Unitary group approach based

Based on the Graphical Unitary Group Approach. 2. Single and Double Replacements From any Set of Reference Configurations. 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

At the ab-initio level, the most obvious possibility is offered by CAS SCF or CAS FCI (i.e., Cl within the CAS or, equivalently, CAS SCF without the orbital reoptimization based on RHF orbitals, cf. [33, 34]) wave functions based on the smallest possible active-space that warrants the correct description of the dissociation channel at hand. This option was also suggested by Stolarczyk [29], although we are not aware of any concrete implementation. Our testing proved to be very encouraging [33, 34], particularly for open shell systems, in which case we employed the spin-adapted CCSD based on the unitary group approach (UGA) [16, 36]. Even in the case of triple bond breaking, the applicability of the CCSD approximation can be significantly extended, as will be shown in Sect. 4. Most recently, we have explored the MR CISD wave function as an external source, as described in the next section. 

The structure of expansion (18) for two electrons in a uniform magnetic field was studied by Kandemir [34], In particular, he reduced the recurrence relation to a closed-form expression. Here, we present a more general analysis. In this derivation, a graphical approach, based on the ideas originally developed by Isaiah Shavitt in his graphical unitary group approach (GUGA) [44, 45], proved to be very useful. 

Spin-orbit Cl (based on graphical unitary group approach) (Yabushita et al. 1999). 

The next step in the formulation of alternatives involves modifications of the cluster operator. Janssen and Schaefer as well as Li and Paldus formulated rigorous spin adapted CC schemes based on a unitary group approach (UGA) para-metrization of the cluster operator T ... 

The state-selective approach to the multi-reference problem was further developed by Banerjee and Simons [118], by Laidig and Bartlett [119], by Hoffmann and Simons [120], by Li and Paldus [121, 122] and by Jeziorski, Paldus and Jankowski [123] who formulated extensive open-shell cc theory, based on the unitary group approach (uga) formalism. The Rayleigh-Schrodinger formulation of a state-selective approach to the multi-reference correlation problem has been developed more recently by Mukherjee and his collaborators [124-130] and also by Schaefer and his colleagues [131-133]. 

X. Li and J. Paldus, /. Chem. Phys., 103, 6536 (1995). Unitary Group Based Open-Shell Coupled-Cluster Approach and Triplet and Open-Shell Singlet Stabilities of Hartree-Fock References. 

Finally, we note that many other important advances have been made in CSF-based approaches, even outside the context of direct CL Much of this effort in recent years has focused on extending the unitary and symmetric group... 

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