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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_0Distribution 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. |

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