[Paper Review] Ab initio instanton rate theory made efficient using Gaussian process regression

Gabriel Laude, Danilo Calderini+2 more|arXiv (Cornell University)|May 7, 2018

Advanced Chemical Physics Studies4 citations

TL;DR

This paper proposes a Gaussian process regression (GPR)-accelerated ab initio instanton method that drastically reduces the number of high-level electronic-structure calculations required for accurate quantum reaction rate predictions. By fitting the potential-energy surface locally around the instanton pathway using GPR, the method achieves convergence to within 1% of benchmark results with up to 10× fewer ab initio evaluations, enabling efficient, high-accuracy rates at UCCSD(T)-F12b level for reactions like H + C2H6.

ABSTRACT

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

Motivation & Objective

• To reduce the computational cost of ab initio instanton theory, which requires many high-level electronic-structure calculations due to the need for energies, gradients, and Hessians along the full instanton path.
• To overcome the inefficiency of on-the-fly ab initio instanton calculations, which are more expensive than transition-state theory due to the large number of required electronic structure evaluations.
• To develop a method that maintains high accuracy using high-level electronic structure methods while significantly reducing the number of expensive calculations needed.
• To enable practical application of ab initio instanton theory to complex polyatomic reactions by making it computationally feasible at high levels of theory.

Proposed method

• Gaussian process regression (GPR) is used to construct a surrogate potential-energy surface (PES) trained only on ab initio data points sampled along the instanton pathway.
• The GPR model is trained on a small, adaptive set of high-level electronic-structure calculations (energies, gradients, Hessians) computed at key points along the ring-polymer instanton path.
• The method adaptively selects new training points based on prediction uncertainty to ensure convergence to the true instanton path and rate constant.
• The GPR surrogate enables accurate instanton rate calculations with far fewer high-level electronic structure evaluations than standard on-the-fly instanton methods.
• The approach is validated by comparing converged rates to benchmark full ab initio instanton calculations, showing agreement within 1%.
• The method is applied to H + CH4 and H + C2H6, achieving full-dimensional instanton rates at the UCCSD(T)-F12b/cc-pVTZ-F12 level with only ~6 Hessians.

Experimental results

Research questions

• RQ1 Can Gaussian process regression be used to accurately approximate the potential-energy surface along the instanton path with minimal high-level electronic-structure calculations?
• RQ2 What is the minimum number of ab initio evaluations required to converge the instanton rate to within 1% of the full on-the-fly result?
• RQ3 How does the GPR-accelerated instanton method compare in accuracy and efficiency to conventional ab initio instanton theory for benchmark reactions like H + CH4?
• RQ4 Can the method be extended to complex polyatomic reactions such as H + C2H6 at high levels of theory with practical computational cost?
• RQ5 Can the GPR framework be combined with low-level electronic structure data to further reduce the number of high-level calculations without sacrificing accuracy?

Key findings

• The GPR-accelerated instanton method converges to within 1% of the benchmark full ab initio instanton rate for the H + CH4 reaction using only a small fraction of the electronic-structure calculations required by standard methods.
• For the H + C2H6 reaction, the method achieved full-dimensional instanton rates at the UCCSD(T)-F12b/cc-pVTZ-F12 level with only about 6 Hessians, making it nearly as efficient as classical TST.
• The method maintains high accuracy even when the instanton pathway deviates significantly from the minimum energy path, demonstrating robustness in complex reaction mechanisms.
• The use of GPR enables systematic convergence with respect to both the number of ring-polymer beads and the size of the training set, ensuring reliable results.
• The approach allows for the use of high-level electronic structure methods in instanton theory, which was previously computationally prohibitive for many systems.
• The method opens the door to systematic inclusion of tunnelling in complex reaction networks by enabling efficient, high-accuracy instanton calculations for key steps only.