Accurate quantum Monte Carlo forces for machine-learned force fields: Ethanol as a benchmark (2404.09755v1)
Abstract: Quantum Monte Carlo (QMC) is a powerful method to calculate accurate energies and forces for molecular systems. In this work, we demonstrate how we can obtain accurate QMC forces for the fluxional ethanol molecule at room temperature by using either multi-determinant Jastrow-Slater wave functions in variational Monte Carlo or just a single determinant in diffusion Monte Carlo. The excellent performance of our protocols is assessed against high-level coupled cluster calculations on a diverse set of representative configurations of the system. Finally, we train machine-learning force fields on the QMC forces and compare them to models trained on coupled cluster reference data, showing that a force field based on the diffusion Monte Carlo forces with a single determinant can faithfully reproduce coupled cluster power spectra in molecular dynamics simulations.
- J. S. Smith, O. Isayev, and A. E. Roitberg, ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost, Chem. Sci. 8, 3192 (2017).
- T. Frank, O. Unke, and K.-R. Müller, So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems, Adv. Neural. Inf. Process. Syst. 35, 29400 (2022).
- J. Gasteiger, F. Becker, and S. Günnemann, Gemnet: Universal directional graph neural networks for molecules, Adv. Neural. Inf. Process. Syst. 34, 6790 (2021).
- J. Behler and M. Parrinello, Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces, Phys. Rev. Lett. 98, 146401 (2007).
- S. Sorella and L. Capriotti, Algorithmic differentiation and the calculation of forces by quantum monte carlo, J. Chem. Phys 133, 234111 (2010), https://doi.org/10.1063/1.3516208 .
- C. Filippi, R. Assaraf, and S. Moroni, Simple formalism for efficient derivatives and multi-determinant expansions in quantum monte carlo, J. Chem. Phys. 144, 194105 (2016), https://doi.org/10.1063/1.4948778 .
- R. Assaraf, S. Moroni, and C. Filippi, Optimizing the energy with quantum monte carlo: A lower numerical scaling for jastrow-slater expansions, J. Chem. Theory Comput. 13, 5273 (2017), https://doi.org/10.1021/acs.jctc.7b00648 .
- R. Assaraf and M. Caffarel, Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces, J. Chem. Theory Comput. 119, 10536 (2003).
- C. Filippi and C. J. Umrigar, Correlated sampling in quantum Monte Carlo: A route to forces, Phys. Rev. B 61, R16291 (2000).
- S. Moroni, S. Saccani, and C. Filippi, Practical Schemes for Accurate Forces in Quantum Monte Carlo, J. Chem. Theory Comput. 10, 4823 (2014).
- K. Nakano, M. Casula, and G. Tenti, Unbiased and affordable atomic forces in ab initio Variational Monte Carlo (2023), arXiv:2312.17608.
- C. Huang and B. M. Rubenstein, Machine Learning Diffusion Monte Carlo Forces, J. Phys. Chem. A 127, 339 (2023).
- A. Tkatchenko and M. Scheffler, Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data, Phys. Rev. Lett. 102, 073005 (2009).
- A. Lüchow, Quantum monte carlo methods, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 1, 388 (2011).
- B. M. Austin, D. Y. Zubarev, and W. A. Lester, Quantum monte carlo and related approaches, Chem. Rev. 112, 263 (2012).
- C. J. Umrigar, M. P. Nightingale, and K. J. Runge, A diffusion Monte Carlo algorithm with very small time-step errors, J. Chem. Phys. 99, 2865 (1993).
- C. Attaccalite and S. Sorella, Stable Liquid Hydrogen at High Pressure by a Novel Ab Initio Molecular-Dynamics Calculation, Phys. Rev. Lett. 100, 114501 (2008).
- S. Pathak and L. K. Wagner, A light weight regularization for wave function parameter gradients in quantum Monte Carlo, AIP Adv. 10, 085213 (2020).
- B. Huron, J. P. Malrieu, and P. Rancurel, Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions, J. Chem. Phys. 58, 5745 (1973).
- P. S. Epstein, The stark effect from the point of view of schrödinger’s quantum theory, Phys. Rev. 28, 695 (1926).
- R. Nesbet, Configuration interaction in orbital theories, Proc. R. Soc. London, Ser. A 230, 312 (1955).
- M. Burkatzki, C. Filippi, and M. Dolg, Energy-consistent pseudopotentials for quantum Monte Carlo calculations, J. Chem. Phys. 126, 234105 (2007).
- S. Sorella, M. Casula, and D. Rocca, Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods, J. Chem. Phys 127, 014105 (2007).
- E. Neuscamman, C. J. Umrigar, and G. K.-L. Chan, Optimizing large parameter sets in variational quantum Monte Carlo, Phys. Rev. B 85, 045103 (2012).
- M. Casula, Beyond the locality approximation in the standard diffusion Monte Carlo method, Phys. Rev. B 74, 161102 (2006).
- T. H. Dunning, Gaussian basis sets for use in correlated molecular calculations. i. the atoms boron through neon and hydrogen, J. Chem. Phys. 90, 1007 (1989).
- G. Fonseca, I. Poltavsky, and A. Tkatchenko, Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope, J. Chem. Theory Comput. 19, 8706 (2023).