Conductance Switching in Expanded Porphyrins through Aromaticity

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Conductance Switching in Expanded Porphyrins Through Aromaticity and Topology Changes Thijs Stuyver, Mickael L Perrin, Paul Geerlings, Frank De Proft, and Mercedes Alonso J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 01 Jan 2018 Downloaded from http://pubs.acs.org on January 1, 2018

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Journal of the American Chemical Society

Conductance Switching in Expanded Porphyrins Through Aromaticity and Topology Changes Thijs Stuyver,† Mickael Perrin,‡,§ Paul Geerlings,† Frank De Proft,† Mercedes Alonso*,† †

Department of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB). Pleinlaan 2, 1050 Brussels, Belgium ‡ Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

§

Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland

ABSTRACT: Expanded porphyrins are flexible enough to switch between different π-conjugation topologies, namely Mobius, Hückel and twisted-Hückel, each with distinct electronic properties and aromaticity. Since these switches can be induced by different external stimuli, expanded porphyrins represent a promising platform to develop a novel type of molecular switches for molecular electronic devices. In this work, the feasibility of conductance switches based on topology and/or aromaticity changes in expanded porphyrins is assessed for the first time. In particular, the electron transport properties of penta-, hexa- and heptaphyrins with different π-conjugation topologies and aromaticity were carefully investigated using the non-equilibrium Green´s function formalism in combination with density functional theory for various configurations of the gold contacts. Our results highlight the importance of the macrocyclic aromaticity and connectivity and, to a lesser extent, the molecular topology, in determining the transmission functions and local currents. When the electrodes are connected along the longitudinal axis of the macrocycle, we found that aromaticity of Hückel expanded porphyrins increases single-molecule junction conductance, contrary to the negative relationship between conductance and aromaticity found in single five-membered rings. For this particular connectivity, antiaromatic Hückel structures with [4n] π-electrons exhibit a sharp reduction in transmission near the Fermi level due to destructive quantum interference between the HOMO and LUMO. Belt-shaped Möbius aromatic structures exhibit a lower conductance as compared to the Hückel aromatic structures and the current flow avoids the molecular twist. Importantly, we show that expanded porphyrins, upon redox and topology interconversions, could act as efficient three-level molecular switches with high ON/OFF ratio, up to 103 at low bias voltage.

INTRODUCTION Single-molecule electronics aims to use individual molecules as active elements in electronic circuits.1 In these devices, electronic functions such as rectifiers, transistors and switches can be incorporated. Among the molecular electronic components, switches are one of the most basic components and they consist of a single molecule that can be reversibly shifted between two or more stable states.2 The switch between the different states is triggered by external stimuli such as light, temperature, pH, voltage or a chemical reaction. Since molecules are the smallest practical switching elements, the design of molecular switches presents an outstanding challenge on the road towards miniaturization in future nanotechnology.3 Given the tunable electronic and photophysical properties of porphyrins, these systems have already attracted considerable attention as promising building block for molecular electronic devices.4 An outstanding example is a four-level conductanceswitching device based on a single proton transfer in a porphyrin derivative induced by the electrons from the scanning tunneling microscope.5 In addition, very recent research on force-induced tautomerization switches underpinned the potential of porphyrins and related macrocycles as switching elements in molecular electronics.6 Expanded porphyrins containing more than four pyrrole rings or alternative heterocyclic subunits have recently emerged as

functional organic chromophores for optoelectronic applications.7 Due to their extended π-system, expanded porphyrins display red-shifted absorption bands and exceptionally large two-photon absorption cross-sections as compared with the regular porphyrin.8 As a consequence, they are excellent candidates for near infrared dyes and nonlinear optical (NLO) materials. One of the most appealing features of expanded porphyrins is their ability to switch between two, and even three, distinct π-conjugation topologies encoding different photophysical and NLO properties.9 Such a change of topology involves a Hückel-Möbius aromaticity switch in a single molecule, which can be induced by solvent, pH, and metalation, among others.10,11 Our recent computational research on expanded porphyrins varying in ring sizes and oxidation states revealed that the conformation of the porphyrinoid macrocycle is clearly dependent on the number of π-electrons and the macrocycle size (Figure 1).12 [4n+2] π-electron expanded porphyrins adopt almost planar and highly aromatic Hückel conformations, whereas Hückel antiaromatic and Möbius conformers coexist in dynamic equilibrium for [4n] π−electron expanded porphyrins. Larger expanded porphyrins, such as heptaphyrins or octaphyrins, adopt a figure-eight conformation in the neutral state but the Möbius topology becomes the most stable in the protonated species.13 Importantly, we found a close relation-

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ship between aromaticity, molecular topology and number of π-electrons.14

Figure 1. Schematic representation of different π-conjugation topologies of expanded porphyrins and the corresponding aromaticity.15

These features make expanded porphyrins interesting candidates for the development of a novel type of molecular switch for nanoelectronic applications. In contrast to other multistate switches based only on Hückel motifs, these Hückel-Möbius aromaticity switches combine both mechanical and π-electron switching, providing a new route to molecular electronic devices.9a,16 In this work, we assess computationally the feasibility of conductance switches based on expanded porphyrins for the first time. In particular, the electron transport properties of single thiol-terminated N-fused penta-, hexa- and heptaphyrins bound to gold electrodes with different π-conjugation topologies and aromaticity were investigated in detail (Figure 2). Based on our findings, the relationship between transport properties, molecular topology and aromaticity is established as well as how this relationship depends on the connectivity of the gold electrodes to the expanded porphyrins. H N

N H E X A

NH

N R

R N

2H+ R

N H

26H-H

28H-H

N

R

N

HN

N

N

N H

HN

NH

NH

N

R

NH

N

N

N H

N HN

N

N

N HN

N

R

R

N H 32H-H

32H-M aromatic weakly aromatic

Nowadays, expanded porphyrins are recognized as the test bed for investigating the correlation between molecular properties and (anti)aromaticity, since they provide congeneric macrocycles with [4n+2] and [4n] π-electrons that can be easily interconverted by two-electron redox reactions.10,21 This unique feature has been exploited by Osuka and Kim to establish the relationship between aromaticity and various photophysical and nonlinear optical properties, including excited-state lifetime, fluorescence, absorption spectra and two-photon absorption cross-sections.22 Even more, expanded porphyrins provide the elusive “yin yang pair” to prove experimentally Baird´s rule for the first time.23 As such, the study of the transport properties of these unique systems is particularly relevant, as they enable linking transmission, a physical phenomenon, and aromaticity, a key concept in Chemistry. COMPUTATIONAL METHODS Geometry optimizations and aromaticity calculations where performed with the Gaussian 09 program24 using the three parameter B3LYP functional25 and split-valence basis sets. The initial structures of the Hückel, Möbius and figure eight topologies of unsubstituted expanded porphyrins were obtained from our previous works, in which an exhaustive conformational analysis was performed for hexaphyrins,12a heptaphyrins13a and N-fused pentaphyrins.14 The performance of the B3LYP hybrid functional on the geometries and relative conformational energies of expanded porphyrins was assessed in our previous benchmarks from comparison with experiment.12-14 The geometries of the different conformations of expanded porphyrins with the linker groups attached to meso-positions were fully optimized and characterized by harmonic vibrational frequency computations at the B3LYP/6-31G(d,p) level of theory. All the structures were found to correspond to minima on the potential energy surface with no imaginary frequencies. The symmetry point group of all the structures is C1. Then, single point calculations using the triple-ζquality 6-311+G(d,p) basis set and the D3-dipersion correction with the Becke-Johnson damping function26 were performed in order to compute more accurate electronic energies for [4n] π-electron expanded porphyrins. The harmonic oscillator model of aromaticity (HOMA),27 defined by Kruszewski and Krygowski [Eq. (1)], was computed as a structural descriptor of aromaticity: HOMA = 1−

H N

NH

R

N H 32H-F

NH

molecular aromaticity does not always hold, since it is highly sensitive to the connectivity between the molecule and the electrodes as well as to the anchoring groups.20

R 24P-M

24P-H

R NH

N

NH

R

22P-H

R

R

N

NH

HN 28H-M

NH

HN

R

N

N

N

2e-, 2H+

N

N

R

HN

N

HN

NH

R

N

R

H E P T A

H N N

NH

HN

R P E N T A

2e-,

R:

C C

SH

antiaromatic

Figure 2. Hückel (H), Möbius (M) and figure-eight (F) conformations of selected expanded porphyrins and their aromaticity character.

