Scale-Up of Room-Temperature Constructive Quantum Interference from Single Molecules to Self-Assembled Molecular-Electronic Films

The realization of self-assembled molecular-electronic films, whose room-temperature transport properties are controlled by quantum interference (QI), is an essential step in the scale-up of QI effects from single molecules to parallel arrays of molecules. Recently, the effect of destructive QI (DQI) on the electrical conductance of self-assembled monolayers (SAMs) has been investigated. Here, through a combined experimental and theoretical investigation, we demonstrate chemical control of different forms of constructive QI (CQI) in cross-plane transport through SAMs and assess its influence on cross-plane thermoelectricity in SAMs. It is known that the electrical conductance of single molecules can be controlled in a deterministic manner, by chemically varying their connectivity to external electrodes. Here, by employing synthetic methodologies to vary the connectivity of terminal anchor groups around aromatic anthracene cores, and by forming SAMs of the resulting molecules, we clearly demonstrate that this signature of CQI can be translated into SAM-on-gold molecular films. We show that the conductance of vertical molecular junctions formed from anthracene-based molecules with two different connectivities differ by a factor of approximately 16, in agreement with theoretical predictions for their conductance ratio based on CQI effects within the core. We also demonstrate that for molecules with thioether anchor groups, the Seebeck coefficient of such films is connectivity dependent and with an appropriate choice of connectivity can be boosted by ∼50%. This demonstration of QI and its influence on thermoelectricity in SAMs represents a critical step toward functional ultra-thin-film devices for future thermoelectric and molecular-scale electronics applications.


Materials and Methods
All reactions were performed with the use of standard air-sensitive chemistry and Schlenk line techniques, under an atmosphere of nitrogen. No special precautions were taken to exclude air during any work-ups. All commercially available reagents were used as received from suppliers, without further purification. 4-Ethynylthioanisole, 4-(ethynyl)phenyl-tert-butylthioether and 1,5dibromoanthracene were synthesised through adapted literature procedures. [1][2][3] Solvents used in reactions were collected from solvent towers sparged with nitrogen and dried with 3 Å molecular sieves, apart from DIPA, which was distilled onto activated 3 Å molecular sieves under nitrogen.

Instrumentation
1 H and 13 C{ 1 H} NMR spectra were recorded on a Bruker Avance 400 MHz spectrometer and referenced to the residual solvent peaks of CDCl3 at 7.26 and 77.16 ppm, respectively. Coupling constants are measured in Hz. Mass spectrometry analyses were conducted by Dr. Lisa Haigh of the Mass Spectrometry Service, Imperial College London. Crystal structure analyses were S3 Figure S2: The 13 C{ 1 H} NMR spectrum of 1 in CDCl3

1,5-Di(4-(ethynyl)phenylthioacetate)anthracene (4)
Synthesised according to an adapted literature procedure. 2 (4A) (0.08 g, 0.14 mmol) was dissolved in DCM (30 mL) and toluene (30 mL). Acetyl chloride (1 mL) was added and the solution was degassed for 20 minutes. BBr3 (1 M in hexanes, 0.72 mL, 0.72 mmol) was added and the solution was stirred overnight at room temperature. The solvent was removed in vacuo and the crude product was exposed to chromatography on a silica column, eluting with chloroform to give the product as a yellow solid (0.05 g, 0.09 mmol, 63%).      The structure of 4A was found to sit across a centre of symmetry at the middle of the anthracenyl moiety. Figure S16: The crystal structure of the Ci-symmetric molecule 4A (50% probability ellipsoids)

DFT and Transport Calculations
The ground state Hamiltonian and optimized geometry of each molecule was obtained using the density functional theory (DFT) code. 8 The local density approximation (LDA) exchange correlation functional was used along with double zeta polarized (DZP) basis sets and the norm conserving pseudo potentials. The real space grid was defined by a plane wave cut-off of 250 Ry. The geometry optimization was carried out to a force tolerance of 0.01 eV/Å. This process was repeated for a unit cell with the molecule between gold electrodes where the optimized distance between Au and the pyridine anchor group was found to be 2.3 Å, whereas Au and SMe 2.7 Å. From the ground state Hamiltonian, the transmission coefficient, the room temperature electrical conductance and Seebeck coefficient was obtained, as described in the sections below. We model the properties of a single molecule in the junction as pervious works 9 have shown the calculated conductance of a SAM differs only slightly from that of single molecules

