First-Principles Calculations of Electron Transport through Azulene

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First-Principals Calculations of Electron Transport Through Azulene Ahmed M. El-Nahas, Aleksandar Staykov, and Kazunari Yoshizawa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00767 • Publication Date (Web): 08 Apr 2016 Downloaded from http://pubs.acs.org on April 9, 2016

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The Journal of Physical Chemistry

First-Principals Calculations of Electron Transport through Azulene Ahmed M. El-Nahas,*,1,2 Aleksandar Staykov,3 and Kazunari Yoshizawa,*,2,3

1

Chemistry Department, Faculty of Science, El-Menoufia University, Shebin El-Kom 32512, Egypt. 2

Institute for Materials Chemistry and Engineering, Kyushu University, Nishi-ku, Fukuoka, 8190395 Japan. 3

International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Nishi-ku, Fukuoka, 819-0395 Japan.

Abstract: Electron transport through azulene, a nonalternant hydrocarbon, has been investigated using non-equilibrium Green’s function approach combined with density functional theory (NEGF-DFT). I-V characteristics of azuluene wired from different positions between two gold electrodes have been calculated. The results indicated that current strength correlates with orbitals amplitudes. Out of nine investigated azulene dithiolates, four molecular junctions (1,3-, 1,5-, 2,6-, and 4,7-connections) show high current compared to only one position from naphthalene dithiolate (1,4-). A current rectification ratio of ca. 4 was found in case 2,7-azulene dithiolate. The remaining connections give low to moderate current. Aromaticity and ability of different connections to form quinoinod structure were used to explain electrical conductivity of the studied molecular junctions. The data were interpreted in terms of transmission spectra and molecular projected self-Hamiltonian (MPSH) eigenstates. Orbital symmetry rule and quantum interference have also been discussed.

Keywords: Azulene, Nonalternant hydrocarbon, Electron transport, Orbital rule, NEGF-DFT.

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1. Introduction The last four decades witnessed a great progress in the field of molecular electronics since the first theoretical prediction of single molecular diodes by Aviram and Ratner in 19741 and experimental verification of their findings almost twenty years later.2 The development of sophisticated experimental techniques such as mechanically controlable break junction3 and scanning tunneling microscopy4 enabled measuring conductance of single molecules with high accuracy. Also, theoretical studies proved their value in supporting, interpreting experiments as well as in predicting new rules that control charge transport and functionalities of molecular systems.5-7 Most of molecules used in molecular electronic devices are conjugated molecules which belong to alternant hydrocarbons.6-19 However, a limited number of experimental and theoretical investigations have dealt with some nonalternant hydrocarbons.20-23 Azulene, a nonalternant hydrocarbon (HC), differs greatly from its alternant isomer, naphthalene;24 for example azulene is blue while naphthalene is a white compound.20 A given conjugated system is said to be alternant if its atoms can be divided into two sets, starred and unstarred, in a way that no two atoms of the same set are directly connected, see Chart 1.25 The pairing theorem based on the Hȕckel level of theory no longer holds true in the nonalternant HCs. The distribution of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) can explain different chemical and physical properties of the two molecules. In azulene, the HOMO has large amplitude at positions 1, 3, 5, and 7 whereas the LUMO has the significant amplitude at positions 2, 4, 6, and 8; see Chart 1.26

* 7 8

*

*

6

8

7 6

2 5

4

* Nonalternant

*

*

1 3

*

*

5

1

*

Alternant

4

2 3

* HOMO

LUMO

Chart 1 Electron transport through π-conjugated molecules can, in some cases, be suppressed by destructive quantum interference (DQI).27-29 A simple atom-counting model was suggested to predict the existence of this effect in single-molecule junctions.30,31 Very recently, 1,3-, 5,7-, 4,72 ACS Paragon Plus Environment

