The computation of nuclear second derivatives (NSD) is an essential routine in quantum chemical investigations of ground and transition state, thermodynamics, and force field. Previous work has contributed to the analytical evaluation of NSD (aNSD) and to the improvement of integral evaluation and storage. Another facet of NSD computations focuses on hardware-enabled faster and more capable integral evaluations based on specialized processors such as graphic processing units. This facet of NSD computation is complimentary to the continuing development of theory and mathematical approximations. Herein, we describe another facet of improving NSD computations focusing on the utilization of grid computing to enable numerical differentiations of analytical first derivatives (aNFD) to calculate NSD (nNSD), nNSD-on-grid. The advantage of nNSD over aNSD is that it circumvents the costly evaluation of the coupled-perturbed self-consisten field (CP-SCF), which could also have convergence issues for near degenerate states. The unfavorable pre-scaling factor, which is twice of the degrees of freedom in central differences, of the nNSD is reduced to unity by distributing each aNFD to a remote computer. Hence, the scaling of nNSD is on the same order as aNFD. For accelerating routine DFT-based NSD, nNSD-on-grid outcompeted aNSD as the ring size grows larger than three for a test set of linear polyacenes (one to seven rings). For a catalytically relevant complex, E-Ag2(tbu3tpy)2OTf(NSO3-2,6-dFPh), with 156 atoms, 2705 Gaussian functions (GFs), and 7094 density fitting GFs, nNSD-on-grid showed 7.7 times faster and 4.4 times less memory intensive than aNSD on 12 processors. For enabling Hessian evaluation for near-degenerate ground state of 2[Rh2(esp)2(NSO3CH3)]+, nNSD-on-grid completed the evaluation in 878 minutes while aNSD failed to converge the CP-SCF for the first out of seven batches in 1440 minutes on 12 processors. For enabling Hessian evaluation using high scaling method, in particular RI-MP2, nNSD-on-grid completed for all the polyacenes, elapsing 153 minutes and using 1367 MB for heptacene. For naphthalene, nNSD-on-grid was 27 times faster and 46 times less memory-intensive than aNSD using 12 processors. Grid computing on numerical methods can outperform analytical methods in terms of computing size and the size of systems treatable. The nNSD-on-grid method presented in this abstract is one example of this concept and a pioneer for future implementations.

Enabling and accelerating Hessian calculations with numerical nuclear second derivatives on computing grid

255th National Meeting (2018)

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