# Efficient Kohn-Sham Density Functional Calculations Using the Gaussian and Plane Waves Approach

Thursday, August 2, 2007 - 11:30am - 12:00pm

EE/CS 3-180

Jürg Hutter (Universität Zürich)

The Gaussian and plane waves (GPW) approach combines

the description of the Kohn-Sham orbitals as a linear combination

of Gaussian functions with a representation of the electron density

in plane waves. The unique properties of Gaussian functions allow

for a fast and accurate calculation of the density in the plane wave

basis. The plane wave representation of the density leads to an

easy solution of Poisson's equation and thereby a representation of

the electrostatic potential. Matrix elements of this potential can

be calculated using the same methods. The auxiliary representation of

the density is further used in the calculation of the exchange-correlation

energy and potential. The resulting approach scales O(N log N) in the

number of electrons and has many additional interesting features,

namely, a small prefactor, early onset of linear scaling, and

a nominal quadratic scaling in the basis set size for fixed system size.

The GPW method is combined with a direct optimization of the subspace

of occupied Kohn-Sham orbitals using an orbital transformation (OT) method.

A variation of this method has recently been implemented that only

requires matrix multiplications. The method combines a small

prefactor with efficient implementation on parallel computers, thereby

shifting the break even point with linear scaling algorithms to

much larger systems. A strategy to combine the OT method with

sparse linear algebra will be outlined.

the description of the Kohn-Sham orbitals as a linear combination

of Gaussian functions with a representation of the electron density

in plane waves. The unique properties of Gaussian functions allow

for a fast and accurate calculation of the density in the plane wave

basis. The plane wave representation of the density leads to an

easy solution of Poisson's equation and thereby a representation of

the electrostatic potential. Matrix elements of this potential can

be calculated using the same methods. The auxiliary representation of

the density is further used in the calculation of the exchange-correlation

energy and potential. The resulting approach scales O(N log N) in the

number of electrons and has many additional interesting features,

namely, a small prefactor, early onset of linear scaling, and

a nominal quadratic scaling in the basis set size for fixed system size.

The GPW method is combined with a direct optimization of the subspace

of occupied Kohn-Sham orbitals using an orbital transformation (OT) method.

A variation of this method has recently been implemented that only

requires matrix multiplications. The method combines a small

prefactor with efficient implementation on parallel computers, thereby

shifting the break even point with linear scaling algorithms to

much larger systems. A strategy to combine the OT method with

sparse linear algebra will be outlined.