Utilizing Two-dimensional Transition-Metal Dichalcogenides As

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C: Energy Conversion and Storage; Energy and Charge Transport

Controlling Band Alignment In Molecular Junctions: Utilizing Two-Dimensional Transition-Metal Dichalcogenides As Electrodes For Thermoelectric Devices Chengjun Jin, and Gemma C. Solomon J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00464 • Publication Date (Web): 30 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry

Controlling Band Alignment In Molecular Junctions: Utilizing Two-dimensional Transition-Metal Dichalcogenides As Electrodes For Thermoelectric Devices Chengjun Jin and Gemma C. Solomon∗ Nano-Science Center and Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark E-mail: [email protected]

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The Journal of Physical Chemistry 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

Abstract While chemical space is vast, there are many instances where chemical modifications make only insignificant changes to the current that can pass through a molecule. This insensitivity comes, in part, from the energy mismatch between molecular resonances and the Fermi level of the electrodes used. Here we present a strategy to overcome this problem by employing two-dimensional transition-metal dichalcogenides as electrodes. The work function of the electrodes can be tuned across the entire molecular energy range (from the highest occupied molecular orbital to the lowest unoccupied molecular orbital) at low bias with the appropriate choice of electrode material. We illustrate the effectiveness of this strategy by investigating the thermoelectric properties of the junctions with a model molecular system, as optimal thermoelectric performance requires a delicate balance between the electronic and heat transport properties. By using Van der Waals contacts between the binding groups and the electrodes, similar to the binding groups used in graphene junctions, we find that we can effectively suppress the phonon contribution to the heat transport while achieving high levels of electron transport and thermopower as the molecular level is tuned into near-resonance.

Introduction A long standing problem for the field of molecular electronics is the question of band-lineup or the alignment of the electrode Fermi energy and the molecular energy levels of interest. 1–7 This problem has captured the attention of chemists and physicists alike as it goes to the heart of understanding molecular electronic structure in the non-traditional environment of a single molecule bound between conducting electrodes and ensuring that the electronic functionality of interest is accessible in the experimentally relevant energy/bias range. One aspect of the problem is the treatment of the electronic structure, and considerable effort has been expended in developing more sophisticated electronic structure methods, such as GW 4,6 for transport applications. The other relates to the inherent mismatch between most

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molecular resonances (where molecular conductance generally becomes more significant and chemical effects more pronounced) and the Fermi energy of the (usually gold) electrodes. While there has been some hope that gating of molecular energy levels might be able to address this issue by tuning the molecule into resonance, this solution has proven to be at best challenging and at worst totally impractical. 8,9 In this paper, we propose that alternative electrode materials will allow the band-lineup to be tuned across the experimentally relevant energy range at low bias. The range of electrode materials that have been employed to date is limited, with most effort focussing on metals (generally gold) 10,11 and some exploration of graphene. 12–16 Here we employ electrode materials that can effectively tune the band-lineup: two-dimensional transition-metal dichalcogenides (TMDs). We hypothesize that the combination of tunable band-lineup and a π-stacked molecular junction will offer significant scope for optimizing the properties of the system and test this with an application to molecular thermoelectrics as the delicate balance required between the electronic and heat transport properties makes this problem particularly challenging.

Molecular thermoelectrics - background A single molecule connected between two metallic electrodes has been proposed as a device for achieving a high figure of merit ZT. 17–20 ZT is defined as S 2 GT /κtotal , which comprises the temperature T, the thermopower S, the electronic conductance G and the thermal conductance κtotal = κel + κph , the sum of the electronic and phononic contributions. Strategies to find devices with ZT > 1, which are considered to be good thermoelectrics, 21 either suppress the thermal conductance κtotal or enhance the power factor S 2 G, or both. In molecular junctions, the typical thermopower S is around 10 µV/K, where S > 150 µV/K is considered for practical applications, 22,23 with an exceptionally high thermopower of 300 µV/K and high ZT of 4 predicted in the edge-over-edge zinc-porphyrin molecular wires. 24 In molecular thermoelectric devices, the phonon propagation needs to be suppressed due 3



