Dynamical mean field theory for diatomic molecules and the exact double counting

Dynamical mean field theory (DMFT) combined with the local density approximation (LDA) is widely used in solids to predict properties of correlated systems. In this study, a parameter-free version of the LDA+DMFT framework is implemented and tested on one of the simplest strongly correlated systems, the ${\text{H}}_2$ molecule. Specifically, we propose a method to calculate the exact intersection of LDA and DMFT that leads to highly accurate subtraction of the doubly counted correlation in both methods. When the exact-double-counting treatment and a good projector to the correlated subspace are used, LDA+DMFT yields a very accurate total energy and excitation spectrum of ${\text{H}}_2$. We also discuss how this double-counting scheme can be extended to solid state calculations.

Figure 1

Total energy curves of the ${\text{H}}_2$ molecule versus interatomic distance $R$ calculated by different methods: LDA+DMFT, HF+DMFT, LDA, and HF. The GW and exact result are also presented for comparison.

Figure 2

(a) Correlation energy of LDA and LDA+DMFT versus interatomic separation in ${\text{H}}_2$ molecule. The DMFT correlation is evaluated by ${\Phi }^{\mathrm{LDA}+\mathrm{DMFT},C}={\Phi }^{\mathrm{LDA},C}+{\sum }_i{E}^{\mathrm{DMFT},i}-{\sum }_i{\Phi }^{\mathrm{DC}}\left[{\rho }_{\mathrm{local}}^i\right]$, where potential energy $E^{\mathrm{DMFT},i}=\frac{1}{2}\mathrm{Tr}\left({\Sigma }_{\mathrm{loc}}^i{\mathcal{G}}_{\mathrm{loc}}^i\right)$. (b) LDA+DMFT double-counting potential $V_{\mathrm{DC}}$ versus $R$, which is defined as the functional derivative of ${\Phi }^{\mathrm{DC}}\left[{\rho }_{\mathrm{local}}^i\right]$ given in Eq. (3).

Figure 3

LDA+DMFT spectral function (red) presented with the HOMO and LUMO energy of LDA (blue), and the exact $\text{−}\mathrm{IE}$ and EA (black).