Some aspects of parallelization of two-electron integrals in molecular orbital programs

Evaluation of two-electron integrals forms a substantial part of the CPU time for any ab initio molecular orbital program. This part of the package, “MICROMOL”, is parallelized. However, this parallelization leads to only sublinear speedups (typically 3 on a 4-node machine). In view of these results, the task of development of an efficient program for two-electron integrals suitable for the parallel environment has been taken up. The program is written in FORTRAN considering specific symmetry features and application of rigorous bounds. This program is further parallelized with a good load balancing strategy. The molecules used as the test cases are: trans-butadiene, benzene, nitrobenzene, naphtalene and cytosine, with 3G and 4–31G basis sets. The results indicate that the parallel version of this program gives a typical speedup of 3.6 for a 3G basis set and approximately 3.4 for a 4–31G basis set for all the molecules tested. The sequential version of this program is ～1.2 times faster than the sequential version of MICROMOL, whereas the parallel version is ～1.4 times faster than the parallelized MICROMOL.