Exploring Anharmonic Nuclear Dynamics and Spectroscopy Using the Kratzer Oscillator

The Kratzer oscillator is useful in modeling anharmonic molecular vibrations; therefore, its underlying theory is briefly explored in this study. The linear dipole moment time correlation function, within the Condon approximation, is analytically evaluated, and linear absorption lineshapes are calculated at different temperatures. An important integral formula of Landau and Liftshitz is, for the first time, utilized to evaluate the anharmonic Franck-Condon factor (FCF) resulting from modeling the initial and final states by Kratzer potentials. In addition, an exact closed-form expression of the FCF for the linearly displaced and shape-distorted final state energy curve, with respect to the ground state, is reported. Within the context of Mukamel formalism, nonlinear spectral/temporal lineshapes, such as hole-burning, photon echo, and pump-probe signals, may not be calculated without nonlinear response theory using the so-called four-point dipole moment time correlation function. The above FCFs will be employed to calculate optical linear and nonlinear spectra at different temperatures utilizing a previously developed formula [Toutounji, M. J. Phys. Chem. C 2010, in press], whereby a hole-burned absorption lineshape may be found using a linear dipole moment time correlation function.