Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy

Abstract

It is demonstrated that the challenging core hole-particle (CHP) orbital relaxation for core electron spectra can be readily achieved by the mixed-reference spin-flip (MRSF)-TDDFT. With the additional scalar relativistic effects on K-edge excitation energies of 24 second- and 17 third-row molecules, the particular ∆CHP-MRSF(R) exhibited near perfect predictions with RMSE ∼ 0.5 eV, featuring a median value of 0.3 and and an interquartile range of 0.4. Overall, the CHP effect is 2 ∼ 4 times stronger than relativistic ones, contributing more than 20 eV in the cases of sulfur and chlorine third-row atoms. Such high precision allows to explain the splitting and spectral shapes of O, N and C atom K-edges in the ground state of thymine with atom as well as orbital specific accuracy. The same protocol with a double hole particle relaxation also produced remarkably accurate K-edge spectra of core to valence hole excitation energies from the first (nO8π∗) and second (ππ∗) excited states of thymine, confirming the assignment of 1s → n excitation for the experimentally observed 526.4 eV peak. Regarding both accuracy and practicality, therefore, MRSF-TDDFT provides a promising protocol for core electron spectra both of ground and excited electronic states alike.

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach

“…[99][100][101][102] Despite its shortcomings, the main tool for routine calculation of XAS is TD-DFT. Furthermore, due to the recent advances in LR-DFT-based theory 103,104 the efficient implementations of DSCF methods, 105 and specialized basis sets, 74 techniques based on mean field approaches will likely remain the workhorses for the calculation of core spectra. Nonetheless, considering an accuracy of less than 0.2 eV attained by the DCCSD schemes S2 and S3 for specific transitions, we expect these to be a promising method for providing benchmark theory-based core excitation/ionization numbers.…”

Solvent Effects and pH Dependence of the X-ray Absorption Spectra of Proline from Electrostatic Embedding Quantum Mechanics/Molecular Mechanics and Mixed-Reference Spin-Flip Time-dependent Density-Functional Theory

“…33,34 The particular formulation of MRSF-TDDFT combined with maximum-overlap method (MOM) also provides a significant advantage in the computation of X-ray absorption. 16,35 Although LR-TDDFT 29 has been the most popular method for valence excited state studies, the accuracy of TDDFT to predict experimental Xray states is very crude, with errors as large as ∼10 eV for second-period elements like C, N, O, and F, 36 and even larger errors for heavier elements. These large shifts are attributed to the lack of description of core-hole orbital relaxation effects in the approximate exchangecorrelation functionals used in TDDFT, which cannot account for the drastic change in the Coulomb interaction of the remaining electrons when a core electron is excited.…”

“…These major challenges can be easily overcome by MRSF-TDDFT with the help of its high-spin triplet reference, which allows a core-hole particle (CHP) pair. The particular ∆CHP-MRSF flavor (referred to for simplicity as ∆MRSF in the following) was designed in our previous work, 16 that we briefly summarize here. In the ∆MRSF approach, the excitation energy is calculated as the energy difference between the X-ray state computed with MRSF-TDDFT using a core-hole triplet state as the reference and the singlet ground state computed at the restricted Kohn-Sham level.…”

“…This simple strategy exhibited near-perfect predictions with RMSE ∼ 0.5 eV, featuring a median value of 0.3 and an interquartile range of 0.4 for Kedge excitation energies of 24 second-and 17 third-row molecules. 16…”

“…MRSF-TDDFT has been recently shown to be able to efficiently and accurately extract XAS, with errors that are within 1 eV of the experimental spectra. 16 In addition, an MRSF-TDDFT/MM coupling was shown to lead to accurate excited-state non-adiabatic dynamics of thymine in water. 17 As a test case, we compute the XAS spectrum of the aminoacid proline in water.…”