Geometry-Dependent Suppression of Quantum Interference in Thiolate- and Nitrile-Terminated Naphthalene Junctions

Abstract

Destructive quantum interference (DQI) in single-molecule junctions can drastically suppress electron transmission, offering a powerful mechanism for modulating molecular conductance. While DQI is often dominated by molecular connectivity, it is also sensitive to molecule-electrode coupling geometry. In this study, we investigate the impact of molecule-electrode coupling geometry, especially those induced by different anchoring motifs, on the manifestation of DQI using naphthalene derivatives substituted at the 2,6- or 2,7-positions and terminated with thiolate or nitrile groups. Conductance measurement using the break junction method revealed that the 2,7-substituted thiolate-anchored molecular junction exhibited strong DQI, while the corresponding nitrile-anchored molecular junction did not, showing conductance level comparable to the 2,6-isomer. Flicker noise analysis and density functional theory-based transmission calculations suggest that the suppression of DQI in the nitrile system arises from a face-on adsorption geometry, which induces direct π-system overlap between the molecule and the Au electrodes. This overlap effectively introduces a through-space conduction pathway that bypasses DQI features present in the through-bond channel. Our findings demonstrate that subtle variations in molecule-electrode geometry can strongly influence quantum interference and provide valuable guidelines for designing molecular devices with tailored transport properties.

1. Introduction

Molecular electronics offers a platform to explore quantum effects in charge transport at the single-molecule level. Among these, quantum interference (QI) plays a pivotal role in modulating conductance, particularly in systems where electron wave functions traversing different molecular orbitals interfere either constructively or destructively. Molecules exhibiting destructive interference (DQI) can show conductance suppression by several orders of magnitude, , a feature exploitable in molecular switches, , transistors, , and thermoelectric devices. , However, while the decrease in conductivity due to DQI has been confirmed for various molecules, ,− there have been only a few instances where the antiresonance peak, an important feature of DQI, has been directly observed. , Additionally, although the antiresonance peak is theoretically expected to significantly improve thermopower and even reverse the sign of Seebeck coefficient by altering the slope of the transmission curve at the Fermi level, , there have been few successful experimental observations of such phenomena at the single-molecule level, leaving a gap between theory and experiment. The expression of QI in single-molecule junctions (SMJs) is generally considered to be governed by molecular connectivity and frontier orbital symmetry, as described by orbital rules. However, recent studies have highlighted the critical influence of molecule-electrode coupling geometryincluding the nature of anchoring groups and adsorption geometryon the electronic conductance of molecular junctions, , only a few studies have experimentally investigated the effect of the interface on the QI. −

In this work, we investigate naphthalene derivatives with 2,6- and 2,7-substitutions (NDT and NDCN, respectively, in Figure ). For the NDT series, CQI and DQI are expected to arise from the phase-coherent superposition of electron transmission amplitudes via molecular orbitals, as described by the orbital rule (Supporting Information 5). In contrast, while the nitrile groups in the NDCN series are not formally part of the π-conjugated core, DFT calculations (Table S2) reveal that the frontier orbitals exhibit finite amplitude at the terminal nitrogen atoms. Therefore, although the strict application of the orbital rule is not valid for NDCN, we employ orbital phase-based considerations as a qualitative framework to interpret trends in conductance. While the orbital rule provides a qualitative guideline based on molecular orbital symmetry and nodal structures, the actual manifestation of QI in our study is confirmed through quantitative transmission functions obtained by DFT-NEGF calculations. We compare junctions formed with thiolate and nitrile anchoring groups, which promote distinct contact geometries: the former favoring well-defined, localized binding via Au–S bonds, and the latter prone to π-system overlap with Au electrodes. While the orbital rule offers a qualitative rationale for anticipating interference behavior based on molecular topology, our conclusions are grounded in quantitative data obtained from break junction (BJ) measurements, flicker noise analysis, and DFT-NEGF simulations. We show that the 2,7-substituted nitrile-terminated junctions exhibit suppressed DQI, in contrast to their thiolate counterparts. This suppression is attributed to face-on molecule–electrode overlap that enables through-space conduction channels, bypassing the DQI node.