to the reduced dimensionality 25,26 or S 2 G needs to be enhanced due to the tunability of the energy level alignment at the molecule/metal interfaces. However it has been difficult to simultaneously control these two factors due to the correlation between the electronic and phononic properties. 27 π-stacked molecular junctions show significant phonon suppression as very few phonon modes can propagate across the non-bonded interface 28,29 and the ZT in such systems can be further improved if the electronic thermal conductance is reduced. 29 We note here that while the prior work on π-stacked molecular junctions for thermoelectrics is theoretical in nature, the geometries employed in that work and this present study are modeled on the structures hypothesized to exist in π-stacked junctions with graphene electrodes. 12,16

A strategy to tune band-lineup

Figure 1: An outline of the strategy employed in this paper. (a) The atomistic structure of the MoX2 (X= O, S, Se, Te) molecular junction. A six-carbon alkyne chain molecule is attached to two semi-infinite MoX2 electrodes via the Van der Waals forces. The chemical drawing of the molecule is shown below. Thermoelectric figure of merit can be improved by (b) a resonant shift in the electronic transmission function (from solid line to dashed line) to increase the power factor and (c) a suppression of the phononic transmission function (from solid line to dashed line). Figure 1 outlines the basic strategy proposed in this work to bring electronic features of interest into the low bias window. A model molecular system (a six-carbon alkyne chain) is connected to the two-dimensional TMDs electrodes via the Van der Waals interactions with anthracene linker groups, as shown in the Fig. 1 (a). The non-bonded contact provides 4


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excellent electrical contact while at the same time being problematic for heat transport, making it possible to simultaneously enhance of the power factor S 2 G and the suppress of the thermal conductance κtotal . On one hand, the energy level alignment at the molecule/metal interfaces can be tuned by utilizing different metallic TMD materials with different work functions, as illustrated in Fig. 1 (b). On the other hand, due to the non-bonding nature at the molecule/metal interfaces, the heat transport is significantly blocked, as illustrated in Fig. 1 (c). Consequently, we find that molecular junctions utilizing certain metallic TMDs can allow ZT to be tuned across a significant range, in this case between almost 0 and 1.2 at room temperature, without any optimization of the molecular component (beyond the choice of a non-bonded system). More specifically, we have not fully optimized the system in terms of the values of S, G and κel in the energy window accessible with the TMDs.

Computational methods The junction structures are optimized until the forces are smaller than 0.02 eV/˚ A using density functional theory (DFT) with the Van der Waals exchange correlational functional 2 (vdW-DF2), 30 as implemented in the GPAW electronic structure code. 31 This gives the binding distances of ∼ 3.4 ˚ A for all the junctions, in agreement with the case of graphene. 32 The wave functions are sampled on a real space grid for optimizations. Double ζ polarized basis sets and PBE xc-functional are employed in the electronic transport calculations. The electronic transport calculations are performed with the Green’s function approach as implemented in the GPAW. 33 The electronic transmission function is calculated from the Landauer formula 34,35

Tel (E) = Tr[G(E)ΓL (E)G† (E)ΓR (E)],

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(1)


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where the retarded Green’s function is obtained from −1 G(E) = ES − H − ΣL/R (E) .

