A PROGRAM SYSTEM FOR ABINITIO MO CALCULATIONS ON VECTOR AND PARALLEL PROCESSING MACHINES .3. INTEGRAL REORDERING AND 4-INDEX TRANSFORMATION

This series of three papers presents a program system for ab initio molecular orbital calculations on vector and parallel computers. Part III is devoted to the four-index transformation on a molecular orbital basis of size NMO of the file of two-electron integrals (pq parallel-to rs) generated by a contracted Gaussian set of size NATO (number of atomic orbitals). A fast Yoshimine algorithm first sorts the (pq parallel-to rs) integrals with respect to index pq only. This file of half-sorted integrals labelled by their rs-index can be processed without further modification to generate either the transformed integrals or the supermatrix elements. The large memory available on the CRAY-2 has made possible to implement the transformation algorithm proposed by Bender in 1972, which requires a core-storage allocation varying as (NATO)3. Two versions of Bender's algorithm are included in the present program. The first version is an in-core version, where the complete file of accumulated contributions to transformed integrals is stored and updated in central memory. This version has been parallelized by distributing over a limited number of logical tasks the NATO steps corresponding to the scanning of the most external loop. The second version is an out-of-core version, in which twin files are alternatively used as input and output for the accumulated contributions to transformed integrals. This version is not parallel. The choice of one or another version and (for version 1) the determination of the number of tasks depends upon the balance between the available and the requested amounts of storage. The storage management and the choice of the proper version are carried out automatically using dynamic storage allocation. Both versions are vectorized and take advantage of the molecular symmetry.