Wave functions, 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-electron correlation effects that are missing in current density functional theory (DFT) calculations. However, there has been relatively little focus on the wave functions from these theories. We present the methodology of the newly developed elk-triqs interface and how to calculate the DFT with DMFT ($\mathrm{DFT}+\mathrm{DMFT}$) wave functions, which can be used to calculate $\mathrm{DFT}+\mathrm{DMFT}$ wave-function-dependent quantities. We illustrate this by calculating the electron localization function (ELF) in monolayer ${\mathrm{SrVO}}_{3}$ and ${\mathrm{CaFe}}_{2}{\mathrm{As}}_{2}$, which provides a means of visualizing their chemical bonds. Monolayer ${\mathrm{SrVO}}_{3}$ ELFs are sensitive to the charge redistribution between the DFT, one-shot $\mathrm{DFT}+\mathrm{DMFT}$, and fully charge self-consistent $\mathrm{DFT}+\mathrm{DMFT}$ calculations. In both tetragonal and collapsed tetragonal ${\mathrm{CaFe}}_{2}{\mathrm{As}}_{2}$ 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.