# 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

parameter.

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.

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

parameter.

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.