1.

Chemical structures of target molecules.

2. Methods Section

2.1. Experiment

2,6-NDT (Sugai Chemical Industry, purity > 99%), 2,7-NDT (Sugai Chemical Industry, purity > 99%), 2,6-NDCN (BLD Pharmatech, purity > 95%), 2,7-NDCN (Tokyo Chemical Industry, purity > 94%) were purchased from commercial sources and used without further purification. The Au tip was prepared by mechanically cutting a Au wire (Nilaco, diameter ≈ 0.3 mm, purity > 99.9%). The Au(111)/mica substrates were prepared via thermal evaporation of Au onto mica, followed by flame annealing. For sample preparation, the Au(111)/mica substrates were immersed in a 1 mM ethanol solution of NDT for few minutes or 1 mM toluene solution of NDCN overnight. After immersion, the substrates were dried under an inert gas flow. Electronic measurements were conducted using a commercially available ambient STM (MS-10 and Nanoscope V, Bruker) equipped with a signal access module III (Bruker), an external piezo driver (M-2141, MES-TEK), and a data acquisition device with LabVIEW2018 (USB-6363, National Instruments).

In the BJ method, a Au tip was repeatedly brought into and out of contact with the Au(111) substrate in the presence of molecules. Upon rupture of the Au point contact, a nanogap with nanosized electrodes was created between the Au tip and the Au substrate. A surface-deposited molecule can be captured into this nanogap, enabling the fabrication of an SMJ using the BJ technique. Figure presents 2D conductance versus stretching distance histograms of the conductance traces of the SMJs, wherein the electronic currents of the SMJs are repeatedly measured during the junction stretching process by applying a constant bias voltage of 100 mV between the Au sample electrodes and the Au-STM tip. In the 2D histograms, the stretching distance at which the conductance falls below 0.5 G ₀ (G ₀ = 2e ²/h) for 2,6-NDT and 0.013 G ₀ for other molecules was set to zero, and the conductance traces were integrated for statistical analysis.

2.

Example of conductance traces for 2,6-NDT (blue), 2,7-NDT (red), 2,6-NDCN (green), and 2,7-NDCN (orange). 2,6-NDT (blue) vertical axis follows the scale on the right.

For the flicker noise analysis, SMJs were formed by the BJ method, and conductance was measured for 0.1 s at a constant bias voltage of 100 mV while the junctions were held in place. The sampling rate was 100 kHz. The time series of conductance data were extracted within a half-width at half-maximum from the peak position of the one-dimensional conductance histogram for each state and Fourier transformed to obtain PSD. Noise power was calculated by integrating the PSD in the region of 100–1000 Hz.

2.2. Calculation

We used the DFT code SIESTA − for geometry optimization and transmission calculations of SMJs. A model electrode was fabricated by attaching a triangular pyramid tip to the surface of a slab electrode fabricated by cutting out a Au(111) surface. The size of the unit cell was set to 4 × 4, and the tip was fabricated with 4 Au atoms. The model structure of the SMJ was fabricated by arranging the electrodes symmetrically and sandwiching the target molecule in the gap between the electrodes. For NDT derivatives, we modeled the junctions with the thiolate form (−S−) bound to Au electrodes, reflecting the deprotonated species typically present under experimental conditions. The electrodes on both sides were separated by 0.025 nm each, for a total of 0.05 nm, and the geometry was optimized by the DFT method at each stage to simulate the junction elongation process in the BJ method. This cycle was continued about 15 cycles. In the geometry optimization calculations, the k-point mesh defining the k-space grid was set to 2 × 2 × 1, the energy cutoff defining the real-space grid was set to 300 Ry, the basis functions were set to single-ζ-polarized (SZP) for Au atoms only and double-ζ-polarized (DZP) for the other atoms, the exchange correlation functionals were set to the Perdew–Burke–Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA), and the convergence threshold was set to 0.02 eV/nm. For the transmission calculations, the k-point mesh was set to 10 × 10 × 1, and the other parameters were set to the same values as for the geometry optimization calculations.

