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Several studies on the transition voltage ($V_t$) are based on calculationsof the tunneling current within the Simmons model. In this paper devoted tovacuum nano-junctions, we compare the Simmons results for $V_t$ with thoseobtained from the exact Schrodinger equation by exactly including the classicalimage effects. The comparison reveals that the Simmons estimates for $V_t$ arecompletely unacceptable for nanogap sizes ($d$) at which image effects areimportant. The Simmons treatment drastically overestimates these effects,because it misses the famous 1/2 factor related to the fact that the imageinteraction energy is a self energy. The maximum of the Simmons curve $V_t$ vs.$d$ turns out to be merely an artefact of an inappropriate approximation.Unlike the Simmons approach, the "exact" WKB method yields results, whichqualitatively agree with the exact ones; quantitative differences areimportant, demonstrating that the transmission prefactor has a significantimpact on $V_t$. Further, we show that a difference between the work functionsof the left and right electrodes, which gives rise to a Volta field, may beimportant for the ubiquitous asymmetry of the measured $I$-$V$-characteristicsin general, and for the different $V_t$-values at positive and negative biasesreported in vacuum nanojunctions in particular. The weak dependence $V_t =V_t(d)$ found experimentally in vacuum nanojunctions contrasts to thepronounced dependence obtained by including the exact electrostatic imagecontribution into the Schrodinger equation. This demonstrates that not only themolecular transport, but also the transport through a vacuum nanogap representsa nontrivial problem, which requires further refinements, e.g., a realisticdescription of contacts' geometry, retardation effects due to the finitetunneling time, local phonons, surface plasmons or electron image states.

Transition voltage spectroscopy: a challenge for vacuum tunneling models at nanoscale