Fully Anharmonic Vibrational Resonance Raman Spectrum of Diatomic Systems

A study is presented on the resonance Raman (RR) spectrum based on fully anharmonic wave functions and energies obtained from ab initio multireference potential energy curves of diatomic systems. The vibrational problem is numerically solved using a variational stochastic method or the Cooley-Numerov method, as implemented in Le Roy's LEVEL program. Anharmonic Franck-Condon and Herzberg-Teller integrals are numerically evaluated, and the RR polarizability is calculated within the time-independent framework of the RR theory. At the harmonic level, the differential cross sections show faster convergence with respect to the number of intermediate vibrational states than what is obtained from anharmonic wave functions. Twice as many intermediate states are required to achieve the same convergence in the RR intensities as observed within the harmonic model. The anharmonic spectra evaluated for H₂, C₂, and O₂ molecules show that RR intensities are strongly affected by anharmonic effects. They differ from their harmonic counterparts not only in the position of the peaks but also in the absolute and relative intensities.