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Construction of an Orbital Dependent Exchange
Correlation Density Functional

By Tobias Schmidt (21.02.2013)

The world's population, and with it the worldwide energy consumption, will increase drastically in the near future. Therefore it is of major importance to perform basic research on alternative and sustainable energy sources. Especially the employment of organic semiconductor systems in photovoltaic devices represents a promising approach in order to efficiently tackle this problem.

Consequently, the academic as well as industrial interest in developing organic semiconductors has been growing significantly in the past decades. Even though these systems work on similar physical principles as the conventional inorganic semiconductors, which are already well established in our common daily usage, organic semiconductors offer decisive advantages compared to their inorganic counterparts. For example, besides being considerably cheaper in the production process, organic semiconductor materials also show remarkable properties like high flexibility and transparency, which extends their possible applicability.

In order to enhance the efficiency and overall performance of organic semiconductors, a detailed theoretical description and modeling of the employed molecules is required. It deserves for instance exact quantum mechanical simulations to understand the process of charge transport in certain organic molecular structures and, based on that, to experimentally develop new materials with improved electronic properties. Unfortunately, all the molecules, which can be considered as promising candidates for organic semiconductor systems because of their appropriate electronic structure, are complex systems containing several hundreds of electrons. In this case, it is a reasonable approach to describe the quantum mechanical many-body problem within the formalism of Density Functional Theory (DFT), for this theory is capable of delivering results with a satisfying accuracy within a moderate computation time.

The crucial component of DFT is the so-called exchange correlation energy. It contains the non-classical part of the electron-electron interaction and allows for transforming the many-body Schrödinger equation into the non-interacting Kohn-Sham equations. To exploit the benefits of DFT in the description of many-electron systems, this functional must be approximated reasonably by an analytic expression. In the course of the development of DFT in the past decades, several ideas of approaching the analytical construction of the exchange correlation energy were investigated. This led to a wide range of varying functional expressions, each tackling the problem from different directions.

Schematic plots of the electron density ρ along the interatomic axis of the two diatomic molecules BH and H2, calculated with LDA and the new functional.

As a result, these exchange correlation functionals differ quite strongly in their abilities as well as efficiencies. Unfortunately, even employing the same functional expression for a certain molecular systems leads to predictions of different physical quantities with greatly varying accuracies. For instance functionals, that are capable of describing geometries and binding energies of complex molecules in great accordance with the experimental data, only deliver insufficient predictions when it comes to the computation of excitation spectra and vice versa.

It is contradictory to the pursuit of a universally valid theory to make use of different methods for each specific application. Therefore I am working on the construction of a new functional, that does not necessarily outrange already existing functionals in computing certain quantities to a high accuracy. My work rather attempts to develop a mathematical expression for the exchange correlation term, that allows for exact thermochemical predictions and, at the same time, holds out the prospect of computing excitation spectra and describing charge transfer processes correctly. In the long term, this may lead to a powerful, universal functional tool, which enables us to a better understanding of the fundamental processes in organic solar cells (e.g. charge transfer) and therefore contributes to a solution to the energy problem mentioned in the beginning.

This functional idea is based on the principle of a spatially resolved exchange correlation energy, which contains certain amounts of other, already well established functionals like exact exchange and the local spin density approximation. This ansatz therefore qualifies as a so-called local hybrid. Furthermore, its construction aims to fulfill crucial analytical requirements for the exchange correlation term, which are exactly known, as for instance the spin scaling behavior or the homogeneous electron gas limit.

The main part of the work on this topic is a collaboration with Prof. Leeor Kronik and Eli Kraisler from the Weizmann Institute of Science in Rehovoth, Israel. My supervisor is Prof. Stephan Kümmel from the department of Theoretical Physics IV at the University of Bayreuth.

Wissenschaftlicher Werdegang
  • September 2005 - Dezember 2011
  • Studium der Physik an der Universität Bayreuth
  • August 2008 bis Juli 2009
  • Teilnahme am europäischen Austauschprogramm ERASMUS, Studium an der Universität Lund in Schweden
  • seit Wintersemester 2009
  • Mitglied des Elitenetzwerks Bayern, Teilnahme am Studiengang "Macromolecular Science"
  • Dezember 2010 - Dezember 2011
  • Arbeit an Diplomarbeit mit dem Titel "Konstruktion eines orbitalabhängigen Austausch-Korrelations-Dichtefunktional" in der Arbeitsgruppe von Prof. Dr. Stephan Kümmel, Theoretische Physik IV

Berufliche Erfahrung
  • 04/2005 - 09/2005
  • Beschäftigung in der "Bernhard Gotzeina und Co. GmbH" in Eisfeld, Thüringen
  • 03/2010:
  • Einwöchiger Forschungsaufenthalt am "Weizmann Institute of Science" in Rehovoth, Israel
  • seit 04/2012
  • Anstellung am Lehrstuhl Theoretische Physik IV als Doktorand, dabei wird die Bearbeitung des Themas der Diplomarbeit weitergeführt