Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.

In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard communication networks like Gigabit Ethernet. While this scheme has disadvantages in the limit of very large numbers of compute nodes, it proves to be an efficient way of reducing the overall computational time for large-scale coupled-cluster calculations. In this way, CCSD(T) calculations of molecular properties such as vibrational frequencies or NMR-chemical shifts for systems with more than 1000 basis functions are feasible. A thorough analysis of the time-determining steps for CCSD and CCSD(T) energies, gradients, and second derivatives is carried out. Benchmark calculations are presented, proving that the parallelization of these steps is sufficient to obtain an efficient parallel scheme. This also includes the calculation of parallel CCSD energies and gradients using unrestricted (UHF) and restricted open-shell (ROHF) Hartree-Fock references, parallel UHF-CCSD(T) energies and gradients, parallel ROHF-CCSD(T) energies as well as parallel equation-of-motion CCSD energies and gradients for closed- and open-shell references. First applications to the calculation of the NMR chemical shifts of benzene using large basis sets and to the calculation of the equilibrium geometry of ferrocene as well as energy calculations with more than 1300 basis functions demonstrate the efficiency of the implementation.