Time domains, wave packet dynamics

In this section, the real-time spectra for two different pump probe cycles, i.e. two-color and one-color real-time experiments, are presented. First, the two essentially different real-time spectra I t) are analyzed in the time domain, followed by a detailed analysis in the frequency domain (/(u )). Introducing the spectrogram technique I At,uj)) enables detailed insight into the investigated wave packet dynamics. In particular, it visualizes directly several total and fractional revivals of induced vibrational wave packets. By comparing the spectrograms of the different pump probe cycles, one can easily assign the different ionization pathways of the laser-induced processes. This nicely demonstrates the different excitation mechanisms in the two experiments. 

The physical picture of the dynamics of the wave packet in the time domain described above provides insight into the absorption spectrum in the frequency domain. The width of the spectrum is determined by the initial decrease of the overlap which in turn is governed by the slope of steepest descent. The larger the distortion, the steeper the slope, the faster the... 

To calculate numerically the quantum dynamics of the various cations in time-dependent domain, we shall use the multiconfiguration time-dependent Hartree method (MCTDH) [79-82, 113, 114]. This method for propagating multidimensional wave packets is one of the most powerful techniques currently available. For an overview of the capabilities and applications of the MCTDH method we refer to a recent book [114]. Additional insight into the vibronic dynamics can be achieved by performing time-independent calculations. To this end Lanczos algorithm [115,116] is a very suitable algorithm for our purposes because of the structural sparsity of the Hamiltonian secular matrix and the matrix-vector multiplication routine is very efficient to implement [6]. 

Perturbed Wave Packet Propagation. The influence of a perturbation on the propagation of the wave packet is now presented in the time as well as the frequency domain. Finally, the mechanism of the build-up dynamics and the time dependence of the induced electronic population dynamics are discussed. 

Equation (13) establishes the connection between the energy- or frequency-domain on one hand and the time-domain on the other. S t) is the key quantity as it reflects in a rather direct way the dynamics of the system in the upper state, for example, how fast the initial wave packet leaves its place of birth, whether it ever comes back to its starting position... 

If the PES is not purely repulsive, i,e if direct dissociation is (partly) prohibited by a potential barrier in the exit channel or some other dynamical effect, some part of the wave packet is trapped for a longer time and performs an oscillatory motion as observed for FNO(Si) in Figures. Whenever a part of the wave packet recurs to its starting position, the overlap with d>ex(0) increases and the autocorrelation function shows a series of recurrences as schematically illustrated in Figure 6(c), The recurrences reflect the vibrational motion of the molecule in the inner region of the PES, before it finally escapes through the transition state (point of no return) and dissociates. If T is the period of the oscillation in the time-domain, the Fourier transformation of S(t) leads to structures in the spectrum. 

---