Time evolution of excited states

Abstract Time evolution of excited state population was studied theoretically for the... 

Pulsed lasers are used to monitor the time-evolution of excited states, the formation of photochemical products and the kinetics of photoprocesses. The high intensity of the laser beam also enables very weak transitions to be excited, so that vibrational photochemistry and multiphoton transitions, which exhibit different selection rules, can be studied. Chap. 15 provides further details about some of the experiments that may be performed using pulsed laser sources. Table 14.2 gives details of the most commonly used lasers in photochemistry today. The key properties to consider for any particular application are wavelength(s), pulse duration, and power. Simplicity of operation is another important factor. 

A major technological innovation that opens up the possibility of novel experiments is the availability of reliable solid state (e.g., TiSapphire) lasers which provide ultra short pulses over much of the spectral range which is of chemical interest. [6] This brings about the practical possibility of exciting molecules in a time interval which is short compared to a vibrational period. The result is the creation of an electronically excited molecule where the nuclei are confined to the, typically quite localized, Franck-Condon region. Such a state is non-stationary and will evolve in time. This is unlike the more familiar continuous-wave (cw) excitation, which creates a stationary but delocalized state. The time evolution of a state prepared by ultra fast excitation can be experimentally demonstrated, [5,7,16] and Fig. 12.2 shows the prin-... 

For bound state systems, eigenfunctions of the nuclear Hamiltonian can be found by diagonalization of the Hamiltonian matiix in Eq. (11). These functions are the possible nuclear states of the system, that is, the vibrational states. If these states are used as a basis set, the wave function after excitation is a superposition of these vibrational states, with expansion coefficients given by the Frank-Condon overlaps. In this picture, the dynamics in Figure 4 can be described by the time evolution of these expansion coefficients, a simple phase factor. The periodic motion in coordinate space is thus related to a discrete spectrum in energy space. 

Fig. 35). The potential energy curves and the transition dipole moment are taken from [117]. The time evolution of the populations on the ground and excited states is shown in Fig. 36 More than 86% of the initial state is excited to the B state within the period shorter than a few femtoseconds. The integrated total transition probability V given by Eq. (173) is P = 0.879, which is in good agreement with the value 0.864 obtained by numerical solution of the original coupled Schroedinger equations. This means that the population deviation from 100% is not due to the approximation, but comes from the intrinsic reason, that is, from the spread of the wavepacket. Note that the LiH molecule is one of the...

The laser intensities are taken to be the possible lowest. The intensity in case (b) is almost three times larger than the others. This is simply due to the fact that the transition dipole moment exponentially decays from the equilibrium position and also the potential energy difference increases. Note again that the coordinate-dependent level approximation works well. In order to demonstrate the selectivity the time evolution of the wave packets on the excited state are shown in Fig 41. As a measure of the selectivity, we have calculated the target yield by... 

Figure 1. The trajectory of ground-state D2 colliding with ground-state NHj" at 8 eV leads to abstraction with the NHsD+ ion highly vibrationally excited. The time evolution of the interatomic distances (c) and of the atomic charges (b) show which product species are generated.

The time evolution of the fluorescence intensity of the monomer M and the excimer E following a d-pulse excitation can be obtained from the differential equations expressing the evolution of the species. These equations are written according to the kinetic in Scheme 4.5 where kM and kE are reciprocals of the excited-state lifetimes of the monomer and the excimer, respectively, and ki and k i are the rate constants for the excimer formation and dissociation processes, respectively. Note that this scheme is equivalent to Scheme 4.3 where (MQ) = (MM) = E and in which the formation of products is ignored. 

The shift of the fluorescence spectrum as a function of time reflects the reorganization of propanol molecules around the excited phthalimide molecules, whose dipole moment is 7.1 D instead of 3.5 D in the ground state (with a change in orientation of 20°). The time evolution of this shift is not strictly a single exponential. 

In this book we shall write the Hamiltonian as an (algebraic) operator using the appropriate Lie algebra. We intend to illustrate by many applications what we mean by this cryptic statement. It is important to emphasize that one way to represent such a Hamiltonian is as a matrix. In this connection we draw attention to one important area of spectroscopy, that of electronically excited states of larger molecules,4 which is traditionally discussed in terms of matrix Hamiltonians, the simplest of which is the so-called picket fence model (Bixon and Jortner, 1968). A central issue in this area of spectroscopy is the time evolution of an initially prepared nonstationary state. We defer a detailed discussion of such topics to a subsequent volume, which deals with the algebraic approach to dynamics. 

Figure 11. The time-evolution of the solvation structure around the benzene-like solute site whose charge increases by e/2. The left panel depicts the pair correlation of this site with the N site of acetonitrile and the right panel the pair correlation with the C site of benzene. The equilibrium pair correlations for the ground (t = 0) arid excited (t = °°) solute states are also shown. The curves depicting the pair correlations for t > 0 are vertically offset from each other by 0.5.

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