State specific MRCC

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]. 

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. 

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... 

In this paper, we have presented several aspects of the unitary group adapted MRCCs of the state-specific and state-universal type ... 

Also in the recently very active field of multireference coupled-cluster theory, first FI 2-extensions have been reported. Demel et al. reported such an development for the case of Mukherjee s state-specific multireference coupled-cluster ansatz (Mk-MRCC), while Liu et al. applied F12 theory to internally contracted multireference theory. 

We note that eq (4) involves the coefficients and c explicitly, indicating that the cluster amphtudes depend on them, as is expected of a state-specific theory. We also note that the sets T and c are coupled through eq (4) and eq (7). Solving these coupled set of equation we obtain both the cluster amplitudes and the converged coefficients from the diagonalization. The number of unknowns in this formalism is exactly the same as in the effective hamiltonian based SU-MRCC theory [12]. 

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