Fractional-Electron and Transition-Potential Methods for Core-to-Valence Excitation Energies Using Density Functional Theory

Abstract

Methods for computing X-ray absorption spectra based on a constrained core hole (possibly containing a fractional electron) are examined. These methods are based on Slater's transition concept and its generalizations, wherein core-to-valence excitation energies are determined using Kohn−Sham orbital energies. Methods examined here avoid promoting electrons beyond the lowest unoccupied molecular orbital, facilitating robust convergence. Variants of these ideas are systematically tested, revealing a best-case accuracy of 0.3−0.4 eV (with respect to experiment) for K-edge transition energies. Absolute errors are much larger for higher-lying near-edge transitions but can be reduced below 1 eV by introducing an empirical shift based on a charge-neutral transition-potential method, in conjunction with functionals such as SCAN, SCAN0, or B3LYP. This procedure affords an entire excitation spectrum from a single fractional-electron calculation, at the cost of ground-state density functional theory and without the need for state-by-state calculations. This shifted transition-potential approach may be especially useful for simulating transient spectroscopies or in complex systems where excitedstate Kohn−Sham calculations are challenging. = c c(1) are estimated as differences between final-state (virtual) energy levels ε υ and the initial-state (core) level ε c . In some cases, a fractional electron may be placed into the lowest unoccupied molecular orbital (LUMO), as described in Section 2, but not into any higher-lying virtual MO. Transition intensities are computed according to

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response

“…SRC functionals tend to be very accurate for LR-TDDFT calculations (and thus for TDKS calculations), yet this appears to benefit from significant error cancellation as evidenced by the fact that these functionals perform very poorly in ΔSCF calculations of the same K-edge transitions. , As such, we have begun to shift our emphasis to functionals such as B3LYP, which perform well in ΔSCF calculations, , and also to functionals such as PBE0 and CAM-B3LYP that perform well for LR-TDDFT and mitigate problems with long-range charge-transfer states. ,− For core-level excitations, LR-TDDFT calculations with B3LYP are often significantly shifted with respect to experiment (by ≥10 eV and worse for heavier elements), ,,− yet relative peak positions and chemical shifts exhibit accuracy on par with many-body methods . In our view, this observation is consistent with ΔSCF results …”

“…106 In our view, this observation is consistent with ΔSCF results. 95 Relativistic corrections are not included in this work. These corrections are ≲0.5 eV for second-row elements, 107−109 and while they are larger for later elements, our goal here (with regard to heavier elements) is to explore how dipole filtering can disentangle L-and K-edge excitation spectra.…”

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations

“…Additionally, ΔSCF approaches can still be impacted by self-interaction error, particularly for heavier elements . The aforementioned simulations of thiyl radical XANES, as well as related studies, employed the transition potential approach based on a fractionally occupied core orbital. , These approaches may be employed with ΔSCF calculations for each excited state of interest, or with Kohn–Sham orbital energies computed from a constrained core hole possibly containing a fractional electron. , Another strategy is to simply shift TDDFT-computed core excitation energies to match experiment, focusing on chemically relevant energy differences . The aforementioned study of acetylacetone combined these strategies, using empirically shifted TDDFT to simulate s core excitations out of a ΔSCF-computed valence excited state .…”

“…42,43 These approaches may be employed with ΔSCF calculations for each excited state of interest, or with Kohn− Sham orbital energies computed from a constrained core hole possibly containing a fractional electron. 44,45 Another strategy is to simply shift TDDFT-computed core excitation energies to match experiment, 46 focusing on chemically relevant energy differences. 47 The aforementioned study of acetylacetone combined these strategies, 3 using empirically shifted TDDFT to simulate s core excitations out of a ΔSCF-computed valence excited state.…”

Correction to “Fractional-Electron and Transition-Potential Methods for Core-to-Valence Excitation Energies Using Density Functional Theory”

“…In our recent paper, several labels were inadvertently swapped in Figure . These include the labeling of the spectra for 4-nitroaniline versus 1,3-butadiene and also labels for the XTPM method versus shifted-XTPM.…”