Unitary group graphical

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

A. Koslowski, M. E. Beck, and W. Thiel. Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach, J. Comput. Chem., 24 714-726 (2003). 

Configuration Interaction Using the Graphical Unitary Group Approach and Relativistic Core Potential and Spin—Orbit Operators. 

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. 

The subset of operators satisfying Eq. (232) is usually known before the MCSCF optimization process is initiated. In fact, many CSF generation methods, including the graphical unitary group approach, allow the specification of the operators of Eq. (232) or the orbital subsets that define these rotation operators. The corresponding orbital rotation parameters may then be deleted from the MCSCF optimization process for any state and for any geometry for wavefunctions expanded in this CSF space. The direct product... 

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 ". ... 

Like any general direct Cl method, the shape-driven graphical unitary group approach can also be used to perform FCI calculations for some cases, but as in Handy s determinantal scheme, matrix elements involving higher than double excitations from the reference CSF are processed using scalar algorithms. Like the Handy determinantal scheme, this approach has been used to provide several benchmarks. 

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 Computational chemistry history Isaiah Shavitt Configuration interaction Electron correlation Graphical Unitary Group Approach COLUMBUS Programs... 

I. Shavitt, The Utilization of Abelian Point Group Symmetry in the Graphical Unitary Group Approach to the Calculation of Correlated Electronic Wave-functions, Chem. Phys. Lett. 63, 421-427 (1979). 

H. Lischka, R. Shepard, F. B. Brown, and 1. Shavitt, New Implementation of the Graphical Unitary Group Approach for Multireference Direct Conhguration... 

R. D. Kent, M. Schlesinger, and I. Shavitt, Graphical Unitary Group Approach to Spin-Spin Interaction, Int. J. Quantum Chem. 41, 89-103 (1992). 

Keywords Multifacet graphically contracted function method Configuration interaction Graphical unitary group approach Shavitt graph Wave function analysis Graph density Node density Arc density... 

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

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