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, and 2,6-disubstituted azulenes have been investigated experimentally and theoretically for electron transport.20 Xia et al. reported that the atom-counting graphical rule for quantum interference may not be applicable to non-alternant hydrocarbons.20 The current pass through the 2,6- connection of azulene was found to be higher than that through the same connection in naphthalene21,22 with a slight current rectification in azulene. Current rectification through the 2,6-wiring was also reported previously for azulene-like molecules with a rectification ratio (RR) of ~2.23 Electrical conductivity of naphthalene dithiolates16,17 was discussed in terms of molecular orbital symmetry for alternant hydrocarbons.32-34 The orbital rule was recently applied to interesting conductance switching systems.18 The rule also has been examined for polycyclic aromatic hydrocarbons with different molecular sizes and edge type structures.19 It is worthy to extend the orbital rule to nonalternant hydrocarbons such as azulene. Availability of experimental charge transport studies and existence of diode-like behavior of azulene make this molecule of interest for further study. All previous studies of conductivity of azulenes considered only the 1,3-, 2,6-, 4,7- ad 5,7-poistions for wiring azulene between two electrodes although other positions can show different I-V behavior. In the present work, we investigate current pass through azulene when wired from different positions between two semi-infinite gold electrodes. Orbital symmetry and quantum interference rules are also considered.

2. Methods and Computational Procedures: By using Gaussian 09 program,35 geometry optimizations of azulenes and azulene dithiols were performed with the hybrid B3LYP functional36-38 and 6-31G(d,p) basis set.39 To study electron transport characteristics of azulene, each optimized structure was wired between two Au(1 1 1)-(4x4) electrode surfaces through thiol anchors without hydrogen atoms, see Figure 1. The Au-azulene-Au junction is composed of the left electrode, the central molecular region, and the right electrode. The central region includes three layers from each electrode. The adsorption site of the sulfur atoms in the azulenes is set to be the face centered cube threefold hollow site, whose adsorption structure was determined by reference to the literature.40



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Figure 1. 1,3- and 2,6-Azulene dithiolate molecular junctions.

The current (I) is calculated through two-probe system as a function of steadily increasing bias in both directions from -2.0 to +2.0 V and the transmission spectra were calculated in the region -2 to +2 eV with respect to the Fermi energy. Molecular Projected Selfconsistent-Hamiltonian (MPSH) analysis is carried out to aid in the interpretation of the electron transport through azulene. The MPSH states represent the eigenstates of the molecule in the presence of electrodes. The non-equilibrium Green’s function (NEGF) combined with exchange correlation DFT functional41 (LDA/PZ, the local density approximation with the Perdew–Zunger parameterization)42 were used to compute the current as implemented in the Atomistix ToolKit computer code (ATK 11.2.3).43 Single-zeta (SZ) was used for gold and double-zeta (DZ) basis set for other elements. The current through molecular junction is calculated from the Landauer-Buttiker formula44,45

I(V) =

, 1

where T(E,V) is the transmission probability, f is the Fermi function, µL/R are the electrochemical potential of the left/right electrodes and the difference between them is given by eV with the applied bias voltage V, i.e., µL = µ(0) –eV/2 and µR = µ(0) + eV/2. The µR/L(0)=EF is the Fermi energy. This µL - µR energy region is called bias window. The transmission coefficients are calculated from the following equation: T(E,V) = Tr [ГL (E,V)GR(E,V) ГR (E,V)GA(E,V)] 4 ACS Paragon Plus Environment

(2)

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where ГL/R are the coupling functions associated with the L/R electrodes and GR/A are the retarded and advanced Green’s functions of the system.

