A simple model to engineer single-molecule conductance of acenes by chemical disubstitution

Journal Name A simple model to engineer single-molecule conductance of acenes by chemical disubstitution† Joel G. Fallaque,a,bSandra Rodríguez-González,b,cCristina Díaz,b,dand Fernando Martín,a,b,e,‡ Understanding and controlling electrical conductivity at the single-molecule level is of fundamental importance for the development of new molecular electronic devices. This ideally requires considering the many different options offered by the molecular structure, the nature of the electrodes, and all possible molecule-electrode anchoring configurations, which is experimentally tedious and theoretically very expensive. Here we present a systematic theoretical study of the conductance of di-amino, di-methylthio and di-(4-methylthio)phenyl acenes, from benzene to pentacene, and for all possible distributions of two identical linkers symmetrically placed on opposite sides of the same ring. We show that, for all investigated compounds, the relative variation of the conductance is well explained by the variations of the HOMO energies as predicted by a simple extendedHückel approach, i.e., without the need for further input from more elaborate calculations. The model predicts quite nicely that diamino acenes are better conductors than their corresponding dimethylthio analogues, and both much better than the di-(4-methylthio)phenyl counterparts, irrespective of the linkers’ relative positions. It also predicts, for a given pair of linkers, the variations in the conductance resulting from changing the acene size and/or the relative position of the linkers. These variations can be as large as an order of magnitude, and therefore can be used to engineer molecular conductance. Finally, we show that a similar approach should be useful to predict trends in the relative conductance of a large variety of disubstituted acene isomers, including various linkers. 1 Introduction Single-molecule conductance studies have been routinely performed over the last 15 years1–3 as a way to investigate transport phenomena at the single-molecule scale. They also provide useful information for the development of improved electronic devices, such as switches4–6, rectifiers7,8 or memories9,10 that can offer alternative points of view to those based on the widespread silicon-based technology11. Previous studies have focused, on the one hand, on understanding the physical mechaaInstituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-Nano), Campus de Cantoblanco, 28049 Madrid, Spain, EU bDepartamento de Química, Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain, EU cDepartamento de Química Física, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain, EU dDepartamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain, EU eCondensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain, EU †Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See DOI: 00.0000/00000000. ‡[email protected] nisms responsible for the observed conductance and, on the other hand, on guiding the design of novel compounds to achieve the desired functionality, mainly by playing with the molecular structure, the nature of the electrodes and the molecule-electrode anchoring configurations. In this respect, existing experiments have investigated the effect of, for example, the length of the molecule or the different binding positions of the anchoring groups in a given molecule12–16. Experimental studies aiming at studying the combined effect of several of these factors are much scarcer, although they have been shown to be crucial in the search for devices with improved properties17,18. In the latter case, the usual procedure is to combine the existing knowledge with trial-anderror approaches with the aim of obtaining improved yields and efficiencies, and/or new functionalities step by step. Brute-force systematic studies would certainly speed up the process, but these are experimentally quite tedious, if possible at all depending of the chosen family of compounds, and in most cases must be accompanied by sophisticated theoretical calculations to interprete the results, for example, to distinguish the arrangement of the molecules in the electronic junction, or to identify physical mechanisms at the quantum level. Journal Name, [year], [vol.], 1–8 | 1 Fig. 1 Disubtituted acenes considered in this work. B: benzene. N: naphthalene. A: anthracene. T: tetracene. P: pentacene. The accompanying subscripts indicate the position if the disubstituted ring from left to right. R2indicates the two identical anchoring groups. In this work, we have used amino (−NH2), methylthio (−SMe) and (4-methylthio)phenyl (−PhSMe) anchoring groups. Similarly, first-principles calculations are too expensive to consider all possibilities, so that it is difficult to extract propensity rules that are valid for a large family of compounds. Hence, the need for simple models that can be massively used at a low computational cost, while preserving the essential physical and chemical ingredients. In this respect, significant insight has already been achieved by combining Hückel molecular orbital theory with non-equilibrium Green’s function (NEGF) methodology14,19–21. However, though computationally cheaper than state-of-the-art first-principles methods, Hückel-NEFG has been so far limited to the study of a small number of compounds, for which experimental data are often