3. Results and Discussion

For each naphthalene derivative, molecular junctions were repeatedly formed several thousand times using the BJ method, and the electrical conductance was measured. Examples of the obtained conductance traces are shown in Figure . These traces exhibit conductance plateaus after the rupture of a Au atomic contact, confirming the formation of molecular junctions. To statistically determine the conductance of the molecule, several thousand conductance traces were integrated to create a two-dimensional (2D) conductance versus elongation distance histogram and a 1D conductance histogram (Figure ). The origin of the elongation distance (Δz) is defined as the point of rupture of the Au atomic contact (see Experimental section for details). During the junction elongation process, two conductance states (H and L states) were observed for 2,7-NDT, whereas a single conductance state (H state) was observed for the other molecules. The conductance of each state was determined from the mean value of the Gaussian distribution fitted to the 1D conductance histogram (Table ). In NDT, the conductance of the H and L states of 2,7-NDT is approximately 16 and 631 times lower than the H state of 2,6-NDT (G_{2,6_H}/G_{2,7_H} = 16 and G_{2,6_H}/G_{2,7_L} = 631). In contrast, in NDCN, the conductance of both isomers was found to be comparable (G_{2,6_H}/G_{2,7_H} = 0.8). Therefore, it is clear that the molecular-electrode coupling geometry has an effect on QI, since no decrease in conductance due to DQI is observed in 2,7-NDCN despite the fact that NDCN has the same naphthalene backbone and the anchoring points to the electrodes (i.e., 2,7-position) as NDT.

3.

Conductance histograms of (a) 2,6-NDT, (b) 2,7-NDT, (c) 2,6-NDCN, and (d) 2,7-NDCN. The bin size for conductivity and elongation distance, Δlog­(G/G0) and Δ­(Δz), were both set to 0.01. See Experimental section for details.

1. Electrical Conductance and Junction Rupture Distance Obtained by BJ Measurements and Distance between Anchor Atoms of Naphthalene Derivatives .

	log (conductance/G 0)	junction rupture distance/nm	distance between anchor atoms/nm
2,6-NDT	[H] – 2.0 (0.4)	1.0 (0.3)	0.9
2,7-NDT	[H] – 3.2 (0.6)[L] – 4.8 (0.6)	1.3 (0.3)	0.8
2,6-NDCN	[H] – 4.5 (1.0)	0.8 (0.3)	1.0
2,7-NDCN	[H] – 4.4 (0.7)	0.8 (0.3)	0.9

^aValues in parentheses represents the half width at half maximum (HWHM).

Next, an analysis of the junction rupture distance was performed to investigate the structural changes during the junction elongation process (see Supporting Information 1 for details). The junction rupture distances obtained from the analysis and the distances between anchor atoms (S–S or N–N distances) are listed in Table for comparison. The junction rupture distance of 2,6-NDT was 1.0 nm, which is about the same as the S–S distance. On the other hand, the junction rupture distance of 2,7-NDT is 1.3 nm, which is about 0.5 nm longer than the molecular length. This is likely because the Au–S bond is stronger than the bond between Au atoms, and the Au atoms are pulled out by the junction elongation to form nanowires. However, we acknowledge that a longer rupture distance alone is insufficient to definitively confirm the formation of Au nanowires. As shown in the DFT-optimized junction geometries (Table S1), elongation of the junction results in the partial extraction of a single Au atom from each electrode at the maximum interelectrode distance. This is consistent with previous reports indicating that Au–S bonds can be stronger than Au–Au bonds, leading to preferential rupture at the Au–Au interface. Nevertheless, we also consider alternative scenarios, such as flexible contact geometries or π–Au interactions. Therefore, we describe Au atom extraction as a possible contributing factor rather than a definitive mechanism. Based on this, the two conductance states of 2,7-NDT observed by conductance measurements are considered to be caused by a structural change from a stable junction geometry in which a thiolate group is adsorbed on the hollow or bridge site to one in which a Au atom is pulled out and adsorbed on the atop site due to junction elongation. , On the other hand, only the H state was observed in 2,6-NDT, and the junction rupture distance did not exceed the molecular length, suggesting that the bond with the Au atom is weaker than in 2,7-NDT. In addition, the L state of 2,6-NDT was observed in the mechanically controllable BJ (MCBJ) measurement, which is not in agreement with the results of the present study. This might be due to the fact that the STM-BJ method used in this study has lower mechanical stability than the MCBJ method, and as a result, L state is not observed. On the other hand, the junction rupture distance for both 2,6- and 2,7-substituted NDCN was shorter than the N–N distance. This suggests that the NDCN adsorbs on the side of the electrode tip where the naphthalene backbone and the electrode overlap significantly and, junction ruptures before the anchor group moves to the neighboring Au atom at the electrode tip due to the junction elongation.

