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. 2024 Feb 22;9(9):10610–10620. doi: 10.1021/acsomega.3c08944

Carbon Nanohoops: Multiple Molecular Templates for Exploring Spectroscopic, Electronic, and Thermoelectric Properties

Oday A Al-Owaedi 1,2,*
PMCID: PMC10918671  PMID: 38463279

Abstract

graphic file with name ao3c08944_0006.jpg

A combination of density functional theory (DFT) methods and quantum transport theory (QTT) has been used to investigate the spectroscopic, electronic, and thermoelectric properties of carbon nanohoop molecules with different molecular templates. The connectivity type, along with inherent strain, impacts the transport behavior and creates a destructive quantum interference (DQI), which proves itself to be a powerful strategy to enhance the thermoelectric properties of these molecules, making them promising candidates for thermoelectric applications.

Introduction

The individual and unique morphology of carbon-based materials has made them a goal of many studies investigating the chemical and physical properties of devices based on these materials over the past century.1−5 One of these materials is the carbon nanohoop (CNH), which has attracted wide interest and many applications, such as organic electronics,6,7 supramolecular sensing,8−10 and bioimaging.11 The planarity of sp2-carbon centers,12 which form π-orbitals, has granted the CNH molecules an attractive functionality as incarnated by their unique charge transport properties. In this context, Terri C. Lovell et al.6 demonstrated that the strain played a central role in defining the properties of carbon nanohoops and controlling the photophysical properties of these molecules, which are particularly exciting. In addition, Ramesh Jasti et al.1 theoretically investigated the structural and optical properties of the carbon nanohoop molecules, and they proved that the favored geometry for the even-membered nanohoops, [12]- and [18]cycloparaphenylene, was a staggered configuration in which the dihedral angle between two adjacent phenyl rings alternated between 33 and 34°, respectively. Furthermore, the effect of the strain in the π-conjugated hoop molecules13 on the structural, spectroscopic, and optical properties of cycloparaphenylacetylene (CPP) and cycloparaphenylene molecules has been studied widely via many research studies.12,14−19 On a few occasions, the charge transport properties of nanohoops were studied. Kayahara et al.7 reported that CPP molecules might be interesting materials for charge storage due to their rigid structure, intrinsic porosity, and tunable properties. However, in only one case was the application of a CPP derivative investigated for charge storage.20,21 The bending of aromatic units could lead to the lack of synthetic generality and low stability, but the property of preservation of the radial conjugation of π-orbitals that distinguished these molecules, assisting the formation of CHN structures in different shapes such as circle, square, and triangle templates, as well as rectangle and star structure shapes.22 Exploring the spectroscopic, electronic, and thermoelectric properties of CNH molecules with different molecular templates provides more insights into the structure–property relationship and may answer fundamental questions on the topic of quantum interference (QI) in single-molecule junctions.23−30 A tunneling process pictures the coherent electron transport through a metal–molecule–metal sandwich structure.31 Quantum interference is not only one of the phenomena that characterizes32,33 the tunneling transport but also controls most of the properties of molecular junctions.23−30 Carbon nanohoop molecules and their derivatives could be a perfect candidate to explore quantum interference (QI), since they provide a powerful way to investigate the propagation of de Broglie waves through source |molecule| drain configuration. If the phases of the propagated waves are identical, then constructive quantum interference (CQI) occurs, leading to effective transport and high electrical conductance.34−38 In contrast, if the waves are out of phase, then destructive quantum interference (DQI) occurs and the transport is blocked.39−43 The spectroscopic1,44−46 and optical47−49 properties of carbon nanohoops have been studied widely, but the investigation of QI effect on electronic and thermoelectric properties of this kind of molecules is limited. Therefore, this work aims to explore the impact of QI on these properties using a combination of density functional theory (DFT) methods49,50 and quantum transport theory (QTT).50−61

Theoretical Methods

The initial optimization of gas-phase molecules, isosurfaces, and spectroscopic calculations was carried out at the B3LYP level of theory62 with the 6-31G** basis set63,64 using density functional theory (DFT) and time-dependent DFT (TD-DFT).65 The geometric optimization of all gold |molecule| gold configurations under investigation in this work was carried out by the implementation of DFT50,51 in the SIESTA50 code, as shown in Figure S2 (see the Supporting Information). The generalized gradient approximation (GGA) of the exchange–correlation functional was used with a double-ζ polarized (DZP) basis set, a real-space grid defined with an equivalent energy cutoff of 250 Ry. The geometry optimization for each structure is performed to force smaller than 20 meV/Å. The mean-field Hamiltonian obtained from the converged DFT calculations was combined with the GOLLUM53 code. The quantum transport theory (QTT)52−61 implemented in GOLLUM has been used to calculate the electronic and thermoelectric properties of all molecular junctions.

