidance for researchers selecting between CREST and GOAT based on their specific research requirements. CREST is generally recommended for larger flexible molecules and budget-constrained projects due to its superior computational efficiency [7] [20]. GOAT demonstrates advantages for metal-containing systems and when the highest accuracy is paramount, though at significantly greater computational cost [5]. For small to medium-sized molecules, both algorithms represent viable options with complementary strengths.

CREST and GOAT represent sophisticated but philosophically distinct approaches to molecular conformational analysis. CREST delivers exceptional computational efficiency and practical utility for drug-like molecules and high-throughput applications, while GOAT offers potentially superior accuracy and methodological flexibility at substantially higher computational cost. The selection between these algorithms should be guided by specific research requirements, system characteristics, and computational resources. CREST remains the practical choice for most conventional drug discovery applications and large-scale virtual screening campaigns. GOAT presents compelling advantages for challenging systems with complex potential energy surfaces and when using high-level quantum chemical methods is methodologically essential. As both algorithms continue to develop, their complementary strengths will further enable computational chemists to address increasingly complex molecular systems with growing accuracy and efficiency.

The accurate identification of global minimum energy structures is a cornerstone of computational chemistry, with direct implications for predicting molecular properties in drug design and materials science. Conformational search algorithms must navigate complex potential energy surfaces to find these structures efficiently. This guide provides an objective comparison of two prominent tools in this field: the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the newer Global Optimization Algorithm (GOAT). We focus on their performance across organic molecules, metal complexes, and water clusters, detailing methodologies and presenting available experimental data to inform researchers and drug development professionals.

The GOAT Algorithm

GOAT introduces a distinct approach to global optimization by eliminating the need for molecular dynamics (MD) simulations, which typically require millions of time-consuming gradient calculations [5]. Its workflow can be summarized as follows:

• Initialization: The algorithm begins from a given molecular structure.
• Random Direction Walk: The structure is perturbed by "walking up" in a random direction on the potential energy surface (PES) [6].
• Barrier Detection: The algorithm detects when a conformational barrier has been crossed.
• Energy Minimization: The energy of the new structure is minimized [6].
• Conformer Identification: The algorithm decides if a new conformer has been found.
• Ensemble Update: New conformers are incorporated into the ensemble based on a Monte Carlo selection criteria, which utilizes simulated annealing to efficiently navigate the PES [6].

A key feature of GOAT is its flexibility; it can be used with any quantum chemical method, including computationally expensive hybrid Density Functional Theory (DFT), to describe the PES [5].

The following diagram illustrates the core iterative workflow of the GOAT algorithm:

The CREST Algorithm

CREST (Conformer-Rotamer Ensemble Sampling Tool) is a well-established state-of-the-art method. It relies on metadynamics-based conformer sampling using the GFN1-xTB method, followed by further refinement [22]. Its core philosophy differs from GOAT, as it utilizes molecular dynamics simulations to explore the potential energy surface, which involves numerous gradient calculations and can be a limiting factor for large systems or high-level quantum methods [5].

Performance Comparison

Comparative Analysis on Diverse Molecular Systems

Independent evaluations and the authors' own testing have benchmarked GOAT against CREST across various chemical systems. The table below summarizes the key performance findings:

Table 1: Performance comparison of GOAT and CREST across different molecular systems

Molecular System	GOAT Performance	CREST Performance	Key Findings
Organic Molecules	Better or very similar for all but one molecule tested [6].	Inferior or similar for all but one molecule [6].	GOAT demonstrates high accuracy and reliability for organic species.
Organometallic Complexes	Better or similar performance [6].	Fails in at least three tested cases [6].	GOAT shows superior robustness for metal-containing systems.
General Systems	More efficient and accurate in finding global minima; succeeds in cases where others cannot [5].	Less efficient and accurate in direct comparison [5].	GOAT's avoidance of MD and free choice of PES are key advantages.
Computational Speed	Slower for small molecules, but usually considerably faster for large molecules [6].	Faster for small molecules, but slower for large molecules [6].	GOAT's efficiency scales favorably with system size.

The Critical Role of Conformational Sampling

The performance of any conformational search tool must be contextualized within the challenge of flexibility. As molecules grow in size and complexity, the number of possible conformers increases exponentially. Benchmark studies, such as those with the FlexiSol dataset, underscore that using a single gas-phase structure can introduce systematic biases when modeling solution-phase properties [16]. For accurate results, especially with drug-like, flexible molecules, exhaustive conformational sampling is essential [16]. Both GOAT and CREST are designed to provide this rigorous sampling, a prerequisite for reliable solvation energy and partition ratio predictions [16].

Essential Research Reagents and Computational Tools

To conduct and compare conformational search studies, researchers utilize a suite of software tools and methodologies. The table below details key resources mentioned in the context of this field.

Table 2: Key research reagents and computational tools for conformational search studies

Tool / Resource	Type	Function in Research
GOAT	Global Optimization Algorithm	Finds global energy minima for molecules and clusters without molecular dynamics [5].
CREST	Conformer Sampling Tool	Metadynamics-based algorithm for generating conformer-rotamer ensembles [22].
GFN1-xTB	Semi-empirical Quantum Method	Fast method used for initial conformer search and pre-optimization in workflows like CREST [22].
ORCA	Quantum Chemistry Package	Used for high-level energy calculations (e.g., DFT) in conjunction with search algorithms [22].
FlexiSol Benchmark Set	Data Set	A public benchmark for testing solvation models on flexible, drug-like molecules [16].
Hybrid DFT (e.g., B3LYP)	Quantum Chemical Method	Costly, high-accuracy method that can be practically used with GOAT for the PES [5].
MCTST (Multi-Conformer Transition State Theory)	Computational Workflow	A cost-efficient workflow for calculating reaction rates, involving conformer searches and quantum chemistry [22].

The comparative data indicates that GOAT represents a significant advance in global optimization algorithms for conformational searching. Its ability to outperform or match the state-of-the-art CREST tool across a wide range of organic and organometallic systems, while offering greater computational efficiency for large molecules, makes it a valuable addition to the computational chemistry toolbox [6]. The choice between GOAT and CREST may depend on the specific system under study. However, GOAT's unique methodology, which avoids molecular dynamics and allows for the use of high-level quantum chemical methods throughout the search, provides a powerful and sometimes more robust alternative for researchers, particularly in drug development where dealing with large, flexible molecules is common.

This guide provides an objective comparison of the performance between the CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimization Algorithm) algorithms for conformational search and global minimum optimization, with a focus on the challenging domain of metal complexes and nanoparticles.

The following tables summarize the key performance metrics and characteristics of CREST and GOAT when applied to complex systems.

Table 1: Quantitative Performance Overview

Feature	CREST	GOAT
Core Methodology	Iterative Metadynamics with Genetic Crossing (iMTD-GC) [1]	Barrier-crossing and ensemble refinement without Molecular Dynamics (MD) [4] [5]
Underlying Engine	Semi-empirical GFN methods (e.g., GFN2-xTB) [1]	Any quantum chemical method in ORCA (XTB, hybrid DFT, etc.) [4] [14]
Performance on Organic Molecules	State-of-the-art [6]	Better or very similar to CREST for all but one tested [6]
Performance on Organometallic Complexes	Fails in some cases [6]	Better or similar to CREST; succeeds where CREST fails [6]
Speed for Large Molecules	—	Usually considerably faster [6]
Gradient Calculations	Requires millions of time-consuming calculations in long MD runs [4]	Avoids millions of gradient calculations by skipping MD [4] [5]

Table 2: Qualitative Strengths and Limitations

Aspect	CREST	GOAT
Key Strengths	Robust, automated workflow with implicit solvation support [1]; Established state-of-the-art for organic molecules [6]	Free choice of Potential Energy Surface (PES) [4] [5]; High accuracy with costlier methods like hybrid DFT [4]; Valuable for large, flexible molecules [6]
Limitations / Challenges	Can fail for certain organometallic complexes [6]; Reliant on its internal GFN methods	A newer algorithm with a less established track record

Experimental Protocols and Workflows

CREST Protocol for Conformational Sampling

CREST employs the iMTD-GC workflow to explore the conformational landscape [1].

• Input Preparation: An initial 3D coordinate file (e.g., struc.xyz) is required.

• Command Execution: A typical command for a calculation with implicit solvation in water using 4 CPU threads is:

  This command specifies the GFN2-xTB Hamiltonian, a GBSA implicit solvation model for water, and parallelization [1].

• Workflow Steps:
  • Initial Optimization: The input geometry is first optimized [1].
  • Meta-MD Sampling: Multiple Meta-Molecular Dynamics (MTD) runs are performed to push the system over conformational barriers. The number and length of these runs are automatically determined based on a system flexibility measure [1].
  • Multilevel Optimization: Structures generated from MTD are crudely pre-optimized, then optimized with tighter thresholds [1].
  • Genetic Crossing (GC): Low-energy conformers are "crossed" to generate new, structurally distinct candidate geometries [1].
  • Final Ensemble Creation: All unique structures are optimized with very tight thresholds. The final output includes a ranked ensemble of conformers with their relative energies and Boltzmann weights [1].

The following diagram illustrates the logical workflow of a standard CREST calculation:

GOAT Protocol for Global Minimum Search

GOAT operates through a cycle of directed walks and local minimizations to locate the global energy minimum [6] [14].

• Input Preparation: An initial 3D coordinate file (e.g., inp.xyz) is required.
• Command Execution: A simple input block is used within an ORCA calculation file. Parallelization is recommended.
  This example uses the fast GFN2-xTB method, but any method in ORCA capable of geometry optimization can be specified (e.g., !GOAT B3LYP D3 def2-SVP) [14].
• Workflow Steps:
  • Initialization: The algorithm starts from the input structure [14].
  • Directed Walk and Barrier Detection: The system is walked up the potential energy surface in a random direction until a conformational barrier is crossed [6].
  • Local Energy Minimization: The geometry is minimized from that point [6].
  • Conformer Identification: The algorithm checks if this minimized structure is a new, unique conformer [6].
  • Ensemble Refinement: New conformers are added to the working ensemble based on a Monte Carlo criterion with simulated annealing, influencing the direction of subsequent walks [6].
  • Convergence: The process repeats until no new low-energy conformers are found [6].
  • Final Output: The calculation concludes by writing the global minimum structure (basename.globalminimum.xyz) and the full final ensemble (basename.finalensemble.xyz), including energies and Boltzmann weights [14].

The following diagram illustrates the core iterative cycle of the GOAT algorithm:

The Scientist's Toolkit

Table 3: Essential Research Reagent Solutions

Item	Function in Context
CREST	A conformer-rotamer ensemble sampling tool that uses GFN-xTB methods and iMTD-GC for robust, automated conformational sampling [1] [6].
GOAT	A global optimizer within ORCA that locates global minima without MD, compatible with a wide range of QM methods from XTB to hybrid DFT [4] [14].
GFN2-xTB	A fast semi-empirical quantum chemical method; the default engine for CREST and a common choice for initial GOAT searches to balance speed and accuracy [1] [14].
Implicit Solvation Models (e.g., GBSA)	Continuum solvation models that approximate solvent effects, crucial for modeling solution-phase conditions in both CREST and GOAT [1] [14].
Hybrid Density Functional Theory (DFT)	High-accuracy quantum chemical methods (e.g., B3LYP); can be directly used in GOAT for reliable results on metal complexes, but are computationally more expensive [4].
L-NABE	L-NABE, CAS:7672-27-7, MF:C13H19N5O4, MW:309.32 g/mol
Loroglossin	Loroglossin, CAS:58139-22-3, MF:C34H46O18, MW:742.7 g/mol

Guidelines for Algorithm Selection Based on Project Goals and System Characteristics

The identification of low-energy molecular conformations is a cornerstone problem in computational chemistry, with critical implications for drug discovery and materials science. [23] [24] The accuracy of downstream property predictions—from protein-ligand binding affinities to spectroscopic behaviors—depends fundamentally on the completeness and reliability of conformational ensembles. [3] Two advanced algorithms currently dominate this research landscape: the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT). [3] [4] This guide provides a structured framework for researchers to select between these tools based on specific project requirements, computational resources, and desired outcomes, supported by comparative experimental data.

Algorithmic Foundations and Methodologies

Understanding the core methodologies of CREST and GOAT is essential for appreciating their performance differences and appropriate application domains.

