New approximations for the exchange-correlation potential using connector theory

In the Kohn-Sham formulation of density functional theory (DFT) [1], the ground-state density of interacting electrons can be obtained from a fictitious system of independent particles in an effective potential. Even though DFT is in principle exact the effective potential contains an unknown quantity called the exchange-correlation (xc) potential. In this talk we propose a new approximation to the xc potential using a general approach called "Connector Theory" (COT) [2]. This approach is a prescription of how to use data from models to calculate quantities in materials. COT is in principle exact but in practice approximations are needed to make it useful. After introducing the general scheme of this approach, we explain how to use the COT in order to build non-local functionals of the density for the xc potential. We show how well the connector approximation describes the non-local functional and we compare with previous approximations. Finally, after implementing the connector xc potential in the self-consistent Kohn-Sham loop, we discuss the quality of the resulting electronic densities and band structures.

[1] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
[2] M. Vanzini, A. Aouina, M. Panholzer, M. Gatti, and L. Reining, arXiv:1903.07930v3