Guided Diffusion Monte Carlo: A Method for Studying Molecules and Ions That Display Large Amplitude Vibrational Motions

Abstract

Diffusion Monte Carlo provides an effective and efficient approach for calculating ground state properties of molecular systems based on potential energy surfaces. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. We recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters [J. Phys. Chem. A201912380638070]. In the present study, we extend this approach and apply it to more strongly bound molecular ions, specifically CH5 + and H+(H2O) n=1–4. For the protonated water systems, we show that the guided DMC approach that was developed for studies of (H2O) n can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H3O+ core of H+(H2O) n and the CH stretches in CH5 +, we develop adaptive guiding functions based on the instantaneous structure of the ion of interest. Using these guiding functions, we demonstrate that we are able to obtain converged zero-point energies and ground state wave functions using ensemble sizes that are as small as 10% the size that is needed to obtain similar accuracy from unguided calculations.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

“…9,10 Recently, we have demonstrated that we can achieve a significant reduction in the ensemble size required for a DMC simulation by introducing a guiding function that describes the dependence of the wave function on the high-frequency intramolecular motions and have applied the approach to neutral water clusters, 10,11 protonated water clusters, and CH 5 + . 12 This development has led to an order of magnitude speed-up in these calculations, which has opened the door to DMC studies of larger molecules and clusters. Even with these advances, the computational requirements for evaluating the potential will quickly limit the size of the systems that can be studied.…”

Multicomponent Coupled Cluster Singles and Doubles with Density Fitting: Protonated Water Tetramers with Quantized Protons

“…To further showcase the power of the NEO-DF-CCSD method, we calculated the relative stabilities of four protonated water tetramer isomers, − treating all nine protons quantum mechanically. This application is particularly challenging because inclusion of zero-point energy contributions is known to change the relative stabilities of these isomers at the coupled cluster level. , According to the electronic energies without zero-point energy contributions at the CCSD­(T) level of theory, the relative stabilities of these isomers are Eigen < ring < cis -Zundel < trans -Zundel (black line in Figure A) .…”

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4+

“…In the present study, we use the GSPA approach to evaluate the spectra of H 7 O 3 + , D 7 O 3 + , H 9 O 4 + , and D 9 O 4 + , as well as the excited state energies of H 3 O + . As inputs for these calculations, we use the ground state probability amplitudes that were obtained as part of a previously reported DMC study of these ions, where we used guided DMC simulations to obtain snapshots of f = Φ 0 Ψ T . In guided DMC studies, f is represented by an ensemble of localized functions, referred to as walkers, Φ 0 is the ground state wave function of the ion of interest, and Ψ T is a guiding function.…”

“…Operationally, the descendant weight is calculated using Based on this expression for d j , the expectation value of an arbitrary multiplicative operator, A can be evaluated using Monte Carlo integration, where N w is the number of walkers in the ensemble. Additional details of the implementation of the DMC calculations are provided in ref and the Supporting Information.…”

“…To explore this possibility, we will use insights gained from the ground state probability amplitudes for H 7 O 3 + and H 9 O 4 + , which were obtained from diffusion Monte Carlo (DMC) simulations . DMC is a stochastic method in which an ensemble of localized functions, referred to as walkers, randomly samples the potential energy surface for the system of interest.…”