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A Variational Approach to Enhanced Sampling and Free Energy Calculations
Omar Valsson, Michele Parrinello
TL;DR
Kinetic bottlenecks make MD and MC sampling of complex free-energy landscapes prohibitively costly, while constructing effective bias potentials is challenging. The paper introduces a variational functional whose minimizing bias relates simply to the free-energy surface, and demonstrates an efficient, flexible sampling method on molecular systems.
Problem
Kinetic bottlenecks hinder MD and MC exploration of complex free-energy landscapes, and constructing effective bias potentials is challenging.
Method
The method minimizes a convex functional of a parameterized bias potential to construct an effective bias and determine free-energy surfaces, with reweighting available during optimization.
Results
The method accurately determines free-energy surfaces in alanine dipeptide and Ala3 examples, including excellent agreement with extensive parallel-tempering reference results for Ala3.
Takeaways & Limitations
The variational approach provides a practical, efficient, and flexible framework for enhanced sampling and free-energy calculations.
Takeaways & Limitations
The method still depends on an appropriate choice of collective variables, while its optimization procedure and basis-set choices may require system-specific improvement.
Abstract
from arXiv · showhide
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variable. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient and flexible sampling method. A number of numerical examples are presented which include the determination of a three dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient standpoint for looking with novel eyes at the sampling problem.