Molecule–Environment Embedding with Quantum Monte Carlo: Electrons Interacting with Drude Oscillators

We present a comprehensive investigation of the El-QDO embedding method [<i>Phys. Rev. Lett.</i> <b>131</b>, 228001 (2023)], where molecular systems described through the electronic Hamiltonian are immersed in a bath of charged quantum harmonic oscillators, i.e., quantum Drude oscillators (QDOs). In the El-QDO model, the entire system of electrons and drudons─the quantum particles in the QDOs─is modeled through a single Hamiltonian which is solved through quantum Monte Carlo (QMC) methods. We first describe the details of the El-QDO Hamiltonian, of the proposed El-QDO ansatz, and of the QMC algorithms implemented to integrate both electronic and drudonic degrees of freedom. Then we analyze short-range regularization functions for the interacting potential between electrons and QDOs in order to accurately treat equilibrium and repulsive regions, resolving the overpolarization error that occurs between the electronic system and the environment. After benchmarking various regularization (damping) functions on the cases of argon and water dimers, the El-QDO method is applied to study the solvation energies of the benzene and water dimers, verifying the accuracy of the El-QDO approach compared to accurate fully electronic ab initio calculations. Furthermore, through the comparison of the El-QDO interaction energies with the components of Symmetry-Adapted Perturbation Theory calculations, we illustrate the El-QDO's explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the electronic subsystem and the environment.