Spectroscopy of linear and circular polarized light with the exact semiclassical light–matter interaction

Khamesian, Marjan; Galván, Ignacio Fernández; Delcey, Mickaël G.; Sørensen, Lasse Kragh; Lindh, Roland

doi:10.1016/bs.arcc.2019.08.004

Cited by 9 publications

(15 citation statements)

References 44 publications

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“…The calculation of the 3d4f RIXS map is based on the Kramers–Heisenberg (see eqs 1 and 2 ) 11 , 21 , 22 , 24 , 30 , 31 expression. The relevant electronic energies and the corresponding complex transition dipole moments 73 of UO 2 2+ are used to calculate the RIXS spectra. Estimates for the lifetime broadenings Γ i and Γ f are derived from Vitova et al 2 and adjusted to fit the experimental data.…”

Section: Methodsmentioning

confidence: 99%

“…The calculated electronic energies of all the relevant states of UO 2 2+ plus the corresponding transition dipole moments 73 are used to calculate the RIXS spectra using the Kramers–Heisenberg formula. 11 , 21 , 22 , 24 , 30 , 31 The polarizability tensor reads 24 with the resonance scattering cross-section as follows μ, ρ = x , y , z : ( x , y , z ) component of the electric–dipole transition operator; |0⟩, E 0 : ground state (3d 10 4f 14 5f 0 ) and corresponding energy; | i ⟩, E i : intermediate states (3d 9 4f 14 5f 1 ) and corresponding energy; | f ⟩, E f : final states (3d 10 4f 13 5f 1 ) and corresponding energy; E ex : excitation energy, E ex = E i – E 0 ; E em : emission energy, E ex = E i – E f ; Γ i : line broadening due to the lifetime of the intermediate states; and Γ f : line broadening due to the lifetime of the final states.…”

Section: Methodsmentioning

confidence: 99%

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Relativistic MulticonfigurationalAb InitioCalculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

et al. 2021

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We applied relativistic multiconfigurational all-electron ab initio calculations including the spin–orbit interaction to calculate the 3d4f resonant inelastic X-ray scattering (RIXS) map (3d 3/2 → 5f 5/2 U M 4 absorption edge and 4f 5/2 → 3d 3/2 U M β emission) of uranyl (UO 2 2+ ). The calculated data are in excellent agreement with experimental results and allow a detailed understanding of the observed features and an unambiguous assignment of all involved intermediate and final states. The energies corresponding to the maxima of the resonant emission and the non-resonant (normal) emission were determined with high accuracy, and the corresponding X-ray absorption near edge structure spectra extracted at these two positions were simulated and agree well with the measured data. With the high quality of our theoretical data, we show that the cause of the splitting of the three main peaks in emission is due to the fine structure splitting of the 4f orbitals induced through the trans di-oxo bonds in uranyl and that we are able to obtain direct information about the energy differences between the 5f and 4f orbitals: Δ5f δ/ϕ – 4f δ/ϕ, Δ5f π* – 4f π, and Δ5f σ* – 4f σ from the 3d4f RIXS map. RIXS maps contain a wealth of information, and ab initio calculations facilitate an understanding of their complex structure in a clear and transparent way. With these calculations, we show that the multiconfigurational protocol, which is nowadays applied as a standard tool to study the X-ray spectra of transition metal complexes, can be extended to the calculation of RIXS maps of systems containing actinides.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Relativistic MulticonfigurationalAb InitioCalculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

et al. 2021

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“…Transition matrix elements up to a full second-order expansion of the wave vector have been calculated using RASSI. 46 In principle, the plane-wave form of the wave vector could also be used, [71][72][73][74] but as that operator depends on the transition energy, the cost of evaluating a scattering processes that includes tens of thousands of individual transitions becomes too high. Here K pre-edge XAS spectra have been simulated using the exact operator for comparison with the multipole expansion.…”

Section: And Si-3 (Esi †)mentioning

confidence: 99%

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering

Källman

Guo

Delcey

et al. 2020

Phys. Chem. Chem. Phys.

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“…24 In a second paper, 25 we presented a mixed analytical-numerical approach to isotropically average oscillator strengths computed with the full light-matter interaction operator. 25 This novel approach has been followed up by Sørensen et al 24,26 Some other works using full lightmatter interaction may be mentioned: Markin and Kaplan calculated the photoionization cross section of the H 2 molecule in both a nonrelativistic 27 and relativistic setting. 28 More recent works along these lines include Refs.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a fourcomponent 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 TiCl 4 , 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.

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Spectroscopy of linear and circular polarized light with the exact semiclassical light–matter interaction

Cited by 9 publications

References 44 publications

Relativistic MulticonfigurationalAb InitioCalculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

Relativistic MulticonfigurationalAb InitioCalculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering

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

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