On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles

Abstract

A new molecular dynamics method for calculating free energy profiles for rare events is presented. The new method is based on the creation of an adiabatic separation between a reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass, thereby allowing the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profile is obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, no unbiasing of the configuration space or postprocessing of the output data is required. The new method is applied to a variety of model problems including a two-dimensional free energy surface and its performance tested against free energy calculations using the “blue moon ensemble” approach. The comparison shows that free energy profiles can be calculated with greater ease and efficiency using the new method.

Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method

“…It must be stressed that this result has been obtained without having to assume adiabatic separation between s and the other variables as in Refs. [29,30,31].…”

Molecular Simulation in the Canonical Ensemble and Beyond

“…The weak dependence of the different parts finally contributes to the derivation of a potential of mean force, so that we can treat the subsystems in a sequential way. A similar technique is used in the setting of Car-Parinello dynamics [9], and a related approach is used for free energy profile calculation [31] in an on-the-fly numerical averaging process.…”

Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions

“…This approach is termed adiabatic free energy dynamics (AFED). 20,21 In the limit of perfect adiabatic decoupling, it can be proved that the CVs move on the correct potential of mean force surface, which is equivalent to the free energy surface. 20 The approach of Refs.…”

“…20,21 In the limit of perfect adiabatic decoupling, it can be proved that the CVs move on the correct potential of mean force surface, which is equivalent to the free energy surface. 20 The approach of Refs. 6 and 13, which we call Crystal-AFED, is an adaptation of the AFED scheme to the isothermal-isobaric ensemble, in which the cell lengths and angles, or equivalently, the elements of the full cell matrix, are employed as the target CVs.…”