On the calculation of internal forces in mechanically stressed polyatomic molecules.

Abstract

We discuss how to define and to compute internal forces in a molecule subjected to mechanical stress. Because of the inherently many-body character of intramolecular interactions, internal forces cannot be uniquely defined without specifying a set of internal coordinates used to describe the molecular structure. When such a set is comprised of 3N - 6 interactomic distances (N being the number of atoms) and includes the bond lengths of interest, we show that the associated forces, while satisfying the equation F = ∂V/∂R (where R is the bond length, F is the internal force in this bond, and V is the potential energy of the molecule), can be determined from the molecular geometry alone. We illustrate these ideas using several toy models ranging from small molecules to a graphene sheet and show that the magnitude of the internal force in a bond is not necessarily a good predictor of its strength in response to mechanical loading. At the same time, analysis of internal forces reveals interesting phenomena such as the force multiplication effect, where weak external forces may, e.g., be used to break strong bonds, and offers insight into the catch-bond phenomenon where chemical reactivity is suppressed through application of a force.