CREST: Metadynamics-Driven Sampling

CREST, developed by the Grimme group, employs a metadynamics-inspired approach to explore molecular potential energy surfaces (PES). [3] Its methodology can be summarized as follows:

• Initial Generation: Creates a diverse set of initial conformers through molecular dynamics (MD) simulations, often using fast semi-empirical methods like GFNn-xTB. [3]
• Ensemble Expansion: Systematically probes different conformers and rotamers by applying kinetic energy to rotatable bonds and ring systems.
• Metadynamics: Uses a history-dependent potential to push molecules out of local energy minima, ensuring broad coverage of the conformational landscape. [3] This approach requires millions of gradient calculations to achieve thorough sampling. [4]

GOAT: Stochastic Basin-Hopping

GOAT, implemented in the ORCA package, utilizes a stochastic global optimization strategy that avoids molecular dynamics. [3] [4] Its algorithm proceeds as:

• Basin Hopping: Starts from an initial geometry, optimizes to the nearest local minimum, then performs "uphill" moves in random directions to cross energy barriers. [3]
• Iterative Refinement: Repeatedly discovers new minima through cycles of perturbation and optimization.
• Ensemble Generation: Collects structures throughout the process, yielding both the global minimum and the conformational ensemble for Boltzmann-averaged property calculations. [3]

The fundamental workflow differences between these algorithms are visualized below:

Performance Comparison and Experimental Data

Direct comparisons between CREST and GOAT reveal significant differences in computational efficiency, accuracy, and resource requirements.

Quantitative Performance Metrics

Table 1: Comparative Performance Metrics for CREST vs. GOAT

Performance Metric	CREST	GOAT
Gradient Calculations	Millions required for thorough sampling [4]	~100× number of atoms (can be reduced to ~3×) [3]
Computational Cost	High (MD-based, many evaluations) [3]	Moderate (avoids MD, efficient parallelization) [3]
Parallelization Efficiency	Good (standard MD parallelization)	Excellent (multinode capable, parallel workers) [3]
Methodology	Metadynamics-driven [3]	Stochastic basin-hopping, taboo search [3]
Typical Applications	Organic molecules, drug-like compounds [24]	Organic molecules to metal clusters & nanoparticles [4]
Global Minimum Location	Reliable for molecular systems [3]	High accuracy, succeeds where others fail [4]

Resource Requirements and System Compatibility

Table 2: Computational Resource Requirements

Resource Factor	CREST	GOAT
Recommended Methods	Primarily GFNn-xTB (for efficiency) [3]	Any method from XTB to hybrid DFT [3] [4]
Hardware Demands	Significant for large systems	Adaptable to available resources
Scalability	Good for small to medium organic molecules	Excellent from clusters to nanoparticles [4]
Theoretical Level Flexibility	Limited to fast methods for practical sampling	High (works with costlier hybrid DFT) [4]

Experimental Protocols and Validation

To ensure reproducible results, researchers should follow standardized protocols when using either algorithm.

Standardized Benchmarking Protocol

System Preparation:

• Select a diverse set of test molecules with known conformational landscapes
• Include flexible drug-like molecules, macrocycles, and small proteins
• Ensure consistent initial geometry formatting across both algorithms

Parameter Settings:

• CREST: Use default settings with GFN2-xTB method
• GOAT: Employ 8 workers with temperature gradient (2904-363 K) [3]

Convergence Criteria:

• CREST: Monitor RMSD and energy criteria until new unique conformers cease to appear
• GOAT: Run minimum 3 global steps until energy difference between iterations is negligible [3]

Validation Metrics:

• Compare found global minimum energies against high-level theory benchmarks
• Calculate Boltzmann populations for thermodynamic properties
• Assess ensemble completeness using known crystallographic data

Research Reagent Solutions

Table 3: Essential Computational Tools for Conformational Search

Tool/Resource	Function	Application Context
GFNn-xTB Methods	Fast semi-empirical quantum mechanical method	Rapid sampling in CREST; initial screening in GOAT [3]
Hybrid DFT Functionals	High-accuracy electronic structure method	Final refinement in GOAT for challenging systems [4]
Boltzmann Weighting	Statistical mechanical population analysis	Thermodynamic property prediction from ensembles [3]
RMSD Filtering	Structural similarity metric (default: 0.125 Ã…)	Eliminating duplicate conformers [3]
Conformer Ensemble Database	Reference structural repositories	Validation against experimental data [24]

Decision Framework for Algorithm Selection

The choice between CREST and GOAT depends on multiple project-specific factors. The following diagram illustrates the key decision points:

Project-Specific Recommendations

Select GOAT when:

• The primary goal is locating the global energy minimum with high confidence [4]
• Systems contain transition metals or complex inorganic components [4]
• Project requires higher-level theory (hybrid DFT) for sufficient accuracy [4]
• Computational resources are limited relative to system size [3]

Choose CREST when:

• A complete conformational ensemble is needed for thermodynamic properties [24]
• Working with organic molecules and drug-like compounds [24]
• Extensive computational resources are available for metadynamics sampling [3]
• Semi-empirical methods provide sufficient accuracy for the research question [3]

Hybrid Approach: For critical projects, consider using both algorithms sequentially: GOAT for global minimum identification followed by CREST for comprehensive ensemble generation around the located minima.

CREST and GOAT represent complementary approaches to conformational searching, each with distinct strengths and optimal application domains. CREST excels at providing comprehensive conformational ensembles for organic molecular systems through its metadynamics-driven approach, while GOAT offers superior efficiency in global minimum location and can handle more diverse system types, including metal complexes and nanoparticles. [3] [4] The selection between these algorithms should be driven by specific project goals, system characteristics, and computational constraints rather than seeking a universally superior option. As both methods continue to evolve, researchers should periodically re-evaluate these guidelines against the latest benchmarking studies to inform their computational strategies for drug discovery and materials development.

Overcoming Computational Hurdles: Accuracy, Efficiency, and System-Specific Tuning

Conformational search, the process of identifying stable three-dimensional structures of a molecule, is a cornerstone of computational chemistry with critical applications in drug design and materials science. The computational cost of these searches, often driven by millions of energy and gradient calculations, is a major bottleneck. This guide objectively compares two algorithms for this task: the established CREST (Conformer-Rotamer Ensemble Sampling Tool) and the newer GOAT (Global Optimization Algorithm). The core of the comparison lies in their fundamental approaches to sampling molecular configurations: CREST relies on molecular dynamics (MD) and metadynamics, requiring extensive gradient calculations, while GOAT employs a strategy that avoids long MD runs, thereby significantly reducing the number of required gradient evaluations [6] [5].

Performance Comparison: CREST vs. GOAT

The following tables summarize the key operational and performance characteristics of CREST and GOAT based on current literature and documentation.

Table 1: Algorithmic Overview and Performance Profile

Feature	CREST	GOAT
Core Sampling Method	MD-based (iMTD-GC) [25] [26]	Non-MD global optimizer [5]
Primary Driver of Cost	Long MD/Metadynamics simulations [5]	Monte Carlo with simulated annealing [6]
Key Efficiency Claim	N/A	Avoids "millions of time-consuming gradient calculations" from long MD runs [5]
Typical Underlying Method	GFNn-xTB (semi-empirical) [26]	Any quantum chemical method, including hybrid DFT [14] [5]
Reported Performance vs. Alternative	Baseline	Better or similar to CREST for most organic molecules and organometallic complexes; faster for larger molecules [6]

Table 2: Experimental Performance on Benchmark Systems

System Category	CREST Performance	GOAT Performance
Organic Molecules	Standard performance [6]	Better or very similar to CREST for all but one organic molecule tested [6]
Organometallic Complexes	Can fail for some systems [6]	Better or similar to CREST; succeeds where CREST fails in some cases [6]
Computational Scaling	Efficient for small to medium systems	A bit slower for small molecules; usually considerably faster for large molecules [6]

Experimental Protocols and Workflows

Understanding the methodologies is key to interpreting their performance data.

CREST Conformational Search Protocol

CREST uses an iterative meta-dynamics and genetic algorithm (iMTD-GC) workflow powered by the semi-empirical GFNn-xTB family of methods to keep computational cost manageable [25] [26].

Detailed Workflow:

• Input Preparation: A reasonable starting geometry for the molecule is provided in a .xyz file.
• Command Execution: A typical command to run CREST with the GFN2-xTB method and implicit water solvation is: crest input.xyz --gfn2 --gbsa h2o --T 24 [26].
  • --gfn2 selects the GFN2-xTB Hamiltonian.
  • --gbsa h2o activates the implicit solvation model for water.
  • --T 24 specifies the use of 24 CPU threads.
• Sampling Steps: The algorithm performs:
  • Meta-dynamics (MTD): Adds a repulsive bias potential to visited areas of the potential energy surface, forcing the exploration of new conformers [25].
  • Genetic Z-Matrix Crossing (GC): Generates new structures by combining parts of different conformers' internal coordinates [25].
  • Geometry Optimization: All generated structures are optimized to the nearest local minimum.
• Output and Post-Processing: The result is an ensemble of conformers. It is considered best practice to refine these structures using more accurate levels of theory, such as density functional theory (DFT) [26].

GOAT Conformational Search Protocol

GOAT is a global optimizer integrated into the ORCA software package that does not rely on molecular dynamics. Its ability to function with costlier hybrid DFT methods is a direct consequence of its reduced need for gradient calculations [14] [5].

Detailed Workflow:

• Input Preparation: A starting geometry is provided in a .xyz file.
• Input File Configuration: An ORCA input file is created to invoke GOAT. The simplest setup uses the integrated GFN2-xTB method:
  Critically, GOAT can also use more accurate methods, such as: !GOAT B3LYP DEF2-SVP D3 to run the search with hybrid DFT [14] [5].
• Sampling Steps: The algorithm operates by:
  • Walking and Minimizing: It walks up from a known minimum in a random direction, detects when a conformational barrier is crossed, and then minimizes the energy of the new configuration [6].
  • Ensemble Expansion: New conformers are included in the ensemble based on a Monte Carlo criterion with simulated annealing [6].
• Output: The output includes the global minimum structure (.globalminimum.xyz) and the full ensemble of unique conformers (.finalensemble.xyz), complete with their relative energies and Boltzmann populations [14].

Workflow Visualization

The diagram below illustrates and contrasts the fundamental operational workflows of CREST and GOAT.

Visual Workflow Comparison: This diagram illustrates the core operational difference between CREST's MD-driven cycles and GOAT's minimization and Monte Carlo-based approach, which underlies their difference in computational cost.

The Scientist's Toolkit: Essential Research Reagents

This table details key software and methodological components referenced in the comparison.

Table 3: Essential Computational Tools and Methods

Tool/Method	Function Description	Relevance to CREST/GOAT
GFN2-xTB	A fast semi-empirical quantum chemical method for geometry optimization and energy calculation [14] [26].	The default or a commonly used level of theory in both CREST and GOAT for efficient sampling.
GFN-FF	A force field for molecules and materials; faster but less accurate than GFN2-xTB [25].	Can be used in CREST for even faster preliminary sampling.
CREGEN	A standalone tool for sorting conformer ensembles and removing duplicate structures based on geometry [25] [19].	Used in CREST and other workflows for post-search ensemble analysis.
Hybrid DFT (e.g., B3LYP)	A more accurate but computationally expensive quantum chemical method [27].	GOAT can use this directly for sampling, while it is typically a post-processing step for CREST ensembles.
Conformational Entropy	A thermodynamic property calculated from a Boltzmann-weighted ensemble of conformers.	The accurate construction of this ensemble is the ultimate goal of both algorithms [19] [14].
Licoagrochalcone B	Licoagrochalcone B|CAS 325144-67-0|RUO	Licoagrochalcone B is a retrochalcone flavonoid for research. Sourced from Glycyrrhiza glabra and Patrinia villosa. For Research Use Only. Not for human or veterinary use.
(R)-Sulforaphane	(R)-Sulforaphane, CAS:142825-10-3, MF:C6H11NOS2, MW:177.3 g/mol	Chemical Reagent

The experimental data and methodological comparison indicate a clear trade-off. CREST provides a robust, highly automated workflow that is efficient for a wide range of systems, but its reliance on MD-based sampling inherently requires a large number of gradient calculations. GOAT's novel non-MD approach directly addresses this computational cost, potentially offering greater efficiency, especially for larger molecules, and the unique flexibility to use more accurate quantum chemical methods like hybrid DFT directly in the search [6] [5]. The choice between them depends on the specific system, the desired level of theory, and the available computational resources. GOAT represents a significant step forward in reducing the cost of conformational searching, though CREST remains a powerful and widely-used benchmark in the field.

In computational chemistry, predicting the three-dimensional structure of a molecule or complex is fundamental to understanding its properties, reactivity, and interactions. The process of conformational search—finding the most stable (global minimum) geometries and all low-energy alternatives—is complicated by the complex, high-dimensional nature of potential energy surfaces (PES). The primary challenge lies in effectively navigating this surface to locate the global minimum while avoiding premature convergence to local minima, which are stable configurations that are not the most optimal.

Algorithms can become trapped in these local minima, leading to incorrect predictions of molecular structure and properties. This article provides a comparative analysis of two modern algorithms for conformational search: the established CREST (Conformer-Rotamer Ensemble Sampling Tool) and the newer GOAT (Global Optimization Algorithm). We evaluate their methodologies, performance, and robustness in managing the critical failures of convergence and local minima entrapment, providing researchers with data-driven insights for selecting appropriate tools.

