Coupled-cluster approximation, open-shell

By adopting the no-pair approximation, a natural and straightforward extension of the nonrelativistic open-shell CC theory emerges. The multireference valence-universal Fock-space coupled-cluster approach is employed [25], which defines and calculates an effective Hamiltonian in a low-dimensional model (or P) space, with eigenvalues approximating some desirable eigenvalues of the physical Hamiltonian. The effective Hamiltonian has the form [26]... 

Recent developments include exact [12-14, 44, 90, 91] and approximate [14, 90, 92-94] iterative schemes to determine Hg, the intermediate Hamiltonian method [21, 24, 95], the use of incomplete model spaces [43, 44] and some multireference open-shell coupled-cluster (CC) formalisms [16-20, 96, 97]. Only some eigenvalues of the intermediate Hamiltonian H, are also eigenvalues of H. The corresponding model eigenvectors of H, are related to their true counterparts as in Bloch s theory. Provided effective operators a are restricted to act solely between these model eigenvectors, the possible a definitions from Bloch s formalism (see Section VI.A) can be used. 

As a result, we may view the orbital invariant SS-MRCEPA, termed by us as SS-MRCEPA(I) (I, for invariant), as the optimal approximation to the parent SS-MRCC method, which includes all the EPV terms exactly and which utilizes only those counter terms of the equations which eliminate the lack of extensivity of the attendant non-EPV terms in an orbital invariant manner [59]. In this article, we will present a couple of invariant SS-MRCEPA methods, viz. SS-MRCEPA(O) and SS-MRCEPA(I), for general open-shell systems using spin-free unitary generator adapted cluster operators starting from explicitly spin-free full-blown parent SS-MRCC formalism. Eor a detailed discussion of the allied issues pertaining to all the SS-MRCEPA-like methods, we refer to our recent SS-MRCEPA papers [58,59] and an earlier expose by Szalay [66]. 

The Pople corrections for higher excitations in CISD calculations result in a method called quadratic (Q) CISD, which can be regarded as an approximation to the coupled-cluster methods discussed in a separate section below. QCISD is available in the Gaussian series of programs, along with analytical derivatives and a method for the estimation of triple excitations called QCISD(T). Note that in Gaussian, CISD on open-shell molecules is performed with UHF MOs. Therefore, for such molecules, the methods just named should really be called UQCISD or UQCISD(T), respectively. 

Well-defined variational (Cl-type see Configuration Interaction), perturbational (MPn see M0ller-Plesset Perturbation Theory), and coupled cluster (CC see Coupled-cluster Theory) techniques have all been employed to determine anharmonic force fields. Important conclusions of these studies include (1) Near equilibrium, the correlation energy is a low-order function of the bond distances,even a linear approximation is meaningful(2) For open-shell species, spin contamination can significantly deteriorate results if a... 

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