Oscillator strength calculation

Table 4.14. De-excitation energies (in eV) and oscillator strengths calculated at the equilibrium structures of excited states of the GeX3 (X = OGeH3) point defect3...

The TDDFT excitation energies and oscillator strengths calculated for the lowest allowed excited states of MgP [138], ZnP [138, 140], and NiP [137, 138] complexes in their optimized D4h geometry, are reported in Table 15 and compared to CASPT2 [150] and Multireference Moller-Plesset perturbation (MRMP) theory [151] results. 

TDDFT methods have also been applied successfully to the description of the linear and nonlinear optical properties of heteroleptic sandwich complexes. The optical spectrum and the hyperpolarizability of Zr(OEP)(OEPz,) for which large first hyperpolarizabilities, /JSHG (SHG=second-harmonic generation) were measured in an electric field induced second-harmonic generation (EFISH) experiment [182], have been investigated by TDDFT methods [134]. The excitation energies and oscillator strengths calculated... 

Table 18- The T, - So oscillator strengths calculated with direct spin-vibronic coupling along 62s modes ( , i=4,5). Results are displayed for different basis sets and for the active space described in text.

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-... 

This holds not only for oscillator strengths calculated from the exact eigenstates of the molecular Hamiltonian, but also for oscillator strengths obtained with certain approximate methods, vide infra. 

It should be noted that in the RPA, the dipole oscillator strengths calculated in dipole velocity, dipole length, or mixed representation and all sum rules would be identical, and the TRK sum rule, Eq. (13), would be fulfilled exactly, that is, be equal to the number of electrons if the computational basis were complete [30,34,35]. Comparison of the oscillator strengths calculated in the different formulations thus gives a measure of the completeness of the computational basis in addition to the fulfillment of the Thomas-Reiche-Kuhn sum rule (vide infra). 

Neglect of the interaction between both states when using the active spaces C1-C2 has more serious consequences for the oscillator strengths calculated, due to the fact that CASSCF wavefunctions are used for this purpose. Indeed, with the active space C1-C2, rather similar transition moments (-2.00 a.u. -2.09 a.u.) are calculated for the pure 2r2g 9fi and 2f2g- 2 2 transitions, leading to an intensity ratio of only 1 1.2 for the two orbitally allowed transitions, much smaller than the experimental value of about 1 9. On the other hand, active space D... 

The emphasis on aquo-ion spectra stems from the ability to identify many relatively isolated bands with single or very limited numbers of SLJ states, the corresponding unambiguous quantitative nature of the oscillator-strength calculation, and the wide range of data available, i.e. most members of the 4f and 5f series can be readily obtained as trivalent aquo ions in dilute acid solution. Intensity correlations for Ln in a great many different host crystals, as well as in vapor complexes, have been developed. For the actinides, systematic and quantitative examination of transition intensities is presently restricted to An (aquo). 

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