Long-time quantum dynamics

To summarize, the results presented for five representative examples of nonadiabatic dynamics demonstrate the ability of the MFT method to account for a qualitative description of the dynamics in case of processes involving two electronic states. The origin of the problems to describe the correct long-time relaxation dynamics as well as multi-state processes will be discussed in more detail in Section VI. Despite these problems, it is surprising how this simplest MQC method can describe complex nonadiabatic dynamics. Other related approximate methods such as the quantum-mechanical TDSCF approximation have been found to completely fail to account for the long-time behavior of the electronic dynamics (see Fig. 10). This is because the standard Hartree ansatz in the TDSCF approach neglects all correlations between the dynamical DoF, whereas the ensemble average performed in the MFT treatment accounts for the static correlation of the problem. 

Model-based experimental design, long time scale dynamics, virtual measurements, force field validation and robustness, quantum dynamics, dispersion,... 

Finally, we consider Model V by describing two examples of outer-sphere electron-transfer in solution. Figures 7 and 8 display results for the diabatic electronic population for Models Va and Vb, respectively. Similar to the mean-field trajectory calculations, for Model Va the SH results are in excellent agreement with the quantum calculations, while for Model Vb the SH method only is able to describe the short-time dynamics. As for the three-mode Model IVb discussed above, the SH calculations in particular predict an incorrect long-time limit for the diabatic population. The origin of this problem will be discussed in more detail in Section VI in the context of the mapping formulation. 

B. Kohler Prof. Fleming, your experimental results clearly indicate that in the case of I2 in hexane the vibrational coherence of an initially prepared wavepacket persists for unexpectedly long times. However, quantum dynamical calculations show that wavepacket spreading due to anharmonicity can be very substantial even for isolated molecules... 

First of all we have to mention that the above described situation of resonance is not related to any quantum effects. Moreover, the role of the transverse electromagnetic field in crystal oscillations in the infrared part of the spectrum was discussed by means of the classical dynamics of crystal lattices a long time ago by Born and Ewald (2) (see also (3) and (4)), and later by a semiphenomenological approach in (5), (6). It is evident, however, that a quantum theory of polaritons in the region of electronic transitions can also be important particularly for the discussion of quantum effects. 

Figure 13 Comparison of the experimental and a quantum mechanically computed (by exact wave packet propagation using an ab initio computed potential energy) spectrum of a nonrotating Na, molecule pumped to its B electronic state. (Courtesy of Experiment by S. Rutz, E. Schreiber, and L. Woste Computations by B. Reischl, all of the Free University of Berlin) (a) The short time dynamics Shown is the population of the excited state vs. time as determined by a pump-probe experiment and by the computation (points connected by a straight-line segments). The periodicity (about 320 fs) is due to the symmetric stretch motion, (b) A frequency spectrum. The long time dynamics (as reflected in the well-resolved spectrum) show the contribution of a different set of vibrational modes. The dominant peaks can be identified as the radial pseudorotation motion of Na,(B) while the splittings are due to the angular pseudorotational motion. (Adapted from B. Reischl, Chem. Phys. Lett., 239 173 (1995) and V. Bonacic-Koutecky, J. Gaus, J. Manz, B. Reischl, and R. de Vivie-Riedle, to be published.)...

In this subsection the more accurate CMD method [4-6,8] is described and analyzed in some detail. The method holds great promise for the study of quantum dynamics in condensed matter because systems having nonquadratic many-body potentials can be simulated for relatively long times. The numerical effort in this approach scales with system size as does a classical MD simulation, although the total overall computational cost will always be larger. Here the CMD method is first motivated by further analysis of the effective harmonic theory. This discussion is an abbreviated form of the historical line of development contained in Paper... 

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