Building Maps in Collective Variable Space

TL;DR

This paper introduces a method to map auxiliary variables in collective variable space, enabling better analysis of molecular systems and the quality of reduced representations in enhanced sampling techniques.

Contribution

It presents a novel approach to visualize and analyze the dependence of functions on collective variables, improving understanding of free energy surfaces and system physics.

Findings

Maps reveal system physics and CV quality

Applied to alanine dipeptide conformations

Analyzed phase transitions in CO2 crystals

Abstract

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables. The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work we discuss how auxiliary variables can be mapped in collective variable (CV) space and how the dependence of the average value of a function of the atomic coordinates on the value of a small number of CVs can thus be visualised. We show that these maps allow one to analyse both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyse the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.