Precise control of single-phenanthrene junction’s conductance

The electronic transmission of fifteen potential configurations of the single-phenanthrene junction has been theoretically investigated. The structures include para–para, para–meta, and meta–meta combined with phenyl pendant group and substituted nitrogen atom. The results show that the para–meta, which offers a tunable anti-resonance in the HOMO–LUMO gap, is the most suitable for synthesizing nanodevice. The anti-resonance is susceptible (unsusceptible) to the hetero-motif location at site four (five). Hence, our paper presents the appropriate hetero-motif conditions—type and location—to synthesize molecular devices with the desired electronic conductance. The paper calculations also deepen the understanding of molecular conductance by demonstrating the active and inactive sites to create and tune anti-resonances. It finally introduces the essential impact of connectivity, quantum interference, and aromaticity in controlling the conductance of single-phenanthrene junction.


Introduction
Molecular electronics have had the potentials [1] to achieve stable and efficient electronic components such as sensors, transistors, and data storages [2,3]. With device dimensions comparable with the wavefunctions of the propagating electrons, quantum phenomena have strongly emerged [4]. The phenomena represent the interactions between the wavefunctions of the nanodevice functional molecule, which refers to the central molecule in the electronic junction that is responsible for the device characteristics, and the wavefunctions of electrons passing through. Meanwhile, prominent examples of the quantum phenomena are the destructive quantum interference (DQI) and constructive quantum interference (CQI) that appear in the benzene ring attached to two external leads [5]. The benzene shows high (CQI), low (DQI), and high (CQI) electrical conductance states associate with para, meta, and ortho connections, respectively [6][7][8][9][10]. Hence, understanding and harnessing these QIs to achieve the aforementioned potentials require developing advanced experimental techniques [4,11] and theoretical methods [12][13][14][15][16]. For instance, enhanced thermal properties of double quantum dots [17] have been captured and controlled using Fano resonance [18]. Moreover, electrochemical gating was used to improve charge transport through biphenyl, triphenyl, and hexaphenyl molecular junctions [19].
In this paper, we follow a different approach that depends on intercalating single or multiple chemical substituents into the same functional molecule [20] provided that the junction retains the same conformation. One possible candidate is the easily synthesized polyaromatic hydrocarbon (PAH) molecules such as phenanthrene. The phenanthrene is an appealing molecule due to its rigid and anti-rotation structure [21][22][23]. It affords low electronic thermal conductance (< 0.005 KB/h) with ignorable phononic thermal conductance that both enhance its thermoelectric efficiency [24]. The phenanthrene also shows a super conductance when it is doped with alkali metals [25,26]. Therefore, in this paper, the phenanthrene was attached to two gold leads in para-para, para-meta, and meta-meta connectivities with one or two carbon atoms substituted with (linked to) nitrogen atom "dopant" (phenyl radical "side group"). Such substituent or side group variation generates 15 molecular structures that may lead to 15 conductance states.
Consequently, the density functional method (DFT) was performed to optimize the structure of the junction so that the Hamiltonian of the junction would be more realistic. Further, the better description of the Hamiltonian leads to a more accurate calculation of the electronic and electric properties of the phenanthrene's fifteen configurations. Hence, the Hamiltonian is crucial to calculate the transmission coefficient via the post-processing technique the nonequilibrium Green's function (NEGF) method. The final method we adopted is the nearest neighbor tight-binding (TB) approach. Such a simple but powerful approach investigates the electronic transmission of each junction in detail. The TB ensures the flexibility for scrutinizing the effect of each segment atom type(s) or bond strength(s) on the transmission of each system.
The results of the above methods show less than one order of magnitude difference between the para-para and meta-meta connectivities in the energy region between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Such insignificant difference, ensuring stable conductance states, results from the variation in the path lengths. However, the para-meta configurations represent the most delicate and essential structures because they offer controllable conductance states. These states essentially rely on the substituents' type and location, but they merely depend on the bond strength between the substituents or the constituents. Hence, various commercial dopants can be embedded in the phenanthrene to manipulate its electrical conductance precisely. Thus, nonhighly purified molecules with less restricted controlling conditions would save expenses and efforts.

