Macroscopic dielectric function within time-dependent density functional theory-Real time evolution versus the Casida approach

Author(s)
Tobias Sander, Georg Kresse
Abstract

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Organisation(s)
Computational Materials Physics
Journal
Journal of Chemical Physics
Volume
146
No. of pages
13
ISSN
0021-9606
DOI
https://doi.org/10.1063/1.4975193
Publication date
02-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics, 103036 Theoretical physics, 103015 Condensed matter, 103009 Solid state physics
Keywords
ASJC Scopus subject areas
General Physics and Astronomy, Physical and Theoretical Chemistry
Portal url
https://ucrisportal.univie.ac.at/en/publications/f6c260b0-9818-42dd-85fb-0a33b2f1cd70