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

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 [Lee, V. G. M.; McCoy, A. B. J. Phys. Chem. A 2019, 123, 8063−8070]. 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.