Results and Discussion

A family of five carbon nanohoop molecules was chosen for the study here, as shown in Figure 1. In the quest to investigate the effect of the strain and connectivity type on the properties of molecules, the molecules under investigation were selected with five different shapes.

Figure 1.

Figure 1

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Schematic illustration of carbon nanohoop molecules in different molecular templates.

Figure 1 shows that the first molecule (CNH-1) has a circular shape, while the second molecule (CNH-2) has a square structure. The third molecule (CNH-3) possesses a structure shape close to triangular. A rectangular shape is the closest picture of the fourth molecule (CNH-4), and the matching description of molecule five (CNH-5) is the star-shaped structure. These molecules are cycloparaphenylene (CPP) molecules, which are typical π-conjugated molecules consisting solely of phenyl rings connected at the para-position, except for the molecule (CNH-5) in which phenyl rings are connected at ortho and meta positions. Shigeru et al.12 mentioned that the strain impact is a crucial parameter in this kind of molecule. Therefore, this work seeks to explore the molecular shape effect on the strain and thus the properties of these molecules. The choice of molecule CNH-5 with a star-shaped structure is to obtain more insights into the role of different connectivities (para or meta) between phenyl rings in creating constructive or destructive interference.

The orbital distribution and the electronic structure of molecules were investigated, and the plots of the optimized structures and the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) are given in Figure 2. The HOMOs of all molecules display a familiar pattern of π–π interactions along the molecular backbone. The LUMOs are also localized over the molecular backbones and could be described as a π-conjugated system. In addition, Figure 2 and Table 1 show that the values of the HOMO–LUMO gap have fluctuated, and the highest value (3.86 eV) was given by molecule CNH-5, while the lowest value (2.59 eV) was exhibited by molecule CNH-4. These results are consistent with previous studies.12 They reported that the HOMO and LUMO of cycloparaphenylenes (CPPs) rings become higher and lower in energy, respectively, as the number of paraphenylene units decreases due to the decrease of the effective π-conjugation. Furthermore, the calculated values of the HOMO–LUMO gap ranged from 2.59 to 3.86 eV, which are close to the HOMO–LUMO gap of the C60 molecule, indicating that the carbon nanohoop is a promising molecule for material applications.66

Figure 2.

Figure 2

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Optimized geometry of all molecules in a gas phase (structure), HOMOs, and LUMOs (isosurfaces ±0.02 (e/bohr3)1/2). The white part has a positive sign, and the blue part has a negative sign. aH.aL is the multiplication of the HOMO and LUMO amplitudes. As an example, when HOMO and LUMO for the CNH-1 molecule possess different signs, then the multiplication of molecular orbital amplitudes (aH.aL) has a negative sign, and the molecule exhibits CQI.

Table 1. H–L Gap is the HOMO–LUMO Gap, A is the Absorption Intensity, Aλmax is the Maximum Absorption Wavelength, E is the Emission Intensity, EλMax is the Maximum Emission Wavelength, fem is Emission Oscillator Strength, and SS is the Stokes Shift.

molecule H–L gap (eV) A (a.u.) Aλmax (nm) E (a.u.) Eλmax (nm) fem SS (nm)
CNH-1 2.64 257.1 374.4 9433.6 399.6 0.13 25.2
CNH-2 2.85 1392.5 379.8 52723.4 406.8 1.3 27
CNH-3 3.39 1492.6 343.6 47238.5 365.2 1.13 21.6
CNH-4 2.59 130.7 396 5355.3 424.8 0.11 28.8
CNH-5 3.86 315.4 326.8 8846.8 345.7 0.22 18.9
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In order to explore the impact of connectivity type and to prove the existence of CQI and DQI in carbon nanohoop molecules, the current investigation performed an orbital analysis and demonstrated that CQI was dominated on the transport of all molecular junctions, except the transport through the CNH-5 molecular junction, which is dominated by DQI, as shown in Figure 2. Lambert et al.67 reported an orbital symmetry rule. The magic ratio theory68 is based on utilizing the exact core Green’s function defined as follows.

