VELOCITY-GAUGE FORMALISM IN THE THEORY OF VIBRATIONAL CIRCULAR-DICHROISM AND INFRARED-ABSORPTION

The first use of velocity-gauge factors in the theory of vibrational circular dichroism (VCD) and infrared absorption intensities is described. The approach involves the exact incorporation of all or part of the dependence of the electronic wave function on an electron-velocity perturbation, such as the vector potential or the velocities of the nuclei, into the atomic orbital basis functions as a gauge transformation. Any remaining dependence of the wave function on these perturbations is carried by the basis-function coefficient derivatives which are determined to first order by coupled Hartree-Fock perturbation theory. The magnetic field perturbation formulations of VCD in the common origin and distributed origin gauges are identified within the new formalism, providing a new direct derivation of the distributed origin gauge theory. The formalism also yields new a priori VCD intensity expressions, derived using nuclear velocity-gauge factors, in the complete adiabatic approximation. Several distinct a priori computational approaches to VCD intensities can now be identified-the vibronic coupling theory implemented with a direct sum over states (VC/SOS), the field adiabatic theory implemented with magnetic field perturbation (FA/MFP), and the complete adiabatic theory implemented with nuclear velocity perturbation (CA/NVP). In addition, basic expressions are presented for an energy gradient theory of VCD that employs both magnetic-field and nuclear-velocity perturbations (EG/MFNVP). It is shown that the CA/NVP theory of VCD possesses a higher Born-Oppenheimer content than the VC/SOS or FA/MFP theories and provides an improved basis for reducing a priori VCD theory to various models of VCD intensity.