Title:

Ab initio molecular diffraction

In 1915, Debye derived his wellknown equation for the Xray scattering from a sample of randomly orientated gasphase molecules. He approximated the molecular scattering by adding the contributions of isolated atomic constituents. This is known as the Independent Atom Model (IAM). However, it omits the redistribution of valence electrons due to bonding, and is limited to the electronic ground state. The main proposition of this thesis is that it is worthwhile going beyond the IAM when interpreting Xray scattering data. In part, this is motivated by the arrival of new Xray sources called Xray FreeElectron Lasers (XFELs). A new method called Ab Initio Xray Diffraction (AIXRD) is introduced. It calculates the elastic Xray molecular scattering factor directly from wave functions calculated by ab initio electronic structure theory, for instance HartreeFock or multiconfigurational selfconsistent field. In this way, the valence electrons are correctly taken into account, and calculations based on electronically excited wave functions become possible. The wave functions must be constructed from spatial orbitals made up of GaussianType Orbitals (GTOs), giving an analytical solution to the Fourier transform integrals involved, and is key to computationally efficient and accurate results. This is compared to a fast Fourier transform (FFT) method, where the electron density is computed on a 3D grid and an FFT algorithm is used to obtain the elastic Xray molecular scattering factor. Inspired by postcrystallography experiments such as serial femtosecond crystallography and singleparticle imaging at XFELs, the AIXRD method is expanded to allow accurate Xray diffraction calculations from large molecules such as proteins. To make the underlying ab initio problem tractable, the molecule is split into fragments. In other words, the electron density is constructed by a sum of fragment contributions, as is the corresponding molecular formfactor. In this way, it is analogous to the IAM approach except that instead of isolated atoms, there are isolated fragments. A pairwise summation of fragment contributions is also used to account for fragmentfragment interactions. Various fragment definitions are compared based on their effect on the Xray diffraction signal, and are compared to the IAM method. Finally, Xray diffraction from molecules in specific quantum states is calculated, revealing a distinct quantum fingerprint in the Xray diffraction, and a comparison to experiment is made. In particular, the elastic Xray diffraction is calculated from gasphase H2 pumped to various electronic, vibrational, and electronic states. This is expanded upon for polyatomic molecules using the harmonic approximation for the vibrational states.
