The electron transport of the 4-(3-nitro-4-tetrafluorophenylthiolate-ethynyl, phenylethynyl) benzenethiolate (S-FNPPB-o) molecule assembled in two Au (111) electrodes, was studied using two approaches: in the first approximate approach an electric field was applied to the pure molecule attached to two thiolate ends fixed, and in the second approach we used the nonequilibrium Green´s function formalism (NEGF) coupled to DFT to calculate the I-V curve and the voltage dependence of the transmission function in the extended system, molecule plus electrodes. By applying an electric field to the pure molecule plus thiolate ends fixed, and visualizing the changes in the spatial distribution of the frontier molecular orbitals, we can expect based on the continuity of the conduction pathway in electron transport, that if electron transport occurs through the frontier orbitals, only the LUMO orbital would create an open channel for electron transport due to its delocalized nature and large orbital density at the thiolate groups. The NEGF calculations indicate that at applied voltages lower than ±0.8 V, the current is related to transmission values through the tails of the broad LUMO orbital, and since this orbital is the one closer to the Fermi energy, and we observed very low current values in this region, higher current values at positive bias than at negative bias. As the voltage exceeds ±0.8 V the current increases from the contribution of more states from the broadened part of the transmission function from the LUMO orbital, and when the voltage approaches ±2 V, the LUMO + 1 orbital enters into the bias window and the current increases again.