Parallelization and vectorization of quantum mechanical methods—I. Integral program for polymers and molecules

The interest in theoretical investigations of macromolecular structures in chemistry with quantum mechanical methods is steadily growing. Many problems can only be attacked when the complexity of the chemical composition is taken into account. Supercomputers are the condition to perform the numerical investigations. The most promising developments in computer science and technology are massively parallel multiprocessor systems, not only with respect to cost-efficiency ratio in comparison with supercomputers. The variety of possible processor units that can be used to build up flexible architectures ranges from transputers, workstations and even large-scale computers. The consequences are for the users to adjust their programs and even to develop new algorithms appropriate for the specific parallel computer system. The calculation of the energy band structure and electronic wave function is the basic step in the theoretical study of physical and chemical properties of polymers. To obtain theoretical results comparable with experimental evidences the ab initio Hartree-Fock Crystal Orbital method has to be applied. We have developed new integral programs (one- and two-electron integrals) for multiprocessor systems with special emphasis on vectorizable structures and algorithms. Speed-up, efficiency and parallelization overhead are analysed for parallel computers with distributed memory and message-passing communication. The results prove that for large chemical systems the parallelization will be very efficient.