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Manuscript Title: MATSUP: a program to obtain two-electron repulsion integrals from a sparse file of P supermatrix elements.
Authors: M. Benard
Program title: MATSUP
Catalogue identifier: AARZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)79
Programming language: Fortran.
Computer: UNIVAC 1100.
Operating system: EXEC 8.
RAM: 31K words
Word size: 36
Peripherals: magnetic tape.
Keywords: Quantum chemistry, Molecular integral, Conversion, Integrals, Electron repulsion, Supermatrix.
Classification: 16.10.

Nature of problem:
The iterative resolution of the Roothaan equations in the SCF procedure can be carried out either from the file of two-electron repulsion integrals (pq/rs), or from a file of supermatrix elements, as defined as P pq,rs = (pq|rs) -1/4 [ (pr|qs) + (ps|qr)]. iterative cycles are intrinsically faster when carried out from the P supermatrix file. However, the file of two-electron repulsion integrals is requested when the wavefunction is improved beyond the Hartree-Fock approximation, by means of configuration interaction. Therefore, there is a clear need for a program designed to convert efficiently a P supermatrix file into a classical file of two-electron repulsion integrals.

Solution method:
If the file P supermatrix elements is assumed to be complete the conversion is performed through a system of three relations involving the elements of P obtained from the three nonequivalent permutations of indices p, q, r, s (assuming p>q>r>s).
(pq|rs) = 1.2Ppq,rs + 0.4[Ppr,qs + Pps,qr],
(pr|qs) = 1.2Ppr,qs + 0.4[Ppq,rs + Pps,qr],
(ps|qr) = 1.2Pps,qr + 0.4[Ppq,rs + Ppr,qs].
This relationship defines a "set" of integrals. If some of these indices are coincident (cases p=q; q=r; r=s and combinations), the size of the set is reduced from 3 to either 2 or 1. Each case is analyzed and processed separately. However, a real P file is usually not complete, but sparse. It means that some of the non- equivalent P elements are omitted in the file either because they are zero by symmetry or because they are lower than a given threshold. For each set of P elements the presence of such "holes" is detected by the program. In the frame of either relation system or its convenient subset, a value of zero is assigned to the deleted permutations of Ppr,rs. Therefore in an intermediate step, a complete set of two- electron integrals is obtained from a set of P elements which may be noncomplete. Then the obtained integrals are checked against a threshold and either kept or deleted.

Running time:
About 210 s for 1 million P elements.