Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis

TL;DR

This paper analyzes the feasibility of a global Hamiltonian in adaptive molecular resolution methods, showing it can be physically consistent and accurate under certain conditions, but practical limitations exist for current implementations.

Contribution

It provides an asymptotic analysis demonstrating conditions for a consistent, accurate Hamiltonian in adaptive molecular resolution, and discusses implications for numerical simulations.

Findings

A Hamiltonian can be physically consistent and accurate under specific mathematical conditions.

Large system sizes are required for the Hamiltonian approach to be practical.

The proposed Hamiltonian offers a foundation for simplifying adaptive resolution algorithms.

Abstract

Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer/transition region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size and thus a Hamiltonian approach as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes.