MAPPING BETWEEN ELECTRON POPULATION AND VIBRATIONAL NORMAL-MODES WITHIN THE CHARGE SENSITIVITY ANALYSIS

The mapping relations between charge displacements (local or normal) and bond stretches (local or normal) are explored within the charge sensitivity analysis (CSA) in the atoms-in-molecules (AIM) resolution. For this purpose the closed-system formulation of the CSA has been developed, to define the internal hardness tenser, corresponding to the constant global number of electrons, and its eigensolutions, which define the internal (polarizational) population normal modes (PNMs). The vibrational (bond stretch) normal modes (VNMs) have been determined using both standard SCF MO (MNDO/AM1) calculations and a novel force field designed especially for use within the CSA approach. Various forms of mapping relations have been numerically tested on small and medium size molecules. The PNMs and VNMs for small molecules are shown to exhibit basically one-to-one correspondence. This provides an extra validation of the physical significance of the PNM reference frame. Possible applications of the present mapping relations to problems in catalysis and in the theory of chemical reactivity, in general, are briefly commented upon. The mapping relations are shown to represent important unifying concepts in the field of chemical reactivity. The proposed formalism offers a diagnostic tool for fast predictions of the system's geometrical/electronic structure responses to real or hypothetical changes along local (or normal) charge/bond length coordinates.