available22,23. Here, we propose a simple model, based on extended Hückel molecular orbital theory, that is able to qualitatively predict, at a negligible computational cost, the trends observed in the conductance of a large number of π-conjugated compounds in which the conduction path length is the same. To demonstrate the appropriateness of this model, a systematic first-principles theoretical study has been performed on di-amino, di-methylthio and di-(4-methylthio)phenyl acenes, from benzene to pentacene, and covering all the possible crosswise distributions of two identical anchoring groups in the same ring. The choice of acenes is based on their promising properties as novel semiconducting material in electronic devices.24–27 Acenes are a family of polycyclic aromatic hydrocarbons with fused benzene rings in a linear arrangement. Their planar and rigid structure favors efficient charge transport owing to the important intramolecular electronic delocalization, and extraordinarily narrow HOMO-LUMO gap (HOMO: highest-occupied molecular orbital; LUMO: lowest-unoccupied molecular orbital). The counterpart of these interesting properties is their high reactivity, which makes more difficult and in some cases prevents the synthesis and long-term storage of pristine acenes containing a high number of fused benzene rings26. Fortunately, the addition of functional groups, as those commonly used for single-molecule break junction experiments, has been shown to efficiently protect long acenes28,29. Therefore, disubstituted acenes are ideal test-beds to perform systematic studies and engineer single-molecule conductivity by varying the conjugation length and the relative positions of the anchoring groups, precluding the conformational changes coming from other non-planar π-conjugated systems30. In order to test the model in different regimes of interfacial electronic coupling and molecular length, three anchor groups have been considered: (i) amino, which has a single lone-pair, (ii) 2 | 1–8 Journal Name, [year], [vol.], Fig. 2 Optimized geometries for two tip-anchoring group-anthracene-anchoring group-surface arrangements with −NH2(a) and −SMe (b) anchoring groups. Yellow spheres: gold atoms. Blue spheres: nitrogen atoms. Grey spheres: carbon atoms. White spheres: hydrogen atoms. Pale yellow spheres: sulfur atoms. Panels (c) and (d) show the corresponding calculated transmissions. methylthio, with two lone-pairs, and (iii) (4-methylthio)phenyl, which separates the acene core from the electrodes12,31,32, and acenes from benzene to pentacene. For all of them, we have considered all possible crosswise distributions of two identical anchor groups bound to the same phenyl ring (see Fig. 1), thus ensuring that the length of the transport pathway is the same for all possible disubstitutions. The latter is the key point that guarantees that the measured conductances are not distorted by different damping factors associated with different pathway lengths, thus reflecting almost exclusively the effect of πconjugation. This strategy is also convenient when conduction occurs in the non-resonant coherent tunneling regime, as one can expect to obtain in this way the highest conductance33,34. To validate our model, we have followed a three-step strategy: (i) single molecule-conductance has been simulated through accurate first-principles calculations for all the above mentioned compounds; (ii) the accuracy of our first-principles methodology has been validated by direct comparison with the few experimental values found in the literature; (iii) the same systems have been investigated by using the extended Hückel approach. We show that, for all the considered systems, the relative variation of the conductances resulting from the first-principles calculations are very well described by just the relative energy position of the HOMO orbital resulting from the simple extended-Hückel approach normalized to the ionization potential of the smallest disubstituted acene. And all this without the need for further input from more elaborate calculations. Therefore, the proposed model should be very useful to predict the relative conductance of a large variety of π-conjugated molecules bearing a huge diversity of anchoring groups at different binding positions. That this is the case is explicitly shown by comparing the predictions of our model with measurements performed in molecules containing an oligophenyleneethynylene core functionalized with acenes of different lengths (and different linkers), for which no first-principles calculations are available. Hence, due to its simplicity, the model should also be ideal to guide experimental research, as those compounds not following the desired behavior could be discarded a priori. 