Next, to further investigate how the different junction geometry of NDT and NDCN affect the occurrence of the QI effect, the flicker noise analysis of the SMJs , was performed, and the mechanism of electron transport at the molecule–electrode interface was investigated (see Supporting Information 2 for details). A 2D histogram of noise power and average conductance G of the junction is shown in Figure . The noise power was normalized by dividing by G. Fitting with a 2D Gaussian function yields a scaling exponent of 0.8 for 2,6-NDT, indicating that through-bond coupling, i.e., electron transfer through a Au–S chemical bond (hereinafter referred to as through-bond tunneling) is occurring in 2,6-NDT. In contrast, the scaling exponents of the H and L states in 2,7-NDT were found to be 1.6 and 2.4, respectively, indicating that the contribution of electron transfer via through-space coupling (hereafter referred to as through-space tunneling) is increased. The through-space tunneling observed in 2,7-NDT was attributed to the suppression of channel conductivity through the Au–S bond by DQI, which is consistent with the measurements of similar molecules in previous studies. Subsequently, the scaling exponents for the 2,6- and 2,7-substituted NDCNs were obtained to be 2.0 and 1.6, respectively, indicating a significant contribution of through-space tunneling in both isomers. It is notable that through-space tunneling was also observed in 2,6-NDCN, which exhibits CQI and is considered to have high through-bond channel conductivity.

4.

Two-dimensional histograms of normalized noise power versus mean conductance for (a) 2,6-NDT, (b) H-state and L-state of 2,7-NDT, (c) 2,6-NDCN, and (d) 2,7-NDCN with data extracted in the conductance region for each molecule. See Supporting Information 2 for details.

Combined with the results of the junction rupture distance analysis, this difference in tunneling mechanisms compared to NDT may be due to the direct coupling between the carbon atoms constituting the naphthalene backbone and the electrode, since NDCN forms a junction structure with a short electrode separation and a large overlap between the electrode and the naphthalene backbone.