Algorithmic Frameworks: Core Mechanisms and Workflows

Understanding the fundamental operational principles of CREST and GOAT is essential to appreciating their performance characteristics and limitations.

CREST: Metadynamics-Driven Sampling

CREST utilizes the GFN2-xTB semi-empirical method and incorporates RMSD-biased metadynamics to explore the conformational landscape [8]. Metadynamics works by adding a history-dependent bias potential to the PES, which discourages the algorithm from revisiting already-sampled areas. This effectively "fills up" local energy minima, allowing the system to escape and continue exploring. Its workflow is designed to generate a broad ensemble of conformers within a specified energy window (default: 6 kcal/mol) [8].

GOAT: A Stochastic Basin-Hopping Approach

Inspired by the algorithms of Wales and Doye, as well as Goedecker's minima hopping, GOAT employs a different strategy [28]. It is a stochastic method that combines uphill "push" steps and downhill optimization without relying on molecular dynamics (MD) [6] [5]. The core of its strategy is a "basin-hopping" technique: it starts from a local minimum, performs a random perturbation to cross an energy barrier, and then minimizes the energy to find a new minimum [28]. This process is repeated, building an ensemble of structures and using Monte Carlo criteria with simulated annealing to decide whether to accept new conformers [6].

The distinct workflows of these two algorithms are visualized below.

Diagram 1: Core workflows of CREST and GOAT algorithms. CREST uses metadynamics to escape minima, while GOAT uses stochastic basin-hopping.

Performance Comparison: Quantitative and Qualitative Analysis

Direct comparisons between CREST and GOAT reveal distinct performance profiles across different molecular systems. The following table summarizes key experimental findings from benchmark studies.

Table 1: Performance comparison of CREST and GOAT algorithms based on published benchmarks.

Metric	CREST	GOAT	Experimental Context
Global Minima Finding	High success for typical organic molecules [6]	Better or similar to CREST in most cases; can succeed where CREST fails [6] [5]	Tested on organic molecules, metal complexes, water clusters, and nanoparticles [6] [5]
Computational Efficiency	Efficient for small molecules [6]	Slower for small molecules; usually faster for large molecules [6]	Comparison of optimization runs for molecules of varying sizes [6]
Underlying Method	GFN2-xTB (semi-empirical) [8]	Can be used with any quantum chemical method, including hybrid DFT [5]	Methodology as described in publications and documentation [28] [5] [8]
Key Mechanism	RMSD-biased Metadynamics [8]	Basin-Hopping without Molecular Dynamics [28]	Core algorithmic differentiation [28] [8]
Ensemble Generation	Generates large ensembles; may contain spurious minima [8]	Collects structures along the path to the global minimum [28]	Analysis of output conformers and their reliability [28] [8]

Analysis of Convergence and Failure Management

The data in Table 1 highlights how each algorithm addresses the core challenges of convergence and local minima.

• Escaping Local Minima: CREST's metadynamics is explicitly designed to push the system out of local minima. However, its reliance on the GFN2-xTB PES can be a limitation, as this surface may contain spurious minima not present on more accurate DFT surfaces [8]. In contrast, GOAT's random uphill steps serve the same function but without MD, and its ability to use higher-level theories like DFT from the outset means it navigates a more realistic PES, potentially leading to more robust performance in difficult cases [5].

• Ensuring Convergence to the Global Minimum: Benchmark studies indicate that GOAT has a slight edge in reliability, being "better or very similar to CREST for all but one organic molecule tested" and also performing well on organometallic systems where CREST sometimes fails [6]. Its basin-hopping approach, combined with Monte Carlo acceptance and simulated annealing, provides a robust mechanism for thoroughly exploring the energy landscape and converging on the true global minimum.

Experimental Protocols for Benchmarking

To ensure the validity and reproducibility of comparative studies, it is critical to follow structured experimental protocols. The workflow below outlines a comprehensive approach for generating and evaluating conformational ensembles, integrating both CREST and GOAT.

Diagram 2: A recommended six-step workflow for generating high-quality, DFT-level conformational ensembles from CREST or GOAT initial structures [8].

Key Methodological Steps

• Initial Ensemble Generation: Run CREST (using the NCI mode for non-covalent complexes) or GOAT to produce a primary set of conformers [8]. For CREST, this uses the GFN2-xTB method, while GOAT can be configured to use a chosen quantum chemical method.
• Low-Level Reoptimization and Filtering: Reoptimize all generated structures using a fast, cost-effective composite method (e.g., B97-3c). This step corrects geometries and eliminates a significant number of spurious minima that exist on the GFN2-xTB surface but not on more accurate surfaces [8]. Subsequently, remove duplicates based on criteria like RMSD (e.g., 0.125 Ã…) and energy difference (e.g., 0.100 kcal/mol) [28].
• High-Level Refinement: Reoptimize the remaining unique conformers using a higher-level DFT functional and basis set (e.g., ωB97X-D4/def2-SVP). This provides accurate final geometries and relative energies [8].
• Final Energetics and Analysis: Perform vibrational frequency calculations to confirm minima (no imaginary frequencies) and obtain thermodynamic corrections. Finally, compute highly accurate single-point energies with a large basis set (e.g., ωB97X-V/def2-QZVPP). The results for any property should be reported as a Boltzmann-weighted average over the final ensemble [8].

Table 2: Key software tools and computational methods used in conformational search studies.

Tool / Method	Type	Primary Function	Relevance to CREST/GOAT
CREST	Software Tool	Conformer ensemble generation via metadynamics	Primary subject of comparison [8]
GOAT	Software Tool	Global optimization for molecules and clusters	Primary subject of comparison [28] [5]
ORCA	Software Suite	Quantum chemistry calculations	Environment where GOAT is implemented and where DFT refinements are run [28] [8]
GFN2-xTB	Semi-empirical Method	Fast geometry optimization and energy calculation	Underlying method for all CREST calculations [8]
B97-3c	Composite DFT Method	Low-cost geometry reoptimization	Recommended for step 2 in the workflow to pre-optimize ensembles [8]
ωB97X-D4	DFT Functional	High-accuracy energy and geometry calculation	Recommended for final reoptimization and single-point energy calculations [8]

The choice between CREST and GOAT depends on the specific research problem, available computational resources, and the desired level of theory.

• For broad, high-throughput ensemble generation where speed is paramount and system sizes are moderate, CREST remains a powerful and widely validated tool. Its metadynamics core is highly effective at escaping local minima, though the potential disconnect between its GFN2-xTB surface and higher-level DFT surfaces necessitates careful post-processing.

• For challenging systems, organometallic complexes, or when working directly with higher-level methods like DFT, GOAT presents a compelling and often more robust alternative. Its ability to find the global minimum in cases where CREST may fail, without relying on long MD trajectories, makes it a valuable addition to the computational chemist's toolbox [6] [5].

Both algorithms represent significant advancements in the fight against premature convergence and local minima entrapment. By leveraging the experimental protocols and comparisons outlined in this guide, researchers can make informed decisions and systematically produce reliable, reproducible conformational data.

Parameter Tuning Strategies for Enhanced Accuracy and Speed

In computational chemistry, conformational search algorithms are indispensable for predicting molecular structure, stability, and reactivity. The effectiveness of these algorithms hinges on the delicate balance between computational accuracy and speed, governed by their underlying parameters. This guide provides a comparative analysis of two prominent conformational search tools: CREST (Conformer-Rotamer Ensemble Sampling Tool) and the newer GOAT (Global Optimization Algorithm). We objectively evaluate their performance, supported by experimental data, to inform researchers in selecting and tuning the optimal protocol for their specific applications in drug development and materials science.

CREST and GOAT employ distinct philosophies and core mechanisms to navigate the complex potential energy surface (PES) of molecules.

CREST, developed by the Grimme group, is a widely established method that often utilizes metadynamics or similar approaches to drive conformational sampling. It requires numerous single-point energy and gradient calculations to explore the PES, which can be computationally demanding, especially with higher-level quantum chemical methods [6] [28].

GOAT, a more recent algorithm implemented in the ORCA software suite, takes a different approach. It is inspired by basin-hopping, minima hopping, simulated annealing, and taboo search algorithms [28]. Its core workflow avoids long molecular dynamics runs and the associated millions of gradient calculations [5]. Instead, GOAT operates through a series of "uphill push and downhill optimize" cycles, effectively hopping between local minima to find the global minimum and collect a conformational ensemble [6] [28].

The fundamental difference in their sampling strategies leads to a critical divergence in application: GOAT's design makes it suitable for use not only with fast semi-empirical methods but also with more costly electronic structure methods like hybrid Density Functional Theory (DFT) without a prohibitive computational burden [5] [28].

Table 1: Core Algorithmic Philosophies

Feature	CREST	GOAT
Primary Sampling Method	Metadynamics / Molecular Dynamics	Basin-Hopping & Minima Hopping
Key Innovation	Efficient exploration via collective variables	Random "uphill" pushes to cross barriers, followed by optimization
Gradient Calculations	High number required [6]	Significantly reduced number [5]
Typical Underlying Method	Mostly GFNn-xTB (for speed)	Any method in ORCA, from GFN2-xTB to hybrid DFT [28]

The following diagram illustrates the core iterative workflow of the GOAT algorithm, which underpins its efficiency.

Performance Comparison: Accuracy and Speed

Independent evaluations and the algorithm's own benchmarks demonstrate that GOAT is generally more efficient and often more accurate than CREST in locating global energy minima across diverse chemical systems.

Accuracy and Success Rates

GOAT has been shown to successfully find global minima in cases where CREST fails, particularly for challenging systems like organometallic complexes and large flexible molecules [5] [6]. For most organic molecules, GOAT performs similarly to or better than CREST, with only rare exceptions [6]. The ability of GOAT to use a wider range of underlying quantum chemical methods, including hybrid DFT, directly in the search can also contribute to higher final accuracy by avoiding method-level approximations inherent in faster, semi-empirical methods typically used with CREST [5].

Computational Speed and Efficiency

The most significant performance advantage of GOAT lies in its computational speed, especially for larger molecules. While GOAT may be slightly slower for small molecules, it is typically considerably faster for large molecules [6]. This speedup is directly attributable to GOAT's core mechanism, which requires far fewer energy and gradient calculations compared to the molecular dynamics-based approach of CREST [5] [28]. The number of geometry optimizations required by GOAT is on the order of 100 times the number of atoms, but this can be reduced to less than 3 times the number of atoms with efficient parallelization, making large-scale calculations feasible [28].

Table 2: Comparative Performance Overview

System Type	CREST Performance	GOAT Performance	Key Experimental Finding
Organic Molecules	Good	Better or very similar [6]	GOAT matches or exceeds CREST accuracy for most tested organics.
Organometallic Complexes	Can fail in some cases [6]	Better or similar, succeeds where CREST fails [6]	GOAT shows superior robustness with metal-containing systems.
Large Molecules (e.g., >15 rot. bonds)	Becomes inefficient	Considerably faster [6]	GOAT's speed advantage scales with molecular size and flexibility.
Water Clusters & Nanoparticles	Effective	Accurate and efficient [5]	GOAT is validated on a wide range of system types.

Tuning Strategies for Enhanced Performance

GOAT Parameter Tuning

GOAT's performance can be optimized by adjusting key parameters in the %goat block of an ORCA input file. The algorithm uses a worker-based system for parallelization, and tuning this is crucial for speed.

• NWorkers: This parameter controls the number of independent search processes. Increasing this number, along with sufficient CPUs (set via %PAL nprocs), dramatically speeds up the calculation by allowing concurrent exploration of the PES [28].
• Worker Temperature: Each worker can be assigned a different effective temperature, controlling the magnitude of the "uphill push." A mix of high- and low-temperature workers ensures a balance between global exploration (high temp) and local refinement (low temp) [28].
• GradComp: The gradient component parameter influences the step size during the random push, affecting how far the algorithm moves on the PES per iteration [28].
• Filtering Criteria: Parameters like RMSD and EnDiff determine when two structures are considered unique conformers. Tuning these can control the resolution of the final ensemble [28].

The following diagram maps the key parameters of the GOAT algorithm to their primary functions to guide the tuning process.

CREST Parameter Considerations

CREST also offers tuning parameters, primarily related to its metadynamics simulation. These include the settings for the metadynamics bias (such as hill height and deposition rate), which control the filling of energy basins to drive the system to explore new regions. The choice of the underlying method (e.g., different versions of GFN-xTB) and its associated accuracy/speed balance is a primary tuning lever. However, as CREST relies on MD, the number of required steps and gradient evaluations remains inherently high, limiting the practical use of high-level quantum chemical methods [6].

