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WIREs Comput Mol Sci
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Modeling of the spectroscopy of core electrons with density functional theory

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Abstract The availability of X‐ray light sources with increased resolution and intensity has provided a foundation for increasingly sophisticated experimental studies exploiting the spectroscopy of core electrons to probe fundamental chemical, physical, and biological processes. Quantum chemical calculations can play a critical role in the analysis of these experimental measurements. The relatively low computational cost of density functional theory (DFT) and time‐dependent density functional theory (TDDFT) make them attractive choices for simulating the spectroscopy of core electrons. An overview of current developments to apply DFT and TDDFT to study the key techniques of X‐ray photoelectron spectroscopy, X‐ray absorption spectroscopy, X‐ray emission spectroscopy, and resonant inelastic X‐ray scattering is presented. Insight into the accuracy that can be achieved, in conjunction with an examination of the limitations and challenges to modeling the spectroscopy of core electrons with DFT is provided. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Electronic Structure Theory > Density Functional Theory
Comparison of standard TDDFT (black line) with fast‐low memory TDDFT where the virtual space is limited to the lowest 50 orbitals (red line) for the calculation of the lowest 50 states to naphthalene, phenanthrene, pyrene and pentacene. The CPU time reflects the time for the TDDFT calculation. The memory represents the fraction of the storage required for the subspace vectors for the modified calculation compared with the standard calculation. The structures are optimized using B3LYP/6−311G**
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Comparison of calculated K‐edge X‐ray emission spectra based upon the Kohn–Sham orbital energies with CAM‐B3LYP (red line) and SRC1r2 (blue line) functionals with experiment (black line) for (a) Cr(CO)6, (b) Cr(η‐C6H6)(CO)3, and (c) Cr(η‐C6H6)2. The cc‐pCVTZ basis set was used and the structures are optimized using B3LYP/6−31G*. Experimental data from reference 183. The calculated spectra have been shifted to align with experiment
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Comparison of calculated K‐edge X‐ray emission spectra based upon the Kohn–Sham orbital energies (red line) and TDDFT (blue line) with experiment (black line) for (a) CH3OH, (b) NH3, (c) CH3Cl and (d) Cr(CO)6 with the CAM‐B3LYP functional and cc‐pCVTZ basis set. The structures are optimized using B3LYP/6−311G**, except for (d) where B3LYP/6−31G* was used. Experimental data from references 180‐183. The calculated spectra have been shifted to align with experiment, the following energy shifts were applied for Kohn–Sham spectra (a) +10.9 eV, (b) +13.0 eV, (c) +62.6 eV, (d) +123.5 eV and (a) −5.7 eV, (b) −7.0 eV, (c) −26.5 eV, (d) −18.3 eV for TDDFT
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Electronic Structure Theory > Density Functional Theory
Theoretical and Physical Chemistry > Spectroscopy
Electronic Structure Theory > Ab Initio Electronic Structure Methods

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