State-reference coupled-cluster

The single-reference coupled cluster (CC) theory [1-5] has become a standard computational tool for studying ground-state molecular properties [6-10]. The basic approximations, such as CCSD (coupled cluster singles and doubles approach) [11-15], and the noniterative CCSD[T] [16,17] and CCSD(T) [18] methods, in which the cleverly designed corrections due to... 

The CASSCF method itself is not very useful for anything else than systems with few electrons unless an effective method to treat dynamical correlation effects could be developed. The Multi-Reference Cl (MRCI) method was available but was limited due to the steep increase of the size of the Cl expansion as a function of the number of correlated electrons, the basis set, and the number of active orbitals in the reference function. The direct MRCI formulation by P. Siegbahn helped but the limits still prevented applications to larger systems with many valence electrons [20], The method is still used with some success due to recent technological developments [21], Another drawback with the MRCI approach is the lack of size-extensivity, even if methods are available that can approximately correct the energies. Multi-reference coupled-cluster methods are studied but have not yet reached a state where real applications are possible. 

X. Li and J. Paldus, ]. Chem. Phys., 102, 2013 (1995). Spin-Adapted Open-Shell State-Selective Coupled-Cluster Approach and Doublet Stability of Its Hartree-Fock Reference. 

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

III. A STATE-SPECIFIC COUPLED CLUSTER THEORY WITH A DECONTRACTED REFERENCE FUNCTION... 

It is now well established by numerous and extensive applications that the single reference (SR) based many-body methods, viz. many-body perturbation theory (PT) [1], coupled cluster (CC) theory [2], coupled electron-pair approximations (CEPA) [3], etc. provide rather accurate descriptions of the energy in and around the equilibrium geometry of the closed-shell states. In particular, the single reference coupled cluster (SRCC)... 

Multireference State-Specific Coupled Cluster Theory with a Complete Active Space Reference... 

Mahapatra US, DtittaB, Bandyopadhyay B,MukheqeeD (1998) State-specific muli-reference coupled cluster formulations two paradigms. In Lowdin PO (ed) Advances in Quemtum Chemistry, vol 30. Academic, San Diego, p 163... 

Li, X, and Paldus, J. (2011) Multi-reference state-universal coupled-cluster approaches to electronically excited states,/ Chem. Phys., 134, 214118-214133. 

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]. 

Although the past 20 years have witnessed a great progress in the Hilbert space multi-reference coupled cluster methods (see, for example, the work of Mukherjee and Pal [99],Paldus [101], Jeziorski and Paldus [102], Jankowski et al. [103],Paldus et al. [104], Paldus et al. [105], Meissner et al. [106], Kucharski and Bartlett [107], Balkovd et al. [108], Baikova and Bartlett [109], Balkovd et al. [110], Baikova et al. [Ill], Berkovic and Kaldor [112]) only a few applications of this approach have been reported, mostly oriented to the simple model systems exploiting a lowdimensional model space. Among the reasons for this paucity of applications are the choice of an appropriate model space, convergence difficulties arising from intruder state problems and from multiple solutions of non-linear coupled cluster equations. 

The application of the Brillouin-Wigner coupled cluster theory to the multireference function electron correlation problem yields two distinct approaches (i) the multi-root formalism which was discussed in Section 4.2.2 and (ii) the single-root formalism described in the previous subsections of this section. Section 4.2.3. The multiroot multi-reference Brillouin-Wigner coupled cluster formalism reveals insights into other formulations of the multi-reference coupled cluster problem which often suffer from the intruder state problem which, and in practice, may lead to spurious... 

Let us consider the simultaneous solution of the Schrodinger and spin equations for high-spin open-shell states. The coupled-cluster wave function may be expressed in terms of a singledeterminant reference function with the excitation operators chosen to yield excitations from this reference state. The full coupled-cluster wave function, being equivalent to the FCI wave function in the same orbital basis, is a simultaneous eigenfunction of the Schrodinger equation and the spin equations ... 

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