Abstract
The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities—in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange–correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2–0.3 eV and ∼10%, respectively, as compared to 0.3–0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.
Highlights
Using aug-cc-pCVQZ/cc-pVQZ with the diffuse functions added to atoms participating in double or triple bonds as a reference, we have investigated the performance of the adopted aT/T/D basis set and of three others
The discrepancies amount to 3−10% and 6−33%, using algebraic diagrammatic construction (ADC)(2)-x as a reference
Using CVSADC(2)-x and fc-core−valence separation (CVS)-EOM-CC singles and doubles (CCSD) as our best theoretical estimates, we investigated the reliability of CC2, the ADC hierarchy, transition potential DFT (TP-DFT), and time-dependent density functional theory (TDDFT) using a suite of different exchange−correlation functionals
Summary
The field of X-ray spectroscopy has progressed rapidly as a result of the development and construction of modern synchrotrons and X-ray free-electron lasers, enabling the investigation of light−matter interactions at unprecedented time resolution and radiation intensity.[1,2] These installations facilitate the study of exotic molecular properties and provide a sensitive experimental tool to questions such as (i) probing chemical reactions in real time, as exemplified by the tracking of the photocatalytic cycle in photosynthesis,[2−6] (ii) considering the structure of molecular samples, such as the local structure of liquid water,[7−9] (iii) identifying the oxidation state of transition metals in organometallic complexes, with examples including the Fe/Mo atoms in nitrogenase,[10−12] (iv) investigating nonlinear properties, such as stimulated emission and two-photon absorption,[13−17] and more. Used in combination with DFT, this method is known as TP-DFT.[65,123] By introducing a shift such that the eigenvalue of the core level is equal to the calculated ionization energy (IE) (ΔKS correction), TP-DFT provides XAS spectra that compare well to experiment in many cases,[50,65,90,123−125] albeit with some occasional difficulties in sufficiently capturing relaxation effects.[92] This motivated the use of a full core-hole on the core-excited atom[92] or alternatively a full core hole in combination with an electron placed in the lowest unoccupied MO (excited-state core hole).[91] Owing to the low computational cost of TP-DFT, Xray absorption spectra of rather large molecules can be calculated with reasonable accuracy in comparison to experiment.[92,126,127] TP-DFT is essentially a ground-state single-particle approach, where orbital relaxation is not included rigorously but via the adjustable core-hole occupation parameter. Each atom-specific spectrum was shifted such that the eigenvalue of the 1s-orbital in the HCH approximation matched the calculated IE
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