Charged excitations made neutral: N-centered ensemble density functional theory of Fukui functions

Abstract

An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative discontinuity problem of DFT for fractional electron numbers, whose contribution is recovered through weight derivatives of the ensemble density functional potential. Thus, it allows for the design of alternative and effective approximations, such as the weight-dependent scaling of regular functionals or the interpolation between known limits of Nc ensembles

Figures (12)

• Figure 1: Performance of the EEXX-scaled EDFA in evaluating Fukui functions (as functions of the external asymmetry potential $\Delta v$) from the zero-weight limit of Nc EDFT in the moderately correlated $U/t=1.5$ regime of the Hubbard dimer.
• Figure 2: Performance of the PT2-scaled EDFA in evaluating the affinity Fukui function (as a function of the interaction strength $U$) up to the stronger correlation $U/t=2.5$ regime of the asymmetric ($\Delta v/t=3.0$) Hubbard dimer.
• Figure 3: Same as Fig. \ref{['fig:onescalevsnwU1.5x0']} for the Padé approximant-based EDFA in the strongly correlated $U/t=5$ regime and away from the zero-weight limit ($\xi_+=\xi_-=0.2$).
• Figure S1: Fukui functions in weak correlation regime for null ensemble weights (parameters in the red inset). Full and dashed lines are $f_{+}$ and $f_{-}$ calculations respectively. Exact results (yellow lines) are compared to EEXX (blue lines) and to the neglect of weight-derivative contributions (grey lines).
• Figure S2: Fukui functions in the low correlation regime for null ensemble weights (parameters in the red inset). We compare EEXX ensemble DFA (blue) to PT2 (green) and neglect of weight derivative terms (grey). Exact results are shown in orange.