Several theoretical and experimental studies have been devoted to finding out the correlation between conductance and aromaticity in single-molecule junctions.17 Experimental evidence showed that aromaticity of single five-membered rings, such as cyclopentadiene, furan and thiophene, reduces the conductance.18 As such, antiaromatic systems are predicted to be better conductors than nonaromatic systems, which, in turn, are predicted to be better conductors than aromatic systems.19 However, the negative relationship between conductance and

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α n ∑(R − Ri )2 n i=1 opt

(1)

where α is an empirical constant fixed for each type of bond and n corresponds to the number of bonds taken into account in the summation. Consequently, HOMA equals 0 for non-aromatic systems whereas HOMA=1 for fully aromatic ones with all bonds equal to the optimal value Ropt. Ri denotes the running bond length along the annulene-type conjugation pathway. For C-C bonds, α = 257.7 and Ropt = 1.388 Å, whereas α = 93.52 and Ropt = 1.334 Å for C-N bonds.28 The GIAO/B3LYP/6-311+G(d,p) method was applied for the NICS (nucleus-independent chemical shift) calculations.29 NICS values were computed at the geometrical center of the heavy atoms of the porphyrinoid macrocycle framework [NICS(0)] and at 1 Å above and below the ring center [NICS(1)], together with its out-of-plane tensor component [NICSzz(1)].30 For non-planar structures, the reference plane was found by least square fitting considering all the coordinates of the heavy atoms of the macrocycle and the ring center.31 When the points located 1 Å above and below the ring center are inequivalent by symmetry, the NICS(1) and NICSzz(1) magnetic indices correspond to the average of the corresponding values computed at 1 Å above and below the ring center. NICS were also evaluated in the geometrical center of the heavy atoms belonging to the classical


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conjugation pathway, but they are similar as shown in Figure S1. The anisotropy of the induced current density (ACID) method was employed complimentarily to visualize the induced delocalization of π electrons.32 For the NICS and ACID calculations, the external magnetic field is applied perpendicular to the least square molecular plane. In the case of the highly non-planar figure-eight structure, the molecule was oriented in such a way that the 2D projection exhibits the largest macrocyclic area, leading to the topology of a ring, and the external magnetic field was applied perpendicular to such projection (Figure 3). It is important to note that when the external magnetic field is applied orthogonal to the least square molecular plane, the corresponding NICS(1) and NICSzz(1) indices are not adequate to measure the macrocyclic aromaticity of twisted-Hückel conformations (Figure S2).

Figure 3. Orientation of the figure-eight structure of 32H-F used for the calculation of the NICS-based indices. The magnetic field is oriented along the z axis. The transmission calculations were performed using the NonEquilibrium Green’s Function (NEGF) method combined with DFT, as implemented in the Artaios code,33,34 a postprocessing tool for Gaussian 09. Gold(111) surfaces were chosen as electrodes and thiol groups were selected as anchor units to connect the molecules to the contacts. Ethynylphenyl spacers were added between the molecule and the thiol anchor unit to avoid steric hindrance between the molecule and the electrode surface. As pointed out recently, the main features of the transmission spectrum of a molecular junction are not influenced by the nature of the anchor units.35 After geometry optimization, the thiol’s hydrogen atoms were removed and Au9 clusters, approximating the electrode surface, were attached in accordance with the methodology outlined in a recent study.36 Fcc-hollow sites were selected as adsorption sites and the AuS distance was set to 2.48 Å.37 In a next step, single-point calculations were performed at the B3LYP/LanL2DZ level of theory using the Gaussian 09 software. A previous study on iron porphyrin complexes showed that the transmission curves with B3LYP and B3P86 functionals are comparable and qualitative results are stable with respect to the functional used in the transmission calculations.38 The Hamiltonian and overlap matrices were extracted to carry out NEGF calculations within the wide-band-limit (WBL) approximation using the post-processing tool Artaios, which yield both transmission spectra and local transmission plots.39 In the WBL approximation, a constant value of 0.036 eV−1 for the local density of states of the electrode surface has been used. This value was taken from the literature.39 For production of the through-bond transmission plots, a threshold was set to 20% of the maximum atom-atom transmission calculated in order to better visualize the preferential paths of the electrons through the molecules. By setting such thresholds, i.e. by not drawing numerous (small) atom-atom contributions, the local transmission plots may falsely appear to not conserve the current.40

RESULTS AND DISCUSSION To investigate the relationship between aromaticity, molecular topology and transport properties in expanded porphyrins, we have selected the most stable configurations of N-fused pentaphyrins, hexaphyrins and heptaphyrins (Figure 2). For pentaand hexapyrrolic macrocycles, the number of π-electrons in the conjugated system can be easily tuned by two-electron redox reactions.8a,41 Two-electron reduction can be experimentally done with NaBH4, whereas two-electron oxidation can be triggered by dichlorodicyanobenzoquinone (DDQ). Accordingly, hexaphyrins with [26] and [28] π-electron peripheries (26H and 28H) have been isolated as well as N-fused pen-

