On the calculation of absolute free energies from molecular-dynamics or Monte Carlo data.
We propose a method for calculating absolute free energies from Monte Carlo or molecular-dynamics data. The method is based on the identity that expresses the partition function Q as a Boltzmann average: 1Q=w(p,x)exp[betaH(p,x)], where w(p,x) is an arbitrary weight function such that its integral over the phase space is equal to 1. In practice, to minimize statistical errors the weight function is chosen such that the regions of the phase space where sampling statistics are poor are excluded from the average. The "ideal" weight function would be the equilibrium phase-space density exp[-betaH(p,x)]Q itself. We consider two methods for constructing the weight function based on different estimates of the equilibrium phase-space density from simulation data. In the first method, it is chosen to be a Gaussian function, whose parameters are obtained from the covariance matrix of the atomic coordinates. In the second, a clustering algorithm is used to attempt partitioning the data into clusters corresponding to different basins of attraction visited by the system. The weight function is then constructed as a superposition of Gaussians calculated for each cluster separately. We show that these strategies can be used to improve upon previous methods of estimating absolute entropies from covariance matrices.
Department of Chemistry and Biochemistry, Institute for Theoretical Chemistry, University of Texas at Austin, 78712, USA.
Lei
L
Huang
Dmitrii E
DE
Makarov
D000465:Algorithms; D016000:Cluster Analysis; D003198:Computer Simulation; D004735:Energy Transfer; D019277:Entropy; D008968:Molecular Conformation; D009010:Monte Carlo Method