Infrared absorption and the Born–Oppenheimer approximation. I. Vibrational intensity expressions

A formalism is presented which permits the expression of corrections to the Born–Oppenheimer approximation without direct reference to the excited electronic states of the molecule. This is accomplished by the introduction of a vibronic gauge function which is the solution of a separate, known differential equation. With this formalism the exact equivalence of the vector potential and dipole moment expressions for infrared vibrational intensities in the Born–Oppenheimer theory is established. The perturbation terms for the corrections to the Born–Oppenheimer approximation are discussed and their meaning is illustrated with the example of a translating hydrogen atom. The vibronic gauge formalism is extended to molecular orbitals where the separability of the problem in terms of individual orbitals is demonstrated. Simple examples of the solution of the vibronic gauge function are presented for inner shell orbitals.