DOI: 10.33612/diss.177486717
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INTERFERENCE
Abstract: Understanding the role and relevance of quantum interference (QI) in molecu- lar junctions for Molecular Electronics devices has been long sought after. Translating molecular features, that are responsible for destructive QI, into an observable like tun- neling current in devices with molecules as the core element builds up the prospect of fu- ture applications. Starting with establishing the origin of QI in tunneling junction, here we discuss four series of molecular wires in which we manipulate QI using their elec- tronic structure properties. Using ab-initio density functional theory calculations com- bined with non-equilibrium green’s function approach, we calculate transmission spectra to study the effects of electron-donating and withdrawing functional groups on the shape, size, and position of QI feature in anthraquinoid-core-based wires; as well explain the two-terminal, QI-induced memory behavior in tetracyanoquinone based molecular junc- tion. Finally, we elucidate on the collective and individual roles of bond-topology and quinoid functional groups in the molecular wire series based on benzodithiophene and thienothiophene cores.
The contents of this chapter are also published as part of the following publications: (i) Results in sec- tion 3.4 are included in M. Carlotti, S. Soni, X. Qiu, E. Sauter, M. Zharnikov, R. C. Chiechi, Nanoscale Adv. 2019, 1, 2018–2028 doi: 10.1039/C8NA00223A (ii) Results in subsection 3.4.1 are included in M. Carlotti, S. Soni, S. Kumar, Y. Ai, E. Sauter, M. Zharnikov, R. C. Chiechi, Angew. Chem. Int. Ed. 2018, 57, 15681 doi: 10.1002/anie.201807879 (iii) Results in section 3.5 are included in Y. Zhang, G. Ye, S. Soni, X. Qiu, T. L. Krijger, H. T. Jonkman, M. Carlotti, E. Sauter, M. Zharnikov, R. C. Chiechi, Chem. Sci. 2018, 9, 4414–4423 doi: 10.1039/C8SC00165K. I would like to thank the contributions of the following collaborators whose crucial work is included in this chapter in the form of supporting data: Dr. Y. Zhang, Dr. G. Ye, Dr. X. Qiu, and Dr. M. Carlotti.
3.1. INTRODUCTION Structure-function relationships have inspired several branches of scientific research in- cluding molecular electronics (ME). Several molecular devices are based on ME func- tionalities, such as molecular switches, rectifiers, transistors, quantum interference, etc., and have potential applications. However, developing more practical systems requires a further understanding of the underlying principles in manipulating and controlling these functions. Quantum interference (QI) has shown importance in mesoscopic elec- tronic systems[1] where two electron waves can interfere constructively or destructively depending on the phase difference between the two. QI is a collection of phenomena re- lated to Fermions whose wave functions can interfere with themselves in molecular tun- neling junctions (MTJ), as explained in section 3.2. Destructive QI can lower the trans- mission probability between the electrodes, significantly lowering conductance without altering the tunneling distance in most cases.
In MTJ, π-conjugated molecules influence tunneling transport in a more non-trivial fashion, rather than posing as a simple, rectangular tunneling barrier. When the pres- ence of different, highly-coupled pathways in a molecular system affect the conductance due to the change in bond-topology, it is typically ascribed to QI,[2] which was originally adapted from the Ehrenberg–Siday–Aharonov–Bohm effect[3,4] to substituted benzenes (section 3.2).[5,6] Solomon et al. further refined the concept in the context of ME where it is now well established that destructive QI suppresses the tunneling probability of tra- versing electron wave, lowering the conductance of the MTJ.[7–13] Experimental evidence of QI has been demonstrated in several experimental platforms with different device geometries and different molecular systems in molecular electronics.[2,5,6,10,14,15] Not- able categories where QI plays a major role include para and meta connections,[5,6,16–24]
varied connectivity in azulene,[25–27] linear versus cross-conjugation,[13,14,28–31] through- space QI,[32–34] and σ-framework QI.[35–37]
Several applications based on QI has shown potential as an intriguing ME element,[38] such as gating via heteroatom substitution,[29,39,40] electrochemical gating,[41] switching using acid and base,,[27,42] two-terminal molecular memory,[43] and parallel-pathways control and manipulation.[42,44–46] The concept “quantum interfer- ence effect transistor” was proposed long ago using meta-benzene structures for device application[47] and lately functioning of a QI-based transistor, consisting of paracyclo- phane core, was also demonstrated.[48]
In this chapter, I will discuss the results of our Density Functional Theory simulations combined with Non-Equilibrium Green’s Function approach for computing transport properties on a series of conjugated molecular wires – with different cores, incorporat- ing functional groups, and manipulating bond-topology – as ideal systems to study QI in large-area EGaIn MTJ, as shown in Figure 3.1.[14,28,43,49] However, before that, I will discuss the origin of QI in MTJ in section 3.2. In section 3.3, I first elucidate on destruct- ive QI in the conjugated and rigid molecular wires AC, AH, and AQ (see Figure 3.1b) that have served as benchmarks since their first reports.[14,50–52] In section 3.4, I study the ma- nipulation of QI feature when the cross-conjugated molecular wire AQ is functionalized by different electron-donating and withdrawing groups. In subsection 3.4.1, I discuss the transmission spectra of different redox states of a unique derivative of AQ – TCNAQ – which has cyano groups at the two carbonyl positions, showing plausible application
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Figure 3.1 (a) Schematic of a MTJ comprising bottom electrode as either AuTS or AuMica, self-assembled mono- layers of molecular wires with the “arms” that are linearly-conjugated phenylacetylenes with varying aryl group (Ar) in the core, and Ga2O3//EGaIn as the top electrode. Molecular cores (Ar) for all the molecular wires stud- ied in this chapter: (b) AC, AH, and AQ benchmark series; (c) several derivatives of AQ molecular wire syn- thesized by functionalizing the carbonyl position with different functional group, including TCNAQ which has been demonstrated as a redox-active QI switch (AMe, A(CH2), AF, A(Alk), and A(All) were not synthetically ac- cessible but were investigated in silico); (d) BDT-n series (n = 1−3) for untangling the effect of quinones and bond-topology on QI, along with other 3 derivatives that were only investigated in silico; (e) Bithiophene (BT as control) and fused thienothiophenes molecules (TT-n; n = 1− 3) for further studying the effect of bond- topology on QI.
as a molecular memory. Further, in section 3.5, I report transmission calculations on a molecular series based on benzodithiophene core that helps us isolate the effects of cross-conjugated bond-topology and electron-withdrawing quinone groups on QI. Fi- nally, in subsection 3.5.1, I present simulations and discuss transmission probabilities of molecular wires with thienothiophene core affecting bond-topology and destructive QI in the process.
