Urban Lars, Laqua Henryk, Ochsenfeld Christian
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany.
Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany.
J Chem Theory Comput. 2022 Jul 12;18(7):4218-4228. doi: 10.1021/acs.jctc.2c00215. Epub 2022 Jun 8.
We employ our recently published highly efficient seminumerical exchange (sn-LinK) [Laqua, H.; Thompson, T. H.; Kussmann, J.; Ochsenfeld, C. 2020, 16, 1456-1468] and integral-direct resolution of the identity Coulomb (RI-J) [Kussmann, J.; Laqua, H.; Ochsenfeld, C. 2021, 17, 1512-1521] methods to significantly accelerate the computation of the demanding multiple orbital spaces spanning Fock matrix elements present in R12/F12 theory on central and graphics processing units. The errors introduced by RI-J and sn-LinK into the RI-MP2-F12 energy are thoroughly assessed for a variety of basis sets and integration grids. We find that these numerical errors are always below "chemical accuracy" (∼1 mH) even for the coarsest settings and can easily be reduced below 1 μH by employing only moderately large integration grids and RI-J basis sets. Since the number of basis functions of the multiple orbital spaces is notably larger compared with conventional Hartree-Fock theory, the efficiency gains from the superior basis scaling of RI-J and sn-LinK (() instead of () for both) are even more significant, with maximum speedup factors of 37 000 for RI-J and 4500 for sn-LinK. In total, the multiple orbital spaces spanning Fock matrix evaluation of the largest tested structure using a triple-ζ F12 basis set (5058 AO basis functions, 9267 CABS basis functions) is accelerated over 1575× using CPUs and over 4155× employing GPUs.
我们采用了我们最近发表的高效半数值交换（sn-LinK）方法[Laqua, H.; Thompson, T. H.; Kussmann, J.; Ochsenfeld, C. 2020, 16, 1456 - 1468]和恒等式库仑积分直接求解（RI-J）方法[Kussmann, J.; Laqua, H.; Ochsenfeld, C. 2021, 17, 1512 - 1521]，以显著加速在中央处理器和图形处理器上对R12/F12理论中存在的、需要大量计算的多个轨道空间的福克矩阵元的计算。针对各种基组和积分网格，全面评估了RI-J和sn-LinK引入到RI-MP2-F12能量中的误差。我们发现，即使在最粗糙的设置下，这些数值误差始终低于“化学精度”（约1 mH），并且通过仅使用适度大的积分网格和RI-J基组，很容易将其降低到1 μH以下。由于与传统哈特里-福克理论相比，多个轨道空间的基函数数量显著更多，则RI-J和sn-LinK的卓越基函数缩放比例（两者均为()而非()）所带来的效率提升更为显著，RI-J的最大加速因子为37000，sn-LinK为4500。总体而言，使用三重ζ F12基组（5058个原子轨道基函数，9267个CABS基函数）对最大测试结构进行多个轨道空间的福克矩阵评估，使用中央处理器时加速超过1575倍，使用图形处理器时加速超过4155倍。
