Exchange-correlation energy functional for solids

Nowadays, the Kohn-Sham version of density functional theory is the most used theoretical method to study the electronic structure of molecules, surfaces, and solids. Unfortunately the exact analytical expression for the exchange-correlation energy functional is unknown, therefore only approximations can be used. The reliability of any Kohn-Sham calculation depends i) on the numerical accuracy when solving these equations and ii) on the approximation used for the exchange-correlation energy. For the solution of the Kohn-Sham equations we use the WIEN2k code, which utilizes a flexible all-electron (L)APW+lo basis set and represents one of the most accurate methods for solid state computations. It is used by more than 1100 groups worldwide. On the other hand this explains why the search for more accurate approximations for the exchange-correlation is an intensive research area both in chemistry and physics. The development, implementation, and testing of exchange-correlation functionals constitute the main topics of this research proposal. More specifically, we plan to implement the (screened) Hartree-Fock method into the WIEN2k code in order to have the possibility to apply hybrid functionals on periodic solids. The last years have seen the emergence of hybrid functionals for solids and it has been shown that hybrid functionals yield very accurate results for various properties (e.g., geometry and structure) of different types of compounds (e.g., semiconductors and strongly correlated systems), in many cases outperforming the standard LDA and GGA approximations for the exchange-correlation energy. Another part of the project will consist of the development of more accurate exchange-correlation functionals of the GGA or meta-GGA type. The GGA functionals in particular (e.g., PBE) are still the most used functionals for solid-state calculations, and one of the main reasons for that is that they are easy to implement and computationally cheap. Several recent publications have shown that this type of approximations can still be improved. An in-depth analysis of the performance of GGA functionals will also be done in order to understand why a given GGA functional works for a given class of elements (or compounds) but not for another. Finally, non-covalent interactions will also be studied. It is well known that the correct description of non-covalent interactions constitutes one of the most difficult challenges for the Kohn-Sham method. Different types of functionals especially designed for non-covalent interactions were proposed in the literature. Some of these functionals are "fully non-local" while others have a simple (but empirical) form. A literature survey of this topic shows that a large part of these works on improved functionals for non-covalent interactions concerns mainly molecules, while for solids such works are rather scarce. We plan to implement such functionals into the WIEN2k code and to test them on solids for which non-covalent interactions play an important role.

The Kohn-Sham version of density functional theory is the most used theoretical method to study the electronic structure of molecules, surfaces, and solids. Unfortunately the exact exchange-correlation energy functional is unknown, therefore only approximations can be used. These approximations determine the quality, reliability and predictability of theoretical simulations and thus the search for more accurate approximations for exchange- correlation is an intensive and very important research area both in chemistry and physics. During this project we have implemented the (screened) Hartree-Fock method into the WIEN2k code in order to have the possibility to apply hybrid functionals to periodic solids. During the last years it has been shown that hybrid functionals yield fairly accurate results for various properties (e.g., geometry or band gaps) of some types of compounds (e.g., semiconductors and strongly correlated systems). In many cases results using hybrid functionals are superior to those from standard LDA and GGA calculations and thus it was important to have this possibility also in our widely used WIEN2k code. In the second part of the project we analyzed the performance of existing GGA functionals. We could identify which regions in space are really important to obtain the proper bond length or lattice parameters. Surprisingly, it is not so much the "bonding" region, but the effective size of an atom is determined primarily by the correct description of the core-valence separation and in open structures or ionic compounds by the tails of the valence orbitals. Common GGAs can either describe lattice parameters of solids or atomization energies of molecules with sufficient accuracy, but not both quantities simultaneously. Based on our analysis we could develop a GGA functional which performs very well for both quantities. This is a milestone development for simulations of heterogeneous catalysis, where the energetics of small molecules adsorbed on solids is very important. The size of the energy band gap in semiconductors and insulators is a key quantity in materials research of semiconductors, photovoltaic or photocatalytic materials. So far gaps had to be calculated by the GW method, which requires huge computational effort and thus is feasible only in relatively small systems. We have developed a new method (mBJ potential) which predicts band gaps with highest accuracy at the cost of standard GGA calculations and thus opens new possibilities in these important research areas.