(2)

Here S and H denote the overlap matrix and the Kohn-Sham (KS) Hamiltonian matrix in the atomic orbital basis, 36 respectively. ΓL/R = i[ΣL/R − Σ†L/R ] accounts for the level broadening due to the electrode coupling, where ΣL/R denotes the retarded lead self-energy of the left/right electrodes. The phononic transport calculations are performed in the Atomistix ToolKit version 2015.1, QuantumWise A/S. 37–39 Double ζ polarized basis sets and PBE xc-functional are employed in the phononic transport calculations. The phononic transmission function Tph (ω) can be calculated from Eq. 1 with the substitution H → K and S → ω 2 M, where K and M denote the force constant matrix and a diagonal matrix with the atomic masses. The force matrix K is calculated by the finite difference method as

KIµ,Jν =

FJν (QIµ ) − FJν (−QIµ ) , 2QIµ

(3)

which is constructed in a such way that each atom is displaced by QIµ = ±0.02 ˚ A in the direction µ = {x, y, z} to obtain the forces FJν (QIµ ) on the atom J 6= I in the direction ν. The intra-atomic elements are calculated by imposing momentum conservation KIµ,Iν = P − K6=I KIµ,Kν . Additionally, the phononic thermal conductance can be calculated from the Landauer-type formula 40

κph

h ¯ = 2πkB T 2

Z

∞

dωω 2 Tph (ω)

0

e¯hω/kB T . (e¯hω/kB T − 1)2

(4)

The dimensionless figure of merit ZT = S 2 GT /(κel + κph ) is calculated to give a measure of the themoelectric properties of the molecular junctions, where T is the temperature.

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Defining an integral 41 2 Lm (µ) = h

∞

∂f (E, µ, T ) dETel (E)(E − µ) − , ∂E −∞

Z

m

(5)

where f (E, µ, T ) is the Fermi-Dirac distribution function, allows all the relevant quantities to be calculated. The electronic conductance, the thermopower and the electronic thermal conductance can be calculated in terms of L as

G = e2 L0 (EF ),

(6)

L1 (EF ) , eT L0 (EF )

(7)

1 L2 (L2 − 1 ). T L0

(8)

S=

κel =

We note that the quantities in Equ. 6, 7 and 8 are defined within the linear response limit, and are thus applicable when ∆T /T is small, where ∆T = TL − TR T and T is the averaged temperature of the left and right electrodes. The non-linear effects are expected to be of minor importance, since the experiments are typically done with T ≈ 300 K and |∆T | ≤ 30 K.

Results and discussion The choice of TMD Two-dimensional transition-metal dichalcogenides (TMDs) exist in either metallic or semiconducting phases, depending on the experimental details. 43 While the semiconducting phases have been widely studied, the metallic phases are of interest in our study because TMDs can then function as metallic electrodes in our molecular junctions. A recent com7



XY-averaged VH (eV)

(a) Φ=5.03 eV

Z (Å)

(b)

−1

Molecule

−2

TMDs

−3

E - Evac (eV)

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

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-EA

MoTe2

−4

MoSe2

−5

MoS2

−6 MoO2

−7 −8

-IP

−9

Energy levels

Figure 2: (a) The XY-averaged Hartree potential along the Z direction for the MoS2 slab. The black dashed line indicates the Fermi level. The work function is indicated by the red dotted line. The atomistic structure of MoS2 is embedded to show its position in the slab calculation. (b) The electron affinity (EA) and ionization potential (IP) of the gas-phase molecule and the work function of 216 of free-standing metallic TMDs. The electron affinity (EA) and ionization potential (IP) are calculated from the ∆SCF method. 42 The work functions of MoX2 (X = O, S, Se, Te) are color-coded.

