The investigation of single and double photoionization effects in small atoms and molecules provides a means to probe fundamental quantum mechanical phenomena concerning electron correlation and interference effects. To consider these concepts accurately from first principles requires the construction of the exact final continuum states of a many body problem in atomic double photoionization and of the complicated continuum states in molecular single photoionization.

Methods designed for incorporating exterior complex scaling (ECS) have proven very successful towards accomplishing these goals, providing a rigorous framework for describing continuum states involving any number of outgoing electrons with numerical exactness. Furthermore, such methods render solutions that can be interrogated to extract the full richness of information about the photoionization process from the wave function.

This work aims to demonstrate the use of exterior complex scaling by first exactly solving the three-body breakup problem of the atomic hydride anion. H^– is the simplest atomic system and is most sensitive to electron correlation effects. The application of ECS with an efficient finite-element discrete variable representation proves quite capable and well-suited for this atomic Coulomb breakup problem.

The evolution of this framework to treat molecular problems efficiently with exactness is furthered by the design of a hybrid basis method. The incorporation of analytic Gaussian basis sets ubiquitous in bound state molecular descriptions seems natural for considering molecular continuum states. The hybrid method is described in full detail and applied to completely describe photoionization of molecular [special characters omitted] and [special characters omitted].

Photoionization of simple molecular systems offers significantly more complexity in the resulting angular distributions of the ejected electron as the target geometry becomes less atomic-like, i.e., as the internuclear separation increases. In this regard, investigation of photoejection from [special characters omitted] provides a molecular environment ideal for considering the role of internuclear distance in molecular continuum states. With its relatively long equilibrium bond length of R = 5.86 bohr, the extreme target geometry of [special characters omitted] offers the possibility of investigating interference effects caused by the photoelectron de Broglie wavelength becoming comparable with the bond length at relatively low photoejection energies. The aid of the hybrid basis in treating this problem proves substantial, providing an intuitive and robust framework for complete solution of processes involving continuum states of molecular targets.