We next performed transmission function calculations for ladder and non-ladder molecules using the non-equilibrium Green's function method by employing the TranSiesta and Tbtrans package (Methods). As shown in Fig. , zero-bias transmission probabilities are plotted as a function of energy relative to the Fermi energy EF, where HOMO and LUMO resonance transport peaks are denoted by dashed and solid arrows. For both L1-PF6 and N1-PF6, the LUMO transmission peaks are located close to the Fermi energy level, which is consistent with a LUMO-dominated charge transport mechanism. This phenomenon was attributed to the highly electron-deficient nature of the positively charged backbones in both molecules. This electron deficiency was evidenced by cyclic voltammogram reduction events at -1.1 V and -1.5 V for L1-PF6 and N1-PF6, respectively, using ferrocene as a reference (Supplementary Figs. ). The transmission function probability at EF for L1-PF6 is an order of magnitude larger compared to N1-PF6, which is qualitatively consistent with the experimental data.