title: Ultranonlocality in Density Functional Theory
Creators: name: Aschebrock, Thilo
Publisher: name: University of Bayreuth
Year: 2019
Subjects: subject: density functional theory
subject: meta generalized gradient approximation
subject: ultranonlocality
subject: charge transfer
subject: band gaps
subject: orbital nodal surfaces
subject: electronic structure of atoms &amp; molecules
subject: density functional theory development
subject: local range separation
subject: gradient expansion
subject: asymptotically nonvanishing potentials
subject: semilocal density functionals
subject: field-counteracting effect
subject: exchange-correlation energy functional
subject: 530

description: The decisive advantage of density functional theory in comparison with other electronic structure methods is its favorable ratio of accuracy to computational cost. In its standard Kohn-Sham formulation, both of these aspects are determined by the density functional that is selected to approximate the exchange-correlation energy. While the computational cost plays a minor role for systems of small to moderate size, its significance rises quickly when one considers extended systems of increasing size as it is common, e.g., in the realms of biology, nano-science, or supramolecular science. These real-world systems, which are areas of great scientific interest, are, thus, typically only accessible with computationally feasible density functional approximations. However, this so-called class of semilocal functionals is known to have hallmark deficits that are closely interconnected by the absence of ultranonlocality. This absence manifests itself, e.g., in the inability to properly describe band gaps or charge transfer. The latter deficit is, for instance, detrimental when one tries to understand light-harvesting systems. Therefore, long-standing effort was and is invested to address this problem and develop semilocal density functional approximations that possess or mimic ultranonlocality. The first part of this thesis focuses on two promising candidates for this task, the Becke-Johnson potential and the Armiento-Kümmel generalized gradient approximation (GGA). Both functionals share a signature asymptotically nonvanishing potential and, as is shown here, also anomalous features that constitute a formidable challenge for their application and the future development of functionals based on their construction concept. Most notably, the corresponding potentials are demonstrated to diverge exponentially in the vicinity of orbital nodal surfaces. These topological challenges of orbital nodal surfaces are also shown to affect many other frequently used density functional approximations. Consequently, exact constraints to avoid such divergences are formulated. In the second part of this thesis, a new construction strategy for meta-GGAs that focuses on the derivative discontinuity is developed and employed. The resulting computationally feasible semilocal functionals are demonstrated to achieve substantial ultranonlocality due to their use of the kinetic energy density. Thereby, considerably more realistic band gaps are obtained in comparison to other semilocal exchange-correlation energy functionals. The meta-GGAs of this thesis are, therefore, promising future candidates for the study of large-scale systems that is presently limited by the above-mentioned deficits of traditional semilocal functionals. Furthermore, the concept of a local range-separation parameter is revisited. It promises formal and practical improvements for the class of range-separated hybrid functionals, which currently spearhead the description of charge transfer in systems of small to moderate size. In particular, a local range-separation parameter is constructed that satisfies additional exact constraints, such as one-electron self-interaction freedom, and exhibits a non-trivial spin-dependence. Lastly, the hyper-GGA approximation, which is based on semilocal exchange hole models and computationally essential to the local range-separation approach, is assessed.