2 Theoretical methods 2.1 Construction of geometries In order to evaluate the conductance of the different molecules (Fig. 1), we consider gold electrodes, which are rather standard in the field. For simplicity, we used identical left and right 3-layer Au(111) electrodes (see Fig. 2). Junction geometries optimization has been carried out at density funcional theory (DFT) level, within the generalized gradient approximation (GGA), by using the PBE functional35 as implemented in the VASP36 code. In all cases, projector augmented waves (PAWs)37 were used in order to describe the interaction between core electrons and the nuclei. The cut-off energy of the plane-wave basis was set at 450 eV. For molecules containing from one up to four rings, we used a 5-layered 6x6 Au(111) slab and a 3x3x1 k-points mesh to sample the first Brillouin zone. For molecules containing five rings, we used a 5-layered 7x7 Au(111) slab and the Γ-point to sample the first Brillouin zone. In all systems, the molecule and the tips of the gold electrodes were relaxed until the forces were lower than 0.01 eVÅ−1, the rest of gold atoms were conJournal Name, [year], [vol.], 1–8 | 3 Fig. 3 Comparison between the calculated conductances from firstprinciples DFT+Σtheory (black triangles) with the available experimental values: B−(SMe)2(pink square) from Park et al. 40, B−(NH2)2, N−(NH2)2 and A2−(NH2)2(blue circles) from Quinn et al. 20, B−(PhSMe)2(yellow triangle) from Sacchetti et al. 41 and A2−(SMe)2(red circle) from Palomino-Ruiz et al. 42. The inset shows the conductances of B−(PhSMe)2and A2−(PhSMe)2in logarithmic scale for easy viewing. strained. From these calculations, we obtained a Au-Au lattice parameter of 2.94 Å, in good agreement with theoretical38 and experimental39 values, 2.94 Å and 2.88 Å, respectively, and junction distances of ∼2.4 Å for Au-N (in −NH2anchoring groups) and Au-S (in −SCH3anchoring groups, SMe), and ∼2.5 Å for Au-S (in (4-methylthio)phenyl anchoring groups, PhSMe). The optimized geometries for two tip-anchoring group-anthraceneanchoring group-surface arrangements with −NH2and −SMe anchoring groups are shown in Fig. 2a,b. 2.2 Evaluation of zero-bias conductance Transmissions were obtained using the TRANSIESTA/TBTRANS packages43.TBTRANS is needed to calculate the transmission curves due to the lack of scissor operator in TRANSIESTA. In these calculations, we first described the system with the TRANSIESTA method, in which we used again the PBE35 exchange-correlation functional, a double-ζbasis set for all atoms, and a mesh cutoff energy of 250 Ry. The first Brillouin zone was described using a 4x4x1 k-mesh (3x3x1 k-mesh for the 7x7 Au(111) slab), including relativistic effects in the Au atoms by means of norm-conserving pseudopotentials. Following the state-ofthe-art, zero-bias self-energy corrected density functional theory (DFT+Σmethod)42,44–48 was used to overcome the shortcomings of standard DFT in providing accurate energy positions of molecular states with respect to the junction Fermi level. We first correct the energies of the frontier orbitals of the free molecule in gas phase and, then, we included the effect of image charges by placing an image plane at 1.47 Å outside the outermost unrelaxed gold layer. After rewriting the Hamiltonian with these corrections, we calculated the transmission with TBTRANS using a 8x8 k-mesh. Finally, by using the Landauer49 formalism, zerobias conductances (G) were obtained as the value of the transmission function at the Fermi level (EF) multiplied by the quantum Fig. 4 Variation of the calculated conductances obtained from firstprinciples DFT+Σtheory (upper panel) and the HOMO energies obtained as described in section 2.3 (lower panel) for all systems investigated in this work. Notations as in Fig. 1. conductance (G0=2e2/h), G=G0T(EF). As experimental conductance values are usually obtained from histograms involving many different electrode-moleculeelectrode geometries, we have considered a few additional geometries to those shown in Fig. 2, corresponding to local minima in the potential energy surface. The results shown in the Supplementary Information show that differences in the calculated conductances are usually smaller than 30%, which are comparable to or even smaller than the typical experimental error bars. A similar conclusion has been reached in a previous study of azaborines42, where calculations were performed by using a larger number of geometries. 2.3 HOMOHückel calculation To elucidate whether frontier orbitals and π-conjugation are the dominant effects that explain the conductance of acenes, taking into account the chemical nature and location of the anchoring groups, we relied on the extended-Hückel model53–55. Due to its simplicity, this model can be massively used to study a large number of compounds at a very low computational cost. In this work, we have applied this model to evaluate the orbital energies for all systems shown in Fig. 1 by using the optimized geometries obtained in section 2.1. The calculations were performed with the Gaussian 16 code56,57.In all cases, the extended Hückel calculations are approximately six orders of magnitude cheaper in terms of computer time than the first principles ones. Due to the intrinsic limitations of the extended-Hückel model, comparison between orbital energies obtained for different systems are only meaningful when the same atoms are involved, i.e., absolute orbital energies for −NH2and −SMe disubstituted systems cannot be directly compared. To overcome this limitation in the case of the HOMOHückel orbitals, which, as shown below, are the ones that allow us to understand the relative conductance of the different systems considered in this work, we have referred the HOMOHückel orbitals of all systems sharing the same anchor4 | 1–8 Journal Name, [year], [vol.], Fig. 5 Molecular electrostatic potentials (MEPs) for pristine anthracene and pentacene (left panel), all SMe (middle panel) and NH2(right panel) disubstituted species considered in this work. ing groups (irrespective of their positions) to the negative of the ionization potential (−IP) of the benzene