Wavefunctions, electronic localization and bonding properties for correlated materials beyond the Kohn-Sham formalism.

Many-body theories such as dynamical mean field theory (DMFT) have enabled the description of the electron exchange-correlation interactions that are missing in current density functional theory (DFT) calculations. However, there has been relatively little focus on the wavefunctions from these theories. We present the methodology of the newly developed Elk-TRIQS interface and how to calculate the DFT with DMFT (DFT+DMFT) wavefunctions, which can be used to calculate DFT+DMFT wavefunction dependent quantities. We illustrate this by calculating the electron localized function (ELF) in monolayer SrVO$_3$ and CaFe$_2$As$_2$, which provides a means of visualizing their chemical bonds. Monolayer SrVO$_3$ ELFs are sensitive to the charge redistribution between the DFT, one-shot DFT+DMFT and fully charge self-consistent DFT+DMFT calculations. In both tetragonal and collapsed tetragonal CaFe$_2$As$_2$ phases, the ELF changes weakly with correlation induced charge redistribution of the hybridized As-p and Fe-d states. Nonetheless, the interlayer As-As bond in the collapsed tetragonal structure is robust to the changes at and around the Fermi level.