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Manuscript Title: A program system for ab initio MO calculations on vector and parallel processing machines. Part 3: integral reordering and four-index transformation.
Authors: R. Wiest, J. Demuynck, M. Benard, M.-M. Rohmer, R. Ernenwein
Program title: ASTERIX-REORD, ASTERIX-TRANSF
Catalogue identifier: ABTA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 62(1991)107
Programming language: Fortran.
Computer: CRAY-2.
Operating system: UNICOS 4.0.
Word size: 64
Peripherals: disc.
Keywords: Molecular physics, Molecular orbitals, Mo, Ab initio, Integral sorting, 4-index transformation, Cray-2.
Classification: 16.10.

Subprograms used:
Cat Id Title Reference
ABRB_v1_0 ASTERIX-INTEGS CPC 58(1990)305
ABRR_v1_0 ASTERIX-SCFCS, ASTERIX SCFOS CPC 60(1990)127

Nature of problem:
The evaluation of the correlation energy through Complete Active Space SCF iterations or CI expansion requires a file of two-electron integrals expressed over the basis of molecular orbitals (MOs) involved in the post-SCF treatment. Assuming that these MOs are known linear combinations of the initial atomic basis set, the present programs compute the integrals over the MO basis starting from a file of randomly distributed two-electron integrals expressed over the atomic orbital basis.

Solution method:
Two-electron integrals over the AO basis, initially labelled by integers pq = p*(p-1)/2 + q and rs = r*(r-1)/2 + s (p,q,r and s referring to orbital labels in the AO basis) are first reordered according to indentical or increasing values of the pq index, using the Yoshimine sorting algorithm. The so-obtained file is then processed through the four-step transformation algorithm proposed by Bender. Advantage is taken of symmetry. The possibilities offered by the vector and parallel architecture of the computer, and by the dynamic storage allocation are fully accounted for.

Restrictions:
These programs are part of the ASTERIX package. It is assumed that all requested input files have been created by ASTERIX-INTEGS and by ASTERIX-SCFCS or -SCFOS (see articles 1 and 2 of this series). The size of the CGTO basis set is limited to 400 functions in program REORD.

Running time:
The cpu time T (seconds) for ASTERIX-REORD on the CRAY-2 is given by
                   T = M *(0.6 + 0.3*NSTEP)
where M is the number of million integrals to be sorted and NSTEP the number of sorting passes, inverse function of the available storage. A typical time for ASTERIX-TRANSF is provided by the transformation carried out over the HMn(CO)5 molecule (151 CGTOs, 89 active MOs, 6541393 nonzero integrals on the AO basis, C2v symmetry, 2061468 integrals computed on the MO basis): 431s on a single processor.