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 (n O8 π * ) 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.

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

“…This restricts the MRSF-TDDFT excitation space from unwanted occupied orbitals. 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 K-edge excitation energies of 24 s- and 17 third-row molecules …”

“…Our model is based on a combination of the electrostatic embedding QM/MM method, used to equilibrate a water droplet around the molecule of interest, and mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) coupled to QM/MM to extract X-ray spectroscopy. 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 . In addition, an MRSF-TDDFT/MM coupling was shown to lead to accurate excited-state nonadiabatic dynamics of thymine in water …”

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory

“…42 The doubles are critical components for the accurate descriptions of excited states, bond breakings, conical intersections, etc., which significantly expands the applicability of MRSF-TDDFT. (6) Recently, it has been demonstrated that the high spin triplet reference of MRSF-TDDFT provides a simple way of ensuring core-hole relaxation for accurate XAS (X-ray absorption), 43 which has been one of the main difficulties of LR-TDDFT. Detailed discussions can be found later in the main text.…”

“…In the case of LR-TDDFT, the corresponding accuracy is crude, with errors as large as ∼10 eV for second-period elements like C, N, O, and F, and even larger errors for heavier elements. With the additional scalar relativistic effects on K-edge excitation energies of 24 s- and 17 third-row molecules, on the other hand, the particular ΔCHP-MRSF­(R) exhibited near-perfect predictions with root-mean-square error (RMSE) ≈ 0.5 eV, featuring a median of 0.3 and an interquartile range of 0.4 . The XAS of valence excited states can also be calculated by the same protocol.…”

“…The XAS of valence excited states can also be calculated by the same protocol. The 1 s core excitation spectra of oxygens either of ππ * (π hole) and nπ * ( n hole) states of the three particular structures (FC, CI 21 , and S 1 min) of thymine were simulated by ΔCHP-MRSF­(R), and the results are presented in Figure b . Remarkably, a near perfect 1 s ( O 8) → n ( O 8) core to valence n hole excitation value of 526.8 eV (exp.…”