  We describe in detail a full configuration interaction (CI) method designed
to analyze systems of quantum dots. This method is capable of exploring large
regions of parameter space, like more approximate approaches such as Heitler
London and Hund Mulliken, though it is not limited to weakly coupled dots. In
particular, this method is well-suited to the analysis of solid state
quantum-dot-based qubits, and we consider the case of a double quantum dot
(DQD) singlet-triplet qubit. Past analyses have used techniques which are
either substantially restricted in the regimes they can be used, or device
specific and unsuited to exploration of a large regions of parameter space. We
analyze how the DQD exchange energy, which is central to the operation of qubit
rotation gates, depends on a generic set of system parameters including
magnetic field, DQD detuning, dot size, and dot separation. We discuss the
implications of these results to the construction of real devices. We provide a
benchmark of the CI by directly comparing results from the CI method with exact
results for two electrons in a single parabolic potential (dot).
