Electronic Theses and Dissertations

Date of Award


Document Type


Degree Name

Ph.D. in Chemistry


Chemistry and Biochemistry

First Advisor

Steven Davis

Relational Format



For few-body systems, the Schrödinger equation can be solved using the linear variational method, where the wavefunction is expanded in a set of parameterized, all-particle functions. However, it remains a challenging task to determine a quality set of nonlinear parameters that result in accurate wavefunctions when the Schrödinger equation is solved from the solution to an eigenvalue problem. In this work, a stochastic optimization algorithm has been implemented to drive the optimization of wavefunctions and first-order perturbed functions. For Z ≤ 10 lithiumlike ions, variational wavefunctions are determined for the 22S, 22P, 32P, 42P, and 52P states. For the Z ≤10 muonic heliumlike ions, comprised of a nucleus, electron, and muon, the ground-state (11S) wavefunctions have been optimized. Using these wavefunctions, relativistic/QED corrections to the ionization energies of the 22S lithiumlike states are determined, in order to assess the most recent experimental results. The n2P (n = 2-5) lithiumlike wavefunctions are used, in combination with multiple optimized first-order perturbed functions, to evaluate frequency-dependent dipole polarizabilities below the 22S→32P absorption frequency. Finally, the muonic heliumlike wavefunctions are used to determine the hyperfine splittings for the Z ≤ 5 muonic heliumlike ions, while properties including radial integrals and their squares are considered as a function of nuclear charge.

Available for download on Thursday, August 15, 2024