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 three-dimensional 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.
%0 Journal Article
%1 PhysRevLett.113.090601
%A Valsson, Omar
%A Parrinello, Michele
%D 2014
%I American Physical Society
%J Phys. Rev. Lett.
%K Carlo Monte chemistry dynamics mechanics molecular physics statistical unread
%N 9
%P 090601
%R 10.1103/PhysRevLett.113.090601
%T Variational Approach to Enhanced Sampling and Free Energy Calculations
%U http://link.aps.org/doi/10.1103/PhysRevLett.113.090601
%V 113
%X 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 three-dimensional 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.
@article{PhysRevLett.113.090601,
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 three-dimensional 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.},
added-at = {2014-09-17T02:23:16.000+0200},
author = {Valsson, Omar and Parrinello, Michele},
biburl = {https://www.bibsonomy.org/bibtex/2c1542329bf4a761ce8b1ed09e95e3eab/drmatusek},
doi = {10.1103/PhysRevLett.113.090601},
interhash = {292f08ed26245346e9ca9adb57fa9487},
intrahash = {c1542329bf4a761ce8b1ed09e95e3eab},
journal = {Phys. Rev. Lett.},
keywords = {Carlo Monte chemistry dynamics mechanics molecular physics statistical unread},
month = aug,
number = 9,
numpages = {5},
pages = 090601,
publisher = {American Physical Society},
timestamp = {2014-09-17T02:23:16.000+0200},
title = {Variational Approach to Enhanced Sampling and Free Energy Calculations},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.090601},
volume = 113,
year = 2014
}