Finally, theoretical calculations were performed to investigate in detail the relationship between junction structure, QI, and electron transport properties (Supporting Information 3 and 4). Although a simplified tight-binding model is included in the Supporting Information (Figure S5) to illustrate the qualitative influence of additional coupling pathways on interference patterns, all conclusions in the main text are based on DFT-NEGF simulations using realistic contact geometries. The junction elongation process was simulated by pulling the electrodes apart by 0.05 nm at each step, stating from an initial structure with a distance of 0.6 nm between the electrodes, and optimizing the structure using the DFT method at each step. The change in total energy during the elongation process is shown in Figure . Here, the origin of Δz is taken to be the point where the distance between electrodes is 0.6 nm, corresponding to the elongation distance in the experimentally obtained conductance trace (see Supporting Information 1 for details). The black arrows in the figure indicate the major energy minima. All junction structures obtained during the elongation process are listed in Table S1. To investigate the change in transmission probability with junction elongation, we focus on structures with the energy minima with short/long interelectrode distances obtained for each molecule (hereafter referred to as short and long geometries). Unlike NDCN, no energy minima appeared in NDT at short elongation distances. Thus, the structure with an elongation distance of approximately 0.1 nm was used as the short structure (Table S1, Structure 2). Figure shows the junction structure and transmission curves of the short and long structures for each molecule. NDT has an electron-donating thiolate group, and the orbital closest to the Fermi level is the HOMO. , Then, the resonance peak around E – E _F ^DFT = 0 eV in Figure c can be assigned to the HOMO peak. The transmission probability of 2,7-NDT is lower than that of 2,6-NDT in both the short and long structures, confirming the occurrence of DQI. The long geometry (i.e., the L state in Figure ) of 2,7-NDT is likely associated with a geometry where destructive DQI is more pronounced, while the short geometry (i.e., the H state) arises from through-space transport pathways where DQI is suppressed. This interpretation is indeed consistent with the results of the flicker noise analysis, which suggests a significant through-space contribution in the H state. Accordingly, this can explain the higher conductance ratio G_{2,6_H}/G_{2,7_L} = 631 than that of G_{2,6_H}/G_{2,7_H} = 16 in the NDT series (Table ).

5.

Energy change during the junction elongation process for (a) 2,6-NDT, (b) 2,7-NDT, (c) 2,6-NDCN, and (d) 2,7-NDCN. The minimum energy value for all steps is taken as the origin of the vertical axis. See Supporting Information 3 for details.

6.

(a,c) Optimized junction geometry and transmission curves of NDT, (b,d) NDCN. See Supporting Information 3 for details.

On the other hand, NDCN has an electron-withdrawing nitrile group, and the orbital closest to the Fermi level is the LUMO. Then, the resonance peak around E – E _F ^DFT = 0 eV in Figure d can be assigned to the LUMO peak. The transmission of 2,7-NDCN is 1 order of magnitude lower than that of 2,6-NDCN over a wide energy range in the long geometry. This trend is similar to the NDT and can be attributed to occurrence of DQI in the 2,7-substituent. However, it is important to note that the nitrile anchors in NDCN are not conjugated directly to the π-system via sp²-hybridized atoms. Therefore, the orbital rule cannot be strictly applied in this case. Nevertheless, as shown in Tables S2, the frontier orbital (LUMO) shows appreciable amplitude at the terminal nitrogen atoms, allowing the use of orbital phase symmetry as a qualitative guideline to interpret the conductance behavior. In support of this approach, Yoshizawa and co-workers have demonstrated that the orbital symmetry rule remains applicable to molecules with π-accepting functionalities such as nitrile and isocyanide anchors. It should be noted, however, that the interpretation based on the orbital rule contradicts the conductance measurement results (Figure c,d), which suggest that the long geometry is not formed during the elongation process. On the other hand, in the short geometry used in the DFT-NEGF simulations, the transmission of 2,7-NDCN exceeds that of 2,6-NDCN, indicating that the DQI feature has disappeared. Although the structure used in the calculations is only one of the various structures that can be formed in the BJ method and therefore does not show quantitative agreement with the experimental data, it does reproduce the trend that conductance is not decreased by DQI in 2,7-NDCN. Therefore, it can be concluded that NDCNs form a junction geometry in which the distance between electrodes is short and the electrodes and naphthalene rings overlap significantly. While conductance measurements show no clear evidence of DQI in 2,7-NDCN with a conductance ratio of G_{2,6_H}/G_{2,7_H} = 0.8 (Table ), our DFT-NEGF simulations of the long geometry, where the electrodes are aligned end-to-end with minimal overlap, exhibit clear DQI features consistent with the orbital rule. This indicates that the suppression of DQI is not caused by a change in the molecular electronic structure due to the nitrile anchor, but rather by the geometric reconfiguration of the junction: specifically, a face-on orientation introduces through-space coupling that bypasses the DQI node, consistent with the flicker noise analysis. This interpretation is further supported by the orbital analysis summarized in Table S2, in which both the NDT and NDCN systems demonstrate consistent interference conditions based on their respective orbital symmetries and anchoring sites. The possible reason for the junction rupture without full elongation is that the bonding force of the nitrile group with the Au atom, which has a large coordination number, is lower than that of anchor groups such as thiolate and pyridyl groups, which have a binding force of 0.8–1.5 nN, and the junction might be easily broken by mechanical vibration of the measuring equipment or thermal diffusion of surface atoms and molecules. Previous studies have shown that alternative transport pathways arising from π-contact configurations can suppress interference features in cross-conjugated systems. Such observations support the idea that not only molecular topology but also electrode coupling geometry plays a critical role in determining the manifestation of quantum interference. However, it should be noted that conductance values alone may not be sufficient to distinguish between CQI and DQI, especially when the Fermi level lies near a frontier orbital. In such situations, CQI and DQI configurations may exhibit similar conductance despite their differing interference characteristics. For example, in junctions with acetylene anchors, conductance measurements failed to differentiate CQI from DQI, whereas junctions with thiol anchors showed clearer interference signatures. Nonlinear current versus voltage (I–V) characteristics have also been proposed as complementary experimental signatures of quantum interference effects. , These additional observables may help further elucidate the presence of DQI in cases where conductance alone is inconclusive.

