Variational Approach to Enhanced Sampling and Free Energy Calculations
Abstract
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, 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 variables. 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 threedimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.
 Publication:

Physical Review Letters
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevLett.113.090601
 arXiv:
 arXiv:1407.0477
 Bibcode:
 2014PhRvL.113i0601V
 Keywords:

 05.10.a;
 02.70.Ns;
 05.70.Ln;
 87.15.H;
 Computational methods in statistical physics and nonlinear dynamics;
 Molecular dynamics and particle methods;
 Nonequilibrium and irreversible thermodynamics;
 Dynamics of biomolecules;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 4 pages, 2 figures