A theoretical scaling relation for length-dependent conductance in oligo (phenylene ethynylene) molecular junctions with different anchoring groups

Charge transport in single-molecule junctions depends strongly on molecular length, backbone conjugation, and molecule–electrode coupling. In this work, density functional theory (DFT) combined with quantum transport calculations is used to investigate length-dependent conductance in oligo (phenylene ethynylene) (OPE) molecular wires terminated with amine (–NH 2 ), thiol (–SH), and direct carbon (–C) contacts. For all anchoring groups, conductance decreases exponentially with increasing molecular length. The extracted attenuation factors show a clear dependence on anchoring groups: thiol- and carbon-terminated junctions exhibit similar decay constants ( β ≈ 0.23–0.24 Å⁻ 1 ), whereas amine-terminated junctions display a smaller value ( β ≈ 0.14 Å⁻ 1 ). The theoretical trends are consistent with previously reported STM, MCBJ, and CP-AFM measurements for OPE junctions. Finally, a theoretical scaling relation is derived that quantitatively connects conductance decay in alkane and OPE molecular wires. The proposed relation reproduces both theoretical calculations and experimental datasets with high accuracy ( R 2 ≈ 0.89–0.93) and provides a theoretical framework for understanding conductance scaling across structurally distinct molecular wires.