MOL: Programs for molecular simulation with Lennard-Jones potential. The 'mol' programs implement simulation of systems of molecules interacting according to the artificial Lennard-Jones potential function. The full range of techniques supported by this software are implemented for this module, including Metropolis Monte Carlo, molecular dynamics, simulated tempering, annealed importance sampling, and Hamiltonian importance sampling. The molecules are simulated in a space of 1, 2, or 3 dimensions, with each dimension wrapping around after some distance (ie, "periodic boundary conditions" are used). The molecules interact according the the Lennard-Jones potential, which for each pair of molecules is given by min { 4 scale [ (width/dist)^12 - (width/dist)^6 ], max (0, maxpe - 4 scale (dist/width)^2) } Here, "dist" is the distance between the two molecules (defined as the distance of the shortest line connecting them in the wrapped-around space). The scale, width, and maxpe parameters are specified when setting up a simulation. The maxpe parameter can be infinite, in which case there is no upper limit on the potential. No "cut off" in the potential is used - the potential for all pairs is calculated, even when the contribution of a pair to the overall potential is tiny. The total potential energy for the system is the sum of the the pair potentials for each distinct pair of molecules in the system. The basic task of the molecular simulation programs is to sample from the canonical distribution with this potential energy, at a temperature of one (using units in which Boltzmann's constant is one). Sampling from both the NVT ensemble (constant number of molecules, volume, and temperature) and the NPT ensemble (constant number of molecules, pressure, and temperature) are supported. For the NPT ensemble, there is an additional term in the potential energy relating to the current volume. If the state were recorded in terms of volume, this term would be the volume times the pressure, P, minus the entropy for N particles in volume V, -N log(V). However, what is recorded in the state is actually the log of the length of a dimension, L, which gives volume equal to exp(LD)), where D is the dimensionality. The appropriately transformed term for the potential energy is then P exp(LD) - (N+1) LD Although the simulation always proceeds as if the desired distribution is that at a temperature of one, the equivalent of the canonical distribution at a temperature other than one can be obtained by changing the "scale" parameter (and "maxpe" if it's not infinite) in the pair potential. For the NPT ensemble, the pressure also needs to be changed. One then needs to also rescale things when interpreting the results - in particular, one should look at the "U" quantity rather than "E", and "p" rather than "P" (see mol-quantities.doc). Some of the Monte Carlo methods involve momentum variables, with associated kinetic energy, for which each molecule is assumed to have unit mass. Copyright (c) 1995-2004 by Radford M. Neal