Institut für Physikalische Chemie, Universität Mainz, Jakob-Welder-Weg 11, D-55099 Mainz, Germany.
Institut für Chemie, Technische Universität Chemnitz, Strasse der Nationen 62, D-09111 Chemnitz, Germany.
J Chem Theory Comput. 2008 Jan;4(1):64-74. doi: 10.1021/ct700152c.
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.
本文介绍了一种高效的耦合簇算法的并行自适应方法，该方法可用于计算耦合簇单双激发（CCSD）和耦合簇单双激发加上微扰三重激发（CCSD(T)）的能量、梯度，并且首次实现了分析二阶导数。提出了一种最小化努力的策略，通过并行化 CCSD 和 CCSD(T) 的时间确定步骤，实现了幅度复制、通信最小化的并行实现。所得到的算法针对的是具有足够内存和本地磁盘空间的计算节点组成的可承受的集群架构，并且通过千兆以太网等标准通信网络连接。虽然在计算节点数量非常大的情况下，这种方案存在缺点，但它证明是一种减少大规模耦合簇计算整体计算时间的有效方法。通过这种方式，对于具有超过 1000 个基函数的体系，可进行分子性质（如振动频率或 NMR-化学位移）的 CCSD(T)计算。对 CCSD 和 CCSD(T)能量、梯度和二阶导数的时间确定步骤进行了深入分析。提出了基准计算，证明了这些步骤的并行化足以获得有效的并行方案。这包括使用非限制（UHF）和限制开壳（ROHF）哈特ree-fock 参考的并行 CCSD 能量和梯度、并行 UHF-CCSD(T)能量和梯度、并行 ROHF-CCSD(T)能量以及用于封闭和开壳参考的并行运动方程 CCSD 能量和梯度的计算。首次将其应用于使用大基组计算苯的 NMR 化学位移和二茂铁的平衡几何结构的计算，以及超过 1300 个基组的能量计算，证明了该实现的效率。
