Quasi-degenerate states

The GMS wave function [1,2] combines the advantages of the MO and VB models, preserving the classical chemical structures, but dealing with self-consistently optimized orbitals. From a formal point of view, it is able to reproduce all VB or MO based variational electronic wave functions in its framework. Besides that, it can deal in a straightforward way with the nonadiabatic effects of degenerate or quasi-degenerate states, calculating their interaction and properties. 

The Two-Time Green s Function and Screened Self-Energy for Two-Electron Quasi-Degenerate States... 

Data in Fig. 9 shows that excitonic bands relevant to states with different n overlap in energy in these conditions ultra-excitonic terms mix up degenerate or quasi-degenerate states and are therefore responsible for large deviations from EM. The exciton number is not even approximately conserved for exact results in Fig.9, and, what is even more impressive, the energy of excited-states shows a... 

Very often the catalyst (unsaturated TM complex) has a low-spin ground state with a high-spin state being very close in energy [23, 36, 37]. This situation is very useful for catalysis it is not necessary to produce a spin-flip and a low barrier is achieved. The metal surface is an ideal catalyst in this sense, since any spin multiplicity can be realized at the local state of the surface, perturbed in the course of the chemisorption process. In other words, a metal cluster which simulates the surface in the course of the chemisorption process has a number of quasi-degenerate state with different spin-multiplicities. 

Nonadiabatic transition of nuclear WPs between the quasi-degenerate states gradually reduces electronic angular momentum. 

L l are close to the eigenvalues fi. We denote H)) by ft)L (o)h)- From the energy gap between the quasi-degenerate states, - -) or —) produced by a linearly polarized laser pulse subsequently evolves in time as a coherent nonstationary state ... 

In a previous section, it was found that time evolutions of WPs taking into account nonadiabatic couplings strongly depend on the initial in-phase or out-of-phase coherent excitation of two quasi-degenerate states. This suggests that the initial direction of K-electron rotation can be identified by analyzing vibrational spectra. It is well known that Fourier transform of the autocorrelation function of WPs gives its frequency spectrum [37]. The frequency spectrum of (Q. 0 after the nonadiabatic transition from H) to L) is defined as... 

Realistic SIC-LDA results for molecules or solids can only be obtained on the basis of some localization prescription for quasi-degenerate states [72]. Such a scheme essentially consists of using the localized linear combinations of for the evaluation of the SIC functional and has to be applied to all core and semi-core states. It is obvious that such a prescription becomes rather difficult to handle in more complicated molecules involving several types of atoms. One thus has to realize that none of the presently available implicit functionals can compete with the standard LDA or GGA for covalently bond molecules. 

Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) How to compute the Fukui matrix and function ftn systems with (quasi-)degenerate states. J Chem Theory Comput 10(1) 202-210... 

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