Graphical Unitary Group Approach GUGA

There are several approaches that may be used to achieve this goal. Many of these methods are discussed in the review of the Cl method of Shavitt, in the review of MCSCF and Cl methodology of McWeeny and Sutcliffe and in the discussion of spin eigenfunctions by Pauncz The method with which the present author is most familiar is the graphical unitary group approach (GUGA) and this approach will be discussed briefly. For more details of this method, the reader is referred, in particular, to the contributions of Paldus and of Shavitt in the volume of Lecture Notes in Chemistry edited by J. Hinze. 

It should be pointed out, however, that the size of the Cl expansion used in a CASSCF calculation is almost always much larger than those normally used in earlier applications of the multiconfigurational SCF (MCSCF) method . It was only when the graphical unitary group approach (GUGA) for full Cl calculations was invented in the years 1975-78 that an efficient computational procedure for CASSCF calculations could be developed ". ... 

Another technique used to speed up Cl calculations is the graphical unitary-group approach (GUGA) for details, see B. R. Brooks and H. F. Schaefer, J. Chem. Phys., 70,5092 (1979) B. R. Brooks et al., /. Chem. Phys.,11,3837 (1980). GUGA has been incorporated into the direct Cl method [P. E. M. Siegbahn, J. Chem. Phys., 72, 1647 (1980)]. 

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

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. 

To perforin the dynamical calculations with SET, we use CSF of the electronic configurations of single and double excitations (CISD), for which the method by graphical unitary group approach (GUGA) has been applied. [310-312, 366, 367] Only the spin-singlet states are considered. Below we outline the practice of our computational scheme. 

In Table 47 we have collected RE and REPE values obtained by the ambitious VB calculations of Wu and Jiang,and those of Alexander and Schmalz, to be compared to the RE values calculated by the simple Hiickel MO method. Both VB calculations used the graphical unitary group technique that have produced highly efficient methods for ab initio calculations, the so-called graphical unitary group approach (GUGA), in which only the non-zero matrix elements are computed.One should recall that the... 

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