A “Surface” Model for the Treatment of Local Vibrations in Macromolecular Systems

Abstract

The accurate theoretical and computational treatment of chemical dynamics and reactivity generally makes use of quantum mechanical analyses of the anharmonic motions of atoms within molecular systems. As reactive dynamics are inherently anharmonic, special potential energy functions that can address the issue are required. The purpose of this paper, therefore, is to discuss a model potential energy function that may accurately represent both local molecular anharmonic and discrete harmonic motions while incorporating the collective harmonic dynamics of the rest of a macromolecule in a parametric form. The model is approximately analogous to a small molecule chemisorbed on or embedded in an elastic surface. As the embedding region in the macromolecule in which the local group resides is generally highly anisotropic, the usual development of continuum elasticity theory is not straightforward. Instead, this approach adopts a local surface model with anisotropic points of attachment between the surface and atoms of the local group. The dynamics of the points of attachment, i.e., anchor pseudo-atoms in a cavity, are proposed to be treated phenomenologically to yield local force constants as fitting parameters to represent the effect of the collective motion ofthe remainder of the macromolecule. A potential energy function of this type should be useful for the analysis of local reactive dynamics in macromolecular systems, such as a reactive polymer or an enzyme. Extension of the model to a closed cavity may also be useful for the treatment of local discrete effects of solvent coordination on solute spectra and dynamics.