Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

Abstract

The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.

Describing strong correlation with fractional-spin correction in density functional theory

“…Work from Becke showed some promise of describing static correlation with XC hole modeling (7,60,61), based on which Johnson and Contreras-García constructed strong-correlation models that improve the description of atoms with fractional charges and spins (58,59). Recent works on recovering the flat-plane condition include the judiciously modified DFT approach (62) and the density matrix minimization model (63). We aim to develop general corrections to common DFAs by imposing the flat-plane condition on global and local regions, to systematically reduce the delocalization and static correlation errors for mainstream DFAs, all within the (G)KS single-determinant description of the electron density.…”

Stable Surfaces that Bind too Tightly: Can Range Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

“…Both such methods are widely used in heterogeneous catalysis modeling to approximately correct energetic DE, and both have been shown 88−90 to equivalently recover exact conditions (i.e., piecewise linearity or the derivative discontinuity 88,90,91 ), albeit at the cost of worsening static correlation error (SCE) 89,92−96 but typically improving densities. 86,87 We have selected hybrids and DFT+U rather than approaches that can eliminate DE and SCE simultaneously 89,96 because of the former methods' widespread use in the catalysis community.…”

“…where I is the Hubbard atom (here, each metal) with a relevant valence subshell (here, 3d, 4d, or 5d), σ is a spin index, and n is the occupation matrix of the subshell obtained by projecting all extended states onto the atomic states obtained during the all-electron calculation of each atom used in pseudopotential generation. 55,57 In a first order approximation, the sensitivity of a property to the +U correction can be estimated from the difference in PBE fractionality 57,[103][104][105] (i.e., ΔTr[n(1-n)]) of the structures being compared. For Eσ, this difference in fractionality is between the surface and bulk metal sites, whereas for ΔE O , this difference is between the pristine surface and the adsorbed surface metal sites (Figure 5).…”

“…Thus, the ability of DFT+U to correct Eσ or ΔE O should be evident from PBE calculations. For large-scale catalysis modeling, modifications to the projections 37 or choice of model Hamiltonian functional form [105][106] could improve DFT+U performance further.…”

Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins

“…Similarly, the +U correction to DFAs improves fractional charge and aggravates fractional spin behavior. 18 While there are hundreds of papers dealing with the curvature errors of DFAs, the understanding of these errors from the wavefunction (WF) perspective is lacking. The few studies that exist are restricted to the conventional formulation (see below) of finite-temperature second-order perturbation theory or density functional theory (DFT)-based many-body perturbation theory (MBPT).…”