X-rays have been widely exploited to unravel the structure of matter since
their discovery in 1895. Nowadays, with the emergence of new X-ray sources
with higher intensity and very short pulse duration, notably X-ray Free Electron
Lasers, the number of experiments that may be considered in the X-ray
regime has increased dramatically, making the characterization of gas phase
atoms and molecules in space and time possible. This thesis explores in the
theoretical analysis and calculation of X-ray scattering atoms and molecules,
far beyond the independent atom model.
Amethod to calculate inelastic X-ray scattering from atoms and molecules
is presented. The method utilizes electronic wavefunctions calculated using
ab-initio electronic structure methods. Wavefunctions expressed in Gaussian
type orbitals allow for efficient calculations based on analytical Fourier
transforms of the electron density and overlap integrals. The method is validated
by extensive calculations of inelastic cross-sections in H, He+, He,
Ne, C, Na and N2. The calculated cross-sections are compared to cross-sections
from inelastic X-ray scattering experiments, electron energy-loss
spectroscopy, and theoretical reference values.
We then begin to account for the effect of nuclear motion, in the first instance
by predicting elastic X-ray scattering from state-selected molecules.
We find strong signatures corresponding to the specific vibrational and rotational
state of (polyatomic) molecules.
The ultimate goal of this thesis is to study atomic and molecular wavepackets
using time-resolved X-ray scattering. We present a theoretical framework
based on quantum electrodynamics and explore various elastic and
inelastic limits of the scattering expressions. We then explore X-ray scattering
from electronic wavepackets, following on from work by other groups,
and finally examine the time-resolved X-ray scattering from non-adiabatic
electronic-nuclear wavepackets in the H2 molecule, demonstrating the importance
of accounting for the inelastic effects
