Ab initio adiabatic dynamics involving excited states combined with Wigner distribution approach to ultrafast spectroscopy illustrated on alkali halide clusters
Authors: Hartmann Michael , Pittner Jiřı́ , Bonačić-Koutecký Vlasta 
Published: July 2002

We investigate the ultrafast multistate nuclear dynamics involving adiabatic electronic excited states of nonstoichiometric halide deficient clusters (NanFn−1) characterized by strong ionic bonding and one excess electron, which is localized either in the halide vacancy or on the alkali atom attached to the ionic subunit depending on the cluster size. For this purpose we developed an ab initio adiabatic nuclear dynamics approach in electronic excited and ground states “on the fly” at low computational demand by introducing the “frozen ionic bonds” approximation, which yields an accurate description of excited states considering the excitation of the one excess electron in the effective field of the other n−1 valence electrons involved in the ionic bonding. We combined this multistate dynamics approach with the Wigner–Moyal representation of the vibronic density matrix forming the ab initio Wigner distribution approach to adiabatic dynamics. This method allows the simulation of femtosecond NeExPo-pump–probe and NeExNe-pump–dump signals based on an analytic formulation which utilizes temperature-dependent ground-state initial conditions (Ne), an ensemble of trajectories carried out on the electronic excited state (Ex) for the investigation of the dynamics of the system, and either the cationic (Po) or the ground state (Ne) for the probing step. The choice of the systems has been made in order to determine the time scales of processes involving (i) metallic bond breaking such as during the dynamics in the first excited state of Na2F, and (ii) fast geometric relaxation leaving the bonding frame intact as during the dynamics in the first excited state of Na4F3. The bond-breaking process via a conical intersection involving nonadiabatic dynamics will be presented in the accompanying paper [Hartmann et al., J. Chem. Phys. 114, 2123 (2001)]. The dynamics in the first excited state of Na2F from triangular-to linear-to triangular structure gives rise to fast geometric relaxation due to Na–Na bond breaking at the time scale of ∼90 fs but no signature of internal vibrational energy redistribution (IVR) is present in NeExNe-pump–dump signals since the broken metallic bond prevents the coupling between stretching and bending modes. Instead, anharmonicities of the bending periodic motion have been identified. In contrast, in the case of Na4F3, which is the smallest finite system for a surface F-center prototype of bulk color centers, after the geometric relaxation in the excited state of ∼100 fs leading to the deformed cuboidal type of structure without breaking of bonds, different types of IVR have been identified in NeExNe signals by tuning the dump laser: one-mode selective energy leaving IVR, resonant, and restricted energy arriving IVR corresponding to the selection of different parts of the phase space. Dissipative IVR could not be identified in NeExNe signals of Na4F3 at low initial temperature on the time scale up to 2 ps in spite of 15 degrees of freedom. Due to similar structural and electronic properties such as F centers in bulk, these findings can serve as guidance for establishing the time scales for geometric relaxation and IVR in excited states of larger systems.