Redefining state-of-the-art in time-dependent density functional theory for core excitations with electron-affinity approaches Kevin Carter-Fenk, Martin Head-Gordon, Leonardo A. Cunha, Juan E. Arias-Martinez University of California, USA In recent years, advances in synchrotron radiation and high-harmonic generation have made high-energy X-ray light sources far more accessible, allowing for more intensive experimental probes into chemical structure and dynamics. Such empirical tools mandate a solid theoretical foundation to build an understanding of chemical phenomena in terms of atomic and electronic structure. The most practical electronic structure approach for valence excitation energies is linear-response time-dependent density functional theory (LR-TDDFT), owing to its low computational cost and an average statistical error of 0.3 eV. However, these errors increase by two orders of magnitude for core excited states due to a lack of particle-hole interactions and orbital relaxation effects in LR-TDDFT, leaving the most affordable quantum chemistry approach in a position where it cannot provide reasonably accurate spectra. We recently reported the derivation of electron-affinity time-dependent density functional theory (EA-TDDFT), 1 a theoretically exact generalization of the static exchange approximation (STEX) to a density functional framework. Using a core-ionized reference density instead of the ground state, EA-TDDFT accounts for orbital relaxation from the creation of a core hole and is naturally free of particle-hole interaction errors. In benchmarking studies across 132 experimental K-edge transitions of second and third-row atoms, EA-TDDFT achieves errors of only 0.5 eV with standard density functionals. Beyond excitation energies, studies on the K-edge X-ray absorption spectra of liquids have revealed that EA-TDDFT provides a nearly quantitative representation of the spectral profile of NH3 (aq), NH 4 + (aq), and H 2 O while LR-TDDFT qualitatively fails to capture the intensities or peak positions. 2 This precludes the simple linear shifts that are often applied to LR-TDDFT spectra to account for errors in the excitation energy and implicates orbital relaxation (or lack thereof) as a key physical contributor to the intensities of solution-phase X-ray absorption spectra. We are now using EA-TDDFT to study the M2,3 -edge of Fe(CO) 5 to track photolysis dynamics of the process: Fe(CO) 5 →Fe(CO) 4 + CO →Fe(CO) 3 + 2 CO. Despite the lower-energy transitions in the M2,3 -edge, we find that orbital relaxation remains a crucial component of the spectra of various Fe(CO) X photolysis products, without which the chemical products cannot be distinguished from one another. Combined with experiment, ab initio molecular dynamics, CASSCF, and EA- TDDFT we can unambiguously identify the atomic structure of the intermediates and products of this photolysis process. Overall, we have found EA-TDDFT to be a powerful tool for computational investigations of X-ray absorption spectra, restoring the balance of accuracy and efficiency that typifies LR-TDDFT calculations without deviating from exact linear-response theory. References 1. K. Carter-Fenk, L. A. Cunha, J. E. Arias-Martinez and M. Head-Gordon, Electron-affinity time-dependent density functional theory: Formalism and applications to core-excited states, J. Phys. Chem. Lett. , 2022, 13 , 9664–9672 2. K. Carter-Fenk and M. Head-Gordon,On the choice of reference orbitals for linear-response calculations of solution-phase K-edge X-ray absorption spectra, Phys. Chem. Chem. Phys. , 2022, 24 , 26170–26179
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