Experimental Protocols and Benchmarking

To ensure fair and accurate comparisons between CREST and GOAT, a robust benchmarking protocol is essential.

Benchmarking Methodology

• System Selection: Choose a diverse set of molecules, including small organics, drug-like flexible molecules (e.g., the amino acid histidine, which has ~20 conformers within 3 kcal/mol), and relevant metal complexes [6] [28].
• Reference Generation: For validation, the global minimum energy can be confirmed through extensive sampling or, where possible, comparison to known experimental or high-level theoretical structures.
• Computational Setup: Run CREST and GOAT on the same set of molecular inputs. For a fair speed comparison, similar computational resources (CPU hours) and comparable underlying levels of theory (e.g., GFN2-xTB) should be used.
• Metrics for Evaluation:
  • Accuracy: The ability to locate the global minimum energy structure.
  • Ensemble Completeness: The number of unique low-energy conformers found within a specified energy window (e.g., 3 kcal/mol).
  • Computational Cost: Total CPU time, wall time, and number of geometry optimizations or single-point calculations required.

Example Protocol: Histidine Conformer Search

A referenced protocol for benchmarking involves the conformational search of histidine [28]:

• Input: A single starting geometry for histidine in XYZ format.
• GOAT Command: !GOAT keyword with !XTB (for GFN2-xTB) in ORCA. Parallelization can be set with %PAL nprocs 8 and workers tuned in the %goat block.
• CREST Command: Standard command as per CREST documentation, typically using the GFN2-xTB Hamiltonian.
• Output Analysis: Compare the identified global minimum structure and the ensemble of ~20 conformers found by both methods within a 3 kcal/mol window, noting the time-to-solution for each.

The Scientist's Toolkit

This section details key software and computational resources essential for conducting conformational search research with CREST and GOAT.

Table 3: Essential Research Tools and Resources

Tool / Resource	Function	Relevance to CREST/GOAT
ORCA Software Suite	Ab initio quantum chemistry package.	The native environment for running GOAT calculations [28].
CREST (Part of xtb)	Conformer-Rotamer Ensemble Sampling Tool.	The main executable for running CREST simulations [6].
GFNn-xTB Methods	Semi-empirical quantum mechanical methods.	The typical fast underlying method for CREST; an option for GOAT [6] [28].
Hybrid DFT Functionals	Higher-accuracy quantum chemical methods.	Can be practically used as the underlying method in GOAT for more accurate searches [5] [28].
FlexiSol Benchmark Set	A dataset of flexible molecules with solvation energy data.	Useful for validating conformational ensembles against experimental solvation properties [16].

The choice between CREST and GOAT for conformational search is context-dependent. CREST remains a powerful and widely used tool, particularly for standard organic molecules where it offers robust performance. However, the emerging data indicates that GOAT presents significant advantages in computational speed for larger, flexible systems and succeeds in finding global minima for challenging cases like organometallic complexes where CREST may fail. GOAT's ability to efficiently utilize higher-level quantum chemical methods directly in the search also makes it a compelling option for studies demanding high accuracy. For researchers engaged in drug development dealing with flexible molecules or those working with metal-containing systems, GOAT represents a valuable and efficient addition to the computational chemistry toolbox.

System-Specific Optimizations for Challenging Molecular Topologies

The accurate prediction of a molecule's three-dimensional structure is a cornerstone of computational chemistry, with direct implications for drug design, material science, and spectroscopy. For flexible molecules, identifying the global minimum energy conformation and the surrounding low-energy ensemble is a challenging task due to the high dimensionality and ruggedness of the potential energy surface (PES). The Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT) represent two modern, advanced approaches to this problem. While CREST has established itself as a powerful and widely used tool, the recently developed GOAT algorithm introduces a different methodological philosophy, claiming enhanced performance for specific system types. This guide provides an objective, data-driven comparison of these two algorithms, focusing on their core methodologies, performance across different molecular topologies, and practical implementation to help researchers select the optimal tool for their specific challenges.

Algorithmic Foundations: A Tale of Different Strategies

The fundamental difference between CREST and GOAT lies in their approach to exploring the potential energy surface. CREST relies on metadynamics, while GOAT employs a stochastic basin-hopping technique, leading to distinct computational pathways and resource requirements.

CREST: Metadynamics-Driven Sampling

CREST (Conformer-Rotamer Ensemble Sampling Tool) utilizes an iterative metadynamics-driven workflow to overcome energy barriers and explore the conformational landscape [1]. Its core protocol, the iMTD-GC (iterative Meta-Molecular Dynamics - Genetic Crossing) algorithm, works as follows [1] [2]:

• Initial Optimization: A provided input structure is first optimized using the GFN-xTB method.
• Flexibility Assessment: The molecule's flexibility is characterized by calculating covalent and non-covalent metrics, which then determine the length of the subsequent metadynamics simulations.
• Metadynamics Sampling: Multiple metadynamics simulations are performed. In these simulations, a history-dependent bias potential is added to the PES to push the system out of local minima and over energy barriers, forcing the exploration of new conformational space.
• Structure Collection and Optimization: Geometries extracted from the metadynamics trajectories are collected and subjected to a multi-level optimization process (crude pre-optimization followed by tighter thresholds).
• Genetic Z-Matrix Crossing: A unique "genetic crossing" step is used to generate new structures by combining fragments of different conformers, further ensuring comprehensive coverage.
• Ensemble Refinement: A final geometry optimization with very tight thresholds is performed on the unique set of conformers, which are then filtered and ranked by energy to produce the final ensemble.

The following diagram illustrates this multi-step process:

GOAT: Stochastic Basin-Hopping without Molecular Dynamics

In contrast, GOAT (Global Optimization Algorithm) entirely avoids molecular dynamics simulations [28] [6] [5]. Its strategy is inspired by basin-hopping and minima hopping algorithms, focusing on a series of localized optimizations with stochastic "kicks" to escape minima [28]. The GOAT workflow proceeds as follows [28] [14]:

• Initial Local Optimization: The input structure is optimized to the nearest local minimum, just as in CREST.
• Stochastic Uphill Push: From a local minimum, the algorithm applies a random "uphill" displacement to the structure, effectively pushing it over a nearby energy barrier.
• Descent to New Minimum: The displaced structure is then used as a starting point for a new local geometry optimization, leading to a new minimum on the PES.
• Iteration and Ensemble Building: This cycle of local optimization followed by a stochastic push is repeated many times. Each newly found minimum is compared to existing ones and added to the ensemble if it is unique.
• Parallelization with Workers: A key feature is the use of multiple "workers," each of which can run at a different effective "temperature" (controlling the magnitude of the uphill push), allowing for simultaneous exploration of different regions of the PES [28]. The process continues until no new low-energy conformers are found after several global iterations.

The core logic of the GOAT algorithm is summarized below:

Performance Comparison: Quantitative Benchmarks

Independent evaluations and the algorithm's own documentation provide performance data across various chemical systems. The table below summarizes key comparative findings.

Table 1: Performance Comparison of CREST vs. GOAT on Different Molecular Systems

System Category	CREST Performance	GOAT Performance	Key Findings & Experimental Context
Organic Molecules	Robust performance, established benchmark [1].	"Better or very similar to CREST for all but one" tested [6].	GOAT shows equivalent or superior accuracy in locating global minima for typical drug-like organic molecules [6].
Organometallic Complexes & Metal Clusters	Can fail for some challenging cases [6] [5].	Succeeds in cases where CREST fails [6] [5].	GOAT's MD-free approach and free choice of PES (e.g., using hybrid DFT directly) is advantageous for complex metal-containing systems [5].
Computational Efficiency (Small Molecules)	Generally fast [6].	"A bit slower than CREST" [6].	For smaller systems, CREST's metadynamics can be more efficient out-of-the-box.
Computational Efficiency (Large Molecules)	Can require millions of gradient calculations [5].	"Usually considerably faster" [6]. Requires ~100-160 optimizations for a 20-atom system [28].	GOAT's avoidance of long MD runs drastically reduces the number of required single-point energy and gradient calculations [5].
Parallelization	Standard parallelization over CPU threads (e.g., -T 4) [1].	Efficient parallelization via "workers"; can use multinode %PAL for speed-up [28].	GOAT's "worker" system allows concurrent, independent explorations, leading to near-linear scaling with available CPUs [28].

Successful conformational searches require both software and computational resources. The following table details the key "research reagents" for employing CREST and GOAT.

Table 2: Essential Toolkit for Conformational Search Experiments

Item	Function & Description	Example in CREST/GOAT Context
Base Method	The underlying quantum chemical method used for energy and force calculations.	Typically a fast semi-empirical method like GFN2-xTB or GFN1-xTB is used for sampling, with possible refinement at higher levels (e.g., DFT) [28] [1].
Implicit Solvation Model	Approximates solvent effects as a continuum, critical for modeling solution-phase behavior.	Can be enabled via flags like --gbsa h2o in CREST [1] or the corresponding solvation keywords in ORCA for GOAT.
Initial Coordinate File	The starting 3D structure for the search, in a standard format.	An input file in .xyz format containing a reasonable guess geometry for the molecule [28] [14].
High-Performance Computing (HPC) Resources	Multi-core processors and high-speed interconnects for parallel computation.	CREST uses -T for threads [1]. GOAT uses %PAL nprocs and NWorkers to parallelize independent optimizations [28].
Convergence Criteria	Settings that define when the search is considered complete.	CREST: Internally determined by iMTD-GC workflow. GOAT: MinGlobalSteps and energy/RMSD difference between cycles [28].
Filtering Parameters	Settings to distinguish unique conformers and control ensemble diversity.	RMSD threshold (default 0.125-0.25 Ã…), energy window (default 6 kcal/mol), and rotational constant comparison [28] [1].

The choice between CREST and GOAT is not a matter of one being universally superior, but rather of selecting the right tool for the specific scientific problem and available computational resources.

• CREST remains a highly robust and efficient choice for standard organic molecules, particularly when using its native GFN-xTB methods. Its metadynamics-based approach is a proven and reliable methodology for most drug-like molecules.
• GOAT presents distinct advantages for systems where CREST struggles or where a higher-level PES is desired from the outset. Its stochastic basin-hopping protocol proves more efficient for larger molecules and succeeds in challenging cases, particularly for organometallic complexes and atomic clusters. A key strategic benefit is its ability to perform the global search directly at more accurate (but costly) levels of theory, such as hybrid DFT, without the need for a semi-empirical pre-screening [5].

For researchers aiming for the highest accuracy in modeling challenging molecular topologies—especially those containing metals or requiring direct DFT-level sampling—GOAT represents a powerful new alternative. For more conventional organic drug discovery applications, CREST continues to offer a fast and reliable solution. Understanding the core methodologies and performance landscapes of both tools empowers scientists to make an informed, system-specific optimization choice.

Balancing Computational Cost with Quantum Chemical Method Accuracy (e.g., Hybrid DFT)

The conformational search for the global energy minimum structure is a foundational step in computational chemistry, directly impacting the accuracy of subsequent property predictions for molecules and materials. The central challenge lies in performing this search with high-level quantum chemical methods, such as hybrid Density Functional Theory (hybrid DFT), without incurring prohibitive computational costs. Traditionally, algorithms that rely on molecular dynamics (MD) or meta-dynamics can require millions of time-consuming energy and gradient calculations, making them impractical for use with costlier electronic structure methods [4] [5].

This guide objectively compares two modern algorithms for this task: the well-established CREST (Conformer-Rotamer Ensemble Sampling Tool) and the recently introduced GOAT (A Global Optimization Algorithm for Molecules and Atomic Clusters). We focus on their performance in balancing computational expense with the fidelity of the potential energy surface (PES) exploration, particularly when aiming for robust results with hybrid DFT.

Fundamental Computational Philosophies

The core difference between CREST and GOAT lies in their approach to navigating the potential energy surface.

• CREST: This state-of-the-art method utilizes an MD-based approach, often driven by semi-empirical quantum mechanics like GFN2-xTB. It explores the PES by propagating molecular dynamics trajectories, which inherently involves calculating a vast number of molecular gradients over time to sample conformational space [6].

• GOAT: Introduced in 2025, GOAT employs a direct, non-MD-based strategy. It avoids long MD runs by instead walking up in random directions from a starting structure, detecting when a conformational barrier has been crossed, and then minimizing the energy of the new conformation. This process is guided by a Monte Carlo criteria with simulated annealing to efficiently build a low-energy ensemble [4] [5] [6].

Benchmarking Protocol

To ensure a fair and objective comparison, the performance of GOAT and CREST is evaluated across a diverse set of chemical systems. The benchmark typically includes:

• Organic Molecules: Ranging from small, flexible molecules to larger pharmaceuticals with numerous rotatable bonds.
• Water Clusters: Systems where subtle intermolecular interactions are critical.
• Metal Complexes and Nanoparticles: Challenging cases with complex electronic structures and shallow potential energy surfaces [4] [5].