Density functional theory (DFT)
Quantum chemistry package, SIESTA [27], was implemented to obtain the ground state geometries of the molecules in the gas phase. We applied PBE version of GGA for the exchange and correlation effects [28,29], double zeta polarized basis sets for the phenanthrene and the anchor group, double zeta basis sets for the gold leads, norm-conserving pseudopotentials for the core electrons [30][31][32], and 200 Ry for the real space grid cutoff energy. When the interatom forces were less than 40 meV/A, the systems were considered fully optimized. Furthermore, the Au-N optimum bond length (2.3 Å) was determined in our previous work by finding the lowest binding energy between the gold tiptop atom and the N of pyridine [33] when they have rigidly shifted away from each other [34]. Such shifting technique proves that the calculated 2.3 Å bond length is the most suitable value according to the applied DFT conditions, namely the exchange and correlation functional, k points, basis set, etc. Therefore, applying different DFT initial conditions leads to various bond lengths and/or energy gaps [9,35]. Moreover, experiments may include additional variables the surrounding solutions [36] or the junction conformation [34] that entails precise and particular simulation [21,37,38] or slight divergence in the theoretical calculations [39]. Hence, as far as we could, no experimental study reports the Au-N bond length between gold tip and pyridine so that we can compare with. The final step was calculating the mean-field Hamiltonians of the whole junctions after fixing the geometry of the junction (metal-anchor group-molecule-anchor group-metal). Further details about the geometry description was included in the supplementary file.

Electron transport
We calculated the phase-coherent electron transport of each system by implementing the DFT mean-field Hamiltonians into Gollum [40]. Gollum calculates the transmission coefficient T(E) by applying the non-equilibrium Green function (NEGF) method using the following for mula: ) defines the broadening of energy levels of the molecule due to the coupling to the left (L) and right (R) leads, and Σ L,R are the retarded self-energies. Besides, GOLLUM utilizes the Landauer formula [41] in calculating electrical conduct- ) . Furthermore, we used a simple tight-binding (TB) code Olife [42] to deal with nearest neighbor TB models. Both Olife and Gollum exploit the same approximation; however, Olife is much easier code than Gollum especially with its build-in graphical user interface (GUI). It is worth mentioning that the reason for studying TB copies of the more realistic DFT structures is that the TB modes offer an initial and clear intuition about the behavior of the systems.

Markussen, Stadler, and Thygesen diagrammatic scheme
These three scientists suggested a diagram drawn on top of the molecule structure. This diagram refers to the path of the electrons traversing through the molecule while they are flowing from the first lead to the second lead. The diagram also predicts the destructive or constructive interferences resulting from the interaction between the passing electrons' wavefunctions and the molecular orbitals wavefunctions. Besides, it represents a mathematical term in the retarded GF (G′); in other words, the scheme provides an analytical description of the electron transport through the molecule near the Fermi level. The MST diagrammatic scheme depends on two rules: (1) only nearest neighbor sites are connected by a path, (2) which has one input and one output ends over all sites except the first and final ones. Fulfilling these rules means continuous electron transport without destructive interferences and vice versa. Consequently, the transmission coefficient shows nodes when it has a disconnected path linking the sites 1 and N. The discontinuity occurs while the Green function goes to zero (G′ = 0). Hence, by adjusting the Fermi level to be zero [43,44] so as the cure will be at the center of the energy band, one can get. where

Results and discussion
Our paper aims to show how the electrical conductance of a single PAH molecule can be precisely adjusted. The work focuses on the phenanthrene's transmission susceptibility to the connectivities and hetero-motifs. The functional phenanthrene was attached to two Au leads through pyridylacetylene anchor groups on both sides, see the Methodology section. It was linked to the anchors with three connection patterns: para-para (pp), para-meta (pm), and meta-meta (mm). Besides, we either substituted nitrogen (N) atom or attached phenyl radical (C 6 H 5 ) at sites X and Y with varied combinations, as shown in Fig. 1. Each combination was referred to as an integer number placed next to the predefined acronyms of connectivities. Hence, the final number of the studied configurations was 15 with five combinations per connectivity pattern. The transmission