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.