Multi-reference MBPT approaches

The main disadvantage of the MBPT/CCM approach, the restriction to a single reference function, is not essential to the theory but only to the current implementation (see references 30-32 for the multi-reference MBPT/CCM theory). To solve open-shell problems we normally use an unrestricted-Hartree-Fock (UHF) reference function. 

Because of its size-extensivity and faster convergence with respect to excitation level Coupled cluster theory has replaced Cl theory as the dominant approach in ab initio correlation calculations. Like MBPT the theory is still mainly applied in cases where the exact wave function is dominated by a single determinant, but multireference methods have been formulated and begin to enter mainstream quantum chemistry. Generalization of the algorithms to the relativistic no-pair level can again be achieved via the spinorbital formulation of the methods. I will first discuss the single reference method and then consider the Fock space method [40] that uses multi-reference wavefiinctions for ionized or excited states. 

PHF methods can, in turn, be classified as the variational and nonvariational ones. In the former gronp of methods the coefficients in linear combination of Slater determinants and in some cases LCAO coefficients in HF MOs are optimized in the PHF calculations, in the latter such an optimization is absent. To the former group of PHF methods one refers different versions of the configuration interaction (Cl) method, the multi-configuration self-consistent field (MCSCF) method, the variational coupled cluster (CC) approach and the rarely used valence bond (VB) and generaUzed VB methods. The nonvariational PHF methods inclnde the majority of CC reaUza-tions and many-body perturbation theory (MBPT), called in its molecular realization the MoUer-Plessett (MP) method. In MP calculations not only RHF but UHF MOs are also used [107]. 

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