Rigorous mathematical results for electronic structure models

In my Ph.D. thesis, I achieve rigorous mathematical results for electronic structure models that arise from problems in Quantum Chemistry. Quantum Chemistry deals with models of how particles move and interact at the atomic and molecular level, and Mathematical Quantum Chemistry lies in a curious intersection of chemistry, physics, and mathematics.

In this thesis, I give a new convergence result for the Collinear Kohn-Sham Spin Density Functional Theory model. In addition, I give a survey of the theory needed for this result. I also give a detailed proof of Lieb’s theorem on maximal ionization for the Restricted and Unrestricted Hartree-Fock models, this is in the form a published joint article: [9].

[9] H. Cox, V. J. J. Syrjanen, and M. Melgaard. Maximum ionization in restricted and unrestricted Hartree-Fock theory. Atoms, 9(1), 2021.