Quantum Chemical Calculations of X-ray Emission Spectroscopy

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 Xray 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 Is 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 (BLYP)-L-66, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, acetone, dimethyl sulfoxide, and CF3Cl in good agreement with experiment.