disubstituted molecule, 7.61 eV58 and 7.74 eV59 for B-(NH2)2and B-(SMe)2systems, respectively. In the case of −PhSMe disubstituted acenes, we used the same correction value as for the −SMe disubstituted ones, since both systems have the same kind of atoms and there is no experimental data available in the literature. This is a legitimate approach in view of the approximate validity of Koopmans’ theorem60.Of course, such a simple model is not useful to obtain quantitative values of the conductance, since, in addition to the above-mentioned limitation, it suffers from all the well-known deficiencies of Hückel theory: complete neglect of σelectrons and electron correlation, and of Coulomb and exchange interactions beyond first neighbors. Still, as shown below, the model is able to correctly catch the observed variations in conductance, showing that these are mainly due to πconjugation effects. 3 Results and discussion Figure 2 shows the calculated DFT+Σzero-bias transmissions as a function of the energy, T(E), for two representative cases, A2−(NH2)2and A2−(SMe)2results for all the other systems are given in the Supplementary Information. As can be seen in the figure, the largest peaks associated with the higher transmission through the HOMO and LUMO lie well below and above the Fermi level, respectively, even in the longer derivatives with narrower HOMO-LUMO gap. Therefore, at zero bias, transport mainly occurs via a non-resonant coherent tunneling mechanism. To check the accuracy of our first-principles calculations, we have compared in Fig. 3 our calculated conductances with those obtained experimentally for B−(NH2)2, N−(NH2)2, A2−(NH2)2, B−(SMe)2, B−(PhSMe)2and A2−(PhSMe)220,40–42, the only data available in the literature for the compounds considered in this work. As can be seen in Fig. 3, the agreement is excellent, with all the theoretical values lying inside the experimental error bars. This suggests that the conductance values obtained for all the other systems should also be accurate and can, therefore, be used as the actual values for the systematic study of these families of compounds. Notice that, for the chosen compounds, the values of the conductance cover three orders of magnitude, thus showing the high degree of control that can be achieved by an appropriate selection of the acene size, the anchoring groups and their relative positions in the chain of phenyl groups. Figure 4 (top panel) shows the calculated zero-bias conductances for all the systems considered in this work in increasing size order. For a given molecule (e.g., P1, P2and P3), the order reflects the position of the two anchoring groups, which goes from the periphery (P1) to the central part of the molecule (P3). As can be seen from Fig. 4, for a given acene molecule and a given position of the anchoring groups, the highest conductance is always found for diamino acenes, except for benzene, where the −SMe disubstituted molecule has a slightly higher conductance than diamino benzene. In all cases, −PhSMe disubstituted acenes exhibit the smallest conductance, between two and three orders of magnitude smaller than that of −NH2and −SMe disubstituted acenes. This is the consequence of (i) the longer charge carrier pathway, (ii) the reduction of the effective conjugation length due to the torsion of the central acene with respect to the phenyl anchoring ring, and (iii) the cross-conjugation effect (see30,42). Although the length of the pathway followed by the electrons from one electrode to the other is nearly the same for all acenes containing the same pair of anchoring groups, Fig. 4 shows that there are important differences in the conductance values (up to a factor of four) within a given family. For a given acene molecule, the conductance increases as the anchor groups move from the outermost ring to the innermost rings, irrespective of the chemical nature of the anchors. The largest variation is found for the pentacene family, where the number of available rings is largest and one of these rings is located in the geometric center of the molecule. Figure 4 also shows that for a given pair of anchoring groups located in more or less equivalent positions (e.g., the central ring or the outermost ring), conductance increases with the size of the acene. Journal Name, [year], [vol.], 1–8 | 5 Fig. 6 Comparison between the conductance trends predicted by the extended Hückel model and those observed in three different experiments performed on systems with an oligophenyleneethynylene core functionalized with acenes of different length and different linkers, in which the conduction path length is the same for all members considered in the experiment. Notations of the different compounds as in Fig. 1. (a) Green empty triangles: HückelHOMO energies, red filled triangles: experimental conductances from Ref.50. (b) Green empty circles: Hückel HOMO energies, red filled triangles: experimental conductances from51. (c) Green empty squares: Hückel HOMO energies, red filled triangles: experimental conductances from Ref.52 . All the above suggests that conductivity in disubstituted acenes depends on both local and non local effects associated with the πconjugated character of these systems, as well as on the nature of the anchoring groups. A minimum theory level that accounts for all these effects in a very simple way is provided by the extendedHückel model. From Fig. 4 (bottom panel), we can see that the energies of the