graphic file with name ao3c08944_m001.jpg 1

In the literature, various approximations to g(E) are discussed, one of which involves the approximation of including only the contributions to g(E) from the HOMO and LUMO. If the amplitudes of the HOMO on sites a and b are denoted ψEHa and ψEHb and the amplitudes of the LUMO are ψELa and ψELb, respectively, and the contributions from all other orbitals are ignored, then a crude approximation to Green’s function gba(E) is

graphic file with name ao3c08944_m002.jpg 2

where EH and EL are the energies of the HOMO and LUMO, respectively. If the HOMO product ψEHbψ(EH)a has the same sign as the LUMO product ψ(EL)bψ(EL)a, then the right-hand side of eq 2 will vanish for some energy E in the range EH ≤ E ≤ EL. In this case, one can say that the HOMO and LUMO interfere destructively. On the other hand, if the HOMO and LUMO products have opposite signs, then the right-hand side of eq 2 will not vanish within the HOMO–LUMO gap and one can say that the HOMO and LUMO interfere constructively within the gap. (They could of course interfere destructively for some other energy E outside the gap.) When the right-hand side of eq 2 vanishes, the main contribution to gba(E) comes from all other orbitals, so in general, eq 2 could be a poor approximation. One exception to this occurs when the lattice is bipartite because the Coulson–Rushbrooke (CR) theorem69 tells us that if a and b are both even or both odd, then the orbital products on opposite sides of eqs 3 and 4 have the same sign. Consequently, when the HOMO and LUMO interfere destructively, all other pairs of orbitals interfere destructively, leading to the trivial zeros in the magic number table,68 for which gba(0) = 0.

graphic file with name ao3c08944_m003.jpg 3
graphic file with name ao3c08944_m004.jpg 4

Here, ± En are eigenvalues in ±pairs, and the eigenstate belonging to −En is related to the eigenstate belonging to En. Obviously, this exact cancellation is a property of bipartite lattices only, but based on its success for bipartite lattices, one might suppose that eq 2 is a reasonable approximation for other lattices. Nevertheless, as pointed out by Yoshizawa et al.,70−73 since orbitals such as those in Figure 2 are often available from DFT calculations, it can be helpful to examine the question of whether or not the HOMO and LUMO (or indeed any other pair of orbitals) interfere destructively or constructively, by examining the colors of orbitals. This is simplified by writing eq 2 in the following form

graphic file with name ao3c08944_m005.jpg 5

where aH = ψ(EH)aψ(EH)b and aL = ψ(EL)aψ(EL)b. If the HOMO product aH has the same sign as the LUMO product aL, then the right-hand side of eq 5 will vanish for some energy E in the range EH ≤ E ≤ EL. In other words, HOMO and LUMO will interfere destructively for some energy within the HOMO–LUMO gap. However, this does not mean that the exact gba(E) will vanish. Indeed, if the right-hand side of eq 5 vanishes, then the contributions from all other orbitals become the dominant terms.74 Nevertheless, this is an appealing method of identifying QI effects in molecules and describing their qualitative features.75

The distinctive properties of carbon nanohoops including for example their spectroscopic properties, especially the absorption and emission spectra, have become the subject of the increased interest for many scientific studies.76 Interestingly, the UV/visible absorption and emission spectra showed asymmetric peaks, since the range of the absorption spectra extends from 326.8 to 396 nm, as shown in Table 1, and the emission spectra ranges from 345.7 to 424.8 nm. These results could be interpreted in terms of strain and molecular shape effects, which are critical qualities that endow molecules with atypical spectroscopic properties and reactivity, since the inherent strain of the molecule increases with the decrease of the carbon nanohoop size and consequently changes the structural and spectroscopic properties. In fact, the carbon nanohoops (CNH-5 and CNH-4) possess the poorest geometry for the orbital overlap and the fewest number of aryl rings. Thus, these molecules are expected to have a small size, which in turn leads to a smaller optical absorption gap47 than that of large-size molecules (CNH-1, CNH-2, and CNH-3). These results are consistent with the results of refs (1,12,77). Furthermore, Figure 3 and Table 1 show that the Stokes shift of these molecules is lowered with a decrease of size, and the values of Stokes shift range from 18.9 to 27 nm. These results may introduce CNH-4 and CNH-2 molecules as promising candidates for encryption and medical applications.78,79

Figure 3.

Figure 3

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UV/vis absorption spectra (solid curves) and emission spectra (dashed curves) for all molecules.

