Valence excited state energy

Eq 7 calculates the energy difference arising from the medium between the thermally equilibrated mixed-valence ground state and a vibrationally nonequilibrium, mixed-valence excited state. The value of Ae depends on the nonequilibrium state 1) For optical charge transfer, Ae = e, the unit electron charge. 2) For thermal electron transfer between chemically symmetrical sites, Ae = e/4. 3) For a chemically unsymmetrical electron transfer... 

The low threshold energies for the production of D( S), 0( P), and 0( D2) show the importance of valence excited states in the BSD of neutral fragments [47]. The pathway for D( S) desorption probably involves D O D -I- OD. Ffowever, the thresholds for producing 0( P2) and 0( D2), which are the same within experimental error, are lower than the 9.5-and 11.5-eV thermodynamic energies required to produce 0( P2) + 2D( S) and 0( D2) + 2D( S), respectively. The low threshold values therefore indicate that the formation of 0( P2) and 0( D2) must occur by a pathway which involves simultaneous formation of D2. Kimmel et al. have in fact reported [46] a threshold for the production of D2 from D2O ice at — 6 to 7 eV, which supports this conclusion. Above the ionization threshold of amorphous ice, these excited states can be formed directly or via electron-ion recombination. 

Docken and Hinze108 have presented a very detailed study of the potential-energy curves for five valence excited states of LiH by the MCSCF method. In this type of calculation, the wavefunction, expressed in the form (5), is variationally optimized... 

The lowest vertical valence excitation energy for this cobalt cluster is 36.6 kcal/mol, which is a higher value than the exothermicity for dissociating Valence excited states will therefore not be available for dissociating either. The reason Co, is at all reactive towards Hg is that the d s atom can transform to a d s atom at a cost of 7.5 kcal/mol (see above). 

The lowest vertical valence excitation energy for Co is 29 kcal/mol, which means that valence excited states will not be available for dissociating H either. The alternative process for dissociating Hg for COg would be to change one of its d s atoms to d s, which only costs 8.8 kcal/mol but is an inner shell rearrangement process. 

Analogous to the PPP method for planar 7r-systems, semiempirical all-valence methods can be and were extended to include Cl, thus giving rise to a family of procedures based on the CNDO, INDO and NDDO variants of the zero-differential overlap (ZDO) approximation, many of which were applied also to the discussion of Cl effects in radical cations. Due to the parametric incorporation of dynamic correlation effects, such procedures often yield rather accurate predictions of excited-state energies and they continue to be the methods of choice for treating very large chromophores which are not amenable to ab initio calculations. 

Figure 7.12 Historical Morse potential energy curves for H2 and its anions, dating back to 1936 [25], 1956 for the excited state [26], 1967 for the polarization ground state [27], and 1981 for the valence excited state [28].

Several extensions to DFT that allow for the treatment of excited states have recently been developed and implemented. The implementation of time-dependent DFT (TDDFT) in Gaussian98 has led to an explosion in the number of calculations using this particular variant of excited-state DFT. The performance of TDDFT for vertical excitation energies to valence excited states is often quite good, ° " with an apparent accuracy similar to some of the best ab initio meth-... 

To conclude this section we might assert that the main techniques for assessing the problem of Rydberg and valence excited states of organic molecules are, in practice, far-UV absorption spectra, photoelectron spectra, and advanced quantum chemical calculations. It should be added that the electronic spectra can also be obtained from electron-impact (energy loss) and circular dichroism spectra. The reader is referred to Robin s Volumes I to III [S, 23] he systematically considers the three kinds of spectra when they are available. 

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