The problems associated with refining a molecular structure using gas-phase electron diffraction (GED) data alone are well known. In particular, similar interatomic distances may be strongly correlated, and the positions of light atoms (particularly hydrogen) are poorly determined due to their low electron scattering ability. These problems make it necessary to fix some geometric parameters at assumed values. This is undesirable for two reasons, which are closely related. First, because this parameter is tacitly assumed to be correct, its effect on other refining parameters cannot be gauged; second, fixing parameters can result in unrealistically low estimated standard deviations for correlated parameters. It has been found that the inadequacies of GED data can, to some extent, be overcome by combining the data with those obtained by other structural techniques, particularly rotational spectroscopy and/or liquid crystal NMR (LCNMR) spectroscopy. This is the ideal approach, as the resulting structure is based entirely on experiment. However, sufficient experimental data are often not available. Work undertaken for this thesis concerned the development of a new technique to complete GED structural refinements using data obtained from ab initio molecular orbital calculations. The new method (called SARACEN - Structure Analysis Restrained by Ab initio Calculations for Electron diffractioN) is fully described in this thesis and illustrated with examples from two different classes of compounds. The first series of compounds are small chlorinated aromatic ring systems which serve as model compounds for larger biological systems. The second series is an extensive array of compounds based on the arachno boron hydride, tetraborane(10), with general formulas H₂MB₃H₈ and (CH₃)₂MB₃H₈, where 'M' represents a Group 13 element B, Al, Ga and In. Wherever possible gas-phase structures obtained are compared to solid-phase structures (either already known or derived as a part of this work).