Use of canonical orbital energy derivatives for closed-shell self-consistent-field wave functions

The characteristics of the first and second derivatives of the canonical orbital energies for the closed shell self-consistent-field (SCF) wave function have been studied. The first derivatives of the orbital energies were determined analytically and the second derivatives by the finite difference method. These derivatives were transformed from the Cartesian coordinate system to the normal coordinate system for a variety of stationary points. It is demonstrated that the first and second derivatives of the orbital energies in terms of the normal coordinates provide very useful chemical information concerning the molecular structures and unimolecular reactions for a range of chemical species. Similarities and differences between the present approach and Mulliken-Walsh method are also discussed.