Excitation functions definition

Fig. 10.9. Left-hand side Rotational excitation functions Ja and Jb for the dissociation of H2O2 through the lowest two excited states, A and B, as functions of the initial torsional angle tpo- IFa and Wb represent the corresponding weighting functions. For definitions see Section 6.3. Right-hand side The resulting final rotational state distributions of the OH products. Reproduced from Schinke and Staemmler (1988).

Another aspect of optical pumping is related to the coherent excitation of two or more molecular levels. This means that the optical excitation produces definite phase relations between the wave functions of these levels. This leads to interference effects, which influence the spatial distribution and the time dependence of the laser-induced fluorescence. This subject of coherent spectroscopy is covered in Chap. 7. 

This chapter provides an introduction to different spectroscopic techniques that are based either on the coherent excitation of atoms and molecules or on the coherent superposition of light scattered by molecules and small particles. The coherent excitation establishes definite phase relations between the amplitudes of the atomic or molecular wave functions this, in turn, determines the total amplitudes of the emitted, scattered, or absorbed radiation. 

Figure 13 shows the cross section for insertion events whose minimum energy was nearly that of the potential energy surface minimum. The cross section for abstraction includes only those reactions whose minimum energy was nearly that of products. Owing to the use of these more restrictive definitions, the excitation functions for insertion and abstraction do not necessarily sum to the overall excitation function but any discrepancy is always quite small. 

With regard to the former, one would like to include as many important configurations as possible. Unfortunately, the definition of an important configuration is often debatable. One popular remedy is the full-valence complete active space SCF (CASSCF) approach in which configurations arising from all excitations from valence-occupied to valence-virtual orbitals are chosen. [29] Since this is equivalent to performing a full Cl within the valence space, the full-valence CASSCF method is limited to small systems. Nevertheless, the CASSCF approach using a well-chosen (often chemically motivated) subspace of the valence orbitals has been shown to yield a much improved depiction of the wave function at all points on a potential surface. Furthermore, the choice of an active space can be adjusted to describe excited state wave functions. 

As has been mentioned above, the inclusion of basis functions (49) with high power values, nik, is very essential for the calculations of molecular systems. It is especially important for highly vibrationally excited states where there are many highly localized peaks in the nuclear correlation function. To illustrate this point, we calculated this correlation function (it corresponds to the internuclear distance, r -p = r ), which is the same as the probability density of pseudoparticle 1. The definition of this quantity is as follows ... 

In his article mainly mode-locked tunable dye lasers are discussed. Giant pulse ruby lasers (3 nsec pulse halfwidth) have been successfully used to probe electron densities as a function of time in a rapidly expanding plasma 22). The electron lifetime in the conduction band can be determined with nanosecond semiconductor lasers. By absorption of the laser pulse the electrons in the semiconductor probe are excited into the conduction band, resulting in a definite conductivity. The mean lifetime is obtained by measuring the decrease of conductivity with time 26). 

That is precisely which is reported say in [123] on example of Pd complexes (and for other systems in Ref. [124]) the TDDFT excitation energies are systematically lower than the experimental ones. In this context it becomes clear that the TDDFT may be quite useful for obtaining the excitation energies in those cases when the ground state is well separated from the lower excited states and can be reasonably represented by a single determinant wave function may be for somehow renormalized quasiparticles interacting according to some effective law, but shall definitely fail when such a (basically the Fermi-liquid) picture is not valid. 

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