Testing Convergence of Different Free-Energy Methods in a Simple Analytical System with Hidden Barriers

Abstract

In this work, we study the influence of hidden barriers on the convergence behavior of three free-energy calculation methods: well-tempered metadynamics (WTMD), adaptive-biasing forces (ABF), and on-the-fly parameterization (OTFP). We construct a simple two-dimensional potential-energy surfaces (PES) that allows for an exact analytical result for the free-energy in any one-dimensional order parameter. Then we chose different CV definitions and PES parameters to create three different systems with increasing sampling challenges. We find that all three methods are not greatly affected by the hidden-barriers in the simplest case considered. The adaptive sampling methods show faster sampling while the auxiliary high-friction requirement of OTFP makes it slower for this case. However, a slight change in the CV definition has a strong impact in the ABF and WTMD performance, illustrating the importance of choosing suitable collective variables.

Keywords

• molecular dynamics
• metadynamics
• adaptive-biasing force algorithm
• temperature-acceleration
• on-the-fly parameterization