Molecular simulation in a pseudo grand canonical ensemble

Pseudo-ensemble simulations and Gibbs–Duhem integrations for polymers

“…The criteria for determining if partial ͓step ͑4͔͒ or overall ͓step ͑5͔͒ convergence has occurred is based on histograms of , P 0 , and eq : empirical fits, as employed by Mehta and Kofke, 6 could also be used but have not been implemented here. Of course, once updates of eq have ceased, the simulation process becomes Markovian.…”

“…For the case of a hard sphere fluid, Mehta and Kofke used ghost particle insertions to evaluate ͑ ͒ and the pressure equation to evaluate Z( ). 6 Subsequently, Camp and Allen 7 pointed out that provided that the functions ͑ ͒ and Z( ) are accurately known, the limiting distribution probed by the pseudo-GC ensemble is that of the isothermal-isobaric (N PT) ensemble. This fact simply restates the dual nature of the problem at hand: The evaluation of the equilibrium density in a VT simulation could be replaced by an NPT simulation if the equilibrium pressure corresponding to the specified were known ͑and vice versa͒.…”

“…To that end, methods to evaluate both and P must also be implemented. Mehta and Kofke 6 accumulated instantaneous values of and P into density histograms; the values of ͑ ͒ and P( ) to be used in Eq. ͑1͒ were then obtained from ͑increasingly refined͒ empirical correlations fitted to histogram data.…”

“…By exploiting the nature of the intensive variable associated with the Helmholtz free energy, Mehta and Kofke 6 arrived at the following Metropolis-type acceptance criterion for volume changes (⌬V) designed to mimic particle insertion or deletion attempts:…”

“…The method requires simultaneous isobaric-isothermal simulations of the two coexisting phases; unfortunately, for multicomponent mixtures the method cannot generally avoid particle insertions. 8 Resorting to a similar combination of molecular simulation and numerical methods, Mehta and Kofke 6 later proposed a pseudo-grand canonical ͑pseudo-GC͒ simulation technique in which particle insertions and deletions are replaced by volume fluctuations. In dense fluids the success rate of molecular insertion and deletion attempts can be prohibitively small; the pseudo-GC approach can therefore lead to faster convergence to the equilibrium density ͑ ͒ than conventional GC simulations ͑as shown in Ref.…”