Perturbation theory, multi-reference

A computationally less expensive alternative to coupled-cluster theory is provided by multireference perturbation theory (MRPT). The currently most widely used form of MRPT in f element chemistry is second-order Complete Active Space Perturbation Theory (CASPT2) [79,80], and we shall focus on this method in this section. 

It will be useful to review certain features of Rayleigh-Schrodinger perturbation theory (RSPT) We start from a partitioning of the Hamiltonian into a zeroth-order part Ho and a first-order part Hi 

Projecting with the zeroth-order solution we obtain 

In order to generate the perturbation corrections to we do not need the other solutions to 

just the orthogonal complement which is not required to form an orthogonal 

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EMERGENCE OE STATE-SPECIFIC MULTI-REFERENCE PERTURBATION THEORY SS-MRPT FROM SS-MRCC THEORY... 

Although the approach described above is presented in its most general form, using a multiple coupled-cluster Ansatz for the SS-MRCC formalism, suitable approxi-mants to it such as the state-specific multi-reference perturbation theory (SS-MRPT) or state-specific multi-reference CEPA (SS-MRCEPA) can be generated by straightforward approximations. Since the new closed component of the wave operator for IMS appear first at the quadratic power, it is evident that the expressions we have derived in this and the earlier papers for the CAS will remain valid if the quadratic powers of are ignored in the approximants to SS-MRCC for IMS. This implies that all the SS-MRPT... 

Determinant based multi-reference perturbation theory... 

Brillouin Wigner based multi-reference perturbation theory for electronic correlation effects Journal of Chemical Physics 108,4714 (1998)... 

Unfortunately, in many situation of interest, both static and dynamic electronic correlation need to be taken into account. This is particularly true for the study of processes involving excited electronic states as in UV spectroscopy or in photochemistry. In this case, methods capable of taking into account the dynamic electronic correlation on top of a multi-determinantal wavefunction of the MCSCF type are needed. These methods are usually called multi-reference methods. The two standard methods that are able to account for both the static and dynamic electronic correlation are the multi-reference configuration interaction (MRCI) and several variants of second-order multi-reference perturbation theory (MRPT). 

Sabbah et a/. also reported calculations of the same sort as described above for CN-I-C2H6, employing second-order multi-reference perturbation theory (CASPT2) to determine the inner barrier heights (the results are shown in Table 2.6). For O -fl propene, the CASPT2 predicted barrier was... 

Keywords Multi-reference Perturbation theory Quasiparticles... 

State-specific multi-reference perturbation theories ... 

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