VB2000: the Implementation of Modern Valence Bond Theory and Group Function Method based on the Algebrant Algorithm and Separability of Quantum Systems

Jiabo Li*, and Roy McWeeny**

* Minnesota Supercomputer Institute, Minneapolis, MN 55415, USA

** Department of Chemistry, University of Pisa, 56100 Pisa, Italy

Abstract: an efficient algorithm based on the successive Laplace expansion of algebrants of many electron wave functions has been implemented for modern valence bond calculation in a simple electronic structure package VB2000. A unique divide-and-conquer approach, the so-called group function method, is adopted for electron correlation calculation of molecular systems. The combination of VB theory and the group function method in VB2000 can be considered as a natural extension of gvb and casscf methods: a molecule can be divided into many electron-groups(rather than two groups as in casscf method), each group may contain many electrons (rather than two as in a GVB pair) and each group can be treated with any variational method, such as Hartree-Fock, casvb(an equivalent of casscf) or any method in between. The method in VB2000 is both variational and size consistent. The algorithm, as a whole, scales formally with N^{5}, where N is the number of basis functions. VB2000 is also compared with Gaussian98 as regard the cpu-timing performance for electron correlation calculations at the mcscf level.