Ab initio calculations of wavefunctions for first- and secondrow diatomic hydrides, and for first-row homonuclear and heteronuclear systems have been performed employing the same Gaussian basis set. This is the first one of a series of papers. In this paper the electronic wavefunctions, orbital energies and total energies of the diatomic hydrides are obtained at the experimental and (or) theoretical internuclear separations. These wavefunctions are solutions to the Restricted Hartree-Fock equations in the form of expansion with Double Zeta Contracted Gaussian functions. The repertory of states includes the ground states AH, a few low-lying excited states AH*, and positive and negative ions AH± , where A denotes the elements Li through F and Na through Cl. The calculations are restricted to states involving either closed-shell electron configurations or open-shell configurations with one incompletely filled open shell. Tables of electronic wavefunctions of three ground states AH, as examples, are presented.