Article pubs.acs.org/JPCC
Single-Molecule Junctions Based on Bipyridine: Impact of an Unusual Reorganization on Charge Transport Ioan Bâldea* Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany S Supporting Information *
ABSTRACT: The (4,4′)-bipyridine molecule (44bpy) has attracted particular interest in molecular electronics because single-molecule junctions can be directly formed via nitrogen−gold affinity, obviating the need of understanding nontrivial invasive effects due to extra anchoring groups. In a recent study, an apparent conundrum related to the transport through 44bpy junctions has been resolved by emphasizing the essential role of the environment (solvent vs ambient conditions). In the present paper, we demonstrate the robustness of the conclusion of that study, by introducing intramolecular reorganization as a new and essential element in the analysis. This extension is necessary in the light of recent investigations drawing attention to the unusual character of intramolecular reorganization in 44bpy as a molecule possessing a floppy, highly anharmonic degree of freedom, which is strongly and nonlinearly coupled to the molecular orbital dominating the charge transport. As a further important effect related to the significant and unusual intramolecular reorganization, we investigate the excess (shot) noise and find values substantially larger than in cases of molecular junctions wherein it has been measured so far. The noise power and Fano factor calculations demonstrate the importance of energydependent transmission, a fact disregarded in the interpretation of experimental data for nanojunctions and molecular junctions investigated so far. According to the theoretical results reported here, the intramolecular reorganization should have a more pronounced overall impact on the charge transport in 44bpy for bias voltages larger than those explored in existing experiments, but not much larger to become prohibitive. These findings should motivate companion experimental investigations in this direction.
■
cm−1), it is thermally activated in experiments conducted at ambient conditions.1,5,7 Rephrasing, the 44bpy molecule reorganizes upon charge transport, and reorganization effects should be considered in order to ensure the robustness of the interpretation given in ref 9. Reorganization effects can and will be discussed within a Newns−Anderson framework14−17 as extended to the specific case of a floppy molecule like 44bpy.11 The related statistical fluctuations will be considered by performing ensemble averaging of the various molecular conformations specified by a distribution in the (dimensionless) coordinate Q of the reorganizable mode mentioned above. A phenomenon related to the aforementioned, namely, the shot (excess) noise, will also be investigated. Important differences from noise measurements done for other single-molecule junctions will be reported.
INTRODUCTION Starting with the seminal work of Tao’s group,1 electron transport through single-molecule junctions based on (4,4′)bipyridine (44bpy) has attracted continuing interest in the molecular electronics community.2−8 Recently, in ref 9 we presented the resolution of an apparent conundrum expressed in ref 5 on the transport through 44bpy junctions. In the latter work, a “working hypothesis” has been proposed to explain differences between own results5 and earlier conductance data of ref 1. In ref 9, our attention was focused on solvent effects, which turned out to make an important difference in the transport under ambient conditions without solvent. This has been demonstrated by resorting to transition voltage spectroscopy (TVS),10 a method becoming increasingly popular in molecular electronics. An important aim of the present work is to investigate the robustness of the conclusions drawn in ref 9 by augmenting the analysis presented there to include the impact of reorganization effects on 44bpy-based single-molecule junctions. This aspect, which was not considered in ref 9, is important in the light of another piece of recent work,11−13 which emphasized it in connection with the most salient structural feature of the 44bpy molecule. This molecule consists of two pyridyl rings, and the twisting angle between them is related to a floppy degree of freedom. The microscopic analysis11−13 revealed that this mode is strongly coupled to the lowest unoccupied molecular orbital (LUMO), which dominates the charge transport through 44bpy junctions. This is important: due to its low frequency (ωf ≃ 60 © 2014 American Chemical Society
■
METHOD The method of calculations employed to obtain the results reported below relies upon the Newns−Anderson model, which is appropriate to describe the electron transport mediated by a single dominant level of energy. As indicated by the negative Seebeck coefficient,5,7,9 this is the lowest unoccupied molecular orbital (LUMO). In view of the significant and specific role Received: December 27, 2013 Revised: March 28, 2014 Published: March 29, 2014 8676
dx.doi.org/10.1021/jp412675k | J. Phys. Chem. C 2014, 118, 8676−8684
The Journal of Physical Chemistry C
Article
played by the reorganization of the floppy mode in 44bpy, the Newns−Anderson model to be utilized below should be extended not only from the form applicable to molecular junctions wherein reorganization effects are irrelevant18−20 but also for that employed to commonly describe reorganizable redox units.14,15,17 As revealed by the recent ab initio analysis,11,12 the impact of the floppy mode (dimensionless coordinate Q) of 44bpy is 2fold: (i) a renormalization of the LUMO energy ε0 ≡ ε0(Q) 2
3
ε(Q ) = ε0 − 2λQ (1 + ε1Q + ε2Q + ε3Q )
