State-specific multi-reference coupled-cluster

U.S. Mahapatra, B. Datta, D. Mukherjee, A state-specific multi-reference coupled cluster formalism with molecular applications. Mol. Phys. 94 (1998) 157. 

State-specific Multi-reference Coupled-cluster Theory and its Approximate Versions... 

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... 

The formulation of a multi-reference bwcc theory can now proceed in two distinct ways. In the first option, we can formulate a multi-root version of the multi-reference BWCC theory which yields all roots of the d-dimensional 9 space simultaneously. This is the approach employed in most multi-reference coupled cluster formulations which are based on the Rayleigh-Schrodinger expansion. In the second option, we can use the state-specific wave operator (4.59) and formulate a state-specific (or single root) version of multi-reference bwcc theory [10]. 

In Section 4.2.3.1, we have defined the wave operator, 12, in the Brillouin-Wigner form (4.92). If we adopt an exponential ansatz for the wave operator, 12, we can develop the single-root (state-specific) multi-reference Brillouin-Wigner coupled-cluster (MR Bwcc) theory. This is the purpose of the present section. 

In Brillouin-Wigner coupled cluster theory, the simple a posteriori correction described above is exact in the case of the single-reference formalism. In the state-specific multi-reference Brillouin-Wigner coupled cluster theory, the simple a posteriori correction is approximate. An iterative correction for lack of extensivity has been studied by Kttner [38], but this reintroduces the intruder state problem. 

Multireference coupled cluster (MRCC) models provide a generalization of the single-reference CC approach (3.1) for applications where several reference determinants contribute with similarly large weights to the wave function of the molecular system under consideration. The MRCC models can be divided into state-specific (SS) and multi-state approaches. One of the state-specific MRCC (SSMRCC) approaches is the active space CC method proposed in the works of Adamowicz and co-workers [14—18]. This method established the foundation for the approach developed and implemented by the authors of this article [19-27]. 

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