E. C. Cyr and S. D. Bond, Using the Method of Weighted Residuals to
Compute Potentials of Mean Force, Journal of Computational Physics,
We propose a general framework for approximating the potential of mean force (PMF) along a reaction
coordinate in conformational space. This framework, based on the method of weighted residuals, can
be viewed as a generalization of thermodynamic integration and direct histogram methods.
Using weighted residuals allows for higher-order approximations to the PMF in the form of a global
spectral method or a finite element method. In addition, the higher degree of continuity provided
by spectral and higher-order elements makes weighted residual methods an attractive choice for
use in tandem with biasing force methods. As an analysis tool, the weighted residuals framework
provides a context for direct comparison of thermodynamic integration and histogram based methods.
For validation of the new method,
numerical experiments are performed on two systems:
a simple double-well and alanine dipeptide in vacuum.
Comparisons between the new weighted residual methods, thermodynamic integration, and
WHAM are performed.
When configuration space is perfectly sampled the high-order weighted residual methods are found to
exhibit exponential convergence. For more realistic sampling, the weighted residual methods performed
comparably to the other two. However, results suggest that spectral type methods are more robust
with respect to parameter choices describing the solution space.