Parallel and Low-Order Scaling Implementation of Hartree–Fock
Exchange Using Local Density Fitting
Christoph Köppl
Hans-Joachim Werner
10.1021/acs.jctc.6b00251.s001
https://acs.figshare.com/articles/journal_contribution/Parallel_and_Low-Order_Scaling_Implementation_of_Hartree_Fock_Exchange_Using_Local_Density_Fitting/3464672
Calculations using
modern linear-scaling electron-correlation methods
are often much faster than the necessary reference Hartree–Fock
(HF) calculations.
We report a newly implemented HF program that speeds up the most time-consuming
step, namely, the evaluation of the exchange contributions to the
Fock matrix. Using localized orbitals and their sparsity, local density
fitting (LDF), and atomic orbital domains, we demonstrate that the
calculation of the exchange matrix scales asymptotically linearly
with molecular size. The remaining parts of the HF calculation scale
cubically but become dominant only for very large molecular sizes
or with many processing cores. The method is well parallelized, and
the speedup scales well with up to about 100 CPU cores on multiple
compute nodes. The effect of the local approximations on the accuracy
of computed HF and local second-order Møller–Plesset perturbation
theory energies is systematically investigated, and default values
are established for the parameters that determine the domain sizes.
Using these values, calculations for molecules with hundreds of atoms
in combination with triple-ζ basis sets can be carried out in
less than 1 h, with just a few compute nodes. The method can also
be used to speed up density functional theory calculations with hybrid
functionals that contain HF exchange.
2016-06-07 00:00:00
processing cores
100 CPU cores
HF calculation scale cubically
default values
domain sizes
1 h
Fock matrix
exchange contributions
Hartree
method
nod
M øller perturbation theory energies
LDF
theory calculations
exchange matrix scales
density
HF program
HF exchange
speedup scales
Local Density