Grand Canonical Adaptive Resolution Simulation for Molecules with Electrons: A Theoretical Framework based on Physical Consistency

TL;DR

This paper introduces a theoretical framework for simulating open molecular systems with electrons using a grand canonical approach, ensuring physical consistency across electronic and classical regions for multiscale modeling.

Contribution

It proposes a novel grand canonical adaptive resolution scheme that couples quantum and classical regions based on thermodynamic principles, ensuring physical consistency.

Findings

Framework maintains electronic chemical potential consistency.

Molecular exchange occurs according to first principles.

Provides guidelines for multiscale simulation protocols.

Abstract

A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic properties of the quantum region are calculated at constant electronic chemical potential equal to that of the corresponding (large) bulk system treated at full quantum level. Instead, the exchange of molecules between the quantum region and the classical environment occurs at the chemical potential of the macroscopic thermodynamic conditions. T he Grand Canonical Adaptive Resolution Scheme is proposed for the treatment of the classical environment; such an approach can treat the exchange of molecules according to first principles of statistical mechanics and thermodynamic. The overall scheme is build on the basis of physical consistency, with the corresponding definition of numerical criteria of control of the approximations implied by the coupling. Given the wide range of expertise required, this work has the intention of providing guiding principles for the construction of a well founded computational protocol for actual multiscale simulations from the electronic to the mesoscopic scale.