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We measure the conductance and current–voltage characteristics of two amine-terminated molecular wires—4, 4'-diaminostilbene and bis-(4-aminophenyl) acetylene—by breaking Au point contacts in a molecular solution at room temperature. Histograms compiled from thousands of measurements show a slight increase in the molecular junction conductance (I/V) as the bias is increased to nearly 450 mV. Comparatively, similar conductance measurements made with 1, 6-diaminohexane, a saturated molecule, demonstrate almost no bias dependence. We also present a new technique to measure a statistically defined current–voltage (I–V) curve. Application to all three molecules shows that 4, 4'-diaminostilbene exhibits the largest increase in differential conductance as a function of applied bias. This indicates that the predominant transport channel for 4, 4'-diaminostilbene (the highest occupied molecular orbital …