taphyrins with [22] and [24] delocalized π-electrons (22P and 24P). Importantly, the aromaticity of the Hückel and Möbius conformations is reversed upon oxidation/reduction of the macrocycle, as we previously demonstrated for a number of congeneric expanded porphyrins with varying oxidation states.12-14 In addition, the enhanced flexibility of the [4n] π-electron macrocycles allows for the realization of Möbius aromatic structures.7 The change of topology is achieved by variation of the internal dihedral angles and can be induced by different external stimuli. In the case of [28]hexaphyrins, Hückel antiaromatic and Möbius aromatic structures coexist in dynamic equilibrium for the neutral free-base42 and the conformational equilibrium is quite sensitive to temperature, solvent, protonation, meso-substituents and metalation.12a,43 For 24P, the Hückel-Möbius aromaticity switch requires very low activation energy barriers and the balance between Möbius and Hückel conformations can be controlled by mesosubstituents.14 Finally, the larger [32]heptaphyrin (32H) is sufficiently flexible to switch between three topologically distinct states (figure-eight, Möbius and Hückel) in a controllable manner by changing the solvent, protonation state and meso-substituents.13a,44 As such, protonation, deprotonation and redox reactions represent ideal external stimuli to induce a topology change from Hückel conformations to Möbius structures in expanded porphyrins. Importantly, the selected expanded porphyrins provide the optimum test bed for investigating the correlation between (anti)aromaticity and conductance. As linker groups, we have selected the thiolphenylethynyl group attached to the meso-positions of the macrocycles. Previous research on porphyrin single-molecule junctions has shown that adding thiol anchor groups increases the stability of the junctions and leads to an increased spread in conductance.45 Furthermore, the linker groups are roughly coplanar with the porphyrinoid core in Hückel topologies, apparently contributing to the extensive overall conjugation (Figure 4). For each expanded porphyrin, we consider one specific contact manner between the macrocycle and the gold electrodes and look at the evolution of the transport properties as the aromaticity and/or topology of the π-system changes. The structure of the molecular junctions considered for Hückel 22P, 26H and 32H is shown in Figure 4. This particular connectivity has little effect on the conformational and aromatic properties of the selected expanded porphyrins, as we demonstrate below. The interplay between the number of π-electrons and the molecular topology to determine the aromaticity of selected expanded porphyrins is shown in Table 1. The structural index HOMA together with the magnetic NICS-based indices were computed in order to quantify the (anti)aromaticity of the different states of the molecular switches. Regarding the magnetic descriptors, we have evaluated the NICS indices at the geometrical center of the expanded porphyrin framework [NICS(0)] and at 1 Å above and below the ring center [NICS(1)], together with the out-of-plane component of the NICS tensor, denoted as NICSzz(1). Both the NICS(1) and the NICSzz(1) are considered to better reflect the magnetic shielding/deshielding by the induced π-electron ring current since perturbations from the σ-system are avoided.46 ,47



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Table 1. Energetic, structural, magnetic, and electronic properties of selected expanded porphyrins. System

Topology

π e-a

ΔGrelb

Πc

Φpc

HOMAc

NICS(0)d

NICS(1)d

NICSzz(1)d

αpolare

ΔEH-Le

26H-H

Hückel

26

0.0

0.90

12.6

0.850

-16.0

-13.4

-30.4

1350

1.49

26H-M

Möbius

26

18.0

-0.41

32.1

0.651

7.7

7.2

32.8

1079

1.19

28H-H

Hückel

28

3.7

0.86

13.3

0.683

25.5

23.6

80.2

1152

1.06

28H-M

Möbius

28

0.0

-0.50

32.3

0.788

-12.9

-10.9

-22.3

1193

1.79

22P-H

Hückel

22

0.0

0.64

21.4

0.822

-17.4

-13.0

-29.6

966

1.66

24P-H

Hückel

24

0.0

0.49

23.1

0.619

10.5

7.8

37.0

839

1.40

24P-M

Möbius

24

2.8

-0.27

38.7

0.711

-11.6

-9.5

-15.2

913

1.83

f

33.6

f

1204

1.01

32H-F

Figure-eight

32

0.0

0.73

18.7

0.701

8.1

8.3

32H-M

Möbius

32

11.3

-0.59

27.1

0.816

-10.3

-10.8

-23.1

1379

1.62

32H-H

Hückel

32

32.5

0.45

30.0

0.698

13.4

12.0

42.8

1319

1.14

a Number of π-electrons along the classical conjugation pathway. b Relative Gibbs free energies (in kcal mol-1) evaluated at the B3LYPD3/6-311+G(d,p) level of theory.c Torsional π-conjugation index (Π), ring strain descriptor (Φp) and HOMA index of the B3LYP/631G(d,p)-optimized geometries. d NICS-based indices (in ppm) calculated with the GIAO/B3LYP/6-311+G(d,p) method. e Polarizability (αpolar in bohr3) and HOMO-LUMO energy difference (in eV). f The NICS(1) and NICSzz(1) values correspond to the molecular orientation relative to the external magnetic field displayed in Figure 3.

Figure 4. Structures of the molecular junctions for Hückel [22] Nfused pentaphyrin (a), Hückel [26]hexaphyrin (b) and Hückel [32]heptaphyrin (c).

Our previous works demonstrate the isotropic NICS(0) values are a reliable descriptor of the degree of aromaticity/antiaromaticity for most of expanded porphyrins,12 in good agreement with the energetic, magnetic and structural indices of aromaticity (Figure S3). The NICS(0) index is highly correlated with the magnetic susceptibility exaltation (Λ) values, a global descriptor of aromaticity computed via the isomerization method (Figure S4).12-14 However, the application of the NICS(1) and NICSzz(1) to describe the aromaticity of twistedHückel topologies is challenging. In these highly non-planar structures, the correct relative orientation of the magnetic field and the doubly twisted molecule corresponds to the one shown in Figure 3. The 2D projection of the molecule exhibits the largest macrocyclic area and has the topology of the ring. With the magnetic field orthogonal to such projection, the NICS(1)

and NICSzz(1) are adequate to determine the (anti)aromaticity of figure-eight structures. Indeed, there is an excellent linear correlation (R2 = 0.992) between NICS(0) and NICSzz(1) values for all the selected expanded porphyrins (Figure S5). Based on the different aromaticity descriptors, the figure-eight structure 32H-F is predicted to be antiaromatic in line with the Hückel aromaticity rules and the experimental 1H NMR spectrum, which exhibits a moderate paratropic ring current.44b Taking into account these considerations, it is clear that aromaticity is closely determined by the number of π-electrons and the molecular topology. Accordingly, Hückel conformations of [4n+2] expanded porphyrins (26H-H and 22P-H) exhibit a strong diatropic ring current, whereas untwisted conformations of [4n] expanded porphyrins (28H-H, 24P-H and 32H-H) exhibit a paratropic ring current, i.e. antiaromatic character. The aromaticity of these macrocycles is totally reverse in the Möbius topology (28H-M, 24P-M and 32H-M), in agreement with the concept of Möbius aromaticity.48 By comparison of the computed NICS values among the Möbius conformations, it is clear that the topological switch in 24P induces smaller changes in the macrocyclic aromaticity than the topological switches in 28H or 32H. In order to further assess the (anti)aromaticity of the different configurations, the so-called ACID (anisotropy of the induced current density) plots were evaluated (Figure 5 and Figure S6).32 These plots display the density and the direction of the induced ring current when an external magnetic field is applied perpendicularly to the π-system. To distinguish between diatropic and paratropic ring currents, we plot the current density vectors onto the ACID isosurface. From these plots, the reversal of (anti)aromaticity upon the change of the number of π-electrons (keeping frozen the molecular topology) as well as upon the topology change (without changing the oxidation state) is clearly visualized. As an example, the overall directions of the current density vectors are changed from clockwise (diatropic) to anticlockwise (paratropic) upon reduction of 26H-H to 28H-H. Similarly, upon the topology change from 28H-H to 28H-M, the direction of the current density vectors changes.


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Figure 5. ACID plots of [26] and [28]hexaphyrins. Isosurfaces and current density vectors are displayed together with the NICS(0) and NICSzz(1) values for each configuration. The large arrow denotes the direction of the induced ring current: clockwise for diatropic ring currents and anticlockwise for paratropic ring currents.