coefficients of the fifteen structures, illustrated in Fig. 2, raise one prominent and common feature, which is the coincidence of the Fermi level (E F ) (the vertical long-dashed line Fig. 2) with LUMO. The concurrence of the Fermi at LUMO is mainly due to the electron-withdrawing pyridyl anchor group [45,46] that shifts the Fermi toward higher energy levels. In addition to the Fermi level, the HOMO-LUMO energy range cannot be overlooked because it defines the chemical reactivity of the molecule [47][48][49][50]. Hence, scanning the HOMO-LUMO energy gap reveals similar and dissimilar behaviors among the studied lattices. The first result is the disappearance of the anti-resonance in the para-para (Fig. 2a) and meta-meta ( Fig. 2c) with no anti-resonances. In contrast, anti-resonances manifest in the transmissions of the five asymmetric para-meta ones, Fig. 2b. One route to rationalizing the results is to focus on the functional molecule alone by excluding the influence of metal leads and anchor groups. The exclusion is justified by the junctions' identical sides [51]. Besides, the 15 configurations were fully optimized in the gas phase under the same relaxation conditions. As a result, all junctions have the same Au-N separation distance (2.3 Å), the same location at the leads' top Au-atom, the same acetylene-phenanthrene distance (1.41 Å), and the same phenanthrene-pyridyl dihedral angle (0°) except for the phenyl-embraced phenanthrene (approximately Fig. 1 The phenanthrene molecule with a para-para, b para-meta, and c meta-meta connections to the pyridylacetylene anchor group. The d shows substituent motifs at X and Y locations 2° = 1.11% change). As the phenanthrene retains planar structure in all the 15 identical junctions, connectivity and substituent motifs were the only factors left to induce the anti-resonances in the para-meta connectivity. The solution to the appearance and disappearance of the anti-resonance lies Fig. 2b, where an anti-resonance is associated with the pristine phenanthrene, pm1 black curve. This curve proves the intrinsic occurrence of anti-resonance due to para-meta connectivity. The figure also depicts that each substituent result in a particular DQI location. Hence, one can conclude that the connectivity generates the anti-resonance, and the hetero-motif tunes the anti-resonance. The dependence of anti-resonance on connectivity has also been approved for hetero-aromatic hydrocarbons in our previous work [33]. So, these two factors control the quality of the electrical conductance of the molecule.
A question now urges, "why do the asymmetric para-meta structures alone show anti-resonances?" The answer may appear from the QI graphical scheme of Markussen, Stadler, and Thygesen (MST), who suggested Hückel-based diagrammatic rules that analytically correlate QI to the molecular topology [51,52], see section 3.2 in the Methodology. Applying the MST scheme to the TB models, we found a continuous line connecting the input site to the output site for all structures (the bold blue line Fig. 3). In addition, pairs of bonded sites (depicted by blue elliptic Fig. 3) have appeared. However, the para-meta case alone illustrates an isolated atomic site, called an onsite loop and shaded by a blue circle Fig. 3. The continuous line and atomic pairs permit the flowing of the electrons in contrast to the onsite loop that turns off the molecules. The conductance inhibition happens when the Green function element, describing the relation between the incoming and outgoing sites, goes to zero. Such a result implies that the onsite loop refers to phase shifting between the superposed electronic de Broglie waves passed along different paths through the molecule. Consequently, the two waves cancel out each other leading to destructive interference in the HOMO-LUMO energy range [53]. It is The MST (left column) and GSS (right column) graphical rules for electron transport through phenanthrene. The LL and RL, respectively, stand for the left and right leads worth mentioning that Garner, Solomon, and Strange (GSS) published a similar paper that tracked the influence of the substituents on the electrical conductance of benzene and naphthalene. They have also suggested a slightly developed MTS approach by relating the anti-resonance location to the substituent onsite energy [20]. However, their presumption is inapplicable to the phenanthrene because they related the transmission coefficient to all possible paths that electrons may take to flow from one end to the other. Such procedure contradicts the DFT and TB calculations, for it shows that the pp and mm connectivities of phenanthrene could manifest anti-resonances near Fermi level, as shown in the three samples in the rightmost column in Fig. 3. Therefore, this paper limits the applicability of Garner's team suggested method. To avoid distracting, we put all possible graphs according to the GSS scheme in Figure S1.
