The origin and the distance dependence of the transition voltage of gold-vacuum-gold junctions are investigated by employing first-principles quantum transport simulations. Our calculations show that atomic protrusions always exist on the electrode surface of gold-vacuum-gold junctions fabricated using the mechanically controllable break junction (MCBJ) method. The transition voltage of these gold-vacuum-gold junctions with atomically sharp electrodes is determined by the local density of states (LDOS) of the apex gold atom on the electrode surface rather than by the vacuum barrier shape. More specifically, the absolute value of the transition voltage roughly equals the rising edge of the LDOS peak contributed by the 6p atomic orbitals of the gold atoms protruding from the electrode surface, whose local Fermi level is shifted downwards when a bias voltage is applied. Since the LDOS of the apex gold atom depends strongly on the exact shape of the electrode, the transition voltage is sensitive to the variation of the atomic configuration of the junction. For asymmetric junctions, the transition voltage may also change significantly depending on the bias polarity. Considering that the occurrence of the transition voltage requires the electrode distance to be larger than a critical value, the interaction between the two electrodes is actually rather weak. Consequently, the LDOS of the apex gold atom is mainly determined by its local atomic configuration and the transition voltage only depends weakly on the electrode distance as observed in the MCBJ experiments.

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The transition voltage of vacuum-spaced and molecular junctions constructed with Ag and Pt electrodes is investigated by non-equilibrium Green's function formalism combined with density functional theory. Our calculations show that, similarly to the case of Au-vacuum-Au previously studied, the transition voltages of Ag and Pt metal-vacuum-metal junctions with atomic protrusions on the electrode surface are determined by the local density of states of the p-type atomic orbitals of the protrusion. Since the energy position of the Pt 6p atomic orbitals is higher than that of the 5p/6p of Ag and Au, the transition voltage of Pt-vacuum-Pt junctions is larger than that of both Ag-vacuum-Ag and Au-vacuum-Au junctions. When one moves to analyzing asymmetric molecular junctions constructed with biphenyl thiol as central molecule, then the transition voltage is found to depend on the specific bonding site for the sulfur atom in the thiol group. In particular agreement with experiments, where the largest transition voltage is found for Ag and the smallest for Pt, is obtained when one assumes S binding at the hollow-bridge site on the Ag/Au(111) surface and at the adatom site on the Pt(111) one. This demonstrates the critical role played by the linker-electrode binding geometry in determining the transition voltage of devices made of conjugated thiol molecules.

The transition voltage of three different asymmetric Au∕poly(phenylene) thiol∕Au molecular junctions in which the central molecule is either benzene thiol, biphenyl thiol, or terphenyl thiol is investigated by first-principles quantum transport simulations. For all the junctions, the calculated transition voltage at positive polarity is in quantitative agreement with the experimental values and shows weak dependence on alterations of the Au-phenyl contact. When compared to the strong coupling at the Au-S contact, which dominates the alignment of various molecular orbitals with respect to the electrode Fermi level, the coupling at the Au-phenyl contact produces only a weak perturbation. Therefore, variations of the Au-phenyl contact can only have a minor influence on the transition voltage. These findings not only provide an explanation to the uniformity in the transition voltages found for π-conjugated molecules measured with different experimental methods, but also demonstrate the advantage of transition voltage spectroscopy as a tool for determining the positions of molecular levels in molecular devices.

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