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putational screening study on the two-dimensional transition-metal dichalcogenides (TMDs) shows that many TMD phases are metallic and thermodynamically stable. 44 Moreover it is experimentally feasible to fabricate these defect-free metallic TMDs. 43,45,46 The metallic phase has shown many interesting applications such as the low-contact resistance, 43 the high hydrogen evolution reaction activity. 47 To the best of our knowledge, we are the first to calculate the work functions of these metallic TMDs using a DFT slab model, which has been very successfully applied to calculate the work functions of conventional metals. 48 The work function of a free-standing TMD is calculated with a slab model, as shown in Fig. 2 (a) for the case of MoS2 . The work function is obtained from the difference between the Fermi level and the Hartree potential in the vacuum. Fig. 2 (b) shows the work functions of 216 metallic free-standing TMDs, 49 where the work functions of MoX2 (X = O, S, Se, Te) are highlighted. This distribution has a mean of 5.4 eV and a standard deviation of 1.1 eV, ranging from 3.6 eV to 8.1 eV. Additionally the electron affinity (EA) and ionization potential (IP) of the gas-phase molecule, calculated from the ∆SCF method, 42 are also shown in Fig. 2 (b). From the simple picture where the molecular levels and the work function of TMD are rigidly combined, we expect to have different energy level alignments at the molecule/metal interfaces because of the wide range of TMD work functions. In the molecular system of interest here, the lowest unoccupied molecular orbital (LUMO) resonance can be probed by using TMDs with small work functions. Consequently it is possible to tune the power factor S 2 G as illustrated in Fig. 1 (b). We note that the realistic energy level alignment at the molecule/metal interface is more complicated than this simple picture because of the molecule-metal interactions at the interface. 50 Therefore the energy level alignment in the metal/molecule/metal junctions are investigated using DFT as the next step.

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Electron Transport The ability to tune the energy level alignment between the metal Fermi level and the molecular levels, gives the possibility of changing the zero-bias electronic conductance in a controlled way. Here, four metallic TMDs with different work functions (4.2 eV to 6.6 eV) are considered, namely MoX2 (X= O, S, Se, Te) as shown in Fig. 2 (b), to test the hypothesis that controlled energy level alignment can be used to optimize thermoelectric properties. Because of the weak Van der Waals interactions between the molecule and the TMD, the energy level alignment at the metal/molecule interfaces are approximately the superposition of the energy levels of the gas-phase molecule and the energy levels of the TMD. 51 This is reflected in the fact that the electronic transport gaps among the molecular junctions are similar to the Kohn-Sham highest occupied molecular orbital and lowest unoccupied molecular orbital (KS HOMO-LUMO) gap of the gas-phase molecule, which is ∼ 1.4 eV indicated by the vertical lines in Fig. 3 (a). While it is clear that while the transmission resonances are, to a large extent, simply shifted with the changing work function, the transmission line shapes also change significantly. The broadenings of the molecular energy levels (responsible for the line shape) are controlled by the strength of the interaction between the molecule and the electrode, and the electrode density of states (DOS). The the DOS of the MoX2 around the Fermi energy is dominated by Mo 4d states and X p states, with qualitatively similar features shifted in a similar fashion to the work function shift. Importantly the DOS of MoX2 is not flat around the Fermi energy, so the work function shift also induces a change in the broadening of the resonances and the variation seen in the transmission line shapes. From the point-of-view of a one-level Lorentzian model for the molecular transport, the position of the LUMO is more important for controlling the magnitude of the electronic conductance than the energy level broadening, as reflected in the electronic transmission shown in the Fig. 3 (a), where the position of the LUMO is indicated by the dashed vertical line and the Fermi level is at 0 eV. From MoO2 to MoTe2 , the Fermi level moves towards 10


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(a)

10 0 10 -2

MoO2

10 0

T el

10 -2

MoS2

10 0 10 -2

MoSe2

10 0 10 -2 10 -4 −1.5

(b)

MoTe 2 −1.0

−0.5

0.0

0.5

1.0

1.5

5.5

6.0

6.5

7.0

E - E f (eV)

10 0 10 -1

G (G 0 )

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 -2 10 -3 10 -4 4.0

4.5

5.0

Work function Φ (eV)

Figure 3: (a) The electronic transmission functions Tel (E) of MoX2 (X = O, S, Se, Te) junctions. The vertical lines indicate the corresponding HOMO and LUMO positions and the Fermi energy is set at 0 eV. (b) The zero-bias electronic conductance as a function of the work function of MoX2 (X = O, S, Se, Te) junctions.