Although the GSS scheme is inappropriate to our molecules, it encapsulates the anti-resonance dependence on the heteroatoms. Figure 2b not only associates the antiresonance with the connectivity but also correlates it with the hetero-motifs. The compounds shift the anti-resonance relative to the Fermi level depending on the number and type of the included hetero-motifs. Here, the molecules should be divided into two groups: (1) compounds with one substituent or one pendant and with (2) two substituents or two pendants. The discrimination allows having a systematic study by focusing on a single variable rather than mixing up between two variables the type and the number of motifs. Accordingly, the shifting of the antiresonances energy away from the Fermi of the two-heteromotif embraced molecules follows the sequence: pristine (pm1) < 2 × phenyl (pm5) < 2 × N (pm3), and the shifting energy of the one-hetero-motif embraced molecules takes the order N (pm2) < phenyl (pm4). A close looking at these sequences reveals the strong influence of electronegativity on the anti-resonance location. Based on the Pauling scale, the electronegativity increases in the sequence H pm1 (2.2) < C pm5 (2.55) < N pm3 (3.04). Hence, it can be concluded that increasing the electronegativity of the hetero-motifs or the pendants will push the anti-resonance away from E F toward the HOMO provided that we have two-hetero-motifs or pendants [54][55][56]. The impact of electronegativity was also reported in the work of Gantenbein et al. for para-and meta-anchored biphenyls [57] and Chen et al. [55]. The phenanthrene behaves differently when a single heteroatom or pendent is added at site five, as shown Fig. 2b. First, the anti-resonance energy difference between the single nitrogen-incorporated phenanthrene and pristine phenanthrene is tiny (ΔE = 0.044 eV). Second, the shifting of single phenyl is higher than the single nitrogen in opposite to the doublemotif cases. Third, the single phenyl's anti-resonance energy excels the double phenyls by 0.095 eV. Before proceeding, one should remember that the polyaromatic phenanthrene consists of a central benzene molecule fused into two aromatic sextets [58]. Besides, the heterocyclic pyridine molecule resembles benzene but with a single substituted nitrogen atom and less aromaticity. Hence, implementing one nitrogen atom in the phenanthrene would retain the same aromatic molecule with less aromaticity due to the nitrogen electronegativity, and it would preserve the charges within the molecule [59]. Thus, adding single nitrogen will not shift the anti-resonance, a result that was also confirmed by our nearest neighbor tight-binding phenanthrene model, Fig. 4c. The TB calculations show that varying the electronegativity between the two modified sites. c, d Show the real and TB structures of phenanthrene molecule, respectively of site five is surprisingly irresponsible for changing the anti-resonance location. However, the previous scenario is inapplicable for the phenyl ring because it is a pendant group, not an annealed motif. Consequently, the phenyl slightly withdraws charges out of the backbone phenanthrene so that it affects not only the adjacent carbon atom but also the total charge distribution of the central ring. When the phenyl ring depletes electrons from carbon atoms (4 and 5), it pushes the anti-resonance away from the LUMO. Unlike the single nitrogen atom which decreases the aromaticity and keeps the charges inside, the phenyl pulls charges outside and increases the phenanthrene aromaticity, cf. table 12 in Ref. [60]. The aromaticity of the phenanthrene with single phenyl spreads charge deficiency all over the central benzene ring. Adding a second phenyl group to site four does not pull extra charges outside the phenanthrene, as we have only two exposable carbon atoms, as shown in Fig. 4f.
