Using arbitrary trial distributions to improve intramolecular sampling in configurational-bias Monte Carlo

A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to generate trial bond lengths, angles and dihedrals is described and shown to provide similar acceptance rates with substantially less computational effort. Several different trial distributions are studied and a linear combination of the ideal distribution plus Gaussian distributions automatically fit to the energetic and ideal terms is found to give the best results. The use of these arbitrary trial distributions enables a new formulation of coupled - decoupled configurational bias Monte Carlo that has significantly higher acceptance rates for cyclic molecules. The chemical potential measured via a modified Widom insertion is found to be ill-defined in the case of a molecule that has flexible bond lengths due to the unbounded probability distribution that describes the distance between any two atoms. We propose a simple standard state that allows the computation of consistent chemical potentials for molecules with flexible bonds. We show that the chemical potential via Widom insertion is not computed properly for molecules with Coulombic interactions when the number of trials for any of the nonbonded selection steps is greater than one. Finally, we demonstrate the power of the new algorithms by sampling the side-chain conformations of a polypeptide.