On the resilience of magic number theory for conductance ratios of aromatic molecules

TL;DR

This paper investigates the robustness of magic number theory in predicting conductance ratios of aromatic molecules, showing that it remains reliable despite electron-electron interactions, with some connectivities exhibiting notable deviations.

Contribution

It demonstrates that magic number theory's predictions are resilient to Coulomb interactions and screening effects, simplifying the analysis of quantum interference in molecular conductance.

Findings

Conductance ratios are resilient to electron-electron interactions due to cancellation effects.

Qualitative trends can be predicted using simple non-interacting models.

Certain connectivities show significant deviations, useful for probing interactions.

Abstract

If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use 'magic number theory'. In contrast with counting rules and 'curly-arrow' descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores. Here we address the question of how conductance ratios are affected by electron-electron interactions. We find that due to cancellations of opposing trends, when Coulomb interactions and screening due to electrodes are switched on, conductance ratios are rather resilient. Consequently, qualitative trends in conductance ratios of molecules with extended pi systems can be predicted using simple 'non-interacting' magic number tables, without the need for large-scale computations. On the other hand, for certain connectivities, deviations from non-interacting conductance ratios can be significant and therefore such connectivities are of interest for probing the interplay between Coulomb interactions, connectivity and QI in single-molecule electron transport.