The dependence of the point properties at the nucleus, electron density (Qe(0) )and spin density (Qs(0) ), on the nuclear cusp is examined for lithium atomic configuration interaction (CI) wave functions. Several series of CI wave functions with 18 and fewer terms, are studied. Importance of the triplet core spin function to Qs(0) is substantiated. Necessary, but not sufficient, spin and electron integral cusp conditions are applied as linear constraints. For the functions studied, Qs(0) improves on applying the spin cusp constraint if the free variational spin cusp is greater than -Z, but becomes worse otherwise. The electron cusp constraint invariably overcorrects Qe(0). The effect of necessary off-diagonal weighting constraints is also examined. No obvious trends could be found. It is concluded that forcing CI functions with a small number of terms to satisfy necessary diagonal or off-diagonal integral cusp conditions has very limited usefulness. A good Qs(0) can be obtained without constraining by (l) including triplet core spin terms. (2) optimizing orbital exponents. Sufficient nuclear cusp constraints are developed for CI wave functions. The generalized cusp-satisfying CI function has multiconfigurational SCF form with the correct cusp for each orbital. Sample calculations with a small basis set are presented. These simple functions give extremely good Qs(0) expectation values but convergence of Qs(0) with respect to basis set size is yet to be tested. The most interesting discovery is the appearance of Dirac [symbol omitted]-like correction basis orbitals from energy minimization of the orbital exponents. A scheme is depicted classifying previous and present work on cusp constraints in terms of necessity and/or sufficiency. / Science, Faculty of / Chemistry, Department of / Graduate

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Thesis (Ph. D.)--Swinburne University of Technology, Centre for Molecular Simulation - 2008. / Dissertation submitted in fulfilment of requirements for the degree Doctor of Philosophy, Centre for Molecular Simulation, Swinburne University of Technology, 2008. Typescript. Includes bibliographical references (p. 188-218).

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xii, 88 p.; also includes graphics (some col.). Includes bibliographical references (p. 83-88). Available online via OhioLINK's ETD Center

In 1915, Debye derived his well-known equation for the X-ray scattering from a sample of randomly orientated gas-phase 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 X-ray scattering data. In part, this is motivated by the arrival of new X-ray sources called X-ray Free-Electron Lasers (XFELs). A new method called Ab Initio X-ray Diffraction (AIXRD) is introduced. It calculates the elastic X-ray molecular scattering factor directly from wave functions calculated by ab initio electronic structure theory, for instance Hartree-Fock or multiconfigurational self-consistent 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 Gaussian-Type 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 X-ray molecular scattering factor. Inspired by post-crystallography experiments such as serial femtosecond crystallography and single-particle imaging at XFELs, the AIXRD method is expanded to allow accurate X-ray 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 form-factor. 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 fragment-fragment interactions. Various fragment definitions are compared based on their effect on the X-ray diffraction signal, and are compared to the IAM method. Finally, X-ray diffraction from molecules in specific quantum states is calculated, revealing a distinct quantum fingerprint in the X-ray diffraction, and a comparison to experiment is made. In particular, the elastic X-ray diffraction is calculated from gas-phase H2 pumped to various electronic, vibrational, and electronic states. This is expanded upon for polyatomic molecules using the harmonic approximation for the vibrational states.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Chemistry / Doctoral / Doctor of Philosophy