Moment functional based spectral density functional theory

We describe a density functional method which aims at computing the ground state electron density and the spectral function at the same time. One basic ingredient of our method is the construction of the spectral function from the first four spectral moment matrices. The second basic ingredient is the construction of the spectral moment matrices from density functionals. We call our method moment functional based spectral density functional theory (MFbSDFT), because it is based on density functionals for the spectral moments and because it allows us to compute the spectral function. If it is implemented in second variation our method consumes only a fraction more computer time than a standard DFT calculation with the PBE functional. We show that MFbSDFT captures correlation effects such as the valence-band satellite in Ni and the formation of lower and upper Hubbard bands in ${\mathrm{SrVO}}_3$. For the purpose of constructing the spectral function from the first four $N\times N$ spectral moment matrices we describe an efficient algorithm based on the diagonalization of one Hermitian $2N\times 2N$ matrix.

Figure 1

Plot of the square of $V_c{r}_s$ vs $r_s$. $r_s$ is the dimensionless density parameter defined in Eq. (68).

Figure 2

Flowchart of the MFbSDFT self-consistency cycle.

Figure 3

DOS of Ni vs energy $E$ in the ferromagnetic state as obtained in KS-DFT. $E_{\mathrm{F}}$ is the Fermi energy.

Figure 4

DOS of Ni vs energy $E$ in the ferromagnetic state as obtained in MFbSDFT when the moment functional is constructed according to Eq. (72). $E_{\mathrm{F}}$ is the Fermi energy.

Figure 5

DOS of Ni vs energy $E$ in the ferromagnetic state as obtained in MFbSDFT when the moment functional is constructed according to Eqs. (66) and (67). $E_{\mathrm{F}}$ is the Fermi energy.

Figure 6

Contributions of the $\mathrm{V}\text{−}3d{e}_g$ and $t_{2g}$ states to the DOS in ${\mathrm{SrVO}}_3$. Results from KS-DFT using the PBE functional.

Figure 7

Contributions of the $\mathrm{V}\text{−}3d{e}_g$ and $t_{2g}$ states to the DOS in ${\mathrm{SrVO}}_3$. Results obtained within MFbSDFT when the moment functionals are constructed according to Eqs. (72) and (73).

Figure 8

Contributions of the $\mathrm{V}\text{−}3d{e}_g$ and $t_{2g}$ states to the DOS in ${\mathrm{SrVO}}_3$. Results obtained within MFbSDFT when the moment functionals are constructed according to Eqs. (66) and (67).

Figure 9

Contributions of the $\mathrm{V}\text{−}3d{e}_g$ and $t_{2g}$ states to the DOS in ${\mathrm{SrVO}}_3$. Results obtained within MFbSDFT when the moment functionals are constructed according to Eqs. (66) and (67). In contrast to Fig. 8 the parameters $c_{\sigma }^{(2+)}$ and $c_{\sigma }^{(3+)}$ are reduced by 18% and 33%, respectively.