New Isospin-Breaking ``USD'' Hamiltonians and their Predictions for Nuclei in the $sd$-shell

Two new USD-type Hamiltonians, USDC and USDI, have been developed that directly incorporate Coulomb and other isospin-breaking interactions. Starting from \textit{ab initio} interactions, linear combinations of two-body matrix elements were constrained by experimental energy levels in \textit{sd}-shell nuclei. With this method, binding energies and excitation energies of proton-rich nuclei in the shell can be added to the data set used in the fit. USDC and USDI contain an analytic Coulomb interaction with Miller-Spencer short range correlations and an effective isotensor interaction. Also presented are the modified interactions, USDCm and USDIm, that have had the Coulomb interaction constrained to better reproduce experimental mirror energy differences. These Hamiltonians are used to provide new predictions for the proton-dripline, to examine isospin level mixing matrix elements, and to calculate the \textit{b-} and \textit{c-}coefficients of the IMME. Several examples of states with large Thomas-Ehrman Shifts are modeled using USDC and a single-particle interaction.