In addition, the structural index of aromaticity HOMA was also used to verify the (anti)aromaticity reversal upon reduction and topology switching.26 The HOMA values along the classical conjugation pathway are maximal for aromatic 26HH, 22P-H and 32H-M, denoting bond-length equalized structures, and minimal for antiaromatic 28H-H, 24P-H and 32HH. Although the correlation between HOMA and NICS(0) is far from perfect (R2 = 0.640, Figure S5), both indices are related, so those conformers characterized by large negative NICSbased indices exhibit a larger degree of bond-length equalization and vice versa. Besides the aromaticity descriptors, several torsional and electronic properties were also evaluated for each configuration of the selected macrocycles. On one side, the extent of effective overlap of neighbouring pz orbitals is measured by the torsional π-conjugation index (Π)7b and the torsional ring strain by the average dihedral angle between neighbouring pyrrole rings (Φp).49 These descriptors together with the aromaticity indices are useful for identifying expanded porphyrins with an optimum balance between the ring strain imposed by the macrocyclic core and the energy stabilization due to aromatic conjugation.12 On the other side, the polarizability and the energy difference between the HOMO and LUMO orbitals have also been computed (Table 1). These electronic properties have been previously connected with the conductance in single-molecule junctions,18d,50 so we will use them to explore their connection with the transport properties of expanded porphyrins. The variation of the static molecular polarizability (αpolar) and the energy gap between the HOMO and LUMO orbitals (ΔEHL) with respect to the number of heavy atoms in the macrocycle are plotted in Figure 6. Figure 6a illustrates that there is a close relationship between the polarizability and the macrocyclic aromaticity for each family of expanded porphyrins. For penta- and hexaphyrin compounds, Hückel aromatic conformations have larger polarizability than the antiaromatic counterparts. The same holds for the Möbius topologies, as can be inferred from the αpolar values of 26H-M and 28H-M. Furthermore, the Möbius aromatic structures exhibit polarizability values smaller than the corresponding Hückel aromatic structures, most likely due to their reduced planarity and decreased aromatic character.

Figure 6. Variation of the static molecular polarizability (a) and the HOMO-LUMO energy gap (b) with respect to the macrocycle size. The aromaticity of each structure is indicated by the dot color.

The effect of the molecular topology on static polarizability can be assessed from the [32]heptaphyrin family. The polarizability decreases significantly when going from the aromatic Möbius topology to the antiaromatic Hückel conformation and then to the figure-eight topology. In addition, by comparison of the polarizability for the different expanded porphyrins, we observe that the polarizability increases as the macrocycle size increases. Thus, the polarizability for the Möbius and Hückel topologies decreases in the following order: 32H > 28H > 24P. Regarding the energy gap between the HOMO and LUMO orbitals (ΔEH-L, Figure 6b), the Möbius aromatic topologies clearly have larger ΔEH-L values (1.6-1.8 eV) than the aromatic Hückel expanded porphyrins (1.5-1.6 eV), which in turn have HOMO-LUMO gaps considerable larger than the corresponding antiaromatic counterparts (1.0-1.4 eV). Moreover, the energy levels and near-degeneracy of the four frontier orbitals (HOMO-1, HOMO, LUMO and LUMO+1) seems to be dictated by the macrocyclic aromaticity (Figure 7 and Figure S7). In the Möbius aromatic topology, HOMO-1 and HOMO orbitals are quasi-degenerate as well as LUMO and LUMO+1.51 On the contrary, the orbital degeneracy is completely broken in the antiaromatic figure-eight and Hückel conformations and the energy gap between HOMO-1/HOMO-2 and LUMO+1/LUMO+2 is reduced as compared with those of aromatic expanded porphyrins. These observations are in line with the molecular orbital diagrams expected for aromatic and antiaromatic expanded porphyrins,8d,10 which, in turn, are in agreement with the absorption and emission spectra.



Page 6 of 27

ture arises from destructive quantum interference from HOMO and LUMO. As a result, the transmission probability around the Fermi level in the aromatic state is significantly larger than in the antiaromatic state. 22P-H and 24P-H therefore represent the high and low conductance configurations of the pentaphyrin macrocycle, respectively.

Figure 7. Schematic diagrams for molecular orbitals of the different π-conjugation topologies of [32]heptaphyrin.51

In a next step, the electron transport properties of the different π-conjugation topologies of selected expanded porphyrins were evaluated by combining density functional theory and the non-equilibrium Green's function (NEGF) method. After optimization of the molecular structure, gold clusters were attached to the thiolphenylethynyl-substituted macrocycles and the transmission spectra were evaluated with the postprocessing tool Artaios.33 The transmission probability at a specific energy E represents the probability for an electron with that particular energy to travel from one contact to the other one without being scattered. It can be related to the electrical conductance g through the Landauer formula:52 𝑔 𝐸 =

!! ! !

𝑇(𝐸)

(2)

From this expression, it is evident that the conductance is directly proportional to the transmission probability of the molecular junctions. Figure 8 shows the transmission functions for the distinct πconjugation topologies of the pentaphyrin macrocycle encoding different aromaticity. In the transmission spectra, energies are shifted by the system´s Fermi energy and the peaks correspond to the individual transport channels through the junction, which can be identified with the molecular orbitals of the isolated molecule. Next to peaks, steep drops in the transmission probability are present throughout the spectrum. These drops are called Quantum Interferences (QI) and they arise from cancelation of the contributions to the transmission probability of the different transport channels due to the fact that different transport channels have an opposite phase.53 The main area of interest of the transmission spectrum is the region around the Fermi level, which is indeed the region experimentally accessible through application of a small bias between the contacts and, consequently, determines the conductance of the system. As such, in the analysis of the transport properties below, we focus on this area with the HOMO and LUMO peaks as outer boundaries. From the transmission spectra in Figure 8, it is clear that the conductance behaviour for the different configurations of the pentaphyrin macrocycle is drastically different. Indeed, the transmission probability is highly dependent on the aromaticity of the π-conjugation system, as well as the molecular topology. Importantly, the transmission probability around the Fermi level for the aromatic 22P-H configuration exhibits a three-fold enhancement as compared with the antiaromatic 24P-H, despite having both a Hückel topology. Remarkably, the antiaromatic 24P-H exhibits a pronounced QI in the window of interest around the Fermi level. The interference fea-

Figure 8. Transmission spectra for Hückel and Möbius topologies of N-fused pentaphyrins. Red lines are linked to aromatic structures, whereas green lines to antiaromatic configurations.

The influence of the molecular topology on the transport properties can be assessed by comparison of the transmission functions of 24P-H and 24P-M. In this case, the number of πelectrons along the conjugation pathway remains equal. In the Möbius topology, a less pronounced quantum-interference feature appears close to the LUMO peak. This interference feature, however, is narrow and far from the Fermi energy, and is therefore unlikely to be observed experimentally. Nevertheless, the transmission probability of 24P-M at the Fermi level is only slightly larger than 24P-H. However, there is a clear decreased transmission probability in 24P-M as compared to 22P-H, despite its weak aromatic character. This reduced conductivity can be ascribed to the less-effective πconjugation overlap (Π = -0.27) in the singly-twisted topology as a result of the larger dihedral angles along the conjugation pathway. In order to generalize these observations, the transmission functions of the [26] and [28]hexaphyrins were computed, both for the Hückel and Möbius topologies (Figure 9). Similarly to pentaphyrins, the Hückel aromatic 26H-H exhibits the highest transmission probability around the Fermi level. Again, a clear quantum interference close to the Fermi level appears upon reduction of the macrocycle without changing the π-conjugation topology. The transmission dip in the 28HH is of the order of 10-5, which is very low in comparison to the ca. 10-2 transmission for 26H-H at the same energy. Accordingly, the ratio between T(E) in the ON state (26H-H), and the OFF state (28H-H) is ∼103. This value is very high and constitutes a proof-of-principle of the potential applicability of aromaticity switches based on expanded porphyrins for nanoelectronic applications.


