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Extensive studies on thin films indicated a generic cubic current-voltage$I-V$ dependence as a salient feature of charge transport by tunneling. A quickglance at $I-V$ data for molecular junctions suggests a qualitatively similarbehavior. This would render model-based studies almost irrelevant, since,whatever the model, its parameters can always be adjusted to fit symmetric(asymmetric) $I-V$ curves characterized by two (three) expansion coefficients.Here, we systematically examine popular models based on tunneling barrier ortight-binding pictures and demonstrate that, for a quantitative description atbiases of interest ($V$ slightly higher than the transition voltage $V_t$),cubic expansions do not suffice. A detailed collection of analytical formulaeas well as their conditions of applicability are presented to facilitateexperimentalists colleagues to process and interpret their experimental data byobtained by measuring currents in molecular junctions. We discuss in detail thelimits of applicability of the various models and emphasize that uncriticallyadjusting model parameters to experiment may be unjustified because the valuesdeduced in this way may fall in ranges rendering a specific model invalid orincompatible to ab initio estimates. We exemplify with the benchmark case ofoligophenylene-based junctions, for which results of ab initio quantum chemicalcalculations are also reported. As a specific issue, we address the impact ofthe spatial potential profile and show that it is not notable up to biases Vsomewhat larger than V_t, unlike at higher biases, where it may be responsiblefor negative differential resistance effects.

Important issues facing model-based approaches to tunneling transport in molecular junctions