One of the most important parameters in optoelectronic applications is the emission oscillator strength (fem).80 Theoretically, for a given PL material, fem is directly proportional to the emission cross section (σem), which is given by81

graphic file with name ao3c08944_m006.jpg 6

where e is the electron charge, ε0 is the vacuum permittivity, me is the mass of the electron, c0 is the speed of light, nF is the refractive index of the gain material, ν is the frequency of the corresponding emission, and g(ν) is the normalized line shape function with ∫g(ν)dν = 1. Table 1 shows that two molecules (CNH-2 and CNH-3) have fem values of 1.3 and 1.13, respectively. These results could be ascribed to the highest intensity value of the emission spectra of these molecules (52723.4 and 47238.5 au, respectively), indicating the highest HOMO → LUMO transition rate in these molecules, which might be attributed to an increase in their emission cross section (σem), suggesting that CNH-2 and NH3 are appropriate molecules for optoelectronic applications.

In this work, T(E) has been calculated by attaching the optimized molecules with two (111)-directed gold electrodes, which involve two small layers (each one consists of 6-atoms pyramidal gold lead), and seven layers of (111)-oriented bulk gold with each layer consisting of 6 × 6 atoms, and a layer spacing of 0.235 nm to create molecular junctions, (see the Supporting Information for all models). These layers were then further repeated to yield infinitely long gold electrodes, which carry the electric current. From these molecular junctions, electronic and thermoelectric properties were calculated using the GOLLUM code.53 The transmission coefficient according to the Landauer–Büttiker82 formalism is given by

graphic file with name ao3c08944_m007.jpg 7

where

graphic file with name ao3c08944_m008.jpg 8

where ΓL,R describes the level broadening due to the coupling between left (L) and right (R) electrodes and the central scattering region, and ∑L,R(E) are the retarded self-energies associated with this coupling.

graphic file with name ao3c08944_m009.jpg 9

Here, GR is the retarded Green’s function, H is the Hamiltonian, and X is the overlap matrix. The transport properties are then calculated using the following Landauer formula

graphic file with name ao3c08944_m010.jpg 10

where f is the Fermi–Dirac probability distribution function.

Figure 4 shows the transmission coefficient T(E)83 of source |molecule| drain molecular junctions. The signature of constructive quantum interference (CQI) is clear for the first four molecules, which leads to high T(E) values, as shown in Figure 4 and Table 2. These outcomes are ascribed to the para connectivity84−89 between phenyl rings. In contrast, an antiresonance feature appears at the middle of the HOMO–LUMO gap in the transport curve of the CNH-5 molecule, which is a representation of the destructive quantum interference (DQI).25−27,32,33,39 Herein, the meta connectivity between phenyl rings results in the lowest T(E) value. In addition, the values of T(E) for CHN-1, CNH-2, and CNH-4 molecules are close to each other and smaller than that of the CNH-3 molecule, as shown in Table 2. These results could be understood in terms of the inherent strain, which resulted in the molecular shape effect (≈ a triangular shape) and in turn decreased the tunneling distance (l) for the CNH-3 molecule and consequently increased T(E), according to eq 11.

graphic file with name ao3c08944_m011.jpg 11

Here, T(E) is the transmission coefficient, β is the electronic decay constant, and l is the tunneling distance. In addition, the molecule length of compounds studied here of ca. > 2 nm is consistent with a dominant contribution from the coherent tunneling mechanism.90−93 The rectangular tunnel barrier model94 states that the electrical conductance through a single molecule (barrier) decreases exponentially with the length of the barrier, according to eq 11.

Figure 4.

Figure 4

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Transmission coefficient T(E) as a function of the electron energies for all molecules.

Table 2. Transmission Coefficient T(E), Molecule Length (l = S···S), Highest Occupied Molecular Orbitals of the Molecules in a Junction (JHOMO), Lowest Unoccupied Molecular Orbitals of the Molecules in a Junction (JLUMO), and HOMO–LUMO Gap (JH–L Gap) of the Molecules in a Junction.

molecule T(E) l (nm) JHOMO (eV) JLUMO (eV) JH–L gap (eV)
CNH-1 5.99 × 10–4 1.361 0.27 0.86 1.13
CNH-2 3.14 × 10–4 1.723 0.25 1.13 1.38
CNH-3 1.63 × 10–3 1.083 0.31 0.98 1.29
CNH-4 1.51 × 10–4 1.292 0.31 0.95 1.26
CNH-5 2.06 × 10–6 1.295 0.34 0.88 1.22
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With the integration of these results with spectroscopic results, there is a prediction that the first four molecules might be promising candidates for electronic and optoelectronic applications.

