A simple state-average procedure determining optimal coordinates for anharmonic vibrational calculations

A simple methodology for calculating state average energies in the context of vibrational self-consistent field (VSCF) is suggested. The suggested state average energy is employed in the optimization of coordinates for anharmonic vibrational wave function calculations where an orthogonal matrix of transformation between normal and optimized coordinates is variationally optimized. The convergence to the exact limit for approximate vibrational configuration interaction and vibrational coupled cluster wave functions is studied, comparing the performance of state average optimized coordinates, ground state optimized coordinates and standard normal coordinates. Exploratory calculations are presented for water, formaldehyde, the water dimer and trimer, and ethylene.