Quasi-degeneracy

The coupling of electronic and vibrational motions is studied by two canonical transformations, namely, normal coordinate transformation and momentum transformation on molecular Hamiltonian. It is shown that by these transformations we can pass from crude approximation to adiabatic approximation and then to non-adiahatic (diabatic) Hamiltonian. This leads to renormalized fermions and renotmahzed diabatic phonons. Simple calculations on H2, HD, and D2 systems are performed and compared with previous approaches. Finally, the problem of reducing diabatic Hamiltonian to adiabatic and crude adiabatic is discussed in the broader context of electronic quasi-degeneracy. 

Quasi-degeneracy Effects.—The convergence properties of the non-degenerate formulation of the many-body perturbation theory deteriorate when quasidegeneracy is present in the reference spectrum. In view of its simplicity, however, there is considerable interest in exploring the range of applicability of the nondegenerate formalism. 

Note that only the same coefficient derivatives are required as in the SCF second derivative case in particular, the exact derivatives of the canonical molecular orbitals are not required. The formulation of Gaw et al. (1984) does apparently use the latter. As discussed in Section III.C, this may lead to numerical difficulties in the case of degeneracies or quasi-degeneracies. Recently Gaw and Handy (1986) eliminated the canonical orbital derivatives from their program, in agreement with the results above. An extension of the closed-shell third derivative program to open-shell and MCSCF wavefunc-tions would be highly desirable for calculating reaction surfaces. 

B. Datta, D. Mukherjee, Treatment of quasi-degeneracy in single-reference coupled-cluster theory. Separation of dynamical and nondynamical correlation effects, Chem. Phys. Lett. 235 (1995) 31. 

The CCSD(T) approach is probably the most often exploited CC method in actual applications, and provides excellent results [145], as long as no quasi-degeneracy is present. This is usually the case for the closed-shell ground states near the equilibrium geometry. However, with the stretching of one or more genuine chemical bonds, the CCSD(T) method... 

Now, let us recall the complementarity of variational and perturbative approaches, specifically of the Cl and CC methods while the former ones can simultaneously handle a multitude of states of an arbitrary spin multiplicity, accounting well for non-dynamic correlations in cases of quasi-degeneracy, they are not size-extensive, and are unable to... 

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. 

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