Transition energies, calculations for

Table 4.22. Optical spectral (one-electron) transition energies ( ) calculated for manganese oxides using the MS-SCF-ATa method, compared with experimentally observed transitions assigned to charge transfer, crystal field, valence band conduction band and crystal field conduction band transitions...

The electronic transition (energy and oscillator strength) calculated for tri-X-substituted cyclopropenium ion by INDO is set out in Table 7. The transition energy calculated for the triaminocycloprope-... 

Figure 4. Evolution with the inverse number of thiophene rings, 1/n, of the INDO/MRD-CI So->S, (solid line, closed circles) and Sq- T4 (dashed line, open circles) energies. Note that the transition energies calculated for Th3 were not included in the linear fits.

For sample III, the transition energies calculated for the strain values of Sxx = —0.73% and Szz = —0.22% agree quite well with the measured ones. The calculated oscillator strength offx = 0.98 Ifz = 0.94) suggests that the Ti (T2) transition is almost completely x polarized (z polarized). Because of the smaller thickness of sample IV in comparison to sample III, Syy in sample IV... 

In the present work, we report on a new semi-empirical theoretical approach which allows us to perform spin and symmetry unconstrained total energy calculations for clusters of transition metal atoms in a co .putationally efficient way. Our approach is based on the Tight Binding Molecular Dynamics (TBMD) method. 

Specifically, the collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions were calculated for weak radiation fields and photon energies Ha> near the atomic transition frequencies, utilizing the concepts and methods of the traditional theory of line shapes for dipole-allowed transitions. The example of the S-D transition induced by a spherically symmetric perturber (e.g., a rare gas atom) is treated in detail and compared with measurements. The case of the radiative collision, i.e., a collision in which both colliding atoms change their state, was also considered. 

Figure 12. Molecular orbital diagram for an FegOjg cluster used to understand the orbitals involved in Fe Fe3 charge transfer. The absorption band observed near 13,000 cm 1 in the spectra of mixed-valence silicates is due to the transition from the Fe2 (t2g)- Fe3+(t2g) orbitals. A transition state calculation for that energy in the cluster presented here gives 10,570 cm"1 in fair agreement with experiment.

SCHEME 107. Relative energies and geometries for the O- and C-addition transition state calculated for the addition of formaldehyde to the lithium enolate of acetaldehyde and the preferred conformations of aldol535... 

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