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Journal of the American Chemical Society clearly between aromatic and antiaromatic configurations based on their transmission spectra.

Figure 9. Transmission spectra for Hückel and Möbius topologies of [26] and [28]hexaphyrins. Red lines are linked to aromatic structures whereas green lines to antiaromatic configurations. Dashed and solid lines correspond to the transmission function of Möbius and Hückel topologies, respectively.

Möbius topologies (Φp ∼ 32°) exhibits a reduced conductivity compared to the relatively planar Hückel 26H-H (Φp ∼ 13°). Moreover, the transmission probability of aromatic 28H-M is almost twice as that of the antiaromatic 26H-M at the Fermi level. A narrow dip in transmission at E = 1.24 eV is also observed in the transmission function of 28H-M near the LUMO orbital, but given the distance from the Fermi energy, this is unlikely to influence the experimentally measured conductance. Despite the presence of a distinct aromaticity in 26H-H and 28H-M, the Möbius topology exhibits a reduced transmission probability around the Fermi level as compared with the Hückel topology. These differences can be attributed to the reduced planarity of the singly-twisted topology, hindering an effective π-conjugation (i.e. Π = -0.50 and Φp = 32º in 28H-M compared to Π = 0.90 and Φp = 13º in 26H-H). In this case, the ratio of conductance for the 26H-H → 28H-M switch is ~ 4-8, which is considerably lower than the predicted ratio of conductance for the redox-based switch 26H-H → 28H-H. These results open the door to redox-triggered molecular switches based on aromaticity changes in hexaphyrins, since upon the two-electron reduction the conductance of 26H-H is expected to be significantly reduced due to the appearance of a quantum interference close to the Fermi level in 28H-H. Topology changes from Hückel to Möbius conformations will also influence the conductance of the macrocycle, but to a lesser extent than the redox interconversions without changing the topology. Finally, the dependence of the transmission functions of [32]heptaphyrins on the π-conjugation topology is investigated (Figure 10). In this topology switch, figure-eight, Möbius and Hückel topologies can be interconverted without changing the number of π-electrons. The aromaticity character is then linked to the π-conjugation topology in such a way that Möbius conformations are aromatic whereas figure-eight and Hückel conformations are antiaromatic. In this case, all the configurations exhibit quantum interference in the HOMO-LUMO gap. As demonstrated below, the presence of quantum interference in the different topologies of 32H is highly dependent on the route of connection to the gold electrodes. Nevertheless, since the transmission dips are not all symmetrically centred around the Fermi level, it is possible to distinguish

Figure 10. Dependence of the transmission function of [32]heptaphyrin with the π-conjugation topology. Red lines are linked to aromatic structures whereas green lines to antiaromatic configurations.

Despite the large differences in topology, antiaromatic 32H-F and 32H-H display very similar transmission function with a transmission dip around 0.5 eV. This similarity in the transport properties can be ascribed to their antiaromaticity and similar molecular orbital diagram and ΔEH-L. In contrast, the interference in the Möbius aromatic topology is shifted to the left (~ 0.2 eV). As a consequence, at the Fermi level, the ratio of transmission between the antiaromatic 32H-F and aromatic 32H-M is approximately 70, which is considerably high and should be clearly measurable experimentally. Therefore, the topology change from antiaromatic to aromatic configurations are predicted to also induce large changes in the conductance of [32]heptaphyrin, which confirms the close relationship between molecular conductance and aromaticity of the πelectron system in expanded porphyrins. From these results, it is evident that the conductance of expanded porphyrins strongly depends on the macrocyclic aromaticity and, to a lesser extent, on the π-conjugation topology. These results provide a proof-of-principle of the applicability of redox-triggered aromaticity switches based on expanded porphyrins as conductance switching elements. In Hückel expanded porphyrins, aromaticity increases single-molecule junction conductance, which disagrees with the previously reported negative relationship between conductance and molecular aromaticity for single five-membered rings based on experimental results.18 Regarding the molecular topology, Möbius aromatic conformations exhibit lowered transmission as compared with the Hückel aromatic state. In addition, the connection between molecular polarizability and transmission in expanded porphyrins can be probed. Contrary to Mujica et al. findings,50b we observe that the conductance rises as the molecular polarizability increases for the systems considered, demonstrating that the link between conductance and polarizability might be more subtle than intuitively anticipated. A recent theoretical investigation of this relation by some of the authors of the present study already hinted in this direction.54 Besides aromaticity and topology switches, expanded porphyrins can provide conductance switches based on single proton transfer inside the junction. The potential of porphyrins and related macrocycles as multilevel conductance switches using tautomerization reactions has been recently demonstrated



experimentally.5,6 Although the position of the hydrogen atom does not influence the structure of the porphyrin, it induces small but significant changes in the current measured through the scanning tunnelling microscope tip, thus confirming that the states have different conductance levels.

Figure 11. Transmission spectra for the two tautomers involved in the molecular switch for the Hückel [22] N-fused pentaphyrin (a) and [26]hexaphyrin (b). Red lines are linked to aromatic structures.

In order to see how tautomerization influences the transmission function, we have evaluated the transport properties of two tautomers for Hückel [22] N-fused pentaphyrin and [26]hexaphyrin (Figure 11). The Hückel molecules contain at least one hydrogen atom inside the cavity that can be flipped between two different tautomeric states. Both tautomers exhibit very similar energies and electronic properties concerning aromaticity, polarizability and energy HOMO-LUMO gap. The molecular orbital diagrams shows that the energy levels of the different orbitals are shifted by c.a. 0.3 eV leading to a very similar ΔEH-L (Figure S8). The transmission functions for both tautomers point to a similar conductance around the Fermi level. It is clear that no destructive quantum interference around the Fermi level is observed for both aromatic Hückel structures, in contrast to the antiaromatic Hückel structures. Accordingly, the tautomerization reactions in pentaphyrins and hexaphyrins are expected to induce significantly smaller changes in the conductance than redox reactions that involve the reversal of the aromaticity. In order to get further insight into the transport properties of expanded porphyrins, we have evaluated the current maps associated to the transmission spectra.40 The Artaios code can also be used to plot the local transmission through Hückel and Möbius expanded porphyrins (Figure 12 and Figures S9-S12). By considering the local transmission plots around the Fermi level, a qualitative understanding of how the current flows through the molecule from contact to contact under small bias can be obtained.55 In these plots, the local transmission is represented by arrows along the molecular geometry, in such a way that the size of

