Efficient Parallel Implementation of the CCSD External Exchange Operator and the Perturbative Triples (T) Energy Calculation.

A new, efficient parallel algorithm is presented for the most expensive step in coupled cluster singles and doubles (CCSD) energy calculations, the external exchange operator (EEO). The new implementation requires much less input/output than our previous algorithm and takes better advantage of integral screening. It is formulated as a series of matrix multiplications. Both the atomic orbital integrals and the corresponding CC coefficients are broken up into smaller blocks to diminish the memory requirement. Integrals are presorted to make their sparsity pattern more regular. This allows the simultaneous use of two normally conflicting techniques for speeding up the CCSD procedure: the use of highly efficient dense matrix multiplication routines and the efficient utilization of sparsity. We also describe an efficient parallel implementation of the perturbative triples correction to CCSD and related methods. Using the Array Files tool for distributed filesystems, parallelization is straightforward and does not compromise efficiency. Representative timings are shown for calculations with 282-1528 atomic orbitals, 68-228 correlated electrons, and various symmetries, C1 to C2h.