Sampling Free Energy Surfaces as Slices by Combining Umbrella Sampling and Metadynamics

TL;DR

This paper introduces a combined umbrella sampling and metadynamics approach to efficiently sample high-dimensional free energy surfaces, especially in flat or broad wells, demonstrated on chemical reactions with ab initio and QM/MM methods.

Contribution

It presents a novel scheme that integrates US and MTD for controlled, efficient sampling of free energy landscapes in complex molecular systems.

Findings

Enhanced sampling efficiency for flat, broad free energy wells.

Successful application to high-dimensional chemical reaction surfaces.

Proposed reweighting method avoids recrossing trajectories for barrier calculations.

Abstract

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, in order to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories.