The art of the possible: computational design of the 1D and 2D materials based on the tetraoxa[8]circulene monomer

Abstract

Novel one- and two-dimensional π-conjugated materials containing a tetraoxa[8]circulene monomer are designed on the basis of density functional theory techniques, including the periodic boundary condition for the infinite structures. These new materials are predicted to be the perspective ambipolar organic semiconductors showing a high mobility for hole and electron charge carriers. Furthermore, we demonstrate that the extension of π-conjugated tetraoxa[8]circulene units in the second dimension leads to a material with the HOMO–LUMO gap being significantly smaller than that for the 1D polymer ribbon. This fact clearly indicates the fundamental difference between the designed 1D and 2D semiconducting polymers, which constitutes the essence of modern “band-gap engineering”. The consistent growth of π-conjugation determines the strong visible light absorption of the studied systems in a great contrast to the initial lack of color of the tetraoxa[8]circulene compound. The possible chemical routes to synthesize the predicted materials are discussed, including free Gibbs energy estimation for the proposed reactions.

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Introduction

One of the main goals of molecular organic electronics is the controlled assembly of polymers, oligomers, molecular blocks or just small organic molecules into the desired architecture of the particular device, simultaneously providing an efficient intermolecular electron and hole transport (or photonic parameters) and a high stability of the whole network on a surface tightly bound by covalent interactions.¹ After the discovery of conductivity in conjugated polymers, the latter have found various applications, as in semiconducting and luminescent materials in OLEDs