Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly correlated solids, but there is much confusion in the literature surrounding the form of these Hamiltonians for shells of p and d orbitals. This thesis derives the most general s, p and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for many body and meanfield calculations. Analytical solutions are found for
s orbital dimers using the full configuration interaction and tight binding methods. The tight binding programme Python Noncollinear Magnetic Tight Binding [1] (PyLATO), developed for this thesis, is introduced and explained. Computational results are found for s, p and d orbital dimers, using the full configuration interaction and tight binding methods, for the Hamiltonians derived herein and the vector Stoner Hamiltonian. Noticeable differences were found between the results of the Hamiltonians derived herein and the vector Stoner Hamiltonian for the magnetic correlation of the groundstate, the time evolution of excited states, and the electronic heat capacity.