Treating quasi-degeneracy

An alternative way to approach the problem is to start out with a hxed MR function, and develop a perturbation theory on it. This is thus an MRPT of the unrelaxed or contracted coefficients variety. The SSMR-based perturbation theories based on contracted description using CAS [43-48] have been widely used as efficient methods to treat quasi-degeneracy. There are usually two ways in which the virtual functions are handled they can be contracted functions themselves or they can be simpler CSFs. Multistate versions of the contracted variety has also been suggested [46]. An SS-based CC formulation of the. frozen variety has been developed [38], where a wave operator is used to generate the exact state by its action on the entire MR function. 

Another approach for treating the quasi-degeneracy is adopted by the various MR-based CEPA methods, which have appeared parallely along with the MRCC and MRPT methods. The earlier developed state-specific MRCEPA methods [37,65-70] avoided the redundancy problem using non-redundant cluster operators to compute the dynamical correlation on the zeroth order MR wave function. The MR version of (SC) CI method, termed as MR-(SC) CI [37], can be viewed as the size-extensive dressing of the MR-CISD method just as the (SC) CI [71] is considered to be the size-extensive dressing of the SR-CISD method. Similar to the SR-case, they include all EPV terms in an exact manner. 

Given the remarkable progress in many-body theories, accurate descriptions of electron correlation in molecular systems of variable near-degeneracies are still challenging and remain an active area of research. One framework that has provided not only accurate results but also qualitative insight is effective Hamiltonian (EH), based on which various multi-reference (MR) or quasi-degenerate (QD) perturbation theories (PT) have been proposed [ 1-26] in the past (see Refs. [27] and [28] for careful comparisons). Yet, the premises of MRPTs and QDPTs that electron correlation can be separated into static and dynamic components and then that they can respectively be treated variationally and per-turbatively are not always justified. As a consequence, low-order MRPTs and QDPTs usually depend strongly on the... 

The lowest vibronic levels may be treated in terms of the weak-coupling case, as sparsely spaced, quasi-stationary v states nearly identical (except for an accidental degeneracy) with zero-order n states. In view of the low vibronic-level density, the conditions for a single-resonance excitation are easily fulfilled so that the excited, radiant v> ( s state decays by emission of the resonance fluorescence. This is the case for benzene, aniline, etc. 

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