Theoretical calculations for the ground states of arsine (AsH\sb3), trimethylgallium (TMG) (Ga(CH\sb3)\sb3), the arsine⋅TMG adduct, gallane (GaH\sb3), the gallane⋅arsine adduct, small Ga\sbxAs\sby clusters (x = y; x = 2-4), and small gallium hydrides are carried out at the self consistent field (SCF) Hartree-Fock level of theory, using analytic energy gradients for rapid geometry optimization. In addition, the SCF results are compared with theoretical predictions obtained at the coupled cluster level of theory including all single and double excitations, (CCSD). The precursors to the formation of GaAs, arsine and TMG, were determined to be of C\sb3v and C\sb3 symmetries, respectively, while gallane was found to be D\sb3h The equilibrium structures for Ga\sb2As\sb2, Ga\sb3As\sb3, and Ga\sb4As\sb4 are found to be of D\sb2h, C\sb1, and C\sbi symmetry, respectively. The adduct binding energies and vibrational frequencies (SCF) are also obtained resulting in two stable bonded adduct species, arsine⋅TMG of symmetry point group C\sb3 and arsine⋅gallane of C\sb3v symmetry. Finally, our theoretical predictions support a slightly exothermic gas-phase reaction yielding GaAs through a TMG⋅AsH\sb3 adduct which is formed without an activation barrier.