Density Functional Theory
The description of excited states in solids is a challenging and
important problem in condensed matter physics since excited states are
needed to determine transport and optical properties of materials.
Untill the mid-eighties, a commonly used way to determine, for example,
band structures of materials was based on density functional theory in
the Kohn-Sham formulation using the local density approximation.
This approach maps the many-body problem onto a system of non-interacting,
fictitious Kohn-Sham particles. While the eigenvalues that result from
the solution of the single-particle Kohn-Sham equations have no physical
meaning within the frame work of the theory they compare rather well
with experiment. The most notable exception is the band gap of
insulators which is generally 0.5 - 2.0 eV too small compared to
experiment.
Very recently, new density functional methods have been presented in
the literature whose energy gaps generally agree much better with
experiment than the LDA. One such method, which has been studied in
much detail for semiconductors, is the so-called exact-exchange density
functional theory which allows the determination of the exact local
Kohn-Sham potential. In particular, self-interaction errors due to
incomplete cancellation of the self-Hartree and the self-exchange
potentials are eliminated in exact exchange density functioanl theory.
Using exact-exchange calculations in combination with LDA or generalized
gradient approximation (GGA) correlation functionals leads to energy gaps
and structural properties (lattice constant, cohesive energy, bulk
modulus, etc.) of standard semiconductors that agree well with
experiment.
An alternative way to describe the excited states of materials is
provided by compuational many-body theory using the dynamically
screened or GW approximation (GWA). In the GWA, the electronic
self-energy, which describes exchange and correlation beyond the
Hartree approximation, is expressed as the product of a single-particle
propagator G and a screened interaction W.
In principle, the GWA requires the self-consistent solution of a set of
four coupled integral equations as is discussed in more detail
in the paper. However, GWA calculations that are non-self-consistent,
use LDA energies and wave functions as input, and neglect the imaginary part
of the self-energy describe the experimental electronic structure of
sp bonded semiconductors and insulators generally to within 0.1 to
0.5 eV.
Here we test the accuracy of wave functions and energies obtained using
exact-exchange plus LDA correlation density functional calculations as
input for quasiparticle calculations. We choose eight standard sp
bonded semiconductors for our test. These provide a hard test, since
LDA plus GWA calculations work very well in these systems. Overall, we
find electronic energies that agree with LDA plus GWA calculations and
experiment.
To cite this page:
Exact-Exchange-Based Quasiparticle Calculations
<http://www.physics.ohio-state.edu/~aulbur/exx/exx.html>