4. Conclusions

In summary, we have demonstrated that manifestation of DQI in molecular junctions is highly sensitive to molecule-electrode contact geometry, particularly in system involving nitrile anchoring groups. While 2,7-substituted thiolate anchored molecular junction exhibits strong DQI signature, its nitrile-anchored counterpart shows comparable conductance to the 2,6-isomer, contrary to expectations based solely on molecular topology. Our combined analysis of conductance and junction rupture distance histograms, flicker noise scaling, and transmission calculations using the DFT-NEGF method indicates that face-on binding of the nitrile groups leads to significant π-overlap with the Au electrodes. This overlap establishes a direct π-coupling between the molecular backbone and the electrodes, enabling through-space transport pathways that bypass the nodal structure responsible for DQI, thereby preserving high conductance even in 2,7-substituted systems. These results highlight the critical role of contact geometry in modulating quantum interference effects, offering design principles for molecular junctions that either preserve or suppress DQI depending on application needs. While CQI/DQI analyses are typically formulated in the context of coherent through-bond tunneling, we emphasize that such frameworks remain conceptually useful even when the dominant experimental transport includes through-space components. In our study, the DFT-NEGF simulations based on idealized junction geometries provide a reference point for the interference behavior expected from the π-conjugated molecular backbone. These theoretical predictions allow us to interpret deviations observed in experimental data as arising from variations in junction geometry, especially those promoting through-space transport. For instance, even though flicker noise analysis indicates a dominant through-space transport component in 2,7-NDCN, our calculations show that DQI is still present in specific geometries with reduced molecule–electrode overlap. Therefore, the suppression of DQI signatures in experiment can be rationalized as a geometric bypassing of the interference node, rather than a complete breakdown of interference principles. This perspective allows CQI/DQI concepts to be employed as a diagnostic framework to assess how contact geometry alters the manifestation of quantum interference. By bridging the gap between ideal molecular topology and realistic experimental configurations, our approach offers new insights into the interplay between molecular structure, contact geometry, and quantum interference in molecular junctions. More broadly, they underscore the need to consider both the electronic structure and the spatial geometry of junctions when engineering functional molecular devices. These findings suggest that the incorporation of molecular spacer units between the π-conjugated core and the anchoring groups may help suppress parasitic through-space interactions and promote through-bond transport. This strategy could serve as a promising design principle for future studies seeking to enhance or isolate quantum interference effects in molecular junctions.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c08235.

• Junction rupture distance analysis, flicker noise analysis, DFT-NEGF, tight-binding NEGF, and orbital rule (PDF)

The authors declare no competing financial interest.