3.2. ORIGIN OF QUANTUM INTERFERENCE
Describing destructive QI in molecular systems is non-trivial. Owing to its quantum- mechanical nature, a physical description of QI can be confusing and misleading if not handled with caution. I will describe the origin and adaptation of QI in ME but, if in-
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3.2. ORIGIN OF QUANTUM INTERFERENCE
terested in detailed reading and formalism of different QI-based concepts, the reader is encouraged to refer to further pedagogical and research texts.[1,2,53,54]
To understand the complexity of this phenomenon, we will first take a step back and recall the classical analogue which served as an inspiration: the famous double- slit experiment performed by the eminent physicist Thomas Young in 1801 investigating the nature of light.[55] Young demonstrated that a beam of monochromatic light upon passing through two closely-spaced slits would create an interference pattern upon re- combination, as shown in Figure 3.2. In Young’s experiment, wherever two peaks or two troughs (i.e., in-phase waves) met, they interfered constructively, resulting in a bright spot; whereas the recombination of a peak and trough (out-of-phase waves) canceled each other (interfering destructively), resulting in a dark spot. However, the quantum- mechanical nature of tunneling electrons makes this analogy inapt—even though it provides a good initial understanding of wave interference—so we move on to meso- scopic ring systems. It was demonstrated that when an electron beam is split around a solenoid, the wavefunctions of the two electron waves experience a phase-shift pro- portional to the magnitude of magnetic flux in the solenoid.[56,57] As a result, the elec- tron beams upon recombination interfere constructively or destructively depending on the phase difference, which is named as Ehrenberg–Siday–Aharonov–Bohm effect.[3,4]
The effect was also demonstrated in normal-metal rings.[58] Naturally, it is tempting to apply this concept to cyclic molecules like para- and meta-substituted benzene rings (Figure 3.2). While para-substituted benzene provides two symmetrical pathways (i.e., φ = 0), meta-connected benzene presents asymmetric pathway consisting of 2 and 4 sp-carbons each (i.e., φ 6= 0). It has been predicted theoretically and shown exper- imentally that meta-benzene is few orders of magnitude lower in conductance com- pared to para-benzene. This path-difference (translating into phase-difference), there- fore, could be considered as a reason for destructive QI in the meta-benzene case.[20]
This analogy, however, breaks down for acyclic systems such as alkenes,[8] more complex systems with through-space QI,[34,59] larger aromatic ring systems,[16,28] and for systems with σ-QI,[35,37] also shown in Figure 3.2. Therefore, neither of the above two phenom- ena can be considered an explanation or QI analogues in MTJ. Furthermore, in Young’s double-slit and Aharonov-Bohm experiments, two waves interfere with one another, but for tunneling transport across molecules, the electron interferes with itself as its wave- function gets ‘scattered’ by the tunneling barrier defined by the molecular bridge. There- fore, we will now move away from the interference analogy of the two experiments to a more quantum-mechanical description from the point of view of molecules and their eigenstates.
Isolated molecules have discrete energy levels, just like individual atoms and quantum dots. Even though these energy modes are perturbed when they are anchored to metal electrodes (especially when the molecule is directly conjugated to the metal), their contribution adds up to the overall transmission probability (T (E)) of the tunnel- ing electron. The contribution will vary for different eigenmodes, hence, the peaks in the transmission can be decomposed by projecting the molecular conductance orbitals from the transport calculation onto the molecular orbitals from fragment DFT calcula- tions, as described earlier in the literature.[9,54] To perceive the difference between the molecular conductance orbitals and molecular orbitals, it helps to realize that both be-
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0
0
Figure 3.2 Schematic showing the evolution of quantum interference phenomenon from wave interference in classical and quantum-mechanical analogues to interference in MTJ. The first panel sketches Young’s double- slit experiment demonstrating interference pattern originating from traveling waves passing through two nar- row slits[55] and the Aharonov-Bohm effect where the wavefunctions of the two electron beams experience a phase-shift proportional to the magnetic flux in the center, giving rise to an interference pattern upon re- combination. The second panel highlights the concept of path-difference between the two available physical pathways for electron traversing across a para- and meta-benzenedithiol in a tunneling junction. The third panel shows examples of molecules in which the analogy of multiple pathways fails as they induce destruct- ive QI via cross-conjugation, through-space, or by sigma framework. The last panel shows an energy diagram of a metal-molecule-metal junction, showing several factors that can govern the total electron transmission, which is the contribution of individual transmissions through these several energetic pathways over the same physical pathway, such as, fermi levels (EFermi) of the two electrodes, energy levels of the molecular bridge, and coupling of molecular levels to the electrodes (ΓL/R ).
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3.3. THE BENCHMARKS: AC, AH, AND AQ SERIES
come the same in the limiting case when the molecule-electrode coupling becomes zero. The simplest system which would give rise to a perfect antiresonance QI dip (T (E) → 0) will be the one in which the contribution of two molecular conductance orbitals dif- fer by a phase of π. This scenario naturally becomes more complicated when we take into account a complete molecule and combination of all the involved eigenstates. Al- though several molecular orbitals contribute to a transmission peak, generally speaking, the ones in the vicinity of the peak in an energy landscape, will contribute the most. For instance, resonance peaks in transmission spectra, where the T (E) → 1, are usually located in the vicinity of the energies of molecular levels. Similarly, the destructive QI feature, which is usually identified in form of a sharp antiresonance dip in the trans- mission spectra (T (E) → 0), is usually located around the energy levels which contrib- ute the most towards its origin. The molecular conductance orbitals could be deloc- alised over the same molecular backbone or separated on different fragments. Thus, the origin of the destructive QI is attributed to the sum of out-of-phase contributions from different energy states spanning the same or neighboring physical pathway on the molecule. This is in contrast to the classical analogue of the double-slit experiment or quantum-mechanical analogue of the Ehrenberg–Siday–Aharonov–Bohm effect where interference occurs between waves traversing two different physical pathways.
The QI antiresonance affects the tunneling conductance the most when it is located near the energy of Fermi level of the electrodes in the transmission spectra (i.e., in the frontier level gap of the molecule). This position of antiresonance can be manipulated by changing the electronic structure and conformation of the molecules in the junction and can be further turned on and off electrochemically, as I will demonstrate later in this chapter.