Page 8 of 27

the arrow represents the value of local transmission for a pair of atoms. Note that the arrows are scaled in each plot, such that the arrow corresponding to the highest local transmission has the same size in every plot and the sizes of the other arrows are determined relative to this one. For aromatic Hückel expanded porphyrins (26H-H and 22PH), we observe that the current flow splits upon entering the molecule and travels equally through both arms and in the same direction close to the Fermi level. It is noteworthy than these Hückel configurations are relatively symmetric, so the degree of bond-length alternation for both transmission paths is equal. Inside the individual pyrrole rings the current splits uniformly, in contrast to the imine-type rings in which the main stream passes through C-N bonds. This observation is in agreement with the annulene-like conjugation pathway, in which the outer C-C bonds are viewed as inert bridges in imine-type rings.56 On the contrary, for Möbius expanded porphyrins (28H-M and 24P-M), the current flow under small bias no longer splits equally along the macrocycle, and the main pathway correspond to the longest arm of the molecule avoiding the molecular twist in the π-conjugated Möbius system. Along the shorter arm, some residual transport occurs but in the opposite direction, reducing the net current from contact to contact. This observation can be understood based on the bond-length alternation, which was shown to play an essential role in determining transmission through the π-system of annulenes.55 In bondalternated annulenes, the current travels in the direction of the shortest bond, i.e. the bond with most double bond character, upon entering the molecule. Bond-equalized annulenes on the other hand exhibit an equal splitting of the current in two paths, both following the same direction. A similar behaviour is observed for Hückel and Möbius topologies. Both, 22P-H and 26H-H exhibit more bond-equalized structures and, importantly, the degree of bond length alternation along the two transmission paths are identical (Figure 12 and Figure S9). However, in singly-twisted topologies, the molecular twist breaks the symmetry of the two plausible transmission paths, which exhibit different bond lengths and torsional strain. Interestingly, the preferred transmission pathway corresponds to the less-strained path, as denoted by ΦARM, and the current travels in the direction of the shortest bond, even when it is the longer-distance path. The changes in dihedral angles and bond-length alternation upon the HückelMöbius topology switch affects the choice of the preferred transmission pathway, which also explains the reduced transmission probability around the Fermi level observed for Möbius aromatic systems as compared to the Hückel aromatic systems. For the antiaromatic Hückel 28H-H with a quantum interference in the window of interest in the transmission spectrum, the local transmission plot at the Fermi level shows triangular cyclic currents at the contact positions. These striking features have previously been connected to signatures of quantum interference.40 Very close to the energy of the quantum interference at -0.16 eV, these cyclic currents become predominant and accordingly, the total transmission vanishes (Figure S10). For the other expanded hexaphyrins with a quantum interference close to the Fermi level, these triangular cyclic currents are also present in their local transmission plots (Figures S11S12). For non-symmetric expanded porphyrins, the two transmission paths are not equal in magnitude in contrast to


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Figure 12. Local transport contributions for the different hexaphyrin configurations at the Fermi energy. Selected bond lengths together with HOMA and torsional strain values for the different transmission paths are also shown. The diameter of the arrows represents the value of the local transmission for a pair of atoms, which are depicted only if they are at least 20% of the maximum local transmission.

28H-H. For antiaromatic 24P-H, besides the triangular cyclic currents, we observe that the current flows in opposite directions along the two arms of the macrocycle, reducing considerably the net transmission from contact to contact (Figure S11). Similar triangular cyclic currents at the contact positions are found for the three different π-conjugated topologies of heptaphyrins (Figure S12). In the last part, we have assessed the orbital selection rule proposed by Yoshizawa to rationalize the occurrence of quantum interference around the Fermi level for the different expanded porphyrins.57,58 This rule has been applied to predict electron transport properties of π-conjugated molecules, demonstrating that the phase and amplitude of HOMO and LUMO orbitals play an essential role in determining the transport properties in single-molecule devices. This rule, which was developed for alternant hydrocarbons, focuses on the zeroth order Green’s function 𝐺 ! !/! (𝐸), which is related to the transmission probability T(E) as follows: 𝑇 𝐸 ~𝐺

! !/! !

𝐸

(3)

When the contacts are connected to the molecule at sites a and b, this zeroth order Green’s function has the following form: ! !/!

𝐺!"

𝐸! =

∗ !!" !!! ! ! !! ±!" ! !

(4)

∗ where the summation runs over all molecular orbitals k, 𝐶!" and 𝐶!! are the kth orbital coefficients k at sites a and b, respectively, 𝜖! is the kth MO energy and 𝜂 is an infinitesimally small number. Exploiting the orbital symmetry for alternant hydrocarbons, only the amplitudes of HOMO and LUMO orbitals at the contact positions need to be considered to know whether the Green’s function (and thus the transmission probability) will be zero at the Fermi level. The contributions from the frontier orbitals can be written as follows: ! !/!

𝐺!"

𝐸! ≈

∗ !!!"#" !!!"#"

!! !!!"#" ±!"

+

∗ !!!"#$ !!!"#$

!! !!!"#$ ±!"

(5)

Since the signs of the denominators are different in Equation 5, the two terms will cancel each other out if the product of the orbital coefficients on the contact positions have the same sign for HOMO and LUMO orbitals, leading to a transmission probability of zero according to Equation 2 and thus, the occurrence of quantum interference at the Fermi level. For molecules that are not perfectly alternant, like expanded porphyrins, the orbital symmetry is not fully conserved. As a result, a perfect cancelation of the two terms in Equation 5

will not necessarily occur at the Fermi level and the terms corresponding to the other orbitals in Equation 4 can no longer be neglected in these cases. Nevertheless, when the orbital coefficients of HOMO and LUMO have the same sign at the contact positions, a cancellation will always occur somewhere in the window of interest, given that the denominators of the terms in Equation 4 become increasingly large as one approaches either the HOMO or LUMO energy.59 Depending on how well the orbitals of the system approximate the symmetrical situation of an alternant hydrocarbon, this cancellation can occur close to the Fermi level, generally leading to a broad dip in the transmission spectrum, or close to the peaks in the transmission spectrum corresponding to the HOMO and LUMO. In the latter case, the presence of the quantum interference will not influence the transmission probability at the Fermi level significantly. The HOMO and LUMO orbitals for the Hückel [26]hexaphyrin and [28]hexaphyrin are displayed in Figure 13. For a symmetric configuration of contacts at mesopositions 1 and 4, we observe that the the CaHOMO is different in sign from CaLUMO (CaHOMO ~ - CaLUMO) and hence, the sign of the product of the orbital coefficients at sites a and b in the HOMO orbital is different from the sign of the product of the orbital coefficients at sites a and b in the LUMO (C*bHOMO CaHOMO ≈ - C*bLUMO CaLUMO). As such, the contributions to transmission from HOMO and LUMO are constructive in 26H-H and no quantum interference is predicted based on the orbital rule for the 1-4 connection. By contrast, is the same as the sign of CaHOMO CaLUMO in 28H-H, so the contributions from HOMO and LUMO are cancelled, resulting in the transmission dip in this state. Furthermore, the large orbital amplitudes of the HOMO and LUMO in the selected contact positions of the hexaphyrin macrocycle further reinforce the suitability of the electrode-molecule-electrode configuration for switching purposes. From the molecular orbital plots, it is clear that the electron transport properties of expanded porphyrins will depend strongly on the route of connection to the gold electrodes. The connections 1-2 and 1-6 (Figure 13c), involving two consecutives meso-carbon bridges, are predicted to be symmetry-forbidden (i.e. containing a quantum interference in the window of interest and thus a reduced transmission probability around the Fermi level) in 26H-H in contrast to connections 1-3, 1-5 and 1-4. Among these symmetry allowed connections, 1-4 is predicted to be the best route for the metal-molecule-metal junction since the expansion coefficients at these contact positions are the largest. In the case of antiaromatic [28]hexaphyrin, the symmetry-allowed connec-


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tions for electron transmission are however 1-3 and 1-6 (Figure 13d).

Figure 13. HOMO and LUMO orbitals for the Hückel aromatic [26]hexaphyrin (a) and antiaromatic [28]hexaphyrin (b). Symmetry-allowed (red) and symmetry-forbidden (green) connections for electron transmission based on the orbital rule (c and d).

