We present Kohn-Sham and hybrid density functional theory calculations on the hydrogen and nitrogen molecules using the Gaussian function exchange energy expression K-G derived by Ghosh and Parr. We compare the potential energy surfaces, equilibrium bond lengths, and exchange energies obtained by using K-G and related models with those predicted from Hartree-Fock theory and the local density approximation to the exchange. Such functionals do not appear to offer promising alternative starting points to the Dirac uniform electron gas exchange functional.