Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory.

Lukas Konecny,Michal Repisky,Kenneth Ruud,Jan Vicha,Stanislav Komorovsky

doi:10.1021/acs.inorgchem.1c02412

Abstract

The simulation of X-ray absorption spectra requires both scalar and spin–orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac–Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange–correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee–Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

Highlights

X-rays were included in the toolbox of chemists shortly after their discovery by Röntgen[1] and are used to probe both the molecular structure in diffraction experiments as well as the electronic structure in absorption, emission, and scattering Xray spectroscopies
For a comprehensive account of quantum-chemical methods addressing X-ray spectroscopies, we refer to recent reviews.[24−27] Since our goal is to target large systems such as heavy-metal complexes, we focus on relativistic density functional theory (DFT) that favorably combines computational cost and accuracy
We first investigate the role of the molecular geometry, basis set, and exchange−correlation functional for 4c relativistic DR-time-dependent DFT (TDDFT) calculations of X-ray absorption spectroscopy (XAS) spectra

Summary

Introduction

X-rays were included in the toolbox of chemists shortly after their discovery by Röntgen[1] and are used to probe both the molecular structure in diffraction experiments as well as the electronic structure in absorption, emission, and scattering Xray spectroscopies. The wavelengths of X-rays are comparable to molecular dimensions, allowing the local electronic structure via excitations from localized core orbitals to be probed. In X-ray absorption spectroscopy (XAS), the spectrum is characterized by absorption edges, i.e., abrupt onsets of absorption at resonant energies corresponding to inner-shell excitations. Higher-energy signals constitute extended X-ray absorption fine structure (EXAFS) spectra that are characterized by weak oscillations originating from resonances in absorptions beyond the ionization energy.[5] While XANES is used to determine the details of the electronic structure, such as oxidation states, EXAFS provides more information about the geometry around the absorbing center than about the electronic structure.

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