MOL-MC: Do Markov chain sampling for a molecular system. The mol-mc program is the specialization of xxx-mc to the task of sampling from the canonical distribution for the states of a molecular system. See xxx-mc.doc for the generic features of this program. The Markov chain state for the system consists of the coordinates of all the molecules (with all coordinates for a molecule in consecutive positions), scaled so their range is [0,1) - in other words, the actual coordinates are obtained from those stored by multiplying by the length of a dimension. If the NPT ensemble is being used, the log of the length of a dimension is stored as a final component of state. The following applications-specific sampling procedures are implemented: wrap Changes the position coordinates of all the molecules so that they range from 0 to the length of a dimension, by adding the appropriate integer multiple of this length. Wrapping the coordinates is generally not necessary, since they are wrapped before being used in any case. Occassional wrapping will prevent them from wandering off to infinity, however, which could eventually cause problems with roundoff error. met-mol [ stepsize ] Does Metropolis updates for the position of each molecule in turn. This is like the standard metropolis and met-1 operations (see mc-spec.doc), except that all coordinates of one molecule are updated simultaneously, by adding independent Gaussian noise with standard deviation given by the stepsize, and the result is then accepted or rejected. In contrast, metropolis updates all coordinates of all molecules at once, and met-1 updates just one coordinate of one molecule at a time. met-len [ stepsize ] Does a Metropolis update for the length of a dimension (actually, for the log of this length). Only allowed when the NPT ensemble is being used. The inverse temperature used in tempering methods is interpreted in the standard way, as a power to raise the (unnormalized) probability density to, or equivalently, a factor to multiply the energy by. The default stepsizes for updating the coordinates (in their [0,1) form) are all equal to N^{-1/D}, where width is the width parameter of the potential, N is the number of molecules and D is the dimensionality of the space. This corresponds roughly to an appropriate stepsize if the molecules are tightly packed. The default stepsize for the log of the length of a dimension (when using the NPT ensemble) is 1/N. These defaults are scaled during tempering and annealed importance sampling by multiplying by the square root of the temperature. When using the NPT ensemble, the length of each dimension is initialized so that the reduced density is 1/2. The positions of the molecules are initialized randomly, from the uniform distribution. Momenta (if needed) are initialized from their canonical distribution at (actual, not reduced) temperature one. Copyright (c) 1995-2019 by Radford M. Neal