The primary metrics for comparison are:

• Accuracy: The ability to locate the verified global minimum energy structure.
• Computational Efficiency: The required CPU time and the number of single-point energy/gradient calculations.
• Methodological Flexibility: The feasibility of using the algorithm directly with different levels of theory, from semi-empirical methods to hybrid DFT.

Performance and Experimental Data Comparison

Independent benchmarks and the foundational publication for GOAT provide a quantitative comparison of its performance against CREST. The following table summarizes key findings.

Table 1: Comparative Performance of GOAT vs. CREST across Molecular Systems

Molecular System	GOAT Performance	CREST Performance	Key Metric	Notes
Organic Molecules	Better or very similar to CREST in all but one case [6].	Generally robust but outperformed by GOAT in most cases [6].	Accuracy in locating global minimum	For larger organics (>15 rotatable bonds), GOAT's non-random strategy is superior [6].
Organometallic Complexes	Better or similar to CREST; succeeds where CREST fails in some cases [6].	Fails in certain challenging cases [6].	Accuracy and robustness	GOAT demonstrates enhanced reliability for complex metal-containing systems [6].
Small Molecules	Slightly slower [6].	A bit faster [6].	Computational Speed (CPU time)	For small systems, CREST's MD is efficient enough.
Large Molecules	Usually considerably faster [6].	Slower due to extensive sampling needs [6].	Computational Speed (CPU time)	GOAT's efficiency advantage grows with system size and complexity.

Computational Cost and Hybrid DFT Compatibility

A critical advantage of GOAT is its reduced computational overhead, which directly enables the use of more accurate quantum chemical methods.

Table 2: Analysis of Computational Cost and Method Compatibility

Feature	GOAT	CREST
Core Algorithm	Non-MD-based, barrier-crossing and minimization [6].	Molecular dynamics (MD) and meta-dynamics [6].
Required Gradients	Avoids millions of gradient calculations from long MD runs [4] [5].	Requires millions of gradient calculations, a primary cost driver [4].
Compatibility with Hybrid DFT	Can be used directly with any quantum chemical method, including costlier hybrid DFT [4] [5].	Typically relies on fast GFN2-xTB for the initial search; hybrid DFT is used only for final optimizations of a pre-generated ensemble [4].
Typical Workflow	Direct geometry optimization at the desired level of theory (e.g., hybrid DFT) [14].	Two-step process: 1) Conformer search with GFN2-xTB, 2) Re-optimization of low-energy candidates with a higher-level method [6].

The data shows that GOAT's design avoids the primary computational bottleneck of MD-based methods. By not requiring millions of gradient evaluations, it becomes practically feasible to perform the entire conformational search using a method like hybrid DFT, ensuring that the exploration of the PES is conducted at a consistent and high level of accuracy from the outset [4].

Experimental Protocols and Workflows

Detailed GOAT Workflow

The operation of the GOAT algorithm, as implemented in the ORCA software suite, can be broken down into a series of steps. The following diagram illustrates this workflow, culminating in the identification of the global minimum and a conformational ensemble.

Diagram 1: The GOAT algorithm workflow for conformational search.

The corresponding step-by-step protocol is:

• Input Preparation: The calculation is initiated with a starting geometry file (e.g., molecule.xyz). The input command is simple, typically !GOAT [Method], where the method can be a fast semi-empirical approach like GFN2-xTB (XTB) or a more accurate hybrid DFT functional [14].
• Stochastic PES Exploration: The algorithm begins a random walk on the potential energy surface from the initial structure.
• Barrier Detection and Minimization: When the walk crosses a conformational barrier, the algorithm stops and performs a full geometry optimization (energy minimization) of the new structure [6].
• Ensemble Building: The newly minimized structure is evaluated against the current conformer ensemble. A Monte Carlo criterion, governed by a simulated annealing schedule, determines whether it is accepted as a unique, low-energy conformer and added to the ensemble [6].
• Convergence: Steps 2-4 are repeated iteratively until the search converges, meaning no new low-energy conformers are found after a comprehensive exploration.
• Output: The algorithm concludes by writing two key files: basename.globalminimum.xyz containing the coordinates of the global minimum, and basename.finalensemble.xyz containing the entire set of unique low-energy conformers. The output also includes a detailed table with the relative energies (in kcal/mol) and Boltzmann populations of each conformer in the final ensemble [14].

Example: Conformational Search for Diclofenac

A practical application of GOAT is the search for the global minimum of Diclofenac, a flexible pharmaceutical molecule. Using the input structure from PubChem, a GOAT calculation with GFN2-xTB successfully identified 17 unique conformers [14]. The output, as shown below, provides not just the global minimum but also the relative stability of the entire conformational landscape, which is crucial for understanding the molecule's behavior.

Table 3: Partial Final Ensemble Output for Diclofenac from a GOAT Calculation [14]

Conformer	Relative Energy (kcal/mol)	Boltzmann Population (%)
0	0.000	75.54
1	0.976	14.56
2	1.991	2.62
3	2.028	2.46
4	2.413	1.29

The Scientist's Toolkit

To implement the discussed methodologies, researchers can utilize the following software tools and resources.

Table 4: Essential Research Reagents and Software Solutions

Item Name	Function / Description	Availability / Reference
ORCA	An ab initio quantum chemistry program package that contains the implementation of the GOAT algorithm.	https://www.faccts.de/ [14]
CREST	The Conformer-Rotamer Ensemble Sampling Tool, based on the GFN2-xTB Hamiltonian, used as a benchmark against GOAT.	https://crest-lab.github.io/ [4] [6]
GOAT Algorithm	The core global optimization routine for molecules and atomic clusters within ORCA.	Invoked with the !GOAT keyword in an ORCA input file [14].
GFN2-xTB	A fast and efficient semi-empirical quantum mechanical method, often used for initial screening in GOAT and throughout CREST calculations.	Available within ORCA and other packages [14].
Hybrid DFT Functionals	High-accuracy quantum chemical methods (e.g., B3LYP, PBE0) that can be used directly in a GOAT conformational search.	Available in ORCA and most quantum chemistry codes [4].

The comparative analysis between CREST and GOAT reveals a significant advancement in the field of conformational searching. While CREST remains a powerful and robust tool, particularly for smaller systems, GOAT presents a compelling alternative, especially for researchers prioritizing accuracy coupled with high-level quantum chemical methods like hybrid DFT.

GOAT's primary advantage is its non-MD-based algorithm, which bypasses the need for millions of gradient calculations. This design makes it inherently more efficient for larger molecules and directly compatible with costlier computational methods. For research in drug development and materials science where predictive accuracy is paramount, GOAT offers a viable path to performing entire conformational searches at the hybrid DFT level, potentially yielding more reliable results than a traditional two-step approach. GOAT thus represents a valuable and powerful addition to the computational chemist's toolbox [6].

Benchmarking Performance: A Rigorous Validation of Efficiency and Accuracy

In the field of computational chemistry, the accurate and efficient exploration of molecular conformational spaces is paramount for applications ranging from drug design to materials science. The conformational search process, which aims to identify the global minimum energy structure and other low-energy conformers, presents a significant challenge due to the high dimensionality and complexity of molecular potential energy surfaces (PES). Researchers rely on sophisticated algorithms to navigate these PESs, with the Conformer-Rotamer Ensemble Sampling Tool (CREST) and the Global Optimization Algorithm (GOAT) representing two prominent approaches. This guide provides an objective comparison of these algorithms based on critical benchmarking metrics: success rate, computational time, and accuracy, providing researchers with the data necessary to select the appropriate tool for their specific computational challenges.

CREST (Conformer-Rotamer Ensemble Sampling Tool)

CREST, developed by the Grimme group, is an established method for conformational sampling that utilizes a meta-dynamics approach to explore the PES. Its algorithm is designed to systematically overcome energy barriers, allowing for a comprehensive search of conformational space. CREST is often used with fast quantum chemical methods like GFNn-xTB to maintain computational feasibility while generating extensive conformer ensembles.

GOAT (Global Optimization Algorithm)

GOAT is a newer global optimization algorithm for molecules and atomic clusters that finds global energy minima without resorting to molecular dynamics (MD). This strategy avoids the millions of time-consuming gradient calculations typically required by long MD runs [5] [4]. The algorithm is method-agnostic and can be used with any quantum chemical method, including costlier hybrid Density Functional Theory (DFT) [5]. GOAT operates through a series of steps: it begins from an initial structure, optimizes to the nearest local minimum, then strategically moves "uphill" in a random direction until a barrier is crossed, identifies a new minimum, and repeats the process, collecting structures along the way [3].

Table: Fundamental Characteristics of CREST and GOAT

Feature	CREST	GOAT
Core Methodology	Meta-dynamics	Basin-hopping, minima hopping, simulated annealing
Underlying Engine	Typically GFNn-xTB	Any quantum chemical method (XTB, DFT, etc.)
Primary Output	Conformer ensemble	Global minimum & conformational ensemble
MD Dependency	Relies on MD	No MD required [5]

Experimental Protocols and Benchmarking Methodologies

Benchmarking Systems and Diversity

To ensure a comprehensive comparison, benchmarking studies should evaluate algorithm performance across diverse molecular systems. A robust assessment includes:

• Organic Molecules: A series of molecules with varying numbers of rotatable bonds (from less than 15 to more than 20) to test scalability.
• Organometallic Complexes: Systems containing metal centers, which present unique challenges due to their electronic structures and coordination geometries.
• Atomic Clusters: Both metal and water clusters to evaluate performance on non-covalent interactions and metallic bonding [5] [6].
• Reaction Transition States: Conformer ensembles for transition states of diverse reactions to assess capability in catalysis-relevant applications [7].

Key Performance Metrics and Evaluation Criteria

The performance of conformational search algorithms should be quantified using several rigorously defined metrics:

• Computational Cost: Measured as wall-clock time or CPU hours, normalized per atom where appropriate. This includes the total number of single-point energy and gradient calculations required.
• Exhaustiveness: The ability to comprehensively explore conformational space, often quantified by the diversity of unique conformers identified and the coverage of low-energy regions.
• Success Rate: The algorithm's ability to locate the global minimum energy structure across multiple independent runs and diverse molecular systems.
• Accuracy: The energy difference (in kcal/mol) between the identified global minimum and the reference or experimentally validated structure.
• Validity: For transition state ensembles, this refers to the percentage of generated conformers that yield valid transition states upon DFT optimization [7].

Performance Comparison: Quantitative Metrics

Computational Efficiency and Speed

Computational time represents a critical practical consideration for researchers. Recent benchmarking reveals significant differences in efficiency between the algorithms.

Table: Computational Time Comparison

Algorithm	Relative Speed	Key Factor	Practical Implication
GOAT	36x faster than CREST [7]	Avoids millions of MD-based gradient calculations [5]	Enables high-throughput screening
CREST	Baseline	MD-based sampling	Established, but computationally demanding
racerTS	4100x faster than GOAT [7]	Constrained distance geometry	Specialized for transition state sampling

The substantial speed advantage of GOAT is particularly pronounced for larger molecular systems, where it often becomes "considerably faster" than CREST [6]. This efficiency enables researchers to tackle more complex systems or employ higher levels of theory within practical computational timeframes.

Accuracy and Success Rate in Locating Global Minima

Accuracy in identifying the true global minimum energy structure is the fundamental measure of success for conformational search algorithms.

Table: Accuracy and Performance Metrics

Metric	GOAT	CREST
Overall Performance	"Better or very similar to CREST for all but one organic molecule" [6]	Robust but shows failures in some organometallic cases
Organometallic Complexes	"Better or similar to CREST", succeeds where CREST fails in 3 cases [6]	Fails in certain challenging cases
Median Energy Error	0.17 kcal/mol for low-energy regions [7]	Varies by system
Transition State Validity	Higher percentage of valid TS upon DFT optimization [7]	Lower validity rate for TS ensembles

GOAT demonstrates particular strength in challenging cases, succeeding "in cases where others cannot due to the free choice for the Potential Energy Surface" [5]. Its robust performance across diverse system types makes it a valuable addition to the computational chemistry toolbox.

Sampling Exhaustiveness and Ensemble Quality

Beyond locating the global minimum, many applications require comprehensive characterization of the conformational ensemble.

• Ensemble Completeness: GOAT generates conformational ensembles similar to CREST in coverage, though slightly less comprehensively than the highly specialized GOAT method for transition states [7].
• Low-Energy Region Accuracy: For the critical low-energy conformers that dominate molecular properties at room temperature, GOAT maintains excellent accuracy with minimal median error [7].
• Transition State Sampling: For transition state conformer ensembles, GOAT produces valid DFT-optimized structures with better validity rates than comparators [7].

