Equilibrium Molecular Thermodynamics from Kirkwood Sampling

We
present two methods for barrierless equilibrium sampling of
molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys. 2009, 130,
134102). Kirkwood sampling employs low-order correlations among internal
coordinates of a molecule for random (or non-Markovian) sampling of
the high dimensional conformational space. This is a geometrical sampling
method independent of the potential energy surface. The first method
is a variant of biased Monte Carlo, where Kirkwood sampling is used
for generating trial Monte Carlo moves. Using this method, equilibrium
distributions corresponding to different temperatures and potential
energy functions can be generated from a given set of low-order correlations.
Since Kirkwood samples are generated independently, this method is
ideally suited for massively parallel distributed computing. The second
approach is a variant of reservoir replica exchange, where Kirkwood
sampling is used to construct a reservoir of conformations, which
exchanges conformations with the replicas performing equilibrium sampling
corresponding to different thermodynamic states. Coupling with the
Kirkwood reservoir enhances sampling by facilitating global jumps
in the conformational space. The efficiency of both methods depends
on the overlap of the Kirkwood distribution with the target equilibrium
distribution. We present proof-of-concept results for a model nine-atom
linear molecule and alanine dipeptide.