Orientational control of molecular scale thermoelectricity

Through a comprehensive theoretical study, we demonstrate that single-molecule junctions formed from asymmetric molecules with different terminal groups can exhibit Seebeck coefficients, whose sign depends on the orientation of the molecule within the junction. Three anthracene-based molecules are studied, one of which exhibits this bi-thermoelectric behaviour, due to the presence of a thioacetate terminal group at one end and a pyridyl terminal group at the other. A pre-requisite for obtaining this behaviour is the use of junction electrodes formed from different materials. In our case, we use gold as the bottom electrode and graphene-coated gold as the top electrode. This demonstration of bi-thermoelecricity means that if molecules with alternating orientations can be deposited on a substrate, then they form a basis for boosting the thermovoltage in molecular-scale thermoelectric energy generators (TEGs).


Optimised DFT Structures of Isolated Molecules
Using the density functional code SIESTA, 1, 2 the optimum geometries of the isolated molecules 1-3 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 local density approximation (GGA) was chosen to be the exchange correlation functional. and pyridine (SnMe 3 -anthracene-Py), 2: anthracene-based molecule with SnMe 3 and thioacetate (SnMe 3anthracene-SAc), 3: anthracene-based molecule with pyridine and thioacetate (Py-anthracene-SAc), and a graphene sheet (Gr). The three asymmetric anthracene-based molecules were combined with Gr and placed between Au electrodes to study their flipping features as we shall discuss later.

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 Energies
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 . It should be noted that for both SAc and SnMe3 groups of molecules 1-3 (see Fig. 1a in the manuscript), some changes occur when SAc and SnMe3 groups attach to a gold metal. In particular, the SAc group cleaves to form a S-Au bond 5 . Similarly, SnMe3 cleaves to form a direct C-Au bond 5 .
Figure SI.5 (B1), 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 Figure 1a   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. ).

Binding Energy of Anthracene Core to Graphene sheet:
This section illustrates the second part of the binding simulations. Another three biding energies have been calculated where, we demonstrate how an asymmetric anthracene-based molecule of different anchor groups binds to a graphene sheet (Gr). Thus, we calculate the binding energy as a function of the optimum binding distance of a Gr sheet to either Py or SnMe 3 or SAc anchor group.
The binding energy between a Gr sheet and pyridine anchor is shown in Figure SI.8, where the right panel shows an asymmetric anthracene molecule linked to a graphene sheet (Gr-Py). The left panel represents the binding energy plot as a function of the optimum binding distance . In this case, is found to be approximately 3Å, and the B.E is approximately -0.14 eV. (Note the optimum distance between the graphene sheet and anchor labelled ).
Next, we connect the Gr sheet with an asymmetric anthracene, this time, and we calculate the binding energy, as shown in Figure SI.9 (B5). The right panel represents an asymmetric anthracene molecule linked to a graphene sheet (Gr-SAc). The left panel shows the binding energy as a function of the optimum distance . and is approximately 5.5 Å, with B.E approximately -0.8 eV.
The last anchor to investigate with graphene sheet is SnMe3, we attach the Gr sheet to an asymmetric anthracene (SnMe3 and Py), as shown in Figure SI.10 (B6). The right panel is an asymmetric anthracene molecule linked to a Gr sheet via SnMe3. In the left panel, is found to be 5.9 Å, and the binding energy is approximately -0.6 eV.

Transmission coefficient ( )
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:

Case 1: Anthracene-based of SnMe3 and Py anchor groups:
Anthracene molecule with two different anchors including SnMe3 and Py, has been studied as shown in Figure SI.11. 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 Figure SI.11, where the TMS pulls the DFT-predict Fermi energy ( eV) slightly -= 0 away from LUMO resonance, as the pyridyl anchor is pinning the Fermi level so -= 0 close to the LUMO resonance 7,8 . 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.

Case 2: Anthracene-based of SnMe3 and SAc anchor groups:
In this case, we consider anthracene with two different anchors including SnMe3 and SAc anchors.

Case 3: Anthracene-based of Py and SAc anchor groups:
Case 3 is an asymmetric anthracene with two different anchors including thioacetate and pyridine, as shown in Figure

Seebeck coefficient
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. (S1) where ( ) is the Fermi function and ( ) is the transmission coefficients, whose moments are denoted as follows is the Fermi energy. The Seebeck coefficient, is then given by (S3) 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. Figure SI.14, shows a negative Seebeck coefficient at the DFT-predicted Fermi eV and this is due to the fact that

Flipping characteristic s
Following the simulations of 3 asymmetric anthracene-based molecules in Au/M/Au junctions. In this section we shall add an extra segment to the Au/M/Au junction, which is a graphene layer (Gr) to form multicomponent Au/Gr+M/Au. Experimentally, this means graphene coated gold contact for more detail about the synthetic and STM measurements we guide the reader to 9 . In the present research, the Gr sheet is stationary, while the asymmetric molecule flips between two orientations, as shown in Figure  2a of the manuscript. For the flipping purpose we shall investigate 3 scenarios a, b and c.

Scenarios a:
We employ molecule 1 for this scenario. Figure SI.17 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 Gr sheet 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 Gr sheet 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.17. 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 Gr sheet, and again place the multicomponent between electrodes as shown the right panel (orientation-1), of Fig. SI.17. We have labelled the two systems as orientation-1 and orientation-2.

Scenarios b:
This scenario employs molecule 2, and the same procedure that described in scenario a, repeats however with different anchors. Here, we mainly focus on SnMe3 and SAc although these anchors cleave during the flipping procedure. In orientation-1 the SnMe3 anchor cleaves from the bottom side to form a Au-C direct contact as shown in the left panel of Fig. SI.19. Similarly, the SAc anchor cleaves from the bottom

Scenarios c:
Here, we repeat the same procedure that described in scenarios a and b. The difference is the two anchors are Py and SAc, in this scenario one anchor cleaves during the flipping procedure. Orientation-1 the SAc anchor cleaves from the bottom side to form a Au-S contact as shown in the left panel of  We attribute that to the conflict between a strong HOMO dominated anchor such as thiol and a strong LUMO dominated anchor such as pyridyl. This is clearly distinguished from molecules 1 and 2, as 1 is a LUMO dominated (see Fig. SI.11), and 2 is a HOMO dominated (see Fig.  SI.12), 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.  Seebeck coefficients of molecule 3 against electron energy E, in two orientations and the Seebeck coefficient switches from a negative to positive sign (yellow to blue respectively).
+ive S -ive S