By direct comparison of (e,2e) measurements with Compton lineshape determinations, we first elucidate whether the (e, 2e) measurement strongly perturbs the molecular system. Specifically, results are presented for N2 and H2O. Although the error bars are somewhat large, excellent agreement is found between the two types of experiment. In order to relate such momentum space information on chemical bonding to other properties of interest, we have then examined: (i) The first moment of the measured molecular Compton profile. We show from the Thomas-Fermi statistical theory for molecules that this moment yields an approximation to the Dirac-Slater exchange energy, and values are given for N2 and H2O. (ii) The asymptotic form far from nuclei of the r space electron density which follows from density functional theory, and the justification it gives for “atomic-like building blocks” at large r or equivalently small momentum p. As predicted by the theory, the small p behavior of the Compton profile can be related between the equilibrium molecule, when the diffraction factor is removed, and the united atom, the link being established via the appropriate ionization potentials in the two configurations.