3.3. THE BENCHMARKS: AC, AH, AND AQ SERIES First experimental evidence of tunneling charge-transport manipulation via QI in large- area MTJ was provided by Fracasso et al.[14] The authors showed that the conduct- ance of molecular wires can be affected by manipulating the bond-topology, thereby changing the conjugation. They studied 3 molecular wires with the same anchoring groups bearing different cores as shown in Figure 3.3a. The cores in AC (anthracene; 4,4’-(anthracene-2,6-diylbis(ethyne-2,1-diyl))dibenzenethiol), AQ (anthraquinone; 2,6- bis((4-mercaptophenyl)ethynyl)anthracene-9,10-dione), and AH (dihydroanthracene; 4,4’-((9,10-dihydroanthracene-2,6-diyl)bis(ethyne-2,1-diyl))dibenzenethiol) introduce linear-, cross-, and broken-conjugation in the 3 molecular wires. Respectively, (i) AC has a continuous single-double bond alternation from one terminal sulfur to the other, (ii) AQ has two non-interacting sequences of single-double bond alternation shown by different colors in Figure 3.1b, and (iii) AH also has two non-interacting sequences of single-double bonds that are bridged by two saturated methylene (–CH2–) groups act- ing as sigma spacers. The authors calculated the geometric and the gaussian means of current densities and deduced that the low-bias conductance follows the trend as AC > AH > AQ. A continuous delocalization of electron density due to the conjugated bonds in linearly-conjugated AC makes it most conductive as shown in Figure 3.3a. Break in the conjugation in AH core compared to the AC results in lower tunneling conductance, while the lowest conductance of AQ is ascribed to destructive QI that occurs near the
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a b
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Figure 3.3 (a) Semilog J −V plots showing geometric means (lines) and Gaussian (µlog) means (symbols) for AC (solid line; squares), AH (dotted line; triangles), and AQ (dashed line; circles). Both statistical methods show that AC is clearly more conductive than either AH or AQ, while meaningful distinction is difficult to make for the latter two. Reprinted with permission.[14] Copyright 2011, American Chemical Society. (b) Transmission spectra of AC, AH, and AQ calculated using ORCA[65,66] and Artaios[67] showing high conductance for linearly- conjugated AC and destructive QI dip for AQ (at ≈ 0.25 eV). The trend in transmission probability at EFermi shows qualitative agreement with the experimentally measured conductance.
EFermi induced by the cross-conjugation in bond-topology. The destructive QI effect in this series was also demonstrated later in single-molecular junctions, and other experi- mental setups (supported by theory).[30,50,51,60–64]
We performed DFT+NEGF simulations on gas-phase optimized geometries of these three molecules using ORCA quantum chemistry software and Artaios program for calculating the transmission spectra, following the same procedure as described in chapter 2. The theoretical QI signature can be seen in the transmission spectra of AQ in Figure 3.3b in form of a significant dip slightly below 0.25 eV. The energy axis has been referenced to the energy of the Fermi level of the EGaIn electrode.[68] The conduct- ance trend at E−EFermi = 0 qualitatively agrees with the experimental conductance trend reported by Fracasso et al.: AC > AH > AQ.
A presence of electron-withdrawing quinone moiety in the core localizes the charge density in the core. This can also be seen in the Figure 3.4, where isoplot of the LUMO level shows charge density localized in the core as opposed to AC which has uniformly distributed charge density. The electron-withdrawing quinone moiety also lowers the energy of LUMO level (−3.24 eV, compared to −2.37 eV for AC and −1.57 eV for AH) be- cause of the non-bonding level originating from the carbonyl groups resulting in the smallest optical bandgap in the series. Despite the smallest bandgap, the presence of de- structive QI feature results in AQ being least conductive. Carlotti et al., in their follow-up work, further elucidate that the conduction in AH can be thought of as "through-space" conduction compared to a "through-bond" conduction in AC, which makes the former less conducting than the latter.[34] The authors demonstrated through-space conduct- ance in AH, which can further depend on the bend in the core of AH.
3.4. MOVING QI DIP BY FUNCTIONALIZING AQ As reported here and in previous literature, the origin of destructive QI feature in AQ SAMs is a result of both cross-conjugation[8,10,69] in the bond-topology and the presence
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3.4. MOVING QI DIP BY FUNCTIONALIZING AQ
Figure 3.4 Frontier molecular orbital isoplots HOMO and LUMO, and HOMO−1 and LUMO+1 of AC, AH, and AQ (isovalue of 0.02) with corresponding gas-phase orbital energies shown next to the orbital diagrams.
of an electron-withdrawing quinone functional group.[70–72] Andrews et al., using theor- etical simulations, showed that width, depth, and entire location of the quantum inter- ference feature can be changed via functionalization of cross-conjugated molecules.[70]
In the case of AQ, the two carbonyl positions offer the possibility of functionalization while preserving the cross-conjugated bond-topology. Even though, as we will discuss further below, not all the AQ derivatives are synthetically accessible, which we have the- oretically investigated (Figure 3.1c). We can divide the proposed AQ derivatives in this work in two separate categories: (i) all-Carbon derivatives comprising AMe, APh, A(CH2), A(All), and A(Alk); (ii) ones with heteroatoms in their core comprising ATTF, TCNAQ, ABr, and AF. The classification will be more clear in this section when we discuss the transmission spectra of these molecular wires.
All the molecular wires studied in this part have identical molecular skeletons and binding groups to the parent anthraquinone wire (AQ),[14] but with different CR2 groups replacing the oxygen in the carbonyl, thus changing molecular geometry, energies and localization of the orbitals, and the distribution of electron density, without altering the cross-conjugated core (Figure 3.1). We investigated the electrical properties of SAMs of anthraquinoid compounds with two different top electrodes (EGaIn and CP-AFM, (AuAFM) and found that their conductance roughly follows the order TCNAQ ≈ AC > ATTF > APh ≈ ABr > AQ. Other AQ derivatives shown in Figure 3.1 were not synthet- ically accessible except AMe which could be synthesized but did not form good SAMs, for unknown reasons, as seen by HRXPS measurements.[49]
We simulated the transmission spectra for all the proposed derivatives in Figure 3.5 clubbing the all-carbon derivatives and the ones with heteroatoms in the core, separ- ately in two graphs allowing easier comparison. As seen in Figure 3.5a, the all-Carbon AQ derivatives split the QI feature into two separate dips occurring just before the two transmission resonance peaks going from EFermi (except for A(All)), in agreement with previously reported transmission for A(CH2).[51]
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a
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AQ ABr TCNAQ ATTF AF
Figure 3.5 Calculated transmission probability as a function of electron energy (with respect to EGaIn’s EFermi = −4.3 eV[68]) of different AQ derivatives. (a) all-carbon wires; (b) wires containing herteroatoms. AQ is reported in both the plots as reference.
