Unitary group approach UGA

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. 

Finite order perturbation theory (PT) for low-spin open-shell singlet states is formulated in terms of spin-free unitary group approach (UGA). Both M0ller Plesset and Bpstein-Nesbet partitionings of the Hamiltonian are considered. The method is tested on low lying excited states of CH2, NH2+ and H2O using various basis sets. 

Keywords Unitary group approach (UGA) Graphical unitary group approach (GUGA) Correlation problem Spin-dependent UGA... 

In the domain of Cl methodology, our close interaction followed the formulation of the unitary group approach (UGA) to the many-electron correlation problem by one of us [2-5]. Professor Shavitt soon fell in love with this formalism and designed an ingenious graphical representation [6-8] of the electronic Gel fand-Tsetlin (G-T) basis as described in terms of the so-called ABC or Paldus tableaux (see below). This development ultimately resulted in his graphical UGA (GUGA) version of UGA (for most recent overviews of these approaches see [4, 9-13]). 

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]. 

The symmetry-adapted CFs introduced in this section, together with their classification according to the U(m) subduction chain, provide the foundations for the unitary-group approach (UGA) to Cl calculations. A useful review is contained in a collection of papers edited by Hinze (1981), while the basic theory is fully presented (with many references) by Matsen and Pauncz (1986). 

ANO = atomic natural orbital CSF = configuration state function DRT = distinct row table FCI = full configuration interaction GUGA = graphical unitary group approach PNO = pseudonatural orbital or pair natural orbital UGA =... 

---