Approximation of the exponential exchange screening function with a scaled complementary error function. Both functions are displayed in the upper panel and their difference is displayed in the lower panel.
Semiconductor band gap errors over HSE space. A subset of functionals with approximately equivalent accuracy extend from (0,0.19) to (0.83,1).
Molecular formation energy errors over HSE space. A subset of functionals with approximately equivalent accuracy extend from (0,0.3) to (0.93,1).
IP and EA errors in HSE space, comparing ΔSCF to eigenvalue-based estimates and including polarization corrections.
IP of a dilute He n cluster, comparing −εHOMO(He n ) to E()−E(He n ) using the HSE06 functional and full Fock exchange with PBE correlation (HF+c), which correspond to the points (0.5, 0.25) and (0.0, 1.0) in HSE space. In HSE06, the ΔSCF and eigenvalue-based results converge for n → ∞. The electron-hole of is localized on one atom with HF+c and uniformly divided among all n atoms with HSE06. Any n-dependence is a size-consistency error.
Binary reaction barrier height, molecular bond length, and semiconductor lattice constant errors in HSE space.
Aggregate error in HSE space. The minimum of this error metric occurs at the HSE12 parameterization. HSE06 and HSE12s lie on a contour of equal error.
Comparison of r TF (from Eq. (4), without semicore d-states in ) and band gaps of the SC/40 set6 using 5 sX-DFT functionals described in the text, labelled by their exchange-correlation model, screening function, and screening length.
Summary of important functionals in HSE space and their performance on various tests discussed in this paper.
Article metrics loading...
Full text loading...