Orientational Effects and Molecular-Scale Thermoelectricity Control

The orientational effect concept in a molecular-scale junction is established for asymmetric junctions, which requires the fulfillment of two conditions: (1) design of an asymmetric molecule with strong distinct terminal end groups and (2) construction of a doubly asymmetric junction by placing an asymmetric molecule in an asymmetric junction to form a multicomponent system such as Au/Zn-TPP+M/Au. Here, we demonstrate that molecular-scale junctions that satisfy the conditions of these effects can manifest Seebeck coefficients whose sign fluctuates depending on the orientation of the molecule within the asymmetric junction in a complete theoretical investigation. Three anthracene-based compounds are investigated in three different scenarios, one of which displays a bithermoelectric behavior due to the presence of strong anchor groups, including pyridyl and thioacetate. This bithermoelectricity demonstration implies that if molecules with alternating orientations can be placed between an asymmetric source and drain, they can be potentially utilized for increasing the thermovoltage in molecular-scale thermoelectric energy generators (TEGs).

Using the density functional theory (DFT) code, 1, 2 the optimum geometries of the isolated molecules 1-3, and ZnTPP were obtained by relaxing the molecules until all forces on the atoms were less than 0.01 eV / Å as shown in Fig. SI.1.A double-zeta plus polarization orbital basis set, norm-conserving pseudopotentials, with an energy cut-off of 250 Rydbergs, defined on the real space grid was used and the generalized gradient approximation (GGA) was chosen to be the exchange correlation functional.

Frontier orbitals of the molecules.
In this section, we show the frontier orbitals of the studied molecules: highest occupied molecular orbitals (HOMO) and lowest unoccupied orbitals (LUMO), in addition to (HOMO-1), and (LUMO+1), along with their energies.

Binding Energy
This section uses a combination of DFT and the counterpoise method.Briefly, the latter removes the basis set superposition errors when calculating the optimum binding distance of two objects; for more details see 3, 4 .

Binding Energy of Anthracene Core to Gold substrate:
Here, we calculated the binding energy of the anthracene-based molecules as shown in Figs

Transmission coefficient 𝑻(𝑬)
This section investigates the transmission function of asymmetric anthracene-based core molecules with different anchor groups including SnMe3, Py and SAc for this purpose we shall explore three different cases:   In this case, we consider anthracene with two different anchors including SnMe3 and SAc anchors.Figure SI.9 shows that this molecule is a HOMO-dominated and that is what one would expect due to the fact that the both anchors (SnMe3 and SAc), are HOMO-dominated.The DFT-predicted Fermi energy  -   = 0  sits so close to the HOMO resonance because both anchors are pinning in the same direction toward HOMO resonance.Again, it should be noted that both anchors (SnMe3 and SAc), cleave to end up with Au-C direct contact (tip side), and Au-S contact (substrate side).

Seebeck coefficient 𝑺
After computing the electronic transmission coefficient for the 3 junctions, we now compute their Seebeck coefficients .To this end, it is useful to introduce the non-normalised probability distribution () defined by.
where () is the Fermi function and () is the transmission coefficients, whose moments  are denoted as follows where,   is the Fermi energy.The Seebeck coefficient,  is then given by where,  is the electronic charge.
The slope of the transmission coefficient () determines the sign and magnitude of the Seebeck coefficient .In other words, whether the curve is HOMO or LUMO dominated.

Scenarios a:
We employ molecule 1 for this scenario.The lower panel displays the Seebeck calculations of molecule 2. This panel proves S of the two orientations to be a positive.This result is expected as the two orientations are a HOMO dominated curves (see top panel).SI.9), even though both molecules are asymmetric.This finding strongly suggests that one of the anchors overcomes the other, for example, for 1 Py > TMS and 2 SH > TMS, therefore, there is either a HOMO or LUMO trend, but not mid-gap likewise 3. Now, one would argue that the thiol anchor is stronger than pyridyl in molecule 3 and therefore should obtain a HOMO domination than a mid-gap.To satisfy this concern, there are many studies [10][11][12] demonstrate the pyridyl anchor is much stronger on a rough Au substrate, thus, we use an ad-atom in our simulations.The second supporting point for this concern is also an experimental evidence (XPS measurements), the percentage of the two orientations as it shall be discussed in the following section.