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the LUMO as a result of the decreasing work function of the TMDs. According to Eq. 6, the zero-bias electronic conductance can be enhanced when the work function of the TMDs decreases as shown in Fig. 3 (b). The electronic conductance at the Fermi energy varies from 10−4 G0 to 10−1 G0 across the series.

Heat transport The weak Van der Waals interactions between the molecule and the electrode are expected to block the heat transport at the molecule/electrode interfaces as they did for the case of graphene electrodes, 29 and indeed this is found to be the case. The phononic transmission functions are shown in Fig. 4 (a). It is clear that the phononic transmission is suppressed across the whole energy range and is most significant below 100 meV, which is similar to the case of graphene as electrodes. 29 The thermal conductance varies from 14.2 pW/K to 38.2 pW/K at room temperature as shown in Fig. 4 (b). Of all the systems considered, MoO2 exhibits the largest thermal conductance as there is reduced mass miss-match between O and C atoms (compared with either Mo or other choices for X). The Debye frequencies of bulk MoX2 (X = O, S, Se, Te) calculated from DFT are ∼ 90 meV, 53 meV, 42 meV and 38 meV, respectively, in agreement with the cut-off observed in the phonon transmission functions. In the the larger X systems (MoS2 , MoSe2 and MoTe2 ), we effectively have two mechanisms of phonon transport suppression in play: the effect of non-bonded contact and energy mismatch between the phonon modes in the electrode and the molecule.The suppression of the phonon thermal conductance to this extent means that the total thermal conductance is now dominated by the electronic part. This leads to a significant modulation of ZT, as shown later.

Thermoelectric properties We now discuss the thermoelectric properties in terms of the thermopower S, the power factor S 2 G, the thermal conductance κtotal = κe + κph and the figure of merit ZT. Fig. 5 shows 12


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(a) 0.8 0.4

MoO 2

T ph (ω)

0.0 0.8 0.4

MoS 2

0.0 0.8 0.4

MoSe 2

0.0 0.8 0.4 0.0

(b) κph (pW/K)

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


MoTe 2 0

50

100

150

Phonon energy ħω (meV)

200

50 40 30 20 10 0

0

200

400

600

Temperature (K)

800

1000

Figure 4: (a) The phononic transmission functions Tph (ω) of MoX2 (X = O, S, Se, Te) junctions. (b) the corresponding thermal conductance κph as a function of the temperature.

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these quantities for four junctions as a function of energy. Because typical thermoelectric measurements are performed at low bias voltages, the thermoelectric properties around the

200 100 0 −100 −200

MoO 2

MoS 2

MoSe 2

MoTe 2

15 10

κtotal

(nW/K)

b

S 2 G (k 2 /h)

S

(µV/K)

Fermi energy will be the focus here.

5 0 5 4 3 2 1 0

1.5

ZT

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

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1.0 0.5 0.0

−1.0−0.5 0.0 0.5 1.0−1.0−0.5 0.0 0.5 1.0−1.0−0.5 0.0 0.5 1.0−1.0−0.5 0.0 0.5 1.0

E - E (eV) f

E - E (eV)

E - E (eV)

f

f

E - E (eV) f

Figure 5: The thermopower S, the power factor S 2 G, the thermal conductance κtotal and the thermoelectric figure of merit ZT of MoX2 (X = O, S, Se, Te) junctions. The thermopower can be calculated from the slope of the transmission function at the Fermi energy, see Eq. 7. The four junctions have a negative thermopower, as expected because there is the LUMO-mediated transport in all cases. MoS2 has the largest thermopower while MoTe2 has thermopower of nearly 0 µV/K as a result of zero slope in the electronic transmission function of MoTe2 at the Fermi energy (the system is on resonance). From MoO2 to MoTe2 , the thermopower increases to the maximum (MoS2 ) and is gradually decreased to 0 µV/K (MoTe2 ). The magnitude of the thermopower plays a critical rule in determining the power factor. It results in a nearly zero power factor for MoTe2 although its electronic conductance is close to 1 G0 . The combination of large S 2 and large G leads 14