Compared to the derivatives with heteroatoms, the electron- donating/withdrawing ability of the functional groups in all- carbon compounds is weaker. The resonance peaks (T(E)→ 1) for E <EFermi is slightly lower compared to AC (Figure 3.3) and for E >EFermi the peaks are about 1 eV higher in en- ergy, except for A(Alk) which tracks with its low LUMO level, tabulated in Table 3.1. The lower LUMO of A(Alk) is a res- ult of the four sp hybridized al- kyne groups having the strongest electron-withdrawing inductive effect compared to their sp2 and sp3 analogues. The cumulative inductive effect results in lower LUMO (and Eg , Table 3.1) as well as the interference feature be- ing closer to EFermi (E−EFermi = 0.78 eV). The inductive effects of
aryl derivative (APh) and sp3 derivative (AMe) are sequentially smaller, resulting in LUMO being higher in energy and the corresponding QI dip being at 1.65 eV and 1.73 eV, respectively. The transmission spectra of A(CH2), on the other hand, is similar to AMe but shifted lower in energies. A(Alk) does not show that big of a shift since the double bonds are next to each other resulting in orthogonal π-orbitals on the sp carbon. The ex- perimental observation of reduced conductance of APh derivative compared to AC and higher conductance compared to AQ can thus be supported using these transmission calculations. A(All) is the only derivative that doesn’t have a CR2 substitution at the car- bonyl position. Instead, it introduces a cumulated diene with sp carbon of the allene functional group instead of oxygen; in allenes, the carbons at 1 and 3 positions are usu- ally considered non-conjugated, this difference seems to result in the (QI) feature-less, suppressed transmission spectrum of A(All). For instance, recently published work by Venkataraman et al.[73] showed that sp-connected carbons in cumulene behaves exactly the opposite of sp2-connected carbon chains of polyyne when it comes to change in tunneling with increasing lengths. With increasing length, tunneling current increases and decreases for cumulene and polyyne, respectively. The authors ascribe this to the reversed trend in bond length alternation between cumulene and polyyne as well as the former having smaller magnitude of bond length alternation. Their study aids answering the question why A(All) having cumulene group behaves differently than the rest of the AQ derivatives. The orbital density localization of LUPS for A(All) is also similar to the strong electron-donating ATTF derivative, discussed in the next paragraph, in contrast
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3.4. MOVING QI DIP BY FUNCTIONALIZING AQ
Figure 3.6 Orthographic projections of Highest Occupied π-States (HOPS) and Lowest Unoccupied π-States (LUPS) of several AQ derivatives described in section 3.4 in metal-molecule single molecule model system, along with AQ itself as a reference.
to the other all-Carbon derivatives.
Meanwhile, AQ derivatives with heteroatoms show a more prominent change in be- havior of the QI feature, and transmission spectra in general, as they affect the elec- tronics of the molecule wires more strongly than the all-Carbon wires. TCNAQ with the well-known, strong electron-withdrawing tetracyanoquinone(TCNQ)-based core pulls the LUMO much lower in energy, even more than the carbonyls in AQ, bringing the in- terference feature to −0.35 eV w.r.t. the EFermi. The bigger effect can also be seen in the frontier orbital plots shown in Figure 3.6. Compared to AQ, the LUPS has even higher electron density localized in the core, while the HOPS has a smaller electron density in the core and even smaller localization in the phenylacetylene arms (compared to AQ). The electron-withdrawing nature is so strong that the transmission resonance peaks for E >EFermi sit right next to EFermi. On the other hand, the strong electron-donating analogue ATTF shifts the entire spectra to higher energies with the resonance peak for E <EFermi at −1.15 eV away from EFermi without any QI feature in the energy range of our interest. This is very small considering the overestimation of Eg that accompan- ies the drawbacks of these simulations. The DFT predicted HOMO and LUMO values in Table 3.1 are higher compared to most other derivatives. While LUPS seems to be the dominating frontier level in TCNAQ, HOPS seems to have a bigger effect on trans- mission at EFermi in the case of ATTF. As seen from Figure 3.6, opposite to AQ, ATTF has HOPS with localized electron density in the core and HOPS with localized density in the phenylacetylene arms. The presence of these energy level proximity to EFermi in the cases of TCNAQ and ATTF supports the experimental observation of their higher conductance compared to the all-Carbon APh and AQ, for which the EFermi sits in the center of the HOMO-LUMO gap. Surprisingly, the halogenated derivatives – AF and ABr – show featureless suppressed transmission where F, being more electronegative, shifts the spectra to lower energies slightly more than Br. Both halogens shift the frontier levels
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AQ AMe APh A(CH2) A(All) A(Alk) ABr ATTF TCNAQ AF LUMO (eV) −3.24 −1.72 −1.87 −2.05 −1.92 −2.79 −2.35 −1.91 −3.99 −2.21 HOMO (eV) −5.98 −5.44 −5.48 −5.62 −5.44 −5.60 −5.80 −4.86 −6.19 −5.77
bandgap (eV) 2.74 3.72 3.61 3.56 3.52 2.80 3.45 2.94 2.20 3.56 φ (degree, ) 0 47 47 (45) 27 0 38 47 (44) 36 36 31
Table 3.1 DFT calculated gas-phase HOMO, LUMO, frontier orbital bandgaps and bend angles of the molecular cores (illustrated in Figure 3.7) for the wires proposed in Figure 3.1. Values shown in parentheses are from X-ray crystal structure obtained by Dr. M. Carlotti.[49]
to lower energy but not as much as TCNAQ or AQ. The transmission spectra near EFermi
are similar in magnitude to most of the all-Carbon derivatives. The molecular orbitals in Figure 3.6 further show that the LUPS has lower localization of electron-density in the core compared to AQ and very delocalized HOPS spanning across the molecule.
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Bent AQ Linear AQ
Figure 3.7 Calculated transmission probability as a function of electron energy (with respect to EGaIn’s EFermi = −4.3 eV[68]) of AQ in planar or linear conformation (red: linear AQ), and with a bend angle of 47° in the core (green: Bent AQ).