Figure
Figure SI.1 shows three structures of asymmetric anthracene-based molecules.These structures are fully relaxed, and are as follows, 1: anthracene-based molecule with two different anchors including SnMe 3

Figure SI. 5 :Figure SI. 6 :
Figure SI.5:An asymmetric anthracene-based molecule configuration with thioacetate and pyridine anchors at the Au lead interface Au-Py (right).Binding energy as a function of the optimum binding distance  ℎ ., where  ℎ . is found to be approximately 2.3 Å. Key: C = grey, H = white, S = light yellow, Au = dark yellow, N = blue, O = red.

Figure SI. 7 :
Figure SI.7:An asymmetric anthracene-based molecule configuration with thioacetate and pyridine anchors at the Au lead interface Au-S (right).Binding energy as a function of the optimum binding distance  ℎ ., where  ℎ . is found to be approximately 2.2 Å. Key: C = grey, H = white, Au = dark yellow.
SnMe3 and Py anchor groups:Anthracene molecule with two different anchors including SnMe3 and Py, has been studied as shown in Figure SI.8.If the two anchors were pyridine, one would expect this molecule to be a LUMOdominated due to the presence of the pyridyl anchor.However, it seems the case is still true even if the molecule is asymmetric, which means two different anchors.We believe this is due to that the Py anchor overcomes the TMS (Au-C), even though the binding energy of TMS is stronger than that Py.It is worth mentioning that, some studies 6 demonstrate that TMS is a HOMO-dominated anchor and that is clearly shown in FigureSI.11,where the TMS pulls the DFT-predict Fermi energy ( -   = 0 eV) slightly away from LUMO resonance, as the pyridyl anchor is pinning the Fermi level  -   = 0  so close to the LUMO resonance7,8 .It should be noted that the SnMe3 group cleaves when it attaches to Au contact to form Au-C direct contact, as we discussed that above.

Figure SI. 8 :
Figure SI.8:Right panel: Schematic illustrations of an asymmetric molecular junction of 1. Left panel: Zero-bias transmission coefficient () of molecule 1 against electron energy E.

Figure SI. 9 :
Figure SI.9:Right panel: Schematic illustrations of an asymmetric molecular junction of 2. Left panel: Zero-bias transmission coefficient () of molecule 2 against electron energy E.

Figure SI. 10 :
Figure SI.10:Right panel: Schematic illustrations of an asymmetric molecular junction of 3. Left panel: Zero-bias transmission coefficient () of molecule 3 against electron energy E.
Figure SI.14, shows a negative Seebeck coefficient at the DFT-predicted Fermi  -   = 0 eV and this is due to the fact that molecule 1 is a LUMO-dominated as shown in Figure SI.8 (anthracene of TMS and Py anchors).

Figure SI. 11 :
Figure SI.11:Right panel: Schematic illustrations of molecular junction of 1. Left panel: Seebeck coefficient  of molecule 1 against electron energy E.

Figure SI. 12 : 2 Figure
Figure SI.12:Right panel: Schematic illustrations of molecular junction of 2. Left panel: Seebeck coefficient  of molecule 2 against electron energy E.
Figure SI.15 illustrates the components that use to build the flipping junction.It also shows molecule 1 where it consists of spacers and two different anchors groups mainly SnMe3 and Py.Then adding a Zn-TPP to form the multicomponent compound.Finally, this structure places between two gold electrodes.To achieve the flipping feature, we first link the Py anchor to the Zn-TPP from one end and the SnMe3 to Au substrate from the other end and then place this structure between the Au electrodes, as shown in the left panel (orientation-1), of Fig. SI.15.It should be noted the SnMe3 anchor cleaves when it attaches to the gold metal to form an Au-C direct contact.Secondly, we flip molecule 1 so that the SnMe3 anchor is now attached to the Zn-TPP, and again place the multicomponent between electrodes as shown the right panel (orientation-1), of Fig. SI.15.We have labelled the two systems as orientation-1 and orientation-2.We repeat the same simulations that described in section 3, to calculate the transmission coefficient T(E).Top panel of Fig.SI.16 illustrate the transmission coefficient curves for orientation-1 and -2.The two curves demonstrate an opposite behaviour, meaning a HOMO dominated curve for orientation-1 and a LUMO dominated for orientation-2.The Fermi energy locates from the LUMO resonance depends on the orientation of molecule 2 between Zn-TPP and Au.In other words, how strong the binding to the Zn-TPP and Au and the type of the anchor.The top panel clearly shows there is a different in the Fermi position when molecule 1 flips from orientation-1 to orientation-2.Similarly, the Seebeck calculations that described in section 4, apply on the flipping simulations.The lower panel of Fig.SI.16 show the Seebeck coefficient of the two orientations.As the top panel illustrates the two orientations to be HOMO and LUMO dominated then that should reflect in the Seebeck sign, means the curves possess a positive and negative Seebeck.

