Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation

We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.

Figure 1

${\mathrm{H}}_2$ (a) and ${\mathrm{H}}_2^{+}$ (b) dissociation curves without breaking spin symmetry. Aug-cc-pVQZ basis sets [24] have been used for all calculations. The total energies of isolated spin-polarized atoms are shown in smaller panels to the right.

Figure 2

${\mathrm{N}}_2$ (a) and ${\mathrm{C}}_2$ (b) dissociations without breaking spin symmetry. Although spin-polarized calculations can provide a qualitatively correct dissociation behavior, enforcing spin symmetry is crucial to achieve a smooth dissociation curve with no Coulson-Fisher singularity [5, 43]. The energy zero for all methods is the total energy of two isolated spin-polarized atoms at the FCI level. All calculations were performed with cc-pV3Z basis sets [24]. For ${\mathrm{C}}_2$, we omit the ZRPS@PBE curve, because PBE calculations for the correct occupation do not converge anymore when the bond becomes stretched. The total energies of two isolated spin-polarized atoms, referenced to FCI, are shown in smaller panels.