Exploring the influence of DQI on the transport behavior and consequently on the thermoelectric properties is one of the main goals of this work. The slope of T(E) determines the Seebeck coefficient (S) and thus the electronic figure of merit (ZelT). The Seebeck coefficient (S), power factor (P), and (ZelT) are given by

graphic file with name ao3c08944_m012.jpg 12

where L is the Lorenz number Inline graphic WΩK–2. In other words, S is proportional to the negative slope of ln  T(E), evaluated at the Fermi energy. Based on the Seebeck coefficient, the power factor was calculated by

graphic file with name ao3c08944_m014.jpg 13

where T is the temperature T = 300 K, G is the electrical conductance, and S is the Seebeck coefficient, and the purely electronic figure of merit (ZelT) is given by95,96

graphic file with name ao3c08944_m015.jpg 14

where kel is the electron thermal conductance. According to previous studies,95,96 the figure of merit in this work has been calculated only based on a purely electronic contribution.

It is well known that the performance of thermoelectric materials is characterized by an efficient conversion of input heat to electricity.97,98 In this context, the enhancement of power factor (P) and electronic figure of merit (ZelT), which depend on the Seebeck coefficient (S), is important. Figure 5bc and Table 3 show that the highest values of S and ZelT (37.24 μVK–1 and 1.17, respectively) have been exhibited by molecule CNH-5. In contrast, molecule CNH-4 presented the lowest values of these parameters (3.13 μVK–1 and 0.036, respectively). These results not only demonstrated the important role of DQI in the improvement of S and ZelT for molecule CNH-5 but also established a crucial role of the inherent strain in the CNH-4 molecule, which might contribute to lowering the values of S and ZelT. In addition, the competition between electrical conductance and the Seebeck coefficient according to eq 13 led to the power factor order of PCNH-3 > PCNH-2 > PCNH-1 > PCNH-5 > PCNH-4. In light of the aforementioned results, these molecules could be considered promising candidates for thermoelectric applications. Furthermore, Figure 5a and Table 3 present the current–voltage (I–V) characteristics of all molecular junctions, which are limited to the first and third quadrants of the I–V plane crossing the origin. Therefore, they are classified as components that consume electric power, and here, the importance of the threshold voltage (Vth) value appears.

Figure 5.

Figure 5

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(a) Current–voltage characteristics, (b) Seebeck coefficient (S), (c) electronic figure of merit (ZelT), and (d) electrical conductance (G/G0) as a function of the voltage of all molecular junctions.

Table 3. Electrical Conductance (G), Seebeck Coefficient (S), Power Factor (P), Electronic Figure of Merit (ZelT), and Threshold Voltage (Vth) of all Molecular Junctions.

molecule G/G0 S (μVK–1) P (WK–1) × 10–17 ZelT Vth (V)
CNH-1 0.46 × 10–7 3.62 6.11 0.048 0.36
CNH-2 0.24 × 10–7 13.45 44.14 0.35 0.21
CNH-3 0.12 × 10–6 12.67 204.06 0.33 0.15
CNH-4 0.11 × 10–7 3.13 1.11 0.036 0.44
CNH-5 0.16 × 10–9 37.24 2.22 1.17 0.29
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The values of Vth range from 0.15 to 0.44 V, which makes these molecules promising candidates for electronic applications. Moreover, I–V characteristics of all molecular junctions exhibited a semiconductor behavior, except for the CNH-5 molecule, which shows the quantum staircase structure in the conductance. Obviously, as the voltage increases, the density of electrons also increases, which leads to an increase in the number of occupied subbands. The dependence conductance, in this case, is a set of plateaus separated by steps of height 2e2/h: a stepwise change in the conductance of the CNH-5 molecule channels occurs each time the Fermi level coincides with one of the subbands. Hence, the quantum staircase behavior could be attributed to the adiabatic transparency of spin-nondegenerate subbands of the CNH-5 molecule.75,99

Conclusions

In conclusion, the type of connectivity whether it is meta or para along with the molecular shape effect is a crucial parameter in controlling and improving the spectroscopic, electronic, and thermoelectric properties of carbon nanohoop molecules. In addition, this work has concluded that the inherent strain plays an important role in governing transport behavior. The most important conclusion is that carbon nanohoop molecules are a perfect host to examine the destructive quantum interference, which proved itself to be a robust strategy to enhance the thermoelectric properties of these molecules, making them a suitable material for thermoelectric applications. The spectroscopic results provided a considerable body of information for designing effective materials for optoelectronic, encryption, and medical applications.

Acknowledgments

O.A.A. thanks the University of Babylon and Al-Zahrawi University College for their support.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c08944.

  • Theories and all details relevant to the computational methods, as well as the theoretical models of all source |molecule| drain configurations100−115 (PDF)

The author declares no competing financial interest.

Supplementary Material

ao3c08944_si_001.pdf (766.5KB, pdf)

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