Obtaining the crystal struc- tures of these molecules would give the best insight into inter- molecular interactions and mo- lecular assemblies in SAMs. In Table 3.1, we tabulate the DFT predicted bend angles of the molecular cores and the ones obtained from X-ray crystallo- graphy in the parentheses.[49]
The data shows that molecules with bulkier functional groups are more bent due to steric crowding. It could be tempting to relate the bent in geometry
with the presence and absence of a sharp QI dip near EFermi. To verify this hypothesis we simulated transmission spectra of AQ, which is inherently planar, by constraining AQ in a geometry with bent angle of 47° – similar to APh and ABr. It can be seen from Fig- ure 3.7 that the transmissions spectra are the same except for the shift in the QI dip by ≈ 0.25 eV. It can be argued that changing the bent in the core could alter the orbital overlap across the arms and change the transmission. Furthermore, it should be considered that in SAMs, the molecular geometries are perturbed by environmental effects such as col- lective effects arising from intermolecular interactions, presence of metal electrodes, de- fects, thermal fluctuations, etc. The QI feature, therefore, will be a result of an averaged distribution of geometries. Thus, by combining our finding from the simulated spectra (Figure 3.7) and keeping in sight the SAM complexity argument, we would like to argue that perturbation in electronic properties by the functional group substitutions affects the QI more than geometrical fluctuations. This is also supported by the findings of So- lomon et al.[8] wherein they demonstrated that while the change in bond-topology and functional groups show a prominent shift in the transmission spectra of acyclic systems, transmission spectra of several geometries of the same molecule obtained via molecular dynamics simulations do not affect the QI dip significantly and is present in all the cases.
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3.4.1. REDOX-ENABLED QI SWITCHING IN TCNAQ
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Figure 3.8 (a) Schematic showing SAM of TCNAQ in the cross- conjugated quinoid form (top) which is reversibly switched to a mixed- SAM in which a fraction of the molecules are reduced to a linearly- conjugated, hydroquinoid form (bottom); the top cross-conjugated neutral form gives rise to destructive QI with lower conductance com- pared to the linearly-conjugated reduced form. (b) Examples of log |J | vs. V traces of junctions comprising SAMs of TCNAQ (top, black) show- ing significant hysteresis in negative bias range, compared with AC as reference showing overlapping forward and reverse traces (bottom, blue) on AuTS. Solid dots represent (data acquired by Dr. M. Carlotti) five forward scans going from −1.00 V to 1.00 V, while open dots repres- ent data acquired during reverse scans from 1.00 V to −1.00 V.[43]
Unlike single-molecular techniques, SAM-based MTJ provide a viable pro- spect as a technologic- ally relevant platform as they can be up-scaled for manufacturing and en- capsulated in stable, static devices.[26,48,74] As dis- cussed in earlier sections, QI lowers the transmission probability between the electrodes, significantly lowering tunneling con- ductance without altering the tunneling distance.[35]
In our published work,[43]
we demonstrate a potential QI-based, two-terminal molecular memory com- prising SAMs of TCNAQ: the AQ derivative with tet- racyanoquinone (TCNQ) core, which is known to be a very electron-withdrawing molecular moiety (also dis- cussed in section 3.4). The QI memory effect occurs due to active redox chemistry between the Au electrode and strongly electron-withdrawing TCNQ. The TCNQ core can reversibly switch between the two redox states which have very different transmission probabilities of the tunneling electrons in MTJ. Thus, in this section, we show how NEGF calculations can be used to explain the difference in conductivity using the different transmission spectra for the neutral and doubly-reduced TCNAQ species.
Figure 3.8a shows a schematic of SAMs of TCNAQ which can be switched (on several coinage metal substrates) between, and addressed in, two conductance states (ON and OFF) in a two-terminal proto-device using EGaIn top-contacts. We will show that the different conductance states can be ascribed to the modulation of the bond-topology of the molecule; TCNAQ—just like TCNQ—can readily accept an electron from the bottom metallic substrate and form a stable (di)anion that converts cross-conjugated pathways to linearly-conjugated pathways, altering the transmission probability similarly to inter- conversion of quinones and hydroquinones.[30] A low-lying LUMO brings the reduction potential of TCNAQ close to the oxidation potential of Au, Ag, and Pt electrodes, elimin- ating the need for a third electrode or redox agent.
Example J−V traces are shown in Figure 3.8b where the black data points for TCNAQ
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show very prominent, reproducible hysteresis between the forward and the reverse traces. SAMs of TCNAQ readily accept an electron from the Au electrode upon the forma- tion of self-assembly, reducing a fraction of molecules to the hydroquinoid forms. When a positive potential is applied on the EGaIn top electrode, the reduced molecules are oxidized back to the neutral form which is cross-conjugated, and hence, is lower in con- ductance due to QI (open-symbols, reverse trace in Figure 3.8b). When a negative po- tential is applied, a few molecules switch again to the reduced, linearly-conjugated form with higher conductance (solid squares, forward trace in Figure 3.8b), causing hyster- esis in every loop. The blue curve in Figure 3.8b corresponds to J −V traces of linearly- conjugated AC molecular wire (section 3.3), as a control, which shows no hysteresis.
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ELUMOEHOMOEfermi
Figure 3.9 Transmission plots from uncorrected DFT calculations: (a) Neut- ral TCNAQ; (b) The α spin channel of TCNAQ•– ; (c) TCNAQ2 – ; (d) The β
spin channel of TCNAQ•– . The black, vertical dashed line corresponds to EFermi = −4.3 eV.[68] The electron configurations of the frontier orbitals, rel- ative to neutral TCNAQ, are shown in the insets. The uncorrected orbital en- ergies under-estimate the HOMO/LUMO gap of TCNAQ and, due to the lack of counterions and solvation, shift the orbitals of the reduced species close to vacuum.
As discussed in the earlier section 3.4, TCNAQ is even more electron-withdrawing than AQ, which results in QI dip being present further lower on the energy scale of the transmission spectra, as shown in Figure 3.5b. The frontier orbitals are also lower in energy for TCNAQ compared to AQ, tabulated in Table 3.1. This trend correlates with the transmission spectra as well where the peak (T (E) → 1) for E > EFermi is lower in energy for TCNAQ than AQ. Next, to elucidate the experimental redox- enabled memory effect, we simulated transmis- sion spectra following
the single-point energy calculations on the singly- and doubly-reduced TCNAQ species, denoted as TCNAQ•– and TCNAQ2 – , respectively.
