Umbrella sampling along linear combinations of generalized coordinates. Theory and application to a glycine dipeptide

Umbrella sampling allows one to calculate potentials of mean force which can be used to determine free energy differences between, e.g., isomeric states. If the potential of mean force is to be determined along a linear combination of generalized coordinates, the proper choice of the umbrella potential energy function requires some care. It is shown what conditions the pathway must fulfil and what umbrella potential energy function must be chosen. As an illustration, the method is applied to a molecular dynamics study of the rotational isomers of a blocked glycine dipeptide.