A Novel Screened Exchange Potential Approach

Density functional theory is the workhorse of theoretical materials investigations. Due to the shortcoming of (semi-)local exchange correlation potentials, hybrid functionals have been established for practical calculations to describe surfaces, molecular adsorption, and defects. These functionals operate by mixing between semi-local and Hartree-Fock exchange semi-emprically. However, their parameters have to be optimized for every material separately. To treat materials with a more physics driven approach and without the need of parameter optimization is possible with many-body approaches like GW, but at an immense increase in computational costs and without the access to total energies and hence geometry optimization.<br/>We have introduced an exchange correlation potential[1] for semiconductor materials, that is based on physical properties of the underlying microscopic screening. We demonstrate that it reprocuduces the low temperature band gap of several materials. Moreover it respects the required linearity condition of the total energy with the fractional occupation number, as expressed by the generalized Koopman’s theorem. We show that this novel functional can be used as a kernel in linear response TDDFT to reproduce excitonic effects in optical spectra.<br/><br/>We will also discuss how to genereralize such a functional to anisotropic systems like surfaces and 2D materials. The presence of interfaces modifies the screening behavior in layered systems in a way, which cannot be described by HSE or any other screened exact exchange functional, which are based on assumptions of isotropy. Defect calculations for 2D systems (or for slab models in general), using hybrids or the sX functional, all suffer from these problems and we could show in Ref. [2] that for some systems such as monolayer hBN, the assumption of isotropy of the screening is bound to fail. Since GW calculations must be based ona priori defect geometries obtained by LDA, GGA, or a hybrid functional, at present there is no method available to achieve the same accuracy in mono- and few-layer systems or their heterostructures as for the bulk. We aim at including the effects of the interface into the model dielectric function of our new screened exact exchange functional and we will present first results of this approach.<br/><br/>[1] Physical Review B <b>102</b>, 235168<br/>[2] Physical Review B <b>100</b>, 235304