Highly Efficient, Linear-Scaling Seminumerical Exact-Exchange Method for Graphic Processing Units

We present a highly efficient and asymptotically linear-scaling graphic processing unit accelerated seminumerical exact-exchange method (sn-LinK). We go beyond our previous central processing unit-based method (Laqua, H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Theory Comput. 2018, 14, 3451−3458) by employing our recently developed integral bounds (Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101) and high-accuracy numerical integration grid (Laqua, H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Phys. 2018, 149, 204111). The accuracy is assessed for several established test sets, providing errors significantly below 1mEh for the smallest grid. Moreover, a comprehensive performance analysis for large molecules between 62 and 1347 atoms is provided, revealing the outstanding performance of our method, in particular, for large basis sets such as the polarized quadruple-zeta level with diffuse functions

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach’s effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latterfrom 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work