Optimised DFT Structures of Isolated Molecules
Using the density functional code SIESTA, 8, 10 the optimum geometries of the isolated molecules 1-4 were obtained by relaxing the molecules until all forces on the atoms were less than 0.01 eV / Å as shown in Figure S17. A double-zeta plus polarization orbital basis set, norm-conserving pseudopotentials, an energy cut-off of 250 Rydbergs defined the real space grid were used and the local density approximation (LDA) was chosen to be the exchange correlation functional. We also computed results using GGA and found that the resulting transmission functions were comparable with those obtained using LDA. 11,12 Figure S17: Fully relaxed isolated molecules. Key: C = grey, H = white, O = red, S = yellow. S12

Frontier orbitals of the molecules
The plots below show isosurfaces of the HOMO, LUMO, HOMO-1 and LUMO+1 of isolated molecules 1-4.

Product rule
Wave function plots for isolated molecules with their optimised geometries ( Figures S18-S21) show iso-surfaces of the HOMO, LUMO, HOMO-1 and LUMO+1 of isolated molecules of the studied molecules. The information of the product rule [13][14][15] is obtained from Figures S18-S21. Product rule predicts a CQI in the HOMO-LUMO gap for the molecules of study, because the product of the HOMO (LUMO) amplitudes at opposite ends of the molecules is negative (positive). Table S1 summarises the signs of these orbital products.

Binding energy of molecules on Au
To calculate the optimum binding distance between pyridyl/thioether anchor groups and Au(111) surfaces, we used DFT and the counterpoise method, which removes basis set superposition errors (BSSE). The binding distance d is defined as the distance between the gold surface and the S/SMe terminus of the thiol/methyl sulphide group. Here, compound 1 is defined as entity A and the gold electrode as entity B. The ground state energy of the total system is calculated using SIESTA and is denoted E AB AB . The energy of each entity is then calculated in a fixed basis, which is achieved using ghost atoms in SIESTA. Hence, the energy of the individual 1 in the presence of the fixed basis is defined as E A AB and for the gold as E B AB . The binding energy is then calculated using the following equation: We then considered the nature of the binding depending on the gold surface structure. We calculated the binding to a Au pyramid on a surface with the thioether sulphide atom binding at a 'top' site and then varied the binding distance d. Figure S22

Optimised DFT Structures of Compounds in Their Junctions
Using the optimised structures and geometries for the compounds obtained as described in section 2.1 (above), we again employed the SIESTA code to calculate self-consistent optimised geometries, ground state Hamiltonians and overlap matrix elements for each metal-moleculemetal junction. Leads were modelled as 625 atom slabs, terminated with 11-atom Au (111) Figure S25: Optimised structure of 3. Figure S26: Optimised structure of 4.

The tilt angle (θ)
In this section, we determine the tilt angle of each compound on a gold substrate, which corresponds to the experimentally measured most-probable break-off distance. In previous work 9 we have demonstrated how the tilt angle calculates for both single molecule and SAM. Table S2 shows each compound for a range of tilt angles. Break-off distance values suggest that compound-

HOMO-LUMO gaps
The calculated and optically measured HOMO-LUMO gaps are listed in Table S3. Theoretical gaps were calculated for isolated molecules and when the compounds are placed in the junctions, the gap between their HOMO and LUMO transmission resonances are quoted. As shown by the third and fourth columns in Table S2, isolated gaps for compounds 1, 2, 3 and 4 are larger than the gaps between the transmission resonances. This is because the latter are shifted by the real part of the self-energy of the contact to the leads, reflecting the fact that the system is more open when contacted to electrodes. In general, theoretical gaps are smaller than the measured gaps, which is consistent with the fact that DFT is known to underestimate its value. 16,17

