Perturbation non-degenerate

The effects of X7 may be treated using ordinary non-degenerate perturbation theory or, as in Dunham s original work, by means of the Wentzel-Kramers-Brillouin method... 

Matsunaga et al. [110] introduced VSCF-DPT2, a method that includes the effects of degeneracies in the anharmonic vibrational spectra. The essential extension is to use Degenerate Perturbation Theory (as opposed to Non-degenerate Perturbation Theory) in introducing correlation effects. Also this method was interfaced with electronic strucmre codes, and is incorporated in gamess. There have been several applications of ab initio spectroscopy calculations with this method. 

To eliminate the restrictions on Se and <5T demanded by non-degenerate perturbation theory, it is necessary to find the eigenvalues and eigenvectors of the complex 2x2 energy matrix, which gives... 

The effect of spin-orbit coupling on mixing of singlet and triplet states can be seen by considering first-order non-degenerate perturbation theory [8). Let us consider the perturbed triplet wavefunction for the state where represents the unperturbed triplet wavefunction for the... 

The non-degenerate perturbation expressions that have been developed in the previous section will result in zero denominators for degenerate systems. As a result, the approach used to obtain the expressions for the various orders of corrections for a degenerate system must be modified from the approach used in non-degenerate systems. 

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