One approach to understanding the phenanthrene behavior is the nearest neighbor TB model. Hence, the realistic pp, pm, and mm molecular connectivities were, respectively, transformed into 1-8, 1-9, and 14-9 TB ones, illustrated in Fig. 4. The general model assumes two left and right onedimensional semi-infinite leads attached to the phenanthrene by the coupling integrals t L = − 0.3 eV and t R = − 0.3 eV, respectively. The two leads have the same onsite energies (ε = 0.0 eV) and resonance integrals (t = − 1.0 eV). The central system has the following parameters: onsite energy ε 0 = 0.0 eV for the carbon-like sites, onsite energy ε 1 for the first modified site, onsite ε 2 for the second modified site, resonance integral t 0 = − 0.5 eV connecting any two nearest neighbors in the molecule except ε 1 and ε 2 that they were connected to each other by α. The pristine case of phenanthrene was envisaged by setting ε 0 = ε 1 = ε 2 = 0.0 eV, and t 0 = α = − 0.5 eV. The increased electronegativity of the sites was implemented in the TB models by increasing the negative value of the related onsite. Increasing the negative (positive) values of the onsite energy means an electronwithdrawing (donating) site. The TB results, Fig. 4, show that the onsite energy of the substituents or pendants could essentially moderate the quantity and quality of the system's electronic transmission. Furthermore, the anti-resonance at the Fermi level of the pristine TB phenanthrene model in the pm connectivity supports the influence of the connectivity on the occurrence of nodes in the transmission, as shown Fig. 4 when ε 1 = 0.0 eV. On the contrary, the bond strength between the two adjacent modified sites does not affect the position of the anti-resonance.
The other feature is the higher electron transport of the pp junctions compared to the mm counterparts, see Fig. 5. The transport curve also reflects the electronic density of states (DOS). Hence, the pp junctions possess higher DOS than the mm due to the different path lengths. Our DFT optimization shows shorter pp junctions (2.546 nm) than the mm ones (2.584 nm). The junction length is the distance between the top atoms of the two gold leads. Hence, the pp length is the direct virtual line connecting the two gold atoms, whereas the mm length was divided into three sections. The first is defined by the distance between the top-gold-lead atom and the phenanthrene carbon atom attached to the linker. The second region is the direct distance between the two phenanthrene carbon atoms connected to the adjacent linkers. The last region is confined by atoms 14, 4, and 9, as shown in Fig. 4c. We first averaged the distances of region two and region three, and we summed the averaged distance with the length of the first section.
In real life, recent decades have witnessed the development of experimental techniques to synthesize PAH with different heteroatoms [61,62]. It is common now to replace one or more carbon atoms in the pristine PAH with single or multiple heteroatoms, but also attach pendant molecules and control the twisting angling between the added molecule and the original functional molecule [21,[63][64][65]. For example, boron and nitrogen atoms can be replaced in the phenanthrene to tune its electrical conductance [66]. Furthermore, Venkataraman et al. investigated the dihedral angle between the functional PAH molecule and the attached side groups [21]. Numerous studies have shown that a single molecule can have multiple conductance states depending on the substituted heteroatoms. A prominent illustration is cyclopentadiene that possesses four conductance states associated with the type of the incorporated heteroatom [55,56,67]. Consequently, our results show the promising role of phenanthrene Fig. 5 A comparison between all para-para (black lines) and all meta-meta (gray lines) connectivities of phenanthrene (a). Fermi level was represented by the vertical long-dashed line. The right panels show the length of the pp junction (b) and mm junction (c) as a highly controllable building block for nano-electronic devices.

Conclusions
Single-phenanthrene (C 14 H 10 ) molecule in pristine and doped with nitrogen and phenyl radical (C 6 H 5 ) was attached in para-para (pp), meta-meta (mm), and para-meta (pm) connection to two gold leads. Hence, 15 configurations were analyzed using density functional theory (DFT), non-equilibrium Green function (NEGF), and nearest neighbor tightbinding method (TB). The results illustrate similar trends of all para-para (mm) and meta-meta (mm) configurations. They have smooth electron transport in the HOMO-LUMO gap with no anti-resonances. Consequently, the pp and mm conductance states are higher than the pm although the electron transport of pp is slightly higher than mm. Even though anti-resonances in pm decrease the transmission coefficient, they allow more sovereignty over the junction electrical properties. Such control is accomplished by two factors: (1) the para-meta connectivity and (2) the type of the heteroatom and/or the pendent group. Hence, we believe that para-meta junction is more favorable for synthesizing nanodevices due to the pm's applicable controlling factors that determine the junction electron transport.