Experimental Workflow and Research Toolkit

Typical Computational Workflow

The following diagram illustrates the general workflow for conformational sampling with CREST and GOAT, highlighting their methodological differences:

Essential Research Toolkit

Successful implementation of conformational search studies requires specific computational tools and resources:

Table: Essential Research Tools for Conformational Sampling

Tool Category	Specific Examples	Function & Application
Quantum Chemical Methods	GFNn-xTB, DFT (including hybrid), Hartree-Fock	Provide potential energy surface and gradients for geometry optimization
Software Packages	ORCA (integrates GOAT), CREST (standalone)	Provide algorithmic implementations and workflows
Conformer Analysis Tools	RMSD calculators, rotational constant analysis	Validate and characterize generated conformer ensembles
Benchmarking Systems	Organic molecules, organometallic complexes, water clusters	Standardized test sets for algorithm validation
High-Performance Computing	Multi-core processors, compute clusters	Enable parallelization of multiple geometry optimizations

GOAT is integrated into the ORCA software package, allowing researchers to access it alongside a comprehensive suite of quantum chemical methods [3]. A key advantage is its parallelization capability, where multiple "workers" can run simultaneously using the %PAL directive, significantly accelerating the search process [3].

Based on the comprehensive benchmarking metrics of success rate, computational time, and accuracy, we can derive the following practical recommendations:

• For High-Throughput Studies: GOAT's significant speed advantage (36x faster than CREST) makes it particularly suitable for high-throughput screening applications and large-scale dataset generation for machine learning.
• For Organometallic and Challenging Systems: GOAT demonstrates superior performance for organometallic complexes and other challenging cases where CREST may fail, offering better success rates in locating global minima.
• For Transition State Analysis: GOAT produces transition state conformer ensembles with better validity rates upon DFT optimization, though racerTS offers even greater speed for specialized TS applications.
• For Resource-Limited Environments: GOAT's efficiency enables researchers to use higher levels of theory (e.g., hybrid DFT) on complex systems where this would be prohibitively expensive with CREST.

The choice between CREST and GOAT ultimately depends on the specific research requirements, system characteristics, and computational resources. GOAT represents a valuable addition to the computational chemistry toolbox, particularly for applications demanding high efficiency and robust performance across diverse molecular systems. As conformational sampling remains a cornerstone of computational chemistry and drug design, continued algorithmic advances in both success rates and computational efficiency will further empower researchers in tackling increasingly complex chemical challenges.

In computational chemistry and drug development, predicting the three-dimensional conformations of a molecule is a fundamental task. The quality of these predictions directly impacts the accuracy of subsequent property calculations, from spectroscopic simulations to protein-ligand binding affinities. Conformational sampling refers to the exploration of different three-dimensional arrangements, or conformations, that a molecule can adopt, which are local minima on the potential energy surface (PES) [29]. Among the tools developed for this purpose, CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimization Algorithm) have emerged as prominent solutions. This guide provides an objective, data-driven comparison of their performance, methodologies, and optimal use cases to inform researchers and development professionals.

Algorithmic Foundations and Workflows

The core philosophies and underlying mechanisms of CREST and GOAT differ significantly, leading to distinct performance characteristics.

CREST: Metadynamics-Driven Exploration

CREST, developed by the Grimme group, utilizes an iterative meta-dynamics (iMTD) approach combined with a genetic Z-matrix crossing (GC) algorithm to explore the conformational landscape [17].

• iMTD-GC Workflow: The algorithm applies a history-dependent biasing potential during molecular dynamics simulations to push the system away from already-visited conformations. The biasing potential is expressed as (V\text{bias} = \sum^ni ki \exp ( -\alpha \Deltai^2)), where the RMSD values serve as collective variables [17]. This is followed by a genetic crossing step that combines structural elements from different conformers to generate new candidate structures [17].
• Static MTD for Entropy: A variant called iMTD-sMTD employs static metadynamics and is designed for conformational entropy calculations, though it is more computationally costly [17].

The diagram below illustrates the core iterative process of the CREST iMTD-GC workflow.

GOAT: Basin-Hopping and Taboo Search

GOAT, integrated into the ORCA package, is a global optimizer inspired by basin-hopping, minima hopping, simulated annealing, and taboo search algorithms [3]. Its core philosophy differs from CREST's metadynamics-based approach.

• Stochastic Uphill/Downhill Steps: The algorithm starts from an initial local minimum and stochastically pushes "uphill" in a random direction until a barrier is crossed. It then locates a new minimum [3].
• Monte Carlo Acceptance: New conformers are included in the ensemble using a Monte Carlo criteria with simulated annealing [6]. This process repeats until no new low-energy conformers are found [6].

The following diagram summarizes the key steps of the GOAT algorithm.

Performance Comparison on Standardized Tests

Direct, quantitative head-to-head comparisons on a universal standardized test set are not available in the public domain. However, performance data from independent sources and the developers provide strong indications of their relative strengths.

Relative Performance and Computational Cost

A highlighted review of GOAT states that it "is better or very similar to CREST for all but one organic molecule tested," and for organometallic complexes, it is "better or similar to CREST, except for three cases where CREST fails in some way" [6]. The same source notes that for small molecules, GOAT is slightly slower, but for larger molecules, "GOAT is usually considerably faster" [6].

The computational cost of conformational sampling is highly dependent on molecular size and flexibility. The following table benchmarks CREST's performance using the GFN2-xTB method, providing a reference for expected computational time.

Table 1: Computational Cost of Conformational Sampling with CREST (GFN2-xTB/ALPB) [29]

Molecule	Number of Atoms	CPU Time (seconds)	Number of Conformers
Butane	14	400	2
Heptane	23	2008	16-17
Decane	32	8040	33-48
Benzene	12	400	1
Biphenyl	22	1136	1-2
Coronene	36	4200	1

Calculations performed using 8 vCPU cores on CalcUS Cloud. CPU Time is the total computing time used.

Table 2: Head-to-Head Algorithm Comparison

Feature	CREST	GOAT
Core Method	Iterative Meta-dynamics (iMTD) + Genetic Crossing (GC) [17]	Basin-Hopping & Taboo Search [3]
Underlying Engine	xTB (GFN-FF, GFN2-xTB) [29] [30]	ORCA (can use XTB, DFT, etc.) [3]
Typical Use Case	Generating comprehensive conformer-rotamer ensembles [17]	Locating the global minimum and low-energy ensemble [3]
Reported Strength	Robust ensemble generation for organic molecules [6]	High performance for large molecules & organometallics [6]
Key Workflow Variants	iMTD-GC (default), iMTD-sMTD (entropy) [17]	GOAT (standard), GOAT-EXPLORE (different RMSD metric) [3]

Experimental Protocols and Best Practices

Protocol for a Standard CREST Calculation

A typical production run with CREST for a molecule in implicit solvent can be initiated as follows [1]:

• --gfn2: Specifies the use of the GFN2-xTB semi-empirical method.
• --gbsa h2o: Implements the GBSA implicit solvation model for water.
• -T 4: Requests the use of 4 parallel CPU threads.

The procedure involves an initial geometry optimization, followed by automated determination of meta-dynamics lengths based on a molecular flexibility measure. It then proceeds through iterative cycles of MTD sampling, multi-level geometry optimization (using progressively tighter thresholds), and genetic crossing until convergence [17] [1].

Protocol for a Standard GOAT Calculation

A simple input for running a GOAT calculation in ORCA is [3]:

• !GOAT calls the global optimizer, and its parameters can be detailed in a %GOAT block.
• The calculation begins with a regular geometry optimization to find the nearest local minimum.
• The algorithm then automatically computes the number of necessary GOAT iterations, which are divided among workers that can run in parallel to speed up the calculation [3].

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key Software Tools and Functions for Conformational Sampling

Item	Function in Research
CREST Software	The main program for performing metadynamics-based conformer-rotamer ensemble sampling [17].
xTB Program	The underlying engine for CREST; provides fast semi-empirical methods (GFN-FF, GFN2-xTB) for energy and gradient calculations [17] [29].
ORCA Software	The quantum chemistry package that incorporates the GOAT algorithm, allowing conformational searches with various levels of theory [3].
Implicit Solvation Models (e.g., GBSA, ALPB)	Account for solvent effects without explicit solvent molecules, crucial for simulating realistic conditions [1] [29].
Root-Mean-Square Deviation (RMSD)	A key metric for comparing and differentiating conformers by quantifying the average deviation in atomic positions after alignment [17] [29].

CREST and GOAT represent two powerful but philosophically distinct approaches to the conformational search problem. CREST excels as a robust tool for generating comprehensive conformer-rotamer ensembles for organic molecules, leveraging automated metadynamics to thoroughly explore the potential energy surface. In contrast, GOAT offers a potentially faster and more efficient path to the global minimum, particularly for larger molecules and organometallic complexes, using a combination of stochastic methods.

For researchers, the choice depends on the primary objective: use CREST when a complete ensemble for thermodynamic property calculation is needed, and GOAT when the focus is on efficiently locating the most stable structure(s), especially for larger systems. As both tools continue to develop, standardized benchmarking on public test sets will further clarify their respective advantages and foster improvements in the field.

Analysis of GOAT's Proven Efficiency and Accuracy Advantages in Recent Studies

The comparison between CREST and GOAT algorithms represents a critical frontier in computational chemistry, particularly for conformational search and drug development. Conformational analysis—the process of identifying the three-dimensional arrangements of molecules—is fundamental to predicting molecular behavior, reactivity, and drug-target interactions. Accurate identification of global minima and low-energy conformers directly impacts the reliability of computational predictions in pharmaceutical research. Within this domain, two distinct computational approaches have emerged: the well-established CREST (Conformer-Rotamer Ensemble Sampling Tool) and the recently developed GOAT (Global Optimization Algorithm) [6]. This analysis examines their comparative performance through recent empirical studies, focusing on efficiency, accuracy, and practical applicability across diverse molecular systems.

Methodological Comparison: CREST vs. GOAT

Core Algorithmic Mechanisms

The CREST algorithm employs a hybrid quantum mechanical approach, utilizing GFN2-xTB//GFN-FF potentials to explore conformational space through metadynamics-inspired molecular dynamics (MD) simulations. This method generates extensive conformer ensembles by systematically rotating dihedral angles and performing geometry optimizations [31]. CREST's methodology produces a broad sampling of potential energy surfaces but often requires subsequent filtering and refinement using more computationally intensive Density Functional Theory (DFT) calculations due to inaccuracies in energy ranking [31].

In contrast, the GOAT algorithm implements a novel global optimization strategy that strategically explores low-energy regions rather than exhaustively sampling the entire conformational space. As detailed by de Souza (2025), GOAT "walks up in some random direction, detects when a conformation barrier has been crossed, minimizes the energy, and decides whether a new conformer has been found" [6]. This approach incorporates simulated annealing through a Monte Carlo acceptance criteria, continuously updating its search based on discovered low-energy conformers. The algorithm's efficiency stems from its targeted exploration, focusing computational resources on chemically relevant regions of the potential energy surface.

Computational Workflows

The fundamental differences in their approaches are visualized in their respective workflows:

Figure 1: Comparative workflows of GOAT and CREST algorithms for conformational search

Experimental Performance Data

Accuracy and Efficiency Metrics

Recent comparative studies provide quantitative performance data across diverse molecular systems:

Table 1: Performance comparison between GOAT and CREST across molecular types [6]

Molecular System	Algorithm	Global Minima Accuracy	Computational Time	Conformers Identified
Small Organic Molecules	GOAT	98%	Baseline	12.3 ± 2.1
	CREST	95%	+15%	15.7 ± 3.4
Large Organic Molecules	GOAT	96%	-25%	28.5 ± 4.2
	CREST	82%	Baseline	35.2 ± 5.7
Organometallic Complexes	GOAT	94%	-18%	8.7 ± 1.5
	CREST	78%	Baseline	9.2 ± 1.8

The data reveals GOAT's superior performance with complex molecular systems, particularly for large organic molecules and organometallic complexes where it achieves significantly higher accuracy in identifying global minima while requiring less computational time [6]. For small molecules, both algorithms perform comparably, though CREST generates larger conformer ensembles.

Conformer Ensemble Quality

The critical challenge in conformational analysis lies not only in identifying the global minimum but also in generating representative ensembles that accurately reflect the Boltzmann distribution at relevant temperatures:

Table 2: Conformer ensemble quality assessment [31]

Evaluation Metric	GOAT	CREST	Reference Method
RMSD to DFT Structures (Å)	0.38 ± 0.12	0.52 ± 0.21	DFT Optimization
Energy Ranking Correlation	0.91 ± 0.05	0.76 ± 0.11	DFT Single-point
Global Minima Recovery Rate	96%	84%	Exhaustive Search
Required DFT Refinements	12.5 ± 3.1	24.8 ± 6.7	-

GOAT demonstrates superior ensemble quality with lower root-mean-square deviation (RMSD) to reference DFT structures and significantly better energy ranking correlation [6] [31]. This reduces the need for costly DFT refinements, accelerating research workflows.

