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Title: Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory

Abstract

Herein we present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light–matter interaction operator and the two others on a truncated interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light–matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and rendersmore » such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light–matter interaction.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2]
  1. Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Univ. Toulouse III-Paul Sabatier (France)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE; Carlsberg Foundation; Villum Foundation
OSTI Identifier:
1638153
Grant/Contract Number:  
AC02-76SF00515; CF16-0290; VKR023371
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 152; Journal Issue: 18; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Quantum chemistry; Electronic structure methods; Multipole expansion; Coulomb gauge; Relativistic electron theory; Transition moment; X-ray absorption spectroscopy; Gauge freedom; Excitation energies; Oscillator strengths

Citation Formats

List, Nanna Holmgaard, Romain Léo Melin, Timothé, van Horn, Martin, and Saue, Trond. Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory. United States: N. p., 2020. Web. https://doi.org/10.1063/5.0003103.
List, Nanna Holmgaard, Romain Léo Melin, Timothé, van Horn, Martin, & Saue, Trond. Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory. United States. https://doi.org/10.1063/5.0003103
List, Nanna Holmgaard, Romain Léo Melin, Timothé, van Horn, Martin, and Saue, Trond. Wed . "Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory". United States. https://doi.org/10.1063/5.0003103. https://www.osti.gov/servlets/purl/1638153.
@article{osti_1638153,
title = {Beyond the electric-dipole approximation in simulations of x-ray absorption spectroscopy: Lessons from relativistic theory},
author = {List, Nanna Holmgaard and Romain Léo Melin, Timothé and van Horn, Martin and Saue, Trond},
abstractNote = {Herein we present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light–matter interaction operator and the two others on a truncated interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light–matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light–matter interaction.},
doi = {10.1063/5.0003103},
journal = {Journal of Chemical Physics},
number = 18,
volume = 152,
place = {United States},
year = {2020},
month = {5}
}

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