Practical approaches to simulating x-ray spectroscopy with quantum chemistry

Developments on simulating X-ray spectroscopy using quantum chemistry are presented. Topics are introduced in Chapter 1 via two separate reviews on X-ray spectroscopy and quantum chemistry. The introduction is followed by four independent investigations across four chapters, aimed at developing robust and accurate simulations to support new experimental findings in X-ray spectroscopy. In Chapter 2, the performance of gaussian basis sets for density functional theory based calculations of core electron spectroscopies is assessed. The convergence of core-electron binding energies and core-excitation energies using a range of basis sets, including split-valence, correlation consistent, polarisation consistent and individual gauge for localized orbitals basis sets is studied. For ∆self-consistent field calculations of core-electron binding energies and core-excitation energies of first row elements, relatively small basis sets can accurately reproduce the values of much larger basis sets but second row element calculations are more challenging. Timedependent density functional theory based calculations of core-excitation energies show less sensitivity to the basis set, in contrast, X-ray emission energies are highly dependent on the basis set. The results are applied to understanding the charge distribution associated with individual components in functionalised ionic liquids being tuned by careful manipulation of the substituent groups. ∆self-consistent field calculations of core-electron binding energies calculated using the pcSseg-2 basis set support X-ray photoelectron spectroscopy experimental findings. The experimental measurements and supporting calculations revealed an unexpected variation in the charge density distribution within the ionic liquid cation when the oxygen atom in a poly-ether containing side chain is moved by just one atomic position. In Chapter 3, the simulation of X-ray emission spectra of organic molecules using time-dependent density functional theory (TDDFT) is explored. TDDFT calculations using standard hybrid exchange-correlation functionals in conjunction with large basis sets can predict accurate X-ray emission spectra provided an energy shift is applied to align the spectra with experiment. The relaxation of the orbitals in the intermediate state is an important factor, and neglect of this relaxation leads to considerably poorer predicted spectra. A short-range corrected functional is found to give emission energies that required a relatively small energy shift to align with experiment. However, increasing the amount of Hartree-Fock exchange in this functional to remove the need for any energy shift led to a deterioration in the quality of the calculated spectral profile. To predict accurate spectra without reference to experimental measurements, we use the CAM-B3LYP functional with the energy scale determined with reference to a ∆self-consistent field calculation for the highest energy emission transition. Chapter 4 sees the resonant inelastic soft X-ray scattering maps for the water molecule simulated by combining quantum chemical calculations of X-ray spectroscopy with ab initio molecular dynamics. The resonant inelastic scattering intensity is computed using the Kramers-Heisenberg formalism which accounts for channel interference and polarisation anisotropy. Algebraic diagrammatic construction and density functional theory based approaches for the calculation of the x-ray transition energies and transition dipole moments of the absorption and emission processes are explored. Conformational sampling of both ground and core-excited intermediate states allows the effects of ultra-fast dynamics on the computed maps to be studied. Overall, it is shown how resonant inelastic scattering maps can be simulated with a computationally efficient protocol that can be extended to investigate larger systems. In Chapter 5, a highly accurate resonant inelastic soft X-ray scattering simulation is performed on the open-shell nitric oxide molecule. The inelastic scattering contains detailed insights into the complex nature of the Rydberg and valence excited states. The high level multi-reference, restricted active space self consistent field and restrictive active space second order perturbation theory methods are employed, performing a comprehensive analysis of the resonant inelastic x-ray scattering map. Furthermore, insights from the simulations are given to the striking vertical broadening feature in the experimental map. The calculations show that excitation and emission energies in this region correspond to π∗ emission from doubly excited core excited states, where a π electron as well as the nitrogen 1s electron have gone into the antibonding π∗ shell. The occurrence of these states is dependant on the nature of the absorption measurement in the RIXS. Potential energy curves between the core excited Rydberg 3sσ and first doubly excited state D1 show an adiabatic state crossing directly in the Franck-Condon region of the ground state. If the RIXS absorption is measured by fluorescence, this indicates the possibility of ultrafast two-electron-one-photon processes happening on the timescale of the absorption process