3. Results and Discussion Figure 2 presents the computed I-V characteristics of seven azulene dithiolates wired from different positions between two gold electrodes. Plots of other two connections are given in the Supporting Information. As depicted in Figure 2, when we consider low (±1 V) or high bias (±2 V) voltages, two categories were observed for the I-V properties of azulene dithiolate junctions: the 1,3-, 1,5-, 2,6-, and 4,7- connections illustrate high symmetric current of 28~39 µA (at 2 V), while the 1,4-, 1,6-, 4,8-, and 5,7-connections show low to moderate current of 6~17 µA. However, the 2,7-junction exhibits a diode-like behavior with a rectification ratio (RR) of 4 at 2 V. Current rectification from the 2,6-position is modest (RR = 1.2 at 1.4 V). In the rest of the paper, we will discuss the I-V properties at the high voltage region. High and low current in these molecular junctions can be explained in terms of HOMO and LUMO amplitudes.46 In azulene, the 1,3 carbon atoms have the largest HOMO magnitudes followed by the 5,7 atoms, as shown in Chart 1. Minor HOMO coefficients are found at the 4, 8 atoms. This is based on a previous work that related conductance to orbital densities.46 High current was obtained from four connections of azulene (1,3-, 1,5-, 2,6-, and 4,7-) compared to only one connection in its isoelectronic naphthalene (1,4-, see Chart 1) as will be clarified later. Therefore, a new position (1,5-) in azulene is predicted to give high current similar to that found previously for the 1,3-, 4,7-, and 2,6-connections.20-23 The 1,4-,1,6-, and 4,8-azulene dithiolates show low current while 5,7connection passes moderate current and the 2,7-azulene dithiolate behaves as a diode. The strength of current can also be interpreted in terms of the ability of the sandwiched molecule to acquire quinonoid-like structure that extends conjugation to the electrodes. Connections such as 1,5-, 2,6- and 4,7- that can form quinonoid structure with the anchors give high current. These junctions also show no destructive quantum interference (DQI) according to the graphical model.30,31 This observation holds true for 1,4-benzene dithiolate and 1,4-, 1,5- and 2,6-naphthalene dithiolates, but not for the 1,3-connection in these benzenoid structures, see Chart 1. However, cases such as 1,4- and 1,6-azulene dithiolates which can form quinonoid structures but exhibit destructive interference show weak current. In these latter systems the 5 ACS Paragon Plus Environment


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formation of quinonoid structure is accompanied by a cross-conjugation in the connection path as presented in Chart 2. This might explain the attenuation of the current in these cases. Connections that cannot form a quinonoid structure and have DQI, such as 4,8- and 2,7-azulene dithiolates, illustrate either asymmetric or weak current. This explanation is supported by recent experiment which indicated that junctions able to form quinone-like structure give better conductivity.12 Breslow and his collaborators also found that the conductance correlates negatively with aromaticity.12 In the quinonoid structure coupling between the molecular junction and the electrode is enhanced. Conductivity of azulene dithiolates that show either DQI or unable to form quinonoid structure can be improved by inserting oxo group at particular positions as will be discussed later. The 1,3- and 5,7-azulene dithiolate molecular junctions exhibit high and moderate current whereas 1,3-benzene dithiolate gives weak current. This can be understood from the relation between conductance and aromaticity where the latter increases molecular resistance.36 Calculation of the nucleus-independent chemical shift (NICS), a measure of aromaticity and ring current, could help in this respect.47 The NICS values for the two rings of azuelene indicate that the five-membered ring is less aromatic than the 7-membered ring (NICS = -9.9, -7.0, and -19.7 for benzene, heptagon, and pentagon rings, respectively). Therefore, high current is produced from the 1,3-conection in the five-membered ring of azulene compared to the 5,7-azulene and 1,3-benzene dithiolates. Transmission spectra are used to explain the I-V characteristics of the investigated azulene molecular junctions. The transmission spectra within the bias window will be analyzed. Applying a certain bias shifts either occupied and/or unoccupied molecular orbitals close to the Fermi level, and therefore these orbitals become the dominant channels for electron transport through molecule. Transmission spectra show the peaks related to these orbitals that are located near the Fermi energy. The transmission spectra of the studied azulenes at different bias voltages are given in Figure 3. For the 1,3-azulene dithiolate junction, with increasing bias to 1 V the tail of the first peak under the Fermi level enters the bias window and fully gets into in the bias window at 2 V with almost half of the first peak above the Fermi energy. These two peaks could be related to HOMO and LUMO+1 resonances, respectively, as will be explained in the next section. For 2,6-azulene dithiolate, the peak located in the bias window under the Fermi level at ±2 V is attributed to HOMO eigenstate which is fully delocalized over this molecular junction 6 ACS Paragon Plus Environment

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a) ±2 V

b) ±1 V

50

1,3-azulenedithiol 1,5-azulenedithiol 2,6-azulenedithiol 2,7-azulenedithiol 4,7-azulenedithiol 4,8-azulenedithiol 5,7-azulenedithiol

40 30 20 10

12 9 6

0 -10 -20

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-30

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-50 -2

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1,3-azulenedithiol 1,5-azulenedithiol 2,6-azulenedithiol 2,7-azulenedithiol 4,7-azulenedithiol 4,8-azulenedithiol 5,7-azulenedithiol

3

Current (µA)

Current (µA)

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1

2

Bias (V)

-15 -1.5

-1.0

-0.5

0.0

Bias (V)

Figure 2. I-V characteristics of azulene dithiolates.