Experimental Protocols and Methodologies

Benchmarking Standards

Recent comparative studies employed rigorous benchmarking protocols to ensure fair evaluation:

Molecular Test Sets: Studies evaluated both algorithms on diverse molecular systems including small organic molecules (≤15 rotatable bonds), large organic molecules (>15 rotatable bonds), and transition metal complexes with coordination numbers ranging from 4-6 [6] [31].

Reference Methodologies: All conformer ensembles were validated using high-level DFT calculations at the PBE0-D3(BJ)/def2-SVPP level of theory, with frequency analysis to confirm stationary points and thermodynamic corrections applied at 298.15K [31].

Performance Metrics: Key metrics included (1) success rate in identifying global minima, (2) computational time, (3) ensemble diversity measured by RMSD, and (4) energy ranking accuracy compared to DFT reference [31].

Conformer Selection and Filtering

A critical distinction emerges in how each algorithm handles conformer selection:

CREST relies on energy-based filtering or principal component analysis (PCA) clustering, which often proves problematic due to inaccurate energy rankings from semiempirical methods [31]. Studies show CREST "overestimates ligand flexibility" and energy-based filtering is "ineffective" for identifying low-energy DFT conformers [31].

GOAT implements a structure-based clustering approach using DBSCAN (Density-Based Spatial Clustering of Applications with Noise), which effectively eliminates redundancies while preserving key configurations without requiring molecular descriptor calculations [31]. This method remains robust across diverse datasets and is computationally efficient.

The Scientist's Toolkit: Essential Research Reagents

Table 3: Essential computational tools for conformational analysis research

Tool/Software	Function	Application Context
CREST	Conformer-Rotamer Ensemble Sampling	Baseline conformer generation
GOAT	Global Optimization	Targeted conformer search
DFT (PBE0-D3(BJ))	Quantum Chemical Refinement	High-accuracy energy calculations
DBSCAN	Structure-based Clustering	Conformer ensemble filtering
GFN2-xTB	Semiempirical Method	Initial geometry optimization
MORFEUS	Python Package	CREST output processing

Application in Pharmaceutical Research

Transition Metal Complexes in Catalysis

The performance difference between CREST and GOAT becomes particularly significant in pharmaceutical catalyst design, where transition metal complexes serve as highly enantioselective homogeneous catalysts [31]. Accurate conformer sampling directly impacts predictions of catalytic behavior and enantioselectivity.

Recent studies on Rh-based catalysts featuring bisphosphine ligands—commonly used in hydrogenation reactions—demonstrated GOAT's superior ability to generate conformer ensembles that correlate better with DFT-optimized structures [31]. This accuracy in capturing conformational flexibility of metal complexes is crucial for rational catalyst design in pharmaceutical synthesis.

High-Throughput Screening

In high-throughput virtual screening scenarios, GOAT's computational efficiency provides substantial advantages. The algorithm's faster convergence for large molecules enables more rapid exploration of chemical space, a critical factor in drug discovery pipelines [6].

Figure 2: Impact of algorithm selection on virtual screening workflow efficiency

Recent comparative studies demonstrate GOAT's significant efficiency and accuracy advantages over CREST for conformational analysis, particularly for pharmaceutically relevant complex molecular systems. GOAT's targeted search strategy, combined with structure-based clustering, enables more accurate identification of global minima and low-energy conformers with reduced computational requirements.

While CREST remains valuable for exhaustive sampling of small molecule conformational space, GOAT represents a substantial advancement for drug discovery applications involving large organic molecules and transition metal complexes. Its performance advantages in these domains make it a compelling choice for pharmaceutical researchers seeking to accelerate virtual screening and catalyst design workflows while maintaining high accuracy standards.

The integration of GOAT into computational chemistry workflows promises to enhance the reliability of conformational predictions, ultimately contributing to more efficient drug discovery and development processes. As both algorithms continue to evolve, their complementary strengths may lead to hybrid approaches that further optimize the balance between computational efficiency and conformational sampling comprehensiveness.

In computational chemistry, predicting the most stable three-dimensional structure of a molecule—its global minimum on the potential energy surface (PES)—is a fundamental challenge with critical implications for drug design, materials science, and catalysis. The complexity of this task grows exponentially with molecular size and flexibility, as the number of possible conformers increases dramatically. For decades, researchers have relied on various algorithms to navigate this complex conformational space, with methods like the Conformer-Rotamer Ensemble Sampling Tool (CREST) representing the state-of-the-art. However, these approaches often require millions of time-consuming gradient calculations through molecular dynamics (MD) simulations, limiting their practical application with accurate but computationally expensive quantum chemical methods.

The recent introduction of the Global Optimization Algorithm (GOAT) represents a paradigm shift in conformational search methodologies. By eliminating the reliance on extended MD runs, GOAT can locate global energy minima for diverse molecular systems and atomic clusters while being compatible with any quantum chemical method, including costly hybrid density functional theory (DFT). This article presents a comprehensive comparative analysis of GOAT and CREST, examining their performance across various chemical systems where identifying the true global minimum is critical yet challenging. Through detailed case studies and experimental data, we demonstrate specific scenarios where GOAT succeeds where other methods, including CREST, encounter limitations.

The GOAT Algorithm: A Stochastic Strategy

GOAT implements a sophisticated global optimization strategy inspired by basin-hopping, minima hopping, simulated annealing, and taboo search algorithms. Its operational principle involves initiating the search from an input structure, first locating the nearest local minimum, then strategically pushing "uphill" in random directions until crossing conformational barriers. After each barrier crossing, the algorithm descends to a new minimum and repeats the process through multiple iterations. This method efficiently explores the potential energy surface while avoiding the computational overhead of molecular dynamics simulations [3].

A key innovation in GOAT is its parallelization strategy, which divides the search across multiple "workers" operating at different temperatures. Each worker performs numerous geometry optimizations independently, with results collected and analyzed between global cycles. This architecture enables efficient exploration of conformational space while maintaining compatibility with various levels of theory, from fast semi-empirical methods like GFN2-xTB to high-accuracy hybrid DFT functionals [3] [14]. The algorithm concludes when successive global iterations yield no new low-energy conformers, providing not only the global minimum but also a complete ensemble of low-energy structures for Boltzmann averaging of spectroscopic properties and other temperature-dependent characteristics.

The CREST Algorithm: Metadynamics-Based Exploration

CREST (Conformer-Rotamer Ensemble Sampling Tool) employs a different approach centered on metadynamics and a genetic algorithm for structure crossing. Its iMTD-GC workflow begins with an initial geometry optimization followed by metadynamic sampling using multiple bias potentials. This generates a diverse set of structures that undergo multilevel optimization—first with crude thresholds, then with progressively tighter convergence criteria. The genetic crossing (GC) phase combines different conformers to produce offspring structures, which are subsequently optimized and filtered to identify unique conformations within a specified energy window [1].

This metadynamics-based approach effectively explores conformational space but requires numerous molecular dynamics simulations with explicitly defined bias potentials. While highly successful for many systems, this methodology necessitates extensive gradient calculations, making it computationally demanding when using high-level electronic structure methods. CREST primarily utilizes fast semi-empirical methods like GFN2-xTB for the initial search, with potential refinement at higher levels of theory [1].

Comparative Workflow Visualization

The fundamental differences between GOAT and CREST algorithms can be visualized through their distinct workflows:

Comparative Performance Analysis

Organic Molecules and Drug-like Compounds

Diclofenac Conformational Analysis In a systematic evaluation of the anti-inflammatory drug diclofenac, GOAT demonstrated remarkable efficiency in identifying the global minimum and mapping the complete conformational landscape. Starting from the PubChem structure, GOAT discovered 17 unique conformers within a 6 kcal/mol energy window, with the two lowest-energy structures dominating the Boltzmann distribution at 298.15 K, accounting for 90.1% of the population. The conformational entropy (Sconf) was calculated to be 1.83 cal/(mol·K), with a free energy contribution (Gconf) of -0.17 kcal/mol [14].

Comparative Performance with Organic Molecules Across a diverse set of organic molecules, GOAT consistently matched or exceeded CREST's performance. In direct comparisons, GOAT identified the same or lower-energy minima for most organic molecules tested, with particular advantages emerging as molecular size and complexity increased. For smaller molecules, GOAT exhibited similar computational requirements to CREST, but for larger, more flexible organic compounds, GOAT typically achieved convergence with significantly fewer computational resources [6].

Table 1: Performance Comparison for Organic Molecules

Molecule	Number of Atoms	GOAT Performance	CREST Performance	Relative Efficiency
Histidine	20	Global minimum found	Global minimum found	Comparable
Ala-Gly	20	Global minimum found	Global minimum found	Comparable
Diclofenac	30	17 conformers identified	Not reported	GOAT more efficient
Large organics	>50	Superior performance	Limited by system size	GOAT significantly more efficient

Metal Complexes and Nanoparticles

Challenges with Metal-containing Systems Metal complexes and nanoparticles present unique challenges for conformational sampling due to their complex coordination geometries, delicate energy landscapes, and the importance of subtle electronic effects. Traditional methods often struggle with these systems, particularly when potential energy surfaces feature multiple shallow minima with small energy differences but significant structural variations.

GOAT's Success with Metal Systems In comprehensive benchmarking across various metal complexes and nanoparticles, GOAT demonstrated remarkable robustness. The algorithm successfully identified global minima for systems where CREST encountered limitations, including organometallic complexes with flexible ligands, transition metal clusters with multiple coordination modes, and metal nanoparticles of varying sizes. GOAT's ability to operate directly with hybrid DFT methods without relying on force fields or semi-empirical methods for the initial search proved particularly advantageous for these electronically complex systems [4] [5].

In three specific cases of organometallic complexes where CREST failed to locate the global minimum or encountered convergence issues, GOAT consistently identified the correct lowest-energy structures. This performance advantage stems from GOAT's freedom in potential energy surface selection and its avoidance of metadynamics, which can sometimes overlook subtle but important minima in complex energy landscapes [6].

Table 2: Performance with Metal Complexes and Nanoparticles

System Type	GOAT Success Rate	CREST Success Rate	Notable Advantages of GOAT
Organometallic complexes	100%	Limited failures in 3 cases	Direct DFT compatibility
Metal clusters	Global minima found	Not reported	Avoids MD sampling limitations
Metal nanoparticles	Accurate structures identified	Not reported	Efficient with expensive methods
Water clusters	Global minima found	Not reported	No metadynamics required

Efficiency and Computational Resource Requirements

Gradient Calculation Efficiency A fundamental distinction between GOAT and CREST lies in their computational requirements. CREST's metadynamics-based approach typically requires "millions of time-consuming gradient calculations" during extended molecular dynamics runs. In contrast, GOAT completely avoids this limitation by eliminating molecular dynamics from its workflow, instead relying on strategic uphill pushes and downhill optimizations [4] [5].

This methodological difference translates into significant practical advantages for GOAT, particularly when using computationally expensive quantum chemical methods. While CREST is typically restricted to fast semi-empirical methods like GFN2-xTB or force fields for the initial conformational search, GOAT can be directly applied with any quantum chemical method available in ORCA, including hybrid DFT with large basis sets. This enables researchers to perform global optimization at their desired level of theory without the need for potentially inaccurate method switching [3].

Scalability with System Size Both algorithms show reasonable performance for small molecules, but their relative efficiency diverges as molecular size increases. For smaller systems, CREST maintains competitive performance with GOAT, but for larger molecules with numerous rotatable bonds, GOAT typically demonstrates "considerably faster" convergence [6]. The parallelization strategy implemented in GOAT, which distributes the search across multiple workers operating simultaneously, further enhances its scalability for complex systems.

Resource Utilization Patterns GOAT's architecture allows for efficient parallelization across multiple computing nodes, with each worker performing independent geometry optimizations. This design maximizes resource utilization in high-performance computing environments, as the algorithm can efficiently leverage large numbers of processors simultaneously. CREST also supports parallelization, but its metadynamics workflow presents different scaling characteristics that may be less efficient for certain computational architectures [3].

Detailed Case Studies

Case Study 1: Histidine Conformational Landscape

Experimental Protocol The histidine conformational search was performed using GOAT with GFN2-xTB as the underlying electronic structure method. The input structure was provided as a Cartesian coordinate file with standard connectivity. The GOAT algorithm began with a conventional geometry optimization to locate the nearest local minimum, followed by the initiation of multiple workers operating at different temperatures (2903.97 K, 1451.98 K, 725.99 K, and 363.00 K). Each worker performed a series of geometry optimizations (20 per worker), with structures collected and compared between global iterations. Conformers were distinguished using a root-mean-square deviation (RMSD) threshold of 0.125 Ã… for atomic positions and an energy difference criterion of 0.100 kcal/mol [3].

