Quantum Chemical Calculations of Electronic Excitation

Quantum chemical calculations of excitation energies and transition dipole moments vary according to the level of sophistication. The HMO model discussed in Section 1.2.3 is the easiest to apply excitation energies are linearly related to orbital energy differences. [Cf. Equation (1.22).] 

It has already been pointed out several times that electron repulsion terms play a major part in the discussion of electronic excitation energies. Within the Hartree-Fock approximation, electron interaction in closed-shell ground states can be taken care of in a reasonable way using SCF methods. In a treatment of excited states, however, configuration interaction usually has to be taken into account. (Cf. Section 1.2.4.) This can be achieved either by semiempirical methods, especially in those cases where the r approximation is sufficient for a discussion of light absorption, or, by ab initio methods in the case of small molecules. 

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Table 7.9. Quantum-chemical calculations of the energies (eV) of the lowest electron-excited states for silicon-centered radicals3...

A possible isomerization pathway for the = 6 cluster has been proposed on the basis of the quantum chemical calculations of Conbariza et al. [59] and Kim et al. [33]. In the predicted most stable structure for the ground state [59], the 1 ion lies on the surface of a V-shaped solvent network. It has been assumed that the initially excited state has a similar geometry, in which the excess electron is weakly bound by the net dipole moment of the solvent network. The supposed form after isomerization resembles the stable half-cage structure for the water hexamer anion [33], in which the excess electron is confined by dangling hydrogens of waters. 

Quantum-chemical calculations ofthe electron structure of the CH4 molecule in the ground and excited states (PM3, MOPAC 6.0) indicate that, upon photoexcitation, Tt-electron density transfers from the LEP of the 0(1) atom into the conjugated system of the annelated substituent and the 7i-antibonding orbital of the C2=C3 double bond of the pyran ring. Such transfer of rc-electron... 

Theoretical methods that combine ab initio MD on the fly with the Wigner distribution approach, which is based on classical treatment of nuclei and on quantum chemical treatment of electronic structure, represent an important theoretical tool for the analysis and control of ultrashort processes in complex systems. Moreover, the possibility to include, in principle, quantum effects for nuclear motion by introducing appropriate corrections makes this approach attractive for further developments. However, for this purpose, new proposals for improving the efficient inclusion of quantum effects for the motion of nuclei and fast but accurate calculations of MD on the fly in the electronic excited states are mandatory. Both aspects represent attractive and important theoretical research areas for the future. 

Early experiments in this new field of femtosecond chemistry took the form of time-resolved spectroscopy since the probing involved absorption or emission spectroscopy. Theoretical interpretation of the spectroscopic data is clearly required in order to obtained the desired information, i.e., snapshots of the time-dependent distribution of atomic positions. To that end, extensive quantum chemical calculations of energies of excited electronic states are needed, which even today can be cumbersome for larger molecular systems. Soon after the first successful experiments using time-resolved spectroscopy, there was, therefore, efforts to use alternative probing techniques like diffraction. The advantage is that a simpler and more direct connection between the diffraction signals and molecular structure is available. 

Dynamic Response Functions. - The perturbation series formula or spectral representation of the response functions can be used only in connection with theories that incorporate experimental information relating to the excited states. Semi-empirical quantum chemical methods adapted for calculations of electronic excitation energies provide the basis for attempts at direct implementation of the sum over states (SOS) approach. There are numerous variants using the PPP,50,51 CNDO(S),52-55 INDO(S)56,57 and ZINDO58 levels of approximation. Extensive lists of publications will be found, for example, in references 5 and 34. The method has been much used in surveying the first hyperpolarizabilities of prospective optoelectronically applicable molecules, but is not a realistic starting point for quantitative calculation in un-parametrized calculations. 

Poor agreement is observed between the experimental and theoretical values [calculated by a combined method, that is, quantum-chemical calculation of the activation energy (Table 37.7 and Table 37.8) and the frequencies of the vibrations of the bonds in the prereaction complex and in the transition state and calculation of the rate constants on the basis of RRKM theory] for certain processes where the effects of electron correlation and the contributions of the excited electronic configurations are not predominant [68-73]. 

According to a large number of experimental studies, the most stable phologen-erated species in the lowest excited stales of conjugated chains are electron-hole pairs bound by Coulomb attraction and associated to a local deformation of the backbone, i.e., polaron-excilons [18]. A good insight into the properties of these species can be provided by quantum-chemical calculations our recent theoretical... 

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