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to the power factor of up to 9.3 k2b /h in the case of MoS2 . The total thermal conductance is, in general, very low ranging from 0.2 to 4.1 nW/K. Because the phononic part is suppressed in these systems to the order of pW/K, the main contribution comes from the electronic part on the order of nW/K. The large electronic thermal conductance can be understood from the Wiedemann-Franz law, 52 recently shown to hold down to metallic nanowires 53 where the κel is proportional to the G. Additionally, the operation of the Wiedemann-Franz law is also reflected in the fact that the κtotal is positively correlated with the G from MoO2 to MoTe2 . By taking the ratio between S 2 G and κtotal to calculate ZT, we can see that the MoS2 shows the most promising high ZT up to 1.2 at the Fermi energy. The nearly zero ZT in the MoTe2 case is due to the nearly zero S, while the extremely small κtotal in the MoO2 case does not leads to a large ZT due to the small S 2 G.

Conclusions In conclusion, the tunability of energy level alignment at the molecule/metal interfaces is achieved by tailoring the work function of the electrode. As a result, a large power factor S 2 G is achieved without further system optimization. On the other hand, the thermal conductance is significantly suppressed due to the weak Van der Waals interactions between the molecule and the TMD materials. We show that with the appropriate choice of electrodes, ZT for a given molecule can be tuned significantly, in this case from almost zero to 1.2, with the possibility of achieving an even higher ZT with optimization of the molecular bridge. This opens the possibility of accessing whichever energy offers the most promising combination of S, G and κel for a given molecule across a wide energy range. While there is undoubtedly a possibility of further optimization of the molecular S and G, the limiting factor for the molecules considered here appears to be the magnitude of κel . A dramatic reduction in κel without a corresponding reduction in G requires a violation of the Wiedemann-Franz law. This is outside the scope of this work but remains a very interesting

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direction for future investigation in molecular thermoelectrics. While we investigated thermoelectric properties here as they are particularly sensitive to band lineup, the principles we have outlined are general. Although gold electrodes have been the popular choice for many molecular electronics investigations, molecular features of interest do not always occur in the energy range accessible from the gold Fermi energy. The series of electrodes studied here show us just how sensitive thermoelectric properties can be to band-lineup, for example in the stark difference between ZT calculated for MoSe2 and MoTe2 . We should stress here however, that the limitations in the accuracy of any DFT calculation for these systems mean that we cannot make definitive predictions, for example discriminating between the choice of MoSe2 or MoTe2 for an experiment. While the many-body perturbation methods such as GW could result in more accurate energy level alignments at the weaklycoupled molecule/metal interface, 4,6 this remains a challenge for large molecules in junctions. Nonetheless, we demonstrate the feasibility of tuning thermoelectric properties in this study and anticipate that DFT is able to qualitatively capture the trends. The binding groups that have been developed to allow Van der Waals contact between molecules and graphene electrodes can be extended to TMDs and this extension allows molecular properties to be tuned into (near) resonance. Many different electronic effects, be they due to conformational switching, chemical substituents or different binding geometries, are all expected to be more significant if the systems can be taken out of the far-off-resonant regime. The chemical identity of the electrode will certainly have consequences for the details of the transmission, seen here in the transmission line shapes, but for these systems, the first order effect was simply to shift the energy levels relative to the Fermi energy. While the use of TMD electrodes will certainly present challenges, as did metal electrodes and graphene electrodes, these systems offer the possibility of a better energetic match between the Fermi energy and molecular energy levels hinting at increased chemical control of transport properties.

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Acknowledgements This work was supported by the funding from the Villum Foundation, Carlsberg Foundation and the Danish Council for Independent Research — Natural Sciences.

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Utilizing Two-dimensional Transition-Metal Dichalcogenides As

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