1ST AND 2ND ENERGY DERIVATIVE ANALYSES FOR OPEN-SHELL SELF-CONSISTENT-FIELD WAVE-FUNCTIONS

A study of first and second derivatives of the orbital, electronic, nu clear and total energies for the self-consistent field (SCF) wavefunct ion has been applied to general open-shell SCF systems. The diagonal e lements of the Lagrangian matrix for the general open-shell SCF wavefu nction are adapted as the 'orbital' energies. The first and second der ivatives of the orbital energies in terms of the normal coordinates ar e determined via the finite difference method, while those of the elec tronic, nuclear and total energies are obtained by analytical techniqu es. Using three low lying states of the CH2 and H2CO molecules as exam ples, it is demonstrated that the derivatives of the SCF energetic qua ntities with respect to the normal coordinates provide useful chemical information concerning the respective molecular structures and reacti vities. The conventional concept of the highest occupied molecular orb ital (HOMO) and the lowest unoccupied molecular orbital (LUMO) has bee n extended to the molecular vibrational motion, and the terminology of vibrationally active MOs (va-MOs), va-HOMO and va-LUMO has been intro duced for each normal coordinate. The energy derivative analysis metho d may be used as a powerful semi-quantitative model in understanding a nd interpreting various chemical phenomena.