HOMO orbitals, calculated as described in section 2.3, exhibit the same trend as the conductance obtained from first-principle calculations irrespective of the length, the nature of the anchoring groups and their position. Therefore, a lower conductance correlates with a higher tunneling barrier (HOMO offset) as the result of the subtle balance between the delocalization of electrons in the acene molecules and the coupling of the anchoring groups with the electrodes. A similar correlation has also been found experimentally in aromatic thiols and isocyanides by Kim et al. 61. To better understand the effect of πconjugation and the chemical nature of the anchoring groups, we have evaluated the molecular electrostatic potentials, MEPs. In Fig. 5, we show the MEPs of the pristine anthracene and pentancene molecules and their -SMe and -NH2disubstituted derivatives obtained from our firstprinciples calculations. From this figure, we can see that, on the one hand, the addition of the two -NH2groups on opposite sides of a ring does not change significantly the electron distribution in the rings in comparison with their pristine acene, thus preserving the original aromatic character. On the other hand, the coupling of the nitrogen lone pair with the πorbitals of acene molecules is rather strong, as this lone pair is nearly perpendicular to the acene plane. Both effects favor the transport of electrons through the disubstituted ring. In contrast, the -SMe lone pairs are weakly coupled to the πorbitals of the acenes and the high electron affinity of sulfur atom tends to favor localization of electrons in its vicinity. As a consequence, electron transport through the disubstituted ring is hindered. The MEPs also show that delocalization of the electrons is favored when the anchoring groups are in the innermost ring, especially in the -NH2family. All these effects are nicely captured by the extended Hückel model. 4Model performance in other acene derivatives To illustrate the predictive power of our extended Hückel model, we have applied it to other families of π-conjugated systems, namely those containing an oligophenyleneethynylene core functionalized with acenes of different length and different linkers, for which first-principles calculations are not available. Again, the systems have been chosen so that the conduction path length is the same for all members belonging to a given family (transverse configuration) and for which experimental results are available. In Fig. 6, we compare the variation of the HOMO energies obtained from the extended Hückel calculations with the variation of the conductances measured in three different experiments performed on systems fulfilling the above conditions. As can be seen, the experimental conductance trends are very well explained by the position of the HOMOs referred to the ionization potential of the smallest member of each series. 5 Conclusions We have shown, by comparison with accurate first principles calculations and experimental measurements, that the HOMO energy of a complex (molecule+anchoring group) computed by means of the extended-Hückel model can be used to estimate rather accurately the trends observed in the conductance of disubstituted acenes and its derivatives. We have applied this approach to study conductance in di-amino, di-methylthio and di- (4-methylthio)phenyl acenes, from benzene to pentacene, and for all possible distributions of two identical anchoring groups symmetrically placed on both sides of a given ring. Our systematic study reveals that, in general, diamino acenes are bet6 | 1–8 Journal Name, [year], [vol.], ter conductors than dimethylthio acenes, and both much better than di-(4-methylthio)penyl acenes, irrespective of relative position of the anchoring groups and the acene size. We have found that for a given pair of identical anchoring groups, conductance values can differ by up to an order of magnitude by simply changing the acene size and by almost a factor of five by changing their relative position in the acene side. These changes are not abrupt, which offers a plethora of possibilities for electronic transport. In summary, our results show that a model based on simple extended-Hückel calculations can be very helpful to engineer single-molecule conductance in acenes without the need for performing systematic experiments and/or expensive first-principle calculations in many different systems. We propose that a similar simple approach should be useful to predict trends in the conductance of a large variety of disubstituted acene isomers and other π-conjugated molecules. Conflicts of interest There are no conflicts to declare. Acknowledgements This work was supported by the Spanish Ministry of Science and Innovation – Ministerio Español de Ciencia e Innovación MICINN – projects PID2019-105458RB-I00, PID2019-106732GB-I00, the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2016-0686) and the María de Maeztu Programme for Units of Excellence in R&D (CEX2018-000805-M). We acknowledge the generous allocation of computer time at the Barcelona Supercomputer Center and the Centro de Computación Científica at the Universidad Autónoma de Madrid (CCC-UAM). Notes and references 1 G. C. Solomon, C. Herrmann and M. A. Ratner, Book Series: Topics in Current Chemistry-Series, Springer-Verlag Berlin Heidelberg, 2012, vol. 313. 2 D. Xiang, X. Wang, C. Jia, T. Lee and X. 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