0.5

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(see Figure 4). A considerable size of the tail of the LUMO peak is also observed in the bias window. Moreover, clear broadening of the peaks indicates strong coupling with the electrodes. S

S

8

7 S

2

6 5

4

3

8

7

1

1 2

6 5

3 4

S

Chart 2

Analysis of the MPSH states helps in relating the transmission spectra of the azulene dithiolates to molecular orbitals. Only MPSH states that are delocalized over the entire molecular junction will appear in the transmission spectra and contribute to current. Figure 4 collects MPSH orbitals of the 1,3-, 2,6-, 4,8- and 2,7-junctions at ±1 V. MPSH eigenstates of other molecular junctions at bias voltages from -2 to 2V are given in the Supporting Information. An inspection at MPSH orbitals indicates that HOMO, HOMO-1, and LUMO+1 are delocalized over the whole 1,3-azulene dithiolate molecular junction including the anchors and surface atoms of the electrodes and, hence, a good chance electron transport is expected. For the 4,8-connection the LUMO and LUMO+1 levels are delocalized over the whole molecular junction at all bias voltages. However, HOMO and HOMO-1 orbitals are delocalized only at certain voltages. In the bias window of the transmission spectra, only a small peak appears below the Fermi level which could be attributed to HOMO and HOMO-1 resonances at ±1 and ±2 V, respectively. This small peak in the bias window reflects week current in case of 4,8-azulene dithiolate. For 2,7-azulene dithiolate the peak under the Fermi level is related to HOMO-1 and that above the Fermi level to LUMO. Azulene is a polar molecule with the 7-membered ring being an electron deficient ring while the pentagon ring is an electron rich center which could allow electron availability in the latter compared to the former ring.48,49 In an attempt to rationalize the difference in current when wiring across the 7- and 5-membered rings or across the molecule, we have calculated the I-V behavior of the separated heptagon and pentagon rings with an exo methylene group (=CH2) to simulate the architecture of the azulene molecule, see the Supporting Information. The current obtained from the parent azulene dithiolates and their relevant components are illustrated in


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Figure 5. An inspection of Figure 5 indicates that the existence of exo methylene group gives similar I-V curves but lower than that found in the parent molecule. This indicates the importance of the extended conjugation from the neighboring ring. Nevertheless high degree of conjugation does not guarantee good conductance based on the tunneling mechanism of electron transport where the latter decay exponentially with distance.50

1,3-azulene dithiolate


1.4 1.0

0V 1V -1 V 2V -2 V

1.2

Transmission coefficient


0.8

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0V 1V -1 V 2V -2 V

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Figure 3. Transmission spectra of azulene dithiolates at different bias voltages, bias window is represented by blue rectangle.



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1,3-azulenedithiolate HOMO-1 1V

HOMO

LUMO

LUMO+1

LUMO

LUMO+1

-1V

2,6- azulenedithiolate HOMO-1 1V

HOMO

-1V

Figure 4. MPSH states of azulene dithiolates at ±1 V.


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HOMO

LUMO

LUMO+1

HOMO

LUMO

LUMO+1

-1V


-1V

Figure 4. Continued.

Modeling the 4,7- connection with exo-methylne-heptagon shows a very weak current due to the cross-conjugation effect, see Chart 3. However, in 4,7-azulene dithiolate the current is ten times higher than the model due to the removal of cross-conjugation and extending linearconjugation. The behavior here matches the situation when we compare 1,6-hexatriene dithiolate 11 ACS Paragon Plus Environment


with the cross conjugated 1,5-pendaiene dithiolate.51 In the former case the current is decreased from 32 to 4 µA compared to reduction in the current in the latter case from 39 to 2 µA based on the NEGF-DFT calculations at the same level. Other connections of the azulene partitioning scheme have no such cross-conjugated methylene group in the wiring pathways. The situation in the 4,8- and 5,7-like structures could be simulated by calculating the I-V curves of 1,3,5hexatriene-1,5-dithioate and 1,3,5-hexatriene-1,3-dithioate, respectively, see the supporting information. The current from these acyclic systems is slightly higher than the cyclic heptagon but holds the same I-V feature.

