Distance-type reaction coordinates for modelling activated processes

A suitably defined distance is the simplest parameter for measuring the difference between two positions, orientations, and/or conformations of a molecular system. Distances also provide a first guess for the reaction coordinates of activated processes. It is shown here that mass-weighted distances possess remarkable mechanical and statistical mechanical properties. They allow us to restrict motions to internal coordinates of a molecule in a simple way where this demand makes sense. Moreover, the computation of free energy changes and rates is facilitated by simple explicit formulae. The numerical treatment of a rate process in a peptide, the ring flip of a phenylalanine, demonstrates the practical application of our results. It also indicates the role of internal friction in macromolecules and the need to consider transmission coefficients.