Linear-Scaling Density-Functional Calculations with Plane-Waves

Thursday, August 2, 2007 - 2:30pm - 3:00pm
EE/CS 3-180
Arash Mostofi (University of Cambridge)
A number of reasons have resulted in plane-waves becoming one of the
basis sets of choice for simulations based on density-functional theory,
for example: the kinetic energy operator is diagonal in momentum space;
quantities are switched efficiently between real space and momentum space
using fast-Fourier transforms; the atomic forces are calculated by
straightforward application of the Hellmann-Feynman theorem; the
completeness of the basis is controlled systematically with a single

The resulting simulations require a computational effort which scales as
the cube of the system-size, which makes the cost of large-scale
calculations prohibitive. For this reason there has been much interest in
developing methods whose computational cost scales only linearly with
system-size and hence bringing to bear the predictive power of
density-functional calculations on nanoscale systems.

At first sight the extended nature of plane-waves makes them unsuitable
for representing the localised orbitals of linear scaling methods. In
spite of this, we have developed ONETEP (Order-N Electronic Total Energy
Package), a linear-scaling method based on plane-waves which overcomes
the above difficulty and which is able to achieve the same accuracy and
convergence rate as traditional cubic-scaling plane-wave calculations.