Figure SI. 15 :Figure SI. 16 :
Figure SI.15:Schematic illustration of molecular junctions for two orientations of molecule 1. Orientation-1 and -2 show how molecule 1 flips between the Zn-TPP and Au.Left panel: Orientation-1 is when the Py anchor linked to the Zn-TPP from one end and the TMS to a Au from the other end.Right panel: Orientation-2 is the opposite, SnMe3 anchor linked to the Zn-TPP and Py anchor to a Au contact.
Top panel of Fig. SI.18 illustrate the transmission coefficient curves for orientation-1 and -2 of molecule 2. The two curves demonstrate a mid-gab curve.the distance between the Fermi energy and the HOMO resonance determines by the orientation of molecule 2 between Zn-TPP and Au.In other words, how strong the binding to the Zn-TPP and Au and the type of the anchor.It's clearly shown by the top panel, there is a different in the Fermi position when the molecule flips from orientation-1 to orientation-2.

Flipped MoleculeFigure SI. 17 :Figure SI. 18 :
Figure SI.17:Schematic illustration of molecular junctions for two orientations of molecule 2. Orientation-1 and -2 show how molecule 2 flips between the Zn-TPP and Au.Left panel: Orientation-1 is when the SAc anchor linked to the Zn-TPP from one end and the TMS to a Au from the other end.Right panel: Orientation-2 is the opposite, SnMe3 anchor linked to the Zn-TPP and S anchor to a Au contact.

Flipped MoleculeFigure SI. 19 :
Figure SI.19:Schematic illustration of molecular junctions for two orientations of molecule 3. Orientation-1 and -2 show how molecule 3 flips between the Zn-TPP and Au.Left panel: Orientation-1 is when the Py anchor linked to the Zn-TPP from one end and the S to a Au from the other end.Right panel: Orientation-2 is the opposite, SAc anchor linked to the Zn-TPP and Py anchor to a Au contact.

Figure SI. 20 :
Figure SI.20:Top panel: Zero bias transmission coefficients T(E) of molecule 2 against electron energy E, of orientation-1 and orientation-2 of Fig. SI.18.The flipping feature shifts the Fermi energy  -   = 0 from 0.01 to 0.15 eV towards a HOMO resonance (left to right respectively).Lower panel: Seebeck coefficients  of molecule 2 against electron energy E, in two orientations and both exhibit a positive and negative Seebeck.

Table of contents 1. Theoretical details 2. Binding energy 3.Transmission coefficient 𝑻
() 5Ac and SnMe3 groups attach to a gold metal.In particular, the SAc group cleaves to form a S-Au bond5.Similarly, SnMe3 cleaves to form a direct C-Au bond 5 .Figure SI.5 (A1), shows that the optimum binding distance  ℎ .between the Py anchor and the Au to be 2.3 Å, and at approximately -0.4 eV.It is worth mentioning that in this case there the molecule remains as it is, meaning no changes as shown in Figure1a(molecule 3), in the manuscript.Similarly, Figure SI.6 (A2) represents the binding energy between the thiol anchor group and the gold lead and  ℎ. is 2.4 Å, at approximately -1.2 eV.This suggests the binding energy of the thiol anchor group is much stronger than that the Py anchor to Au electrode (compare Fig. SI.6 against Fig. SI.5).This result in agreement with the literature review, it should be noted that the SAc group cleaves when this group brought close to the Au metal to form S-Au bond.Figure SI.7 (A3) exhibits the binding energy between the TMS anchor group and the gold lead.The TMS's (Au-C), binding energy lies between the S and Py, however, it is more towards the stronger binding energy (i.e.thiol) to Au with binding energy of -1 eV at  ℎ.= 2.3 Å.These calculations suggest that both thiol and TMS bind to Au substrate approximately 3 times stronger than that Py anchor.Again, the SnMe3 group cleaves when this group brought close to the Au metal to form C-Au direct bond, (Note the optimum distance between the Au and Anchor labelled  ℎ. ) . SI 5-7, on a gold substrate.These asymmetric molecules have different anchor groups including: Py, thiol, and TMS (see Figs.SI 5-7).It should be noted that for both SAc and SnMe3 groups of molecules 1-3 (see Fig.1ain the manuscript), some changes occur when