Four-index integral transformation exploiting symmetry
We present a Fortian implementation of four-index integral transformation in the LCAO-MO (linear combination of atomic orbitals-molecular orbitals) framework that exploits symmetry. Electron correlation calculations, such as configuration interaction (CI) calculations, usually require electron repulsion integrals to be transformed to a molecular orbital basis from a basis using atomic orbitals. In large molecular systems it is vital to exploit the sparsity of integrals in making this transformation. By exploiting symmetry, the sparsity of integrals is fully utilized, the size of intermediate file is minimized, and the computational cost is reduced. The present algorithm is simple and can readily be added to existing quantum chemistry program packages. Program summary Title of program: SYM4TR (symmetry adapted 4-index integral transformation) Catalogue identifier: ADUW Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUW Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: IBM/AIX, HP Alpha server/Tru64, PC's/Linux Program language used: Fortran 95 Number of lines in distributed program, including test data, etc.: 4519 No. of bytes in distributed program, including test data, etc.: 32 095 Distributed format: tar gzip file Nature of physical problem: Molecular orbital calculations including electron correlation effects usually require electron repulsion integrals to be transformed from an atomic orbital (AO) basis to a molecular orbital (MO) basis. By exploiting the sparsity of molecular integrals, the computational cost and memory needed for the transformation are minimized. Method of solution: The sparsity of molecular integrals is exploited. The program treats only nonzero integrals. The length of running indices in DO loops is reduced using the block-diagonal form of the MO coefficient matrix. In the present program, the point group is limited to D-2h and its subgroups. (C) 2004 Elsevier B.V. All rights reserved.
four-index integral transformation electron repulsion integral sparsity symmetry adaptation point group two-electron integral