Quantum supercharger library: hyper-parallel integral derivatives algorithms for ab initio QM/MM dynamics

This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two-electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one- and two-electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree-Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS-UK, which uses the efficient Schlegel method for s- and l-orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6-31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.