K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory

Abstract

X-ray absorption spectra of carbon, silicon, germanium, and sulfur compounds have been investigated by means of damped four-component density functional response theory. It is demonstrated that a reliable description of relativistic effects is obtained at both K- and L-edges. Notably, an excellent agreement with experimental results is obtained for L2,3-spectra-with spin-orbit effects well accounted for-also in cases when the experimental intensity ratio deviates from the statistical one of 2 : 1. The theoretical results are consistent with calculations using standard response theory as well as recently reported real-time propagation methods in time-dependent density functional theory, and the virtues of different approaches are discussed. As compared to silane and silicon tetrachloride, an anomalous error in the absolute energy is reported for the L2,3-spectrum of silicon tetrafluoride, amounting to an additional spectral shift of ∼1 eV. This anomaly is also observed for other exchange-correlation functionals, but it is seen neither at other silicon edges nor at the carbon K-edge of fluorine derivatives of ethene. Considering the series of molecules SiH4-XFX with X = 1, 2, 3, 4, a gradual divergence from interpolated experimental ionization potentials is observed at the level of Kohn-Sham density functional theory (DFT), and to a smaller extent with the use of Hartree-Fock. This anomalous error is thus attributed partly to difficulties in correctly emulating the electronic structure effects imposed by the very electronegative fluorines, and partly due to inconsistencies in the spurious electron self-repulsion in DFT. Substitution with one, or possibly two, fluorine atoms is estimated to yield small enough errors to allow for reliable interpretations and predictions of L2,3-spectra of more complex and extended silicon-based systems.

X-ray circular dichroism signals: a unique probe of local molecular chirality

“…83 Recently a damped response study showed that this branching ratio in L-edge XANES was reproduced well from four-component full relativistic density function theory. 84 Similarly, SOC should also play an important role in L-edge XCD. However, the sizes of the molecules in this study and the numbers of the involved excited states prohibit a full relativistic calculation.…”

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations

“…The computational cost is similar to the eigenvalue response equation and DFT kernels are required also in this case. In the context of relativistic theories with variational SO interaction, the methodology has been developed in the spin-orbit ZORA 42 , and 4c 43,44 framework and applied to the calculation of frequency-dependent dipole polarizabilities 45 , electronic absorption spectra in valence and X-ray regions 46,47 , and electric dipole dispersion interaction coefficients 48 . An extensive list of review texts on eigenvalue and damped response theory can be found in Table 1 in Ref.…”

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements

“…The effects of correlation and relativity are not additive, and non-perturbative theories are ideally suited for handling them together. We should also mention that this is not only true for core IP processes but also for more complex processes 9,[88][89][90][91][92][93] leading all the way to multi-reference theories with relativistic Hamiltonians which are being actively investigated. [94][95][96][97][98][99][100][101] We have also assessed the lowest order Quantum Electrodynamic (QED) correction to the core IP.…”

“…[3][4][5] Recently, advances in electron correlation theories have made the accurate prediction of Xray ionization and excitation spectra viable. [6][7][8][9] A high level correlation theory should, in principle, take care of correlation and orbital relaxation in a generic situation involving energy differences of the ground and ionized, electron attached, or excited states. However, for core IP in particular, a proper correlation theory must also accurately capture not only a partial cancellation of dynamic correlation between the states but also take account of the large orbital relaxation in an explicit manner.…”