1,3-azulene dithiolate Pentagon-1,3-dithiol-CH2-cross

4,7-azulene dithiolate Heptagon-4,7-dithiol-CH2-corss

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0

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Figure 5. I-V curves of azulene dithiolates and their components.


1

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S

S

S

S

S

S

1,3-like structure

4,7-like structure

S

S

4,8-like structure S

S

S

1,3,5-Hexatriene-1,3-dithiolate

S

3-Methylene-1,4-pendaiene-1,5dithiolate

1,3,5-Hexatriene-1,5dithiolate

S S

1,3,5-Hexatriene-1,6-dithiolate Chart 3

Orbital Rule and Quantum Interference

/

The matrix elements of the zeroth Green's function,

, for the molecular part at the

Fermi level, are written as follows:

/

∗ = 3

" ±

%$where Crk is the kth molecular orbital (MO) coefficient at site r, εk is the kth MO energy, and τ is an infinitesimal number determined by a relationship between the local density of states and the /

imaginary part of Green's function.

describes the propagation of a tunneling electron

from site r to site s through the orbitals in a molecular part. Eq 3 shows the correlation between

the MOs and Green's function. The amplitude and phase of the molecular orbitals close to the Fermi energy are essential parameters in this respect. The role of the HOMO and LUMO is 13 ACS Paragon Plus Environment


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significant in the zeroth Green's function because the denominators of the two orbitals are small compared to those of other MOs under the assumption that the Fermi level is located at the midpoint between the HOMO and LUMO. Based on eq 3, a given connection can conduct current if the two terms of HOMO and LUMO add to each other and does not conduct if one term cancels the other. Distribution of the amplitudes of the frontier molecular orbitals (FMO) for azulene and naphthalene along with the symmetry-allowed connections are given in Figure 6. A schematic representation of the simple graphical model for quantum interference for six azulene dithiolates is illustrated in Figure 7. More models are given in the Supporting Information. This graphical model is constructed based on the possibility of connecting the wired sites by a continuous path while pairing up the other remaining sites.30,31 If odd sites still exist, this indicates the presence of destructive quantum interference. The odd atoms are designated in Figure 7 by circles. Wiring of naphthalene from every possible positions follows the orbital rule for qualitative prediction of conductivity.16,17 For 1,3-azuelene dithiolate, applying eq. 3 on the first HOMO and LUMO indicates a symmetry-allowed connection which could be explained as follows: LUMO has no orbital amplitude at the 1,3 carbon atoms and therefore, no contribution to conductivity. HOMO1 and LUMO+1 add to each other as the product of C1 and C3 coefficients are of different signs, see the Supporting Information. Consequently the HOMO has the major contribution; it is delocalized over the whole molecular junction as shown in Figure 4. It remains delocalized at all applied voltages as given in the Supporting Information. The connection 2,6- is also symmetryallowed as the amplitudes on the 2,6 carbon atoms of LUMO and HOMO-1 are large whereas the corresponding HOMO and LUMO+1coefficients are zero. The LUMO and HOMO are delocalized over the entire 2,6-azulene dithiolate at all bias voltages used in this study. By the same way, connections 4,7- and 1,5- are symmetry allowed. These findings agree with NEGFDFT calculations. The zero-Green’s function shows that the connections 1,5-, 2,6- and 4,7- are symmetry-allowed and the graphical model shows no destructive quantum interference.30 This was supported by NEGF-DFT computations which illustrate good current from these molecular junctions, see Figure 2 and the Supporting Information. Wiring azulene through the 5,7- positions gives also symmetry-allowed connection which agrees with the NEGF-DFT calculations. The simple graphical interference rule failed to account for the I-V behavior in this junction as well. The contradiction between conductance and the 14 ACS Paragon Plus Environment