In order to verify the predictions for electron transmission based on the orbital model, the transmission spectra of Hückel [26] and [28]hexaphyrins with different connectivity to the gold electrodes were computed using NEGF combined with DFT calculations (Figure 14). Importantly, the obtained transmission spectra are fully consistent with the qualitative prediction based on the phase and amplitude of the frontier orbitals given above. For Hückel aromatic 26H-H, connections 1-4 and 1-5 do not show quantum interference between HOMO and LUMO in contrast to connection 1-6. As expected, connection 1-4 has the largest transmission probability at the Fermi level. For the antiaromatic 28H-H, the inverse situation is found, so the largest transmission probability corresponds to connection 16. This connection involving consecutive meso-positions is analogous to the single-molecule junction containing individual five-membered rings, for which it was experimentally found that aromaticity decreases conductance (Figure S13).18 Only for this particular connectivity, antiaromatic configurations are expected to show higher conductance than aromatic counterparts. Therefore, the relationship between aromaticity and conductance is more complex than initially envisaged and strongly depends on the connectivity of the molecule to the electrodes. Importantly, for all the different configurations of the single-molecule junctions based on Hückel hexaphyrins, the transmission function is highly dependent on the aromaticity of the π-electron system, so redox interconversions provide efficient conductance switches with high ON/OFF ratio. Similarly to hexaphyrins, the orbital selection rule explains successfully the occurrence of quantum interference for pentaphyrin and heptaphyrin devices (Figures S14-S16). Thus, the phase and amplitude of the frontier orbitals are very useful to rationally control electron transport properties in expanded porphyrins.

Figure 14. Transmission spectra for various connections of the [26] and [28]hexaphyrins with the gold electrodes. The solid and dashed lines indicate symmetry-allowed and symmetry-forbidden connections for electron transport according to the orbital rule.

In summary, our theoretical study underpins the potential of expanded porphyrins to act as efficient three-level molecular switches with high ON/OFF ratio upon redox and topology interconversions. To reliably form metal-molecule-metal junctions in experiments, the proposed single molecules are designed with ethylene spacers and thiol anchoring groups, which possess a high binding affinity to gold electrodes.60 Single-molecule junctions can be routinely formed using the scanning tunneling microscope or mechanically controlled break-junction method, both in vacuum and in solution.1,61 Appealingly, conductance switching has been experimentally measured in situ for molecular switches based on redox and (de)protonation reactions.5,62 On top of that, aromaticity switching in such molecular junctions has been reported at the single-molecule level using electrochemical control of the charge state of the molecule.19e On the basis of the recent experimental setup and taking into account that expanded porphyrins are able to switch their topology between Hückel and Möbius conformations in a controllable manner when external stimuli such as temperature and protonation or (de)protonation reactions are applied,9-11 molecular switches based on redox and topology changes should therefore be feasible.


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CONCLUSIONS The feasibility of conductance switches based on topology and/or aromaticity changes in expanded porphyrins has been assessed for the first time. Through electron transport calculations of Hückel and Möbius expanded porphyrins varying in oxidation state, we have demonstrated that the conductance strongly depends on the macrocyclic aromaticity and connectivity to the gold electrodes and, to a lesser extent, on the π-conjugation topology. When the electrodes are connected along the longitudinal axis of the macrocycle, we found that the single-molecule junction conductance is enhanced in aromatic Hückel penta- and hexaphyrins, whereas the antiaromatic Hückel counterparts exhibit a sharp reduction in transmission near the Fermi level due to the appearance of a destructive quantum interference between the HOMO and LUMO. As a consequence, redox-triggered aromaticity switches based on expanded porphyrins are proven to be efficient conductance switching elements, leading to much higher ON/OFF transmission ratios than experimentally realized tautomerization-based switches. Möbius aromatic conformations exhibit lowered transmission as compared with the Hückel aromatic state, which we attribute to the current flow avoiding the molecular twist. Our results reveal that the negative relationship between conductance and molecular aromaticity or polarizability does not hold for most of the configurations of the molecular junctions based on expanded porphyrins, which provide the optimum test bed for investigating the correlation between (anti)aromaticity and molecular properties. Eventually, the

transport properties of expanded porphyrins are successfully rationalized in terms of the orbital rule, demonstrating that the phase and amplitude of the HOMO and LUMO orbitals play a major role in determining the fundamental aspects of molecular conductance of πconjugated molecules.

ASSOCIATED CONTENT Supporting Information Relationships between aromaticity indices, ACID plots, molecular orbital diagrams, local transport contributions, orbital selection rule for pentaphyrins and heptaphyrins and B3LYP/631G(d,p)-optimized geometries. See DOI: 10.1039/x0xx00000x. The Supporting Information is available free of charge on the ACS Publications website.

AUTHOR INFORMATION Corresponding Author * [email protected]

ORCID Mercedes Alonso: 0000-0002-7076-2305 Author Contributions The manuscript was written through contributions of all authors. / All authors have given approval to the final version of the manuscript.

Funding Sources M. A. thanks the Fund for Scientific Research–Flanders (FWO12F4416N) for a postdoctoral fellowship and the Free University of Brussels (VUB) for financial support. F. D. P and P. G. wish to acknowledge the VUB for a Strategic Research Program. T.S. acknowledges the Research Foundation-Flanders (FWO) for a position as research assistant (11ZG615N).

Notes The authors declare no competing financial interest.

ABBREVIATIONS NLO, nonlinear optical; HOMA, harmonic oscillator model of aromaticity; NICS, nucleus-independent chemical shift; ACID, anisotropy of the induced current density; NEGF, nonequilibrium Green’s function; WBL, wide-band-limit; QI, quantum interference.

