Mixing of configurations

This mixing of configurations is commonly termed configuration interaction. Since application of the configuration mixing model is non-mathematical, the cumbersome mathematical description of various wave-functions in... 

Correlations between electrons in initial and final states lead not only to the shift of photoelectron lines, changes of their forms and redistribution of their intensities, but also to the occurrence of so-called satellite lines, corresponding to photoionization with the excitation of the other electron. Correlation effects in photoelectron spectra are caused by mixing of configurations separately in the initial state, in the final ion and in the final state of continuum. 

Mixing of configurations with opposite parity can occur if the contributions from V to the Hamiltonian contain terms with odd parity. The contribution from V arises due to the interaction of electrons of the ion with the crystal electric field which may be written as... 

The interpretation of these autoionizing excited states even from the outset recognized the inadequacy of the independent-particle picture.2 To account for the number of observed series and their intensities, it was necessary to invoke strong mixing of configurations, each with its own individual-particle quantum numbers. To obtain even a minimally satisfactory description of the... 

Encyclopedia of Physics/Handbuch der Physik, Springer, New York, 1961, Volume 37, pages 110-115). Hybridization gives a mixing of configurations in the valence state. 

The theoretical picture for the mass 19 nuclei in intermediate coupling has been given by Elliott and Flowers [i5] and by Redlich. These treatments differ in the type of central potential and in the method of calculation, but lead to comparable results both allow for the mixing of configurations of the id and 2s shells. This is necessary because it is clear from the and spectrum that the ds/ and si/ levels are close together as is indeed expected for the levels of a harmonic oscillator. The d j — d j splitting is taken from 0 ". The calculations account... 

The diagonalization of the one-particle density matrix P on the Cl level yields the natural orbitals (NOs) and the occupation numbers of the molecule. In an RHF-SCF calculation, all occupation numbers are either 0 or 2, which means that an MO is either doubly occupied by 2 electrons or not occupied. If we invoke a Cl calculation, the mixing of configurations results in fractional occupation numbers of the NOs. Still in a normal molecule, such as ethane, water, ammonia, etc., the occupation numbers for the ground state will be close to 0 or 2. The occupation numbers of at least two NOs of excited states usually deviate from the values 0 and 2. In a biradicaloid structure occupation numbers will change and typically two of them will be close to 1. However, this method cannot characterize zwitterions since occupation numbers should be close to 0 and 2, respectively, in this case. The approach by Jug and Poredda yields both zwitterionic and diradical character of species, based on the valence criterion of Gopinathan and Jug. The valence is defined according to equation (5), which can be reformulated as equation (6). 

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