Hightlight Paper:

Hartree-Fock calculations with linearly scaling memory usage

We present in this paper an implementation of a set of algorithms for performing Hartree-Fock calculations with resource requirements in terms of both time and memory directly proportional to the system size. In particular, a way of computing the Hartree-Fock exchange matrix directly in sparse form is described which gives only small addressing overhead. Linear scaling in both time and memory is demonstrated in benchmark calculations for system sizes up to 11650 atoms and 67204 Gaussian basis functions on a single computer with 32 GB of memory.

The sparsity of overlap, Fock, and density matrices as well as band gaps are also shown for a wide range of system sizes, for both linear and three-dimensional systems.

This paper is probably the first ever demonstration that Hartree-Fock calculations can scale on a single computer up to such a large number of basis functions. We also demonstrate that matrix sparsity - the parameter that determines whether linear scaling in memory is achieved - is appears in three-dimensional systems late. For example, water clusters with a thousand water molecules have significant sparsity in the overlap matrix (20% non-zero elements), little sparsity in the Kohn-Sham matrix (75%) and basically no sparsity in the density matrix (99% non-zero elements). Fortunately, the sparsity starts to appear before in clusters smaller than 3000 water molecules. One has to remember that full three-dimensional systems represent a worst case. Sparsity appears much earlier for (semi-)one or two-dimensional systems as we demonstrate for glutamine-alanine helix systems.

Figures: Timings, memory usage, matrix sparsity, and computed HOMO--LUMO gaps for Hartree-Fock/3-21G calculations on glutamine-alanine helix systems of varying size. The right-most points in the graphs are for GluAla₄₄₈, with 11650 atoms and 67204 basis functions.

Publication reference >> J. Chem. Phys. 128, 184106 (2008)

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