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(47) (a) M. Solà, M.; Feixas, F.; Jiménez-Halla, J. O. C.; Matito, E.; Poater, J., Symmetry 2010, 2, 1156. (b) Lazzeretti, P., Prog. Nucl. Magn. Reson. Spectrosc. 2000, 36, 1. (c) Lazzeretti, P., Phys. Chem. Chem. Phys. 2004, 6, 217. (d) Monaco, G,; Zanasi, R. J. Phys. Chem. A 2014 118, 1673. (48) (a) Heilbronner, E. Tetrahedron Lett. 1964, 5, 1923. (b) Rzepa, H. S. Chem. Rev. 2005, 105, 3697. (c) Herges, R. Chem. Rev. 2006, 106, 4820. (49) Toganoh, M.; Furuta, H. J. Org. Chem. 2010, 75, 8213. (50) (a) Nacci, C.; Ample, F.; Bleger, D.; Hecht, S.; Joachim, C.; Grill, L., Nat. Commun. 2015, 6, 7397. (b) Mazinani, S. K. S.; Meidanshahi, R. V.; Palma, J. L.; Tarakeshwar, P.; Hansen, T.; Ratner, M. A.; Mujica, V., J. Phys. Chem. C 2016, 120, 26054. (51) The degeneracy of the orbitals is not perfect. The energies of the HOMO-3, HOMO-2, HOMO-1 and HOMO orbitals of 32H-M are -5.95, -5.81, -4.88 and -4.80 eV, respectively. The respective energies of the LUMO, LUMO+1, LUMO+2 and LUMO+3 are -3.19, -3.10, -2.08 and -1.92 eV. Therefore, orbital energy differences lower than 0.2 eV are represented as degenerate orbitals in Figure 7. (52) Datta, S. Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, UK, 1997. (53) Solomon, G. C.; Andrews, D. Q.; Hansen, T.; Goldsmith, R. H.; Wasielewski, M. R.; Van Duyne, R. P.; Ratner, M. A., J. Chem. Phys. 2008, 129, 054701 (54) (a) Stuyver, T.; Fias, S.; De Proft, F.; Geerlings, P., Chem. Phys. Lett. 2015, 630, 51. (b) Stuyver, T.; Fias, S.; De Proft, F.; Fowler, P. W.; Geerlings, P., J. Chem. Phys. 2015, 142, 094103. (c) Stuyver, T.; Fias, S.; De Proft, F.; Geerlings, P., J. Phys. Chem. C 2015, 119, 26390. (55) (a) Tsuji, Y.; Movassagh, R.; Datta, S.; Hoffmann, R., ACS Nano 2015, 9, 11109. (b) Tsuji, Y.; Hoffmann, R., Chem. Eur. J. 2016, 22, 4878. (56) (a) Bröring, M., Angew. Chem. Int. Ed. 2011, 50, 2436. (b) Aihara, J.-i.; Nakagami, Y.; Sekine, R.; Makino, M., J. Phys. Chem. A 2012, 116, 11718. (57) (a) Yoshizawa, K.; Tada, T.; Staykov, A., J. Am. Chem. Soc. 2008, 130, 9406. (b) Yoshizawa, K., Acc. Chem. Res. 2012, 45, 1612. (c) Taniguchi, M.; Tsutsui, M.; Mogi, R.; Sugawara, T.; Tsuji, Y.; Yoshizawa, K.; Kawai, T., J. Am. Chem. Soc. 2011, 133, 11426. (58) A careful investigation on the performance of the different selection rules for the occurrence of quantum interference in expanded porphyrins is currently underway in our lab. (59) Li, X.; Staykov, A.; & Yoshizawa, K., Theor. Chem. Acc. 2011, 130, 765-774. (60) Leary, E.; La Rosa, A.; Gonzalez, M. T.; Rubio-Bollinger, G.; Agrait, N.; Martin, N., Chem. Soc. Rev. 2015, 44, 920. (61) Wang, L.; Wang, L.; Zhang, L.; Xiang, D., Top. Curr. Chem. 2017, 375, 61. (62) (a) Darwish, N.; Díez-Pérez, I.; Da Silva, P.; Tao, N.; Gooding, J. J.; Paddon-Row, M. N., Angew. Chem. Int. Ed. 2012, 51, 3203. (b) Baghernejad, M.; Zhao, X.; Baruël Ørnsø, K.; Füeg, M.; Moreno-García, P.; Rudnev, A. V.; Kaliginedi, V.; Vesztergom, S.; Huang, C.; Hong, W.; Broekmann, P.; Wandlowski, T.; Thygesen, K. S.; Bryce, M. R., J. Am. Chem. Soc. 2014, 136, 17922. (c) Li, Y.; Baghernejad, M.; Qusiy, A.-G.; Zsolt Manrique, D.; Zhang, G.; Hamill, J.; Fu, Y.; Broekmann, P.; Hong, W.; Wandlowski, T.; Zhang, D.; Lambert, C., Angew. Chem. Int. Ed. 2015, 54, 13586. (d) Li, L.; Lo, W.-Y.; Cai, Z.; Zhang, N.; Yu, L., Chem. Sci. 2016, 7, 3137. (e) Xiang, L.; Palma, J. L.; Li, Y.; Mujica, V.; Ratner, M. A.; Tao, N., Nat. Commun. 2017, 8, 14471.


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Figure 1. Schematic representation of different π-conjugation topologies of expanded porphyrins and the corresponding aromaticity. 210x73mm (300 x 300 DPI)


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H N

N H E X A

NH

N R

R N

N

NH R N H

26H-H

28H-H

N

R 2e-,

N

N

N

HN

NH N

N

N H

HN

NH

NH

N

R

NH

N

N

N H

N HN

N

N

H N N

NH

R R

HN

N

R

N H

N H

32H-H

32H-M

32H-F

NH

R 24P-M

24P-H

R

N

NH

R

22P-H

R

R

N

NH

HN 28H-M

NH

HN

R

N

N

N

2H+

R

H E P T A

R

HN

N

HN

NH

R

N

HN

R P E N T A

2e-, 2H+

H N

aromatic weakly aromatic

R:

C C

antiaromatic


SH


Figure 3. Orientation of the figure-eight structure of 32H-F used for the calculation of the NICS-based indices. The magnetic field is oriented along the z axis. 29x7mm (300 x 300 DPI)


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Figure 4. Structures of the molecular junctions for Hückel [22] N-fused pentaphyrin (a), Hückel [26]hexaphyrin (b) and Hückel [32]heptaphyrin (c).

139x163mm (300 x 300 DPI)



Figure 5. ACID plots of [26] and [28]hexaphyrins. Isosurfaces and current density vectors are displayed together with the NICS(0) and NICSzz(1) values for each configuration. The large arrow denotes the direction of the induced ring current: clockwise for diatropic ring currents and anticlockwise for paratropic ring currents. 170x99mm (300 x 300 DPI)


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Figure 6. Variation of the static molecular polarizability (a) and the HOMO-LUMO energy gap (b) with respect to the macrocycle size. The aromaticity of each structure is indicated by the dot color. 119x168mm (300 x 300 DPI)



Figure 7. Schematic diagrams for molecular orbitals of the different π-conjugation topologies of [32]heptaphyrin.51 145x80mm (300 x 300 DPI)


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Figure 8. Transmission spectra for Hückel and Möbius topologies of N-fused pentaphyrins. Red lines are linked to aromatic structures, whereas green lines to antiaromatic configurations. 71x43mm (300 x 300 DPI)



Figure 9. Transmission spectra for Hückel and Möbius topologies of [26] and [28]hexaphyrins. Red lines are linked to aromatic struc-tures whereas green lines to antiaromatic configurations. Dashed and solid lines correspond to the transmission function of Möbius and Hückel topologies, respectively. 140x90mm (300 x 300 DPI)


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Figure 10. Dependence of the transmission function of [32]heptaphyrin with the π-conjugation topology. Red lines are linked to aromatic structures whereas green lines to antiaromatic configurations. 124x90mm (300 x 300 DPI)



Figure 11. Transmission spectra for the two tautomers involved in the molecular switch for the Hückel [22] N-fused pentaphyrin (a) and [26]hexaphyrin (b). Red lines are linked to aromatic structures. 175x209mm (300 x 300 DPI)


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Figure 12. Local transport contributions for the different hexaphyrin configurations at the Fermi energy. Selected bond lengths together with HOMA and torsional strain values for the different transmission paths are also shown. The diameter of the arrows represents the value of the local transmission for a pair of atoms, which are depicted only if they are at least 20% of the maximum local transmission. 299x70mm (300 x 300 DPI)



Figure 13. HOMO and LUMO orbitals for the Hückel aromatic [26]hexaphyrin (a) and antiaromatic [28]hexaphyrin (b). Sym-metry-allowed (red) and symmetry-forbidden (green) connections for electron transmission based on the orbital rule (c and d). 119x119mm (300 x 300 DPI)


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Figure 14. Transmission spectra for various connections of the [26] and [28]hexaphyrins with the gold electrodes. The solid and dashed lines indicate symmetry-allowed and symmetry-forbidden connections for electron transport according to the orbital rule. 119x189mm (300 x 300 DPI)


Conductance Switching in Expanded Porphyrins through Aromaticity

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