Odd-even effects in molecular junctions: A Solomonic resolution of conflicting reports on conductance trends, metal...

Odd-even conductance alternation in alkanethiol (CnT, $n=7$ -12) self-assembled monolayers has been debated for two decades, with conflicting reports on trends, metal dependence, and microscopic origin. Using conducting probe atomic force microscopy (CP-AFM) with Ag, Au, and Pt electrodes, we extract low-bias conductance $G$ and effective molecule-electrode coupling $\Gamma$ via the off-resonant single-level model, combined with rigorous $z$ -score statistics (Welch's $t$ -test for unequal variances). We present a Solomonic resolution-meaning a balanced compromise that recognizes truth on both sides-to these long-standing controversies. First, the odd-even effect has a dual origin, manifesting in both the contact conductance prefactor ( $G_c$ , ${\Gamma }_c$ ) and the length-decay constant ( $\beta$ , $\bar{\beta }$ ). Interface and bulk contributions are therefore not mutually exclusive. The assignment to interface versus bulk remains inferential from transport parameters; independent structural characterization would be desirable but faces substantial experimental challenges. Second, the relative conductance of odd versus even chains reverses with length: odd chains are more conductive at short lengths, while even chains become superior beyond a crossover. A point estimate near $n_c\approx 12$ -13 emerges from the global fits, yet the limited experimental window ( $n=7$ -12) and the small difference in decay constants produce a wide uncertainty interval; the precise location of the crossover therefore remains undetermined. The qualitative inversion itself (from $G_o>G_e$ to $G_e>G_o$ ), however, is a robust finding and offers a natural reconciliation of prior opposing claims. Third, the effect is observed in CP-AFM junctions under the present experimental conditions. Earlier CP-AFM analyses of CnT junctions did not report it because they employed parity-agnostic fitting; once the data are deliberately split by parity the effect becomes statistically clear. Fourth, metal dependence follows parity-insensitive work-function scaling $G\propto \exp \left(\xi \Phi \right)$ with $\xi \approx 3.1{\text{eV}}^{-1}$ . Paradoxically, although absolute odd-even differences are smallest on Ag (conductances ∼20 times lower than on Au), statistical confidence is highest for Ag ( $>99.999$  %), owing to exceptional reproducibility of even-chain data. This analysis demonstrates that "weaker" does not imply "absent" and highlights the necessity of variance-aware statistics. Apparently contradictory literature findings arise from different regimes of a single underlying phenomenon.