UC Berkeley

In this thesis, we present our work in pursuit of black-box, \textit{ab initio} methods for computing positions and widths of molecular resonances. The method of complex basis functions is efficiently implemented and applied in the context of various electronic structure approximations. Within the static exchange approximation, basis set effects are investigated and the method is applied to a series of N-containing hetercycles. The extension to Hartree-Fock theory allows for more accurate calculations. These methods have been applied to several small molecules, and the computation of properties within this framework is discussed. The application of complex basis functions to shape and Feshbach resonances at correlated levels of theory including M\o ller-Plesset perturbation theory at second order and equation of motion coupled cluster singles and doubles is also investigated from a practical perspective, and the prospect of using these methods for computing accurate potential energy surfaces is explored. Finally, we describe some theoretical and practical aspects of computing positions and widths of low-energy shape resonances by analytic continuation in the coupling constant. We find that the properties of attenuated Coulomb potentials make them ideal for such calculations.