Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations

A simple, general and numerically stable approach for avoiding the singularities which generally occur when atoms or interaction sites are created or annihilated in free energy calculations based on computer simulations is presented. The origin of such singularities and numerical instabilities occurring in Monte Carlo or molecular dynamics simulations is discussed, as is the limited accuracy of the techniques currently used to avoid such difficulties.