Efficient Implementation of Gaussian Process Regression Accelerated Saddle Point Searches with Application to Molecular Reactions

2025-05-18

AI Summary

To address the low efficiency of first-order saddle point searches on high-dimensional potential energy surfaces and the high computational cost of electronic structure calculations, this work proposes the GPR-dimer method. It tightly couples Gaussian process regression (GPR) with dimer-based minimal-mode-following dynamics in Cartesian coordinates, constructing an energy surrogate model without internal coordinate transformations. By integrating Hessian lowest-eigenmode estimation and a C++-based high-performance implementation, the method drastically reduces the number of electronic structure evaluations. This is the first Cartesian-coordinate-based GPR-accelerated saddle point search achieving both robustness and efficiency across a broad range of force constants. On a benchmark set of 500 molecular reactions, the method reduces electronic structure evaluations by 90% on average; total wall-clock time decreases in 75% of cases, matching the performance of the specialized internal-coordinate software Sella.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Kernel Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.

Problem

• Locating saddle points on high-dimensional energy surfaces efficiently
• Reducing electronic structure calculations for saddle point convergence
• Accelerating saddle point searches using Gaussian process regression

Innovation

• Gaussian process regression accelerates saddle point searches
• Surrogate energy surface updated after each calculation
• Cartesian coordinates reduce electronic structure calculations