A systematic optimization scheme for configurational bias Monte Carlo

We present a simple method that allows us to optimize the efficiency of Monte Carlo schemes that employ trial moves composed of a sequence of elementary steps. One such scheme, namely the Configurational Bias Monte Carlo (CBMC) method, has resulted in great advances in the simulation of phase behavior of chain molecules. Until now the construction of efficient CBMC trial moves was more an art than a science. In this paper we show that there exist simple relations that allow us to design the most efficient CBMC trial moves, for a given temperature and density. The best strategy will vary between random regrowth (in the case of an almost ideal chain) and reptation (in the limit of a dense melt), both of which are special cases of a CBMC trial move. We also show how the same approach can be used to optimize the calculation of the chemical potential of a chain molecule, using the Rosenbluth particle insertion scheme.