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The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted second-order Møller-Plesset perturbation theory, as well as for both restricted and unrestricted Hartree-Fock and density functional theory. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores are also discussed.

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Benchmark timings are presented for the fragment molecular orbital method on a Blue Gene/P computer. Algorithmic modifications that lead to enhanced performance on the Blue Gene/P architecture include strategies for the storage of fragment density matrices by process subgroups in the global address space. The computation of the atomic forces for a system with more than 3000 atoms and 44 000 basis functions, using second order perturbation theory and an augmented and polarized double-ζ basis set, takes ∼7 min on 131 072 cores. Disciplines Chemistry CommentsReprinted (adapted) ABSTRACT: Benchmark timings are presented for the fragment molecular orbital method on a Blue Gene/P computer. Algorithmic modifications that lead to enhanced performance on the Blue Gene/P architecture include strategies for the storage of fragment density matrices by process subgroups in the global address space. The computation of the atomic forces for a system with more than 3000 atoms and 44 000 basis functions, using second order perturbation theory and an augmented and polarized double-ζ basis set, takes ∼7 min on 131 072 cores.

The analytic gradient expression for second-order Z-averaged perturbation theory is revised and its parallel implementation is described in detail. The distributed data interface is used to access molecular-orbital integral arrays stored in distributed memory. The algorithm is designed to maximize the use of local data and reduce communication costs. The iterative solution and the preconditioner used to induce the convergence of the coupled-perturbed Hartree-Fock equations are presented. Several illustrative timing examples are discussed. KeywordsLagrangian mechanics, Gold, Integral equations, Integral transforms, Perturbation theory Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 124 (2006) The analytic gradient expression for second-order Z-averaged perturbation theory is revised and its parallel implementation is described in detail. The distributed data interface is used to access molecular-orbital integral arrays stored in distributed memory. The algorithm is designed to maximize the use of local data and reduce communication costs. The iterative solution and the preconditioner used to induce the convergence of the coupled-perturbed Hartree-Fock equations are presented. Several illustrative timing examples are discussed.

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