An electronic structural study of the complete valence shell of [1.1.1]propellane is reported. Binding energy spectra were measured in the energy regime of 3.5-46.5 eV over a range of different target electron momenta, so that momentum distributions (MDs) could be determined for each ion state. Each experimental electron momentum distribution is compared with those calculated in the plane wave impulse approximation using both a triple-xi plus polarization level SCF wave function and a further 13 basis sets as calculated using density functional theory. A critical comparison between the experimental and theoretical momentum distributions allows us to determine the optimum wave function for [1.1.1]propellane from the basis sets we studied. In general, the level of agreement between the experimental and theoretical MDs for this optimum wave function for all of the respective valence orbitals is fair. The determination of this wave function then allows us Eo derive the chemically interesting molecular properties of [1.1.1]propellane. A summary of these results and a comparison of them with those of other workers are presented with the level of agreement typically being good. In particular, we note that we confirm the existence of the C1-C3 bridging bond with a bond order of 0.70.