**Coarse-Graining of Imaginary Time Feynman Path Integrals: Inclusion of
Intramolecular Interactions and Bottom-up Force-Matching**

WH Ryu and GA Voth, JOURNAL OF PHYSICAL CHEMISTRY A, 126, 6004-6019 (2022).

DOI: 10.1021/acs.jpca.2c04349

Feynman's imaginary time path integral formalism of quantum statistical mechanics and the corresponding quantum classical isomorphism provide a tangible way of incorporating nuclear quantum effect (NQE) in the simulation of condensed matter systems using well-developed classical simulation techniques. Our previous work has presented the many-body coarse graining of path integral (CG-PI) theory that builds an isomorphism between the quantum partition function of N distinguishable particles and the classical partition function of 2N pseudoparticles. In this present work, we develop a generalized version of the many-body CG- PI theory that incorporates many-body interactions in the force field. Based on the new derivation, we provide a numerical CG-PI (n-CG-PI) modeling strategy parametrized from the underlying path integral molecular dynamics (PIMD) trajectories using force matching and Boltzmann inversion. The n-CG-PI models for two liquid systems are shown to capture well both the intramolecular and intermolecular structural correlations of the reference PIMD simulations. The generalized derivation of the many-body CG-PI theory and the n CG-PI model presented in this work extend the scope of the CG-PI formalism by generalizing the previously limited theory to incorporate force fields of realistic molecular systems.

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