We followed the same procedures for the calculations as mentioned earlier. The Hamiltonian (Fock) and overlap matrices were generated from the output of single-point energy calculations. In the case of the radical anions, Hamiltonian matrices were gen- erated for both the α and β spin states. The Hamiltonian and overlap matrices were then used as inputs for Artaios-030417 to generate the transmission curves using the non-equilibrium Green’s function.[67,75] This method separates the finite cluster system into a bulk calculation/approximation for the electrodes and a central subsystem that
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3.4. MOVING QI DIP BY FUNCTIONALIZING AQ
may or may not include some of the atoms from the electrodes. We omitted the elec- trodes and computed the transmission between the terminal sulfur atoms. As before, we chose EFermi value of −4.3 eV[68] to scale the E−EFermi energy axis. This value is both an approximation of the work function of EGaIn[68] and the value of Au modified with a thiol-SAM.[76]
a
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Figure 3.10 Transmission plots from DFT calculations corrected using exper- imental values: (a) Neutral TCNAQ; (b) The α spin channel of TCNAQ•– ; (c) Neutral TCNAQH2, the formally-reduced hydroquinoid form of TCNAQ in which the cross-conjugation has been deliberately broken by the addi- tion of H2; (d) The β spin channel of TCNAQ•– . The energy-axis were shif- ted to align ELUMO and ESOMO to their experimental values from cyclic voltammetry.[43] EHOMO for TCNAQ was estimated by subtracting the on- set of the reported UV-vis absorption (525 nm) from ELUMO obtained from reported CV measurements;[43] for TCNAQH2 values were taken from DFT, hence the large difference in Eg from the neutral TCNAQ. The black, vertical dashed line corresponds to EFermi=−4.3 eV. The electron configuration of the frontier orbitals relative to neutral TCNAQ are shown in the insets. The cor- rected values place the energies of ELUMO and ESOMO very close to EFermi, in agreement with our proposed mechanism of switching. The sharp dip and depressed transmission near EFermi for TCNAQ are absent for both spin channels of TCNAQ•– , but the influence of the conjugation patterns is more clearly resolved in the comparison between the two neutral species, TCNAQ and TCNAQH2.
We omitted the electrodes because we could not capture the collective effects of the SAM, particularly in a mixed-state of neutral and reduced molecules. Thus, the energies of the orbitals for the two anionic forms, TCNAQ•– and TCNAQ2 – were pushed very close to vacuum due to the absence of electrodes, coun- terions, solvation, and the near-by molecules that would be other- wise present in a SAM. Figure 3.9 shows the physically unrealistic result of these calcula- tions, which places un- occupied orbitals below EFermi in some calcu- lations and occupied above EFermi in others. The doubly-reduced species, TCNAQ2 – is particularly illustrative, placing both frontier orbitals just below 0 eV.
To try to com- pensate for the unknowables and assumptions in these model DFT calculations, we re-plotted the transmission curves using experimental values taken from CV and UV-Vis data,[43] which provide the energies of the LUMO and SOMO of TCNAQ and TCNAQ•– (from CV) and the frontier orbital gap of TCNAQ (from UV-Vis), from which the HOMO can be estimated. Note that this is a linear shift that does not correct the under-estimated Eg, which would broaden the dip near EFermi, but would not affect the interpretation of the results. Figure 3.10 shows the results of these calculations,
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a
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BDT1 BDT2 BDT3 AQ
Figure 3.11 (a) Plots of log |J (Acm−2)| versus V of Au/SAM//EGaIn junctions comprising SAMs of BDT-1 (green), BDT-2 (red), BDT-3 (blue) and AQ (black). Each datum is the peak position of a Gaussian fit of log |J | for that voltage. The error bars are 95 % confidence intervals taking each junction as a degree of freedom. (b) Transmission spectra for isolated molecules of BDT-n and AQ. The spectrum of BDT-1 is featureless between the resonances (transmission→ 1) near the frontier orbitals. The sharp dips in the spectra of BDT-2, BDT-3 and AQ are destructive QI features. The energies on the bottom axis are with respect to the EFermi value of EGaIn at −4.3 eV.
which place the LUMO and SOMO orbitals very close in energy to EFermi. The loss of the suppressed transmission and sharp dip near EFermi for TCNAQ is evident in both the α and β spin channels of TCNAQ•– . We interpret this difference as the loss of QI when the cross-conjugated core of TCNAQ is replaced by the linearly-conjugated core that is expected to be (by far) the dominant resonance structure of TCNAQ•– , however, the introduction of unpaired spins strongly affects the features of the transmission plots. Thus, we also plotted the formally reduced, but neutral hydroquinoid form, TCNAQH2, in which the cross-conjugation is deliberately removed by the addition of H2. The comparison between TCNAQ and TCNAQH2 clearly highlights the role of conjugation patterns. Taken together, the data in Figure 3.10 support our proposed mechanism, which localizes spin and charge on the central carbons of the malononitrile substituents, favoring the re-aromatization of the anthracene core.
3.5. BDT SERIES: EFFECT OF QUINONE ON QI Experimental studies on conjugation patterns other than AC/AQ are currently lim- ited to ring substitutions such as meta-substituted phenyl rings,[17–24] or varied con- nectivity in azulene.[25–27] These molecular systems differ fundamentally[2,8,32,38,46] from cross-conjugated bond topologies[30,77,78] because they change tunneling pathways or molecular-lengths or bond-topology, simultaneously. Isolating these variables is how- ever important because the only primary observable is conductance, which varies ex- ponentially with molecular length. More recent work has focused on “gating” QI effects by controlling the alignment of π-systems through-space[32–34] and affecting the orbital symmetry of aromatic rings with heteroatoms.[29,39,40] These studies exclusively invest- igate the effects of the presence and absence of QI features; to date—and despite recent efforts[79]—the specific effects of bond-topology and electronegativity on the depth and position of QI features have not been isolated experimentally.