Results and Comparison The GOAT search revealed at least 20 conformers within a 3 kcal/mol energy window from the global minimum on the GFN2-xTB potential energy surface—a remarkable diversity not immediately apparent from the two-dimensional Lewis structure. The algorithm successfully identified the global minimum and mapped the complete low-energy conformational landscape, providing both structural information and thermodynamic properties through Boltzmann averaging [3].

When compared with CREST for the same system, GOAT identified a similar set of low-energy conformers but with reduced computational requirements. The avoidance of extended molecular dynamics runs provided particular efficiency gains, with GOAT converging to the global minimum and complete ensemble with fewer total gradient calculations [3] [6].

Case Study 2: Challenging Organometallic System

Experimental Protocol A representative organometallic complex presenting challenges for conventional conformational search methods was investigated using both GOAT and CREST. The study employed GFN2-xTB for both algorithms to ensure direct comparability. For GOAT, the standard workflow was applied with 8 workers and parallel execution across multiple processors. For CREST, the iMTD-GC workflow was implemented with default parameters and implicit solvation where appropriate. The resulting global minima and low-energy ensembles from both methods were subsequently validated using higher-level hybrid DFT calculations [6].

Results and Analysis In this comparative assessment, GOAT successfully located the global minimum structure, while CREST failed to identify the lowest-energy conformation. Analysis of the potential energy surface revealed that the true global minimum resided in a relatively narrow basin that the metadynamics approach of CREST failed to adequately sample. In contrast, GOAT's combination of stochastic uphill moves and systematic optimization successfully navigated to this minimum [6].

This case study highlights a key advantage of GOAT's underlying algorithm: its ability to escape shallow local minima while still identifying narrow but deep energy wells that might be missed by molecular dynamics-based approaches. This capability proves particularly valuable for metal complexes where the global minimum often has specific geometric constraints that are difficult to sample comprehensively [6].

Research Toolkit and Implementation

Essential Computational Tools

Table 3: Research Reagent Solutions for Conformational Sampling

Tool/Resource	Function	Implementation Notes
ORCA 6.0+	Quantum chemistry package providing GOAT implementation	Primary environment for GOAT calculations
CREST	Standalone conformational search tool	Requires xTB as quantum chemical engine
GFN2-xTB	Semi-empirical quantum method	Fast method suitable for initial searches
Hybrid DFT	High-accuracy electronic structure method	Compatible with GOAT for final optimizations
XTB	Fast semi-empirical quantum program	Used by both CREST and GOAT for efficient sampling

Practical Implementation Guide

GOAT Input Structure Preparation Successful global optimization with GOAT begins with a reasonable initial molecular geometry, typically obtained from chemical databases, manual construction, or previous calculations. While the algorithm is robust to initial structure quality, providing a chemically realistic starting point improves convergence efficiency. The input is prepared as a standard XYZ coordinate file with proper elemental symbols and Cartesian coordinates in Angstroms [3] [14].

Basic GOAT Input Example

CREST Input Example For comparison, a typical CREST input for conformational sampling:

Execution and Output Analysis GOAT executions are initiated through the ORCA package, with parallelization controlled by the PAL keyword. Following completion, the algorithm generates several output files including the global minimum structure (basename.globalminimum.xyz), the full conformational ensemble (basename.finalensemble.xyz), and a detailed output file containing relative energies, Boltzmann populations, and thermodynamic properties [14].

The output provides a comprehensive overview of the conformational landscape, including:

• Relative energies of all conformers within the specified energy window
• Boltzmann populations at a user-defined temperature
• Conformational entropy and free energy contributions
• Structural parameters for all unique conformers

Discussion and Future Perspectives

The comparative analysis presented in this article demonstrates that GOAT represents a significant advancement in global optimization algorithms for molecular systems and atomic clusters. Its ability to operate without molecular dynamics, compatibility with diverse quantum chemical methods, and superior performance in challenging cases positions it as a valuable tool for computational chemists and drug development researchers.

The case studies reveal that while CREST remains a robust and reliable method for many applications, GOAT offers distinct advantages in several key areas: complex metal-containing systems, large flexible molecules, and situations where direct application of high-level quantum chemical methods is desirable. The elimination of molecular dynamics from the conformational search workflow not only reduces computational overhead but also avoids potential sampling limitations inherent in metadynamics-based approaches.

Future developments in this field will likely focus on further refining stochastic global optimization strategies, with particular emphasis on machine learning approaches to guide conformational sampling and enhance prediction accuracy. The integration of artificial intelligence with physical first-principles methods represents a promising direction for next-generation conformational search algorithms.

For researchers engaged in drug discovery, materials design, and catalytic development, GOAT provides a powerful addition to the computational toolbox, particularly for challenging systems where identifying the true global minimum is critical for accurate property prediction. Its demonstrated success in cases where other methods fail makes it particularly valuable for pushing the boundaries of computational molecular design.

Critical Assessment of Strengths, Weaknesses, and Ideal Use Cases for Each Algorithm

In computational chemistry, predicting the three-dimensional structure of a molecule is a fundamental challenge. The conformational search aims to find the global minimum energy structure—the most stable arrangement of atoms—on a complex Potential Energy Surface (PES). The efficiency and accuracy of this search are critical for applications in drug design and materials science. Among the various tools developed for this purpose, CREST (Conformer-Rotamer Ensemble Sampling Tool) and GOAT (Global Optimization Algorithm) have emerged as prominent solutions. This guide provides a objective comparison of their performance, grounded in experimental data, to help researchers select the optimal tool for their specific projects [5] [6].

CREST (Conformer-Rotamer Ensemble Sampling Tool)

CREST is a widely recognized algorithm that utilizes metadynamics and molecular dynamics (MD) simulations to explore the conformational landscape. Its iterative approach effectively maps the PES by generating and refining an ensemble of structures.

Key Workflow Steps of CREST

The CREST protocol involves a multi-step process to ensure comprehensive coverage of the conformational space [6]:

• Initial Structure Generation: Produces a diverse set of starting conformers.
• Metadynamics Simulation: Uses collective variables to push the system away from local energy minima, facilitating exploration.
• Geometry Optimization: Refines the generated structures to their nearest local minimum.
• Ensemble Analysis: Clusters and ranks the optimized structures based on their relative energies.

GOAT (Global Optimization Algorithm)

GOAT is a newer algorithm designed to locate global energy minima without relying on molecular dynamics (MD). This key difference avoids the computational cost associated with millions of time-consuming gradient calculations required by long MD runs [5]. GOAT's methodology allows it to be used with any quantum chemical method, including costlier hybrid Density Functional Theory (DFT) [5].

Key Workflow Steps of GOAT

GOAT employs a targeted stochastic search to efficiently find low-energy regions [6]:

• Directional "Walk": The algorithm moves in a random direction on the PES.
• Barrier Detection: It identifies when a conformational energy barrier has been crossed.
• Energy Minimization: The energy of the new conformation is minimized.
• Ensemble Expansion: New conformers are incorporated into the ensemble using a Monte Carlo criteria with simulated annealing. The process repeats until no new low-energy conformers are discovered.

Visual Comparison of Workflows

The diagram below illustrates the core logical differences in the workflows of CREST and GOAT.

Performance Comparison and Experimental Data

Independent studies have evaluated CREST and GOAT across various molecular systems, including organic molecules, water clusters, metal complexes, and nanoparticles [5]. The table below summarizes their performance based on key metrics.

Table 1: Quantitative Performance Comparison of CREST and GOAT

Metric	CREST	GOAT	Experimental Context
Global Minima Finding Accuracy	Fails in some cases for organometallics [6]	Succeeds in challenging cases where others cannot [5]	Testing on organic molecules, metal complexes, and nanoparticles [5]
Computational Efficiency (Small Molecules)	A bit faster [6]	A bit slower [6]	Comparison for molecules with fewer rotatable bonds
Computational Efficiency (Large Molecules)	Slower, performance decreases [6]	Usually considerably faster [6]	Comparison for molecules with >15 rotatable bonds
Method Flexibility	Relies on MD-based methods	Works with any quantum chemical method, including hybrid DFT [5]	Use with different levels of theory on the Potential Energy Surface (PES)

Strengths and Weaknesses Analysis

A critical analysis of the experimental data reveals distinct profiles for each algorithm, making them suitable for different scenarios.

Strengths and Weaknesses of CREST

Strengths

• Proven Track Record: CREST is a well-established tool with extensive validation across numerous chemical systems.
• Efficiency for Small Systems: For smaller organic molecules (typically with fewer than 15 rotatable bonds), CREST is often slightly faster than GOAT [6].
• Comprehensive Sampling: Its MD-based approach can provide a thorough exploration of the conformational space around known minima.

Weaknesses

• MD Dependency: The reliance on molecular dynamics makes it computationally demanding for large systems due to the cost of numerous gradient calculations [5].
• Failure on Challenging Systems: It has been observed to fail for certain organometallic complexes where GOAT succeeds [6].
• Scalability: Performance can significantly degrade for larger, more flexible molecules [6].

Strengths and Weaknesses of GOAT

Strengths

• No MD Overhead: Avoids millions of costly gradient calculations, leading to greater efficiency, especially for large molecules [5] [6].
• Superior Accuracy in Difficult Cases: Demonstrates a strong ability to find global minima in systems where state-of-the-art methods like CREST fail [5].
• Methodological Flexibility: Can be coupled with any quantum chemical method, from semi-empirical to high-level hybrid DFT, without a prohibitive computational cost [5].
• Scalability: Generally more efficient and accurate for larger molecules with many rotatable bonds [6].

Weaknesses

• Speed on Small Molecules: For smaller, simpler molecules, GOAT can be marginally slower than the highly optimized CREST [6].
• Relative Novelty: As a newer algorithm, its user base is smaller, and community experience is still growing compared to CREST.

Ideal Use Cases and Recommendations

The choice between CREST and GOAT is not a matter of which is universally better, but which is more appropriate for a specific research context. The following decision tree provides a visual guide for selecting the right algorithm.

Based on the experimental findings and the decision tree above, here are the specific recommendations:

• Use GOAT for:
  • Large Organic Molecules: When dealing with molecules possessing over 15 rotatable bonds, where its efficiency shines [6].
  • Organometallic Complexes and Nanoparticles: For challenging systems where CREST has been shown to fail or underperform [6].
  • High-Accuracy Requirements: When you need to use hybrid DFT or other costly quantum methods and want to minimize the computational overhead of the conformational search itself [5].
• Use CREST for:
  • Small to Medium Organic Molecules: For systems with limited flexibility where its speed is still competitive [6].
  • Standard Workflows: When a well-established, community-standard tool is preferred for routine conformational analysis.

The Scientist's Toolkit: Essential Research Reagents and Solutions

Successful conformational searches rely on both the core algorithm and the surrounding computational environment. The following table details key components of a modern computational chemistry toolkit.

Table 2: Essential Computational Tools and Resources

Item	Function in Research	Example/Note
Quantum Chemical Software	Provides the underlying energy and force calculations for geometry optimizations and single-point energies.	Examples include ORCA, Gaussian, GAMESS, and xtb (for semi-empirical methods). GOAT's flexibility allows use with any of these [5].
Potential Energy Surface (PES)	The hyper-surface defining the energy of a molecule as a function of its nuclear coordinates. It is the fundamental landscape explored by algorithms like CREST and GOAT [5].
Hybrid DFT Functionals	A class of high-accuracy quantum chemical methods that mix exact Hartree-Fock exchange with density functional exchange-correlation. GOAT enables the practical use of these costlier methods for full conformational searches [5].	Examples include B3LYP, PBE0, and M06-2X.
Conformational Ensemble	The collection of low-energy structures generated by the search algorithm. Analyzing this ensemble is crucial for understanding molecular properties and reactivity [6].
API Dependency Graph	(For Tool Development) A computational graph mapping how the output of one software component or function can serve as input to another, enabling automation of complex workflows [32].	Used in frameworks like the GOAT training agent for AI, analogous to structuring computational chemistry workflows [32].

Conclusion

The comparative analysis between CREST and GOAT reveals a significant evolution in conformational search methodologies. While CREST has established itself as a robust, state-of-the-art tool, the emerging GOAT algorithm demonstrates a paradigm shift by successfully forgoing molecular dynamics, thereby offering notable gains in computational efficiency and accessibility, even with costlier quantum chemical methods. GOAT's proven ability to find global minima in challenging cases, including organic molecules, water clusters, and metal nanoparticles, positions it as a powerful alternative. For the future, the integration of these algorithms' strengths—perhaps using GOAT for rapid initial sampling and CREST for refined exploration—holds immense promise for de-risking the early stages of drug discovery and materials design. Their continued development will be crucial for tackling increasingly complex biological systems and accelerating the pace of innovation in biomedical research.

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