Transport Calculations
The transmission coefficient curves T(E), obtained from using the Gollum transport code, were calculated for compounds 1-4 based on the tilt angle range in Table S2. The LUMO resonance is predicted to be pinned near the Fermi Level of the electrodes for the four molecules, however, we choose Fermi Level to be in the mid gap at approximately ±0.5 eV (black-dashed line), as shown in Figure S28. In previous works 9 we have demonstrated that the transmission coefficient T(E), for single molecule is approximately the same for SAM, by comparing T(E) for single molecule against SAM consists of 7 molecules. S18

Seebeck coefficient
After covering the electronic transport for the four molecules, the study of some thermoelectronic properties such as thermopower for the same groups is made.
To calculate the thermopower of these molecular junctions, it is useful to introduce the nonnormalised probability distribution ( ) defined by where ( ) is the Fermi-Dirac function and ( ) are the transmission coefficients and whose moments are denoted as follows where is the Fermi energy. The thermopower, , is then given by where is the electronic charge.
Supplementary Figure S29 shows the thermopower evaluated at room temperature for different energy range − .

Magic number table for anthracene core
To demonstrate that conductances are not simply a reflection of the path lengths between injection and collection points, it is useful to examine the full magic number table for the anthracene core, which is shown below. This captures the effect of connectivity by noting that if electrons are injected at pi orbital and collected at pi orbital , then the electrical conductance, then the contribution to electrical conductance from the pi system of the core is proportional to ( ) 2 , where is the , th entry in the magic number table. The diagonal blocks (coloured yellow) in this table correspond to DQI, whereas the off-diagonal block correspond to CQI. In the case of CQI, 71 ′ is greater than 62 ′ , even though the distances between 7 and 1 ′ is the same as the distance between 6 and 2 ′ . This demonstrates that connectivity dependence of electrical conductances is not simply a reflection of the distances between sites. This lack of correlation with the distances between sites is even more clear when one notes that the entries in the diagonal blocks between unprimed and unprimed numbered sites (such as 12 ), or primed and primed numbered sites (such as 1 ′ 2 ′ ) are zero, which demonstrates that even though these are close to each other, their conductances are lower than those between more distant sites, such as 72 ′.

QCM monitoring of SAMs growth
The QCM substrate (International Crystal Manufacturing, USA) was rinsed by acetone (>99%), methanol (>99%) and iso-propanol (>99%) in series and cleaned by oxygen plasma for 5 minutes. The stabilised, initial resonance frequency (f0) of the cleaned QCM substrate was recorded. The cleaned QCM substrate was then immersed in 1 mM solution of molecules 1-4 in 1:2 ethanol:THF mixture (>99.9%, bubbling with nitrogen for 20 min to remove oxygen) from 12 hours to 48 hours. Optimised assembly times were established over multiple depositions. The substrate was subsequently rinsed by THF and ethanol several times to remove excess physisorbed molecules before drying in vacuum (10 -2 mbar, 40oC). The frequency of substrate after SAMs growth was again measured by the QCM. The equivalent measurement, where the QCM substrate was immersed in 1:2 ethanol:THF mixture without any molecules 1-4 present was also pre-formed as a reference. The difference between the measured frequency and initial frequency, ∆ , related with the amount of molecule on Au surface is given by the Sauerbrey equation: Where n the amount of molecule adsorbed on Au surface, A the electrode area, NA the Avogadro's number, Mw the molecular weight, µ the shear modulus of quartz, ρ the density of quartz, f0 the initial frequency.
The single molecular occupation area on Au surface can be calculated by: S20 the corresponding results were listed in Table S3.

TS gold preparation for SPM
A Si wafer (5 mm x 5 mm) was cleaned in an ultra-sonication bath with acetone, methanol and isopropanol in series, before cleaning with oxygen plasma for 5 minutes. The cleaned wafer was glued onto the top surface of a thermal evaporated gold sample previously grown on Si (100 nm thickness) with Epotek 353nd epoxy adhesive to form Si/Glue/Au/Si sandwich structure. The adhesive was cured for 40 minutes at 150 o C, then the original, bottom Si substrate was carefully removed using a sharp blade leaving an atomically-flat Au surface which was templated on the original Si surface. The prepared gold was scanned by AFM for 3-5 random spots for quality tests. For all cases, only the substrates with roughness below 0.2 nm were used for SAMs growth.

SAMs Growth
Following the optimised procedure for QCM, the gold was immersed in solution immediately after cleavage without any further treatment for 12 h (molecules 1, 2 and 4) and 24 h (molecule 3). The substrates were rinsed after molecular assembly by ThF and ethanol and dried in vacuum for 12 hours (10 -2 mbar, 40 o C).

Single molecular conductance calculation
The plot of dI/dV (S) vs. bias voltage was shown in Figure S26. The number of molecules contacted by the probe was calculated using contact area between sample and probe dividing the occupation area of a single molecule. The contact area between sample and probe was estimated by Hertzian model: Where r the contact radius, F the loading force from probe to sample, R the radius of the probe (~10 nm from the supplier), v1 and v2 the Poisson ratio of the material, E1 and E2 the Young's Modulus for probe (~ 100 GPa) and SAMs (~10 GPa, estimated by nano-mechanical mapping under peak force mode). 3.5 SAMs characterization SAM topography was characterized by AFM (MultiMode 8, Bruker Nanoscience) in peak force mode, a low force intermittent-contact mode with combines high resolution imaging, sample nanomechanical information and low sample damage. The peak force setpoint was set to the range of 500 pN to 1 nN and the scan rate was set to 1 Hz. The nano-scratching was performed in contact mode at high set force (F = 15 -40 nN) using a soft probe (Multi-75-G, k = 3 N/m) to 'sweep away' the molecular film from a defined area ( A = 300 nm x 300 nm). The topography of sample after scratching was again characterized in peak force mode, the scratched window is easily observed. Nano-scratching was also conducted on a bare gold sample under the same conditions to ensure no gold is scratched away in used force range. The height difference between the scratched part and un-scratched part indicates the thickness of SAMs.

Conductive AFM (cAFM)
The electrical transport properties of the SAMs were characterized by a custom cAFM system. The cAFM setup is based on a multi-mode8 AFM system (Bruker nanoscience). The bottom gold substrate was used as the source, and a Pt/Cr coated probe (Multi75 E, BugetSensor) was used as the drain. The force between probe and molecule was controlled at 2 nN, as this force is strong enough for the probe to penetrate through the water layer on the sample surface but not too strong to destroy the molecular thin film. The driven bias was added between the source and drain by a voltage generator (Aglient 33500B), the source to drain current was amplified by a current preamplifier (SR570, Stanford Research Systems), and the IV characteristics of the sample was collected by the computer.

Thermal-Electrical Atomic Force Microscopy (ThEFM)
The Seebeck coefficients of SAMs were obtained by a ThEFM modified from the cAFM system used for electrical transport measurement. A peltier stage driven by a voltage generator (Aglient 33500B, voltage amplified by a wide band amplifier) was used to heat up and cool, thus a temperature difference can be created between sample and probe. The sample temperature was measured by a Type T thermal couple, and the probe temperature was calibrated by using an SThM (scanning thermal microscopy) probe (KNT SThM 2an) under the same conditions (F = 2 nN). We made an assumption that the SThM probe and the cAFM probe have similar probe temperatures at the apex part when finding contact with the molecules. The thermal voltage between sample and probe was amplified by high impedance differential pre-amplifier (SR551, Stanford Research Systems), and recorded by a computer.      Table 1. Black corresponds to molecule 1 and red to molecule 2. This shows that at all measured temperature points, the thermal voltage of molecule 2 is higher than that of molecule 1. (e-f) same as (a-d) but on a different sample prepared with same recipe, inset value the calculated Seebeck coefficient of different SAMs from the slope of the curve.

Figure S38
Representative QCM data sets for molecules 1-4 (a-d respectively)