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

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.

Advances and challenges in single-molecule electron transport

“…As has been put forward by several groups, quantitative comparison becomes much better when considering ratios of experimental data [see, e.g., the switching of conductance for two magnetic states of a molecule (Schmaus et al, 2011) or a comparison of different connection sites on a molecule, as in the "magic ratios" discussed by Geng et al (2015) and further reviewed by Ulčakar et al (2019)]. The results for ratios compare quantitatively because many of the aspects of the theory that are sensitive to matrix elements drop out.…”

Extended curly arrow rules to rationalise and predict structural effects on quantum interference in molecular junctions

“…MRRs are best suited to analysis of CQI. 54 They can impressively predict the ratio of conductances for different connectivities through a molecular core, 18,30 and have been applied to bipartite lattices containing heteroatoms 29 and non-alternant hydrocarbons. 31 However, MRRs require increasing levels of matrix manipulation as the molecular core gets larger and, to our knowledge, have not been applied to systems containing 5-membered heterocycles or cross-conjugation.…”

Scale-Up of Room-Temperature Constructive Quantum Interference from Single Molecules to Self-Assembled Molecular-Electronic Films

“…This simple theory illustrates how connectivity alone contributes to conductance ratios, without including chemical effects or Coulomb interactions. When the latter are included, recent studies 35 indicate that the qualitative trend in the ratio is preserved (i.e., that G 1 / G 2 ≫ 1), but the precise value should be calculated using ab initio methods. Our aim is to determine if this single-molecule signature of QI is preserved or modified in a SAM, where intermolecular interactions are also expected to play a role.…”