The Loop-Driven Graphical Unitary Group Approach: A Powerful Method for the Variational Description of Electron Correlation
Abstract
The graphical unitary group approach (UGA) has been cast into an extraordinarily powerful form by restructuring the Hamiltonian in terms of loop types. This allows the adoption of the loop-driven formulation which illuminates vast numbers of previously unappreciated relationships between otherwise distinct Hamiltonian matrix elements. Several new developments are presented and discussed. Among these developments are the use of new segment coefficients, improvements in the loop-driven algorithm, implicit generation of loops wholly within the external space adopted within the framework of the loop-driven methodology, and comparisons of the diagonalization tape method to the direct method. It is also shown how it is possible to implement the GUGA method without the time-consuming full (m5) four-index transformation. A particularly promising new direction involves the use of the graphical UGA methodology to obtain one-electron and two-electron density matrices. Once these are known, analytical gradients (first derivatives) of the CI potential energy can be easily obtained. Several calculations have been performed and times are compared with our preliminary implementation [J. Chem Phys. 70, 5092, (1979)] of the method. Also included is a calculation on the asymmetric 21A' state of SO2 with 23 613 configurations to demonstrate methods for the diagonalization of very large matrices on a minicomputer.
- Publication:
-
Physica Scripta
- Pub Date:
- January 1980
- DOI:
- 10.1088/0031-8949/21/3-4/013
- Bibcode:
- 1980PhyS...21..312B