Dissipative vibrational dynamics in a curve–crossing system

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Abstract
The density matrix theory is utilized for the description of ultra fast optical properties and related vibrational wave packet dynamics of molecular systems in condensed media. As an example, optically induced vibrational wave packets in the so-called curve–crossing system are considered. Such a system goes beyond the standard treatment of optical phenomena since the vibrational wave packet moves in a double well potential and is subject to environmental influences like wave function dephasing and relaxation. The complete theoretical description has been carried out in a representation of the vibrational wave functions of the diabatic states which refer to the two coupled vibrational surfaces. Solving the corresponding density matrix equations by numerical methods allows us to incorporate the static coupling between the crossed surfaces in a nonperturbative manner. Standard projection operator technique is used to treat environmental contributions up to the second order. For the case of a bilinear coupling between the molecular system and the environment we determine the time development of an initially prepared Gaussian wave packet. Corresponding time-resolved spectra of a pump–probe configuration are also derived. The developed formalism is finally applied to the system of the coupled electronic states c′ 1Σ+u and b′ 1Σ+u of the N2 molecule.