Quantum Chemical Calculations of X-ray Emission Spectroscopy

Abstract

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time dependent density functional theory (TDDFT) and resolution of the identity single excitation configuration interaction with second order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s orbitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment, however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D)gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range corrected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B 66 LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, acetone, dimethyl sulfoxide and CF 3 Cl in good agreement with experiment.

Assessment of basis sets for density functional theory-based calculations of core-electron spectroscopies

“…However, in this study we use the B97-1 functional throughout since we are not primarily concerned with a direct comparison with experiment. X-ray emission energies where computed for the highest occupied molecular orbital (HOMO) → core transition by applying TDDFT to a Kohn-Sham determinant with a core hole in a procedure described in more detail elsewhere [21]. All calculations use an unrestricted Kohn-Sham formalism except the TDDFT calculations of core-excitation energies.…”

“…X-ray absorption spectra can be computed using the transition potential method [12], time-dependent density functional theory (TDDFT) [13,14], Bethe-Salpeter equation [15], coupled cluster theory [16,17], the algebraic diagrammatic construction (CVS-ADC) scheme [18] and multi-reference methods [19]. TDDFT and EOM-CCSD methods have also been used to study X-ray emission spectroscopy through the use of a reference determinant with a core-hole [20][21][22][23]. More recently, resonant inelastic X-ray scattering spectra have been simulated based upon multi-reference wavefunction methods [24] and also using Kohn-Sham density functional theory with a core-excited reference determinant [25].…”

Multireference X-ray emission and absorption spectroscopy calculations from Monte Carlo configuration interaction

“…We compare MCCI values using c min = 5 × 10 −4 with the results of Ref. [9] for molecules that contain first row atoms and with one example (HCl) of a molecule containing a second row atom. We use the experimental geometry of the neutral molecule throughout except for methanol and CH 3 F where we optimize the geometry when using MP2 with cc-pVTZ.…”

“…Table 1 MCCI emission energies and oscillator strengths at c min = 5 × 10 −4 with a 6-311G** basis when using the lowest-lying core hole in the ionized molecule compared with experimental and EOM-CCSD results as listed in Ref. [9]. The results for emission energies are displayed in table 1 and, except for CH 3 OH, CH 3 F and CO, are close to, but slightly higher than, the available EOM-CCSD results of Ref.…”

Kohn-Sham density functional theory calculations of non-resonant and resonant x-ray emission spectroscopy

“…This approach has been applied to study organic and inorganic systems, and functionals have been parameterised to more accurately reproduce experiment. [42][43][44] One potential limitation of this approach is that inaccurate intensities can arise when the transition is described by a mixture of single excitations within the TDDFT calculation. 44 Alternatively X-ray emission spectra can be computed directly from Kohn-Sham DFT using the following:…”