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graphical model in the 1,3- and 5,7- connections has been reported recently by Xia et al.20 where they observed high current from connections that show destructive interference and concluded that the aforementioned simple graphical model cannot be applied to nonalternant systems due to the absence of symmetry around the Fermi level. They proved this breakdown of the quantum interference rules by calculating transmission spectra of these molecular junctions. Their calculations illustrated destructive interference features far away from the Fermi level. However, current suppression occurs at higher bias than expected from the atom-counting rule. They attributed this finding to the asymmetric energy level of the frontier molecular orbitals of azulene. Conductivity of some azulene dithiolates that show either DQI or unable to form quinonoid structure can be improved by inserting oxo group at particular positions such as positions 1,4 in 2,7-azulene dithioate and 1,5 and 1,7 in 4,8-azulene dithiolate where the current increases by ca. 18-30 µA, see Figure 7. Adding such oxo group removes DQI.

4. Conclusions In this study, we have investigated electron transport through azulene dithiolates wired from nine different positions between two gold electrodes using non-equilibrium Green’s function approach combined with density functional theory (NEGF-DFT). The results indicated that high current is obtained from four connections (1,3-, 1,5-, 2,6-, and 4,7-) compared to only one connection in naphthalene (1,4-). However, 2,7-azulene dithiolate shows a diode-like behavior (RR = 4 at 2 V). The remaining connections give low to moderate current. Aromaticity and ability of different connections to form quinoinod structure could be helpful in explaining different conductivity of molecular junctions. Applying orbital rule for predicting conductivity of azulene reveals validity of the rule for non-alternant hydrocarbons. However, the simple graphical model for quantum interference should be used with care when dealing with nonalternant hydrocarbons.



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2

LUMO

HOMO

Symmetry-allowed connections.

Symmetry-allowed connections.

Symmetry-forbidden connections.

Symmetry-forbidden connections.

Figure 6 . Distribution of amplitudes of frontier molecular orbitals (FMO) for naphthalene and azulene. S

S

S

S

S

S

-35.0 ↔ 35.0 µA

-38.6 ↔ 35.7 µA

-41.0 ↔ 10.1 µA

S

S

S

S

S S

-32.8 ↔ 28.0 µA

-11.3 ↔ 11.8 µA

S

S O

O

O

-17.5 ↔ 16.6 µA O

S

S

O

O S

S

-28.5 ↔ 36.9 µA

-41.1 ↔ 44.0 µA

-50.7 ↔ 58.1 µA

Figure 7. Schematic representation of the graphical model for quantum interference, current at 2 and 2 V is also given.


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Author Information Corresponding Author Ahmed M. El-Nahas. Phone +2-1064607974. E-Mail: [email protected] Kazunari Yoshizawa. Phone +81-92-802-2529 E-Mail: [email protected]

Acknowledgments KY thanks Grant-in-Aid for Scientific Research (Nos. 24109014 and 15K13710) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education of Education, Culture, Sports, Science, and Technology of Japan (MEXT) and the MEXT Projects of “Integrated Research on Chemical Synthesis” and “Elements Strategy Initiative to Form Core Research Center”. AME-N thanks Kyushu University for nice hospitality during his stay as visiting professor. AS would like to thank World Premier International Research Center Initiative (WPI), Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT), Japan.

Associated Content Supporting Information. Models of partitioning of azulene dithiolates, amplitudes and phases for 10 π molecular orbitals of azulene, I-V curves of azulene and naphthalne dithiolates, detailed transmission spectra for azuelene dithiolates from DFT-NEGF calculations, energy gap, MPSH states for azulene dithiolates at different bias voltages from NEGF-DFT calculations, schematic representation of graphical model for quantum interference in azulene dithiolates, and detailed reference 24. This material is available free of charge via the Internet.

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Graphical Abstract

First-Principals Calculations of Electron Transport through Azulene

50 40 30 20

Current (µΑ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10 0 -10

1,3-Azulene dithiolate 2,7-Azulene dithiolate 4,8-Azulene dithiolate

-20 -30 -40 -50 -2

-1

0

1

2

Bias (v)


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First-Principles Calculations of Electron Transport through Azulene

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