In this section, I will discuss our work[80] where we demonstrate that the electron-
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3.5. BDT SERIES: EFFECT OF QUINONE ON QI
Figure 3.12 Molecular orbital isoplots of BDT-1, BDT-2, and BDT-3 for isovalue of 0.02 with corresponding gas-phase orbital energies shown next to the orbital diagrams.
withdrawing quinone group in AQ and the cross-conjugated bond-topology of AQ sep- arately influence the destructive QI feature. Stressing on the fact that, ‘while cross- conjugation can induce QI, quinone groups (among other electron-withdrawing groups) pull it closer to EFermi’. To understand this further, we introduced the new BDT-n series in Figure 3.4d, where we compare two structurally similar isomers, changing the position of one of the two S atoms, converting the molecule from linearly- to cross- conjugated, reducing the overall tunneling current. Dr. Y. Zhang and Dr. G. Ye de- signed and synthesized the series of benzodithiophene derivatives: benzo[1,2-b:4,5- b’]dithiophene (BDT-1, linearly conjugated), benzo[1,2-b:4,5-b’]dithiophene-4,8-dione (BDT-2, cross-conjugated with quinoid core), and benzo[1,2-b:5,4-b’]dithiophene (BDT- 3, cross-conjugated without quinone, and an isomer of BDT-1). These compounds isol- ate the influence of cross-conjugation (bond-topology: BDT-1↔BDT-3) from that of the electron-withdrawing effects of the quinone functionality (BDT-1↔BDT-2↔BDT- 3) while controlling for the molecular formula and length. The variation in the end- to-end lengths of these compounds is within 1 Å and the linear- and cross-conjugated compounds BDT-1 and BDT-3, respectively, differ only by the relative position of sul- fur atoms. This series helps us to study the effect of cross-conjugation and electron- withdrawing group independently, unlike in AQ. Here we show, how with the help of DFT and transition voltage spectroscopy, that the cross-conjugation introduces QI dip while carbonyl groups move it closer to EFermi.
The J −V data for the BDT-n series and AQ are plotted in Figure 3.11a, showing that cross-conjugation lowers the conductance of BDT-3 by an order of magnitude compared to BDT-1 but the quinone functionality of BDT-2 and AQ lowers it further by another order of magnitude, latter being in agreement with the analogous behavior of AC and AQ.[14,51] The simulated transmission spectra of the four molecules are shown in Fig- ure 3.11b. The linearly conjugated BDT-1 is featureless with high transmission, identical to AC in Figure 3.3. BDT-3 (the cross-conjugated isomer of BDT-1) has lower transmis- sion compared to BDT-1 with a destructive QI dip at −2 eV, quite far away from EFermi.
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The destructive QI dip of BDT-2 on the other hand is very close to EFermi and has same shape of the curve as AQ. Further it can be seen from Figure 3.12 that the DFT calculated frontier energy levels of BDT-2 are lower in energy than BDT-1 and BDT-3, same as AQ. The localization of the LUMO at the core of the molecule is also similar to that of AQ, as seen from Figure 3.4. This shows that the presence of an electron-withdrawing quinone group pulls the frontier orbitals lower in energy and subsequently the QI dip closer to EFermi. Because of the proximity of the QI dip to the EFermi, its effect on the conductance is more significant than in the case of BDT-3 where the QI dip is far away. The theoret- ically predicted transmission spectra, performed on single-MTJ, thus agrees remarkably with the experimentally observed tunneling conductance from MTJ comprising SAMs, exhibiting the low-bias conductance trend: BDT-1 > BDT-3 > BDT-2 ≈ AQ.
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BDT-1 BDT-2 BDT-3 BDT-1F BDT-2CH2 BDT-2S
Figure 3.13 Transmission probabilities of BDT-1, BDT-2, and BDT- 3 along with their derivatives BDT-1F , BDT-2S, BDT-2C H2 as a function of the energy of tunneling electron.
Many molecules can be difficult to synthesize, but in- silico simulations provide us with tools to investigate as many variations only limited by our creativity. Similar to the AQ derivatives described in section 3.4, we studied 3 derivatives of BDT-n series: linearly-conjugated BDT-1F containing two F atoms at the two benzylic positions of BDT-1; quinoid, cross-conjugated BDT- 2S containing S atoms instead of
O in BDT-2; quinoid, cross-conjugated BDT-2C H2 with two CH2 groups instead of O in BDT-2. The transmission spectra are shown in Figure 3.13 and the molecular orbital diagrams with the energies of the gas-phase frontier levels are shown in Figure 3.14. BDT-1F slightly shifts the transmission spectra compared to BDT-1 to lower energies and also the frontier orbitals showing the influence of the electron-withdrawing fluorine groups on the linearly-conjugated molecules. BDT-2C H2 on the other hand has two split QI dips just like the all-carbon AQ derivatives discussed earlier in the chapter. BDT-2S pulls the QI dip further down in energy just like AQ derivatives functionalized with strong electron-withdrawing groups. The effect is also evident from the molecular orbital plots in Figure 3.14 where LUMO of BDT-2S, which is the dominant frontier level participating in charge transport has similar localization of electron density as BDT-2 but with higher density on the sulfur atoms compared to oxygen atoms and the same in the rest of the orbitals. These calculations show the flexibility and opportunities that these molecular systems offer us to study and utilize QI as a feature for potential molecular electronic devices.
To demonstrate that the intrinsic molecular properties are preserved when the mo- lecule is attached between two metal clusters, we compare the isoplots of the dominant gas-phase HOMO or LUMO orbitals with the Highest Occupied π-State (HOPS) or Low- est Unoccupied π-State (LUPS) in the MTJ in Figure 3.15. HOPS and LUPS correspond to those “frontier" orbitals in these metal-molecule-metal systems in which the majority
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3.5. BDT SERIES: EFFECT OF QUINONE ON QI
Figure 3.14 Molecular orbital isoplots of BDT-n derivatives for isovalue of 0.02 with corresponding gas-phase orbital energies shown next to the orbital diagrams.
Figure 3.15 Frontier molecular orbital isoplots of BDT series (isovalue of 0.02) showing both gas-phase mo- lecular orbitals (HOMO/LUMO) and in presence of electrodes (HOPS/LUPS).
of orbital density is localized on the molecules and not the metal electrodes. It is evident that the orbital coefficients and symmetry are preserved in these calculations.
3.5.1. FUSED THIENOTHIOPHENE MOLECULAR WIRES. As an extension to our above findings with the BDT series, we further studied molecu- lar wires with fused thienothiophene rings in the core. The molecular structure of TT- 1, TT-2, and TT-3, along with the linearly-conjugated reference molecule BT is shown in Figure 3.1. All TT-n (n = 1− 3) molecular wires are structural isomers of each other where the only thing that changes is the position of the two sulfur atoms, along with the connectivity of “arms” in TT-3. This makes TT-1 linear-conjugated, while TT-2 and TT-3 cross-conjugated with one and two cross-conjugated double bonds in TT-2 and TT-3, re- spectively. Unlike BDT-n series, these molecules are devoid of any quinone functionality and help us independently investigate the effect of bond-topology and heteroatoms on QI. While TT-1 and TT-2 can be considered analogous to BDT-1 and BDT-3, respectively, TT-3 offers a different topological pattern, wherein, the single-double bond alternation is broken twice highlighted by blue and red double bonds in Figure 3.1e. If the involvement of the heteroatoms is ignored in the core, TT-2 and TT-3 can be considered equivalent to a cross-conjugated alkene with 1 and 2 nodes, respectively.
Large-area SAM based J −V measurements using EGaIn as a top electrode and CP-
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AFM were performed by Dr. Y. Zhang and Dr. X. Qiu, respectively, while single-molecule MCBJ measurements were performed by Hong et al. at Xiamen University. In all three experimental platforms, the obtained conductance trend was TT-1 > BT > TT-2. After the experiments were already performed, Dr. G. Ye also proposed TT-3 molecular wire. The synthesis and measurements of TT-3 are yet to be performed, however, that doesn’t stop us from already predicting the plausible transmission behavior of TT-3 in silico. The trend in optical bandgap (Eg ) obtained from UV-Vis spectroscopy is BT (2.76 eV) < TT-1 (2.98 eV) < TT-2 (3.26 eV) following the same trend as predicted by DFT: BT (2.82 eV) < TT-1 (3.01 eV) < TT-2 (3.59 eV). The trend in experimentally observed conductance does not follow Eg , suggesting that the tunneling change between the wires is not just a simple band-gap effect.
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BT TT-1 TT-2 TT-3
Figure 3.16 Transmission probability as a function of energy of the tunneling electron for isolated molecules of TT-1, TT-2, and TT-3 molecules with reference to the control molecule BT. The sharp dip in the spectrum of TT-2 is the destructive QI feature.
On the other hand, the trans- mission spectra obtained using DFT (using ORCA quantum chemistry package[65,66]) + NEGF (using Artaios[67]) sim- ulations, shown in Figure 3.16, exactly reproduces the experi- mentally observed trend. Just like AC and BDT-1 molecular wires, the linearly-conjugated BT and TT-1 show featureless spectra with bowl-shaped trans- mission spectra between the two resonances (transmission→ 1) around the HOMO and LUMO
energies. The cross-conjugated TT-2 shows a sharp QI dip at ≈ 1.9 eV. This QI dip even though is far away from EFermi is also accompanied by a reduction in transmis- sion probability around EFermi. This cross-conjugated induced QI dip results in the reduced conductance of TT-2. These calculations also explain why the conductance of TT-2 molecular wire is only 1 order of magnitude lower than TT-1; compared to the benchmark AQ whose QI dip is closer to EFermi and the experimental conductance is about 2 order of magnitude lower than AC, its linear analogue (section 3.3).[49] The takeaway from this series so far is the same as that from the other series discussed earlier. However, TT-3 is a unique molecule, as it now helps us study another molecule with same chemical formula but with different connectivity. As pointed out earlier, TT-3 has two cross-conjugated nodes. As can be seen in Figure 3.16, TT-3 shows the transmission further suppressed but without the presence of any QI feature. This is in agreement with the reported transmission spectra by Andrews et al.,[70] (if the presence of heteroatoms is ignored) where the addition of multiple cross-conjugated nodes re- duce the transmission systematically. Our systems present the advantage of conserving the molecular geometry across the entire series and selectively studying the effect of bond-topology on QI. If the future performed experiments agree with the transmission trend at EFermi in Figure 3.16 – TT-1 > BT > TT-2 > TT-3 – these insights gained on the role of heteroatoms will be useful from these thieonthiophenes for designing molecules
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3.6. CONCLUSIONS Combined with ab-initio Density Functional Theory calculations & Non-equilibrium Green’s Function approach on the model single-molecule tunneling junctions, we estab- lish structure-function relationship. We have shown that manipulating bond-topology and functional group effects on QI can be utilized to elucidate conductance fluctuations across series of molecules observed in large-area based MTJ. Without performing ex- cruciating DFT simulations on periodic systems, or molecular dynamics simulations on self-assembled monolayers, we show that single-molecule models can be used to draw excellent qualitative agreements with experimental observations, apart from acting as crucial support behind the laid hypotheses.
Establishing the origin of QI in linear- and cross-conjugated systems, we have estab- lished that the relative effects of QI on tunneling conductance can be tuned by substi- tuting cross-conjugated molecules, such as AQ with several electron-withdrawing and donating functional groups. We have investigated molecules in silico that are other- wise synthetically inaccessible. We have shown that we can vary the position, width and depth, and even split the QI feature by functionalization of AQ with groups such as CN, TTF, F, Br, Ph, CH2, CH3, etc. Strong electron-withdrawing tetracyanoquinone containing TCNAQ was also shown to act as a molecular switch, switching between mul- tiple redox states that enable effective QI switching for two-terminal molecular memory application, explained using DFT+NEGF simulations.
We further secluded the effects of bond-topology and quinone on destructive QI by investigating tunneling transmission in BDT-n SAMs. We conclusively demonstrated that while destructive QI is induced in cross-conjugated systems, the presence of a strong electron-withdrawing quinoid core brings the feature next to EFermi, prominently affecting its conductance. This was consequently verified in the thieonthiophene series where we could study two isomers that preserve the molecular formula but change the bond-topology from linear to cross-conjugation, making the latter less conductive than the former due to destructive QI. In another isomer of the thieothiophene series, we also studied transmission that could provide insight into the role of S as a heteroatom in mo- lecular wires, incorporating more than one cross-conjugated node in the bond-topology.
3.6.1. OUTLOOK Finally, in all the molecules discussed above, especially the AQ derivatives, the two path- ways in the molecules are always similar (in terms of conjugation pattern) formed by either two linearly-conjugated pathways in case of AC, or two broken-conjugated in AH, or two cross-conjugated pathways in AQ (including the derivatives). We have discussed how to manipulate QI by functionalizing the two pathways symmetrically. However, the presence of two different physical pathways opens the possibility of studying different intramolecular pathways in parallel. I will discuss a molecular wire system based on a fluorenone core that lets us study the effects of parallel pathways with varying conjuga- tion on QI in the next chapter.
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