Recent scanning tunneling microscopy studies of individual organic molecules on Si(001) reported negative differential resistance (NDR) above a critical applied field, observations explained by a resonant tunneling model proposed prior to the experiments. Here we use both density functional theory and a many-electron GW self-energy approach to quantitatively assess the viability of this mechanism in hybrid junctions with organic molecules on Si. For cyclopentene on p-type Si(001), the frontier energy levels are calculated to be independent of applied electric fields, ruling out the proposed mechanism for NDR. Guidelines for achieving NDR are developed and illustrated with two related molecules, aminocyclopentene and pyrroline.