Dutta Achintya Kumar, Neese Frank, Izsák Róbert
Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany.
J Chem Phys. 2016 Jan 21;144(3):034102. doi: 10.1063/1.4939844.
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm(-1) (59 μHartree) for excitation energies and 6.799 cm(-1) (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.
在本文中，球交换链（COSX）近似被应用于含单双激发的运动方程（EOM）耦合簇方程中的最高标度项，特别是涉及带有四个虚指标积分的项。结果发现，即使仅加速这一项也能带来显著的计算增益，同时不影响该方法所需的精度。对于使用585个基函数对五个水分子簇进行激发能计算，使用宽松网格的COSX计算含四个虚指标的项比使用标准实现快9.4倍，这使得整个EOM计算加速了2.6倍。对于电子附着计算，对于同一体系，含四个虚指标的项比标准计算快15倍，整个EOM计算快10倍。使用与本文所讨论方式相同的设置，通过Thiel激发态测试集对新方法的精度进行了测试，发现整个测试集中激发能的最大绝对偏差为12.945 cm⁻¹（59 μHartree），电子附着的最大绝对偏差为6.799 cm⁻¹（31 μHartree）。结合本文讨论的方式对完整EOM方程进行并行评估，使用基态的MP2振幅，使我们能够对大体系进行计算。使用英特尔至强E5 - 2670处理器的4个核心，每个核心分配10 GB内存，在3天19小时内获得了锌原卟啉模型化合物两个最低态的电子亲和能值（224个相关电子和1120个基函数）。使用同一处理器的8个核心，每个核心分配相同内存，计算反式视黄醛的最低两个激发能（114个相关电子和539个基函数）耗时1天21小时。
