Four-index integral transformation exploiting symmetry

We present a Fortran 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: ADUWProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUWProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers: IBM/AIX, HP Alpha server/Tru64, PC's/LinuxProgram language used: Fortran 95Number of lines in distributed program, including test data, etc.: 4519No. of bytes in distributed program, including test data, etc.: 32 095Distributed format: tar gzip fileNature 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.     

A parallel method for large sparse generalized eigenvalue problems using a GridRPC system

In this paper we present a master–worker type parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem , where A and B are large sparse matrices. A moment-based method that finds all of the eigenvalues that lie inside a given domain is used. In this method, a small matrix pencil that has only the desired eigenvalues is derived by solving large sparse systems of linear equations constructed from A and B. Since these equations can be solved independently, we solve them on remote servers in parallel. This approach is suitable for master–worker programming models. We have implemented and tested the proposed method in a grid environment using a grid RPC (remote procedure call) system called OmniRPC. The performance of the method on PC clusters that were used over a wide-area network was evaluated.     

Numerical accuracy on Fm(z) for molecular integral calculations

Large-scale SCF calculations require more accurate numerical results. We investigated numerical accuracy on various F_m(z) evaluation methods. We found that the polynomial of z, which are often used for the Taylor series expansion and the Chebyshev approximation in molecular orbital programs, contains unexpectedly large numerical errors even if a polynomial degree is cubic. The numerical accuracy is allowable for small molecules, but may be insufficient for large molecules. On the other hand, the polynomial of δ, which requires only one more calculation step than that of z, maintains sufficient numerical accuracy because round-off errors are hardly propagated in the polynomial of δ.