Making Many-Body Interactions Nearly Pairwise Additive: The Polarized Many-Body Expansion Approach

TL;DR

The paper introduces the Polarized Many-Body Expansion (PolBE) method, which enhances the accuracy of condensed phase simulations by treating each energy contribution as an embedding problem with polarized environments, achieving near pairwise additivity.

Contribution

The novel PolBE approach improves the accuracy of many-body expansions by incorporating polarized environments, reducing the need for higher-order terms and enabling efficient simulations with hybrid density functionals.

Findings

PolBE accurately predicts non-covalent interaction energies across various systems.

PolBE interaction energies are predominantly pairwise, unlike traditional MBE.

PolBE outperforms other embedded MBE methods like electrostatically embedded MBE.

Abstract

The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve quantitative accuracy. In this work, we propose the Polarized MBE (PolBE) method where each MBE energy contribution is treated as an embedding problem. In each energy term, a smaller fragment is embedded into a larger, polarized environment and only a small region is treated at the high-level of theory using embedded mean-field theory. The role of polarized environment was found to be crucial in providing quantitative accuracy at the 2-body level. PolBE accurately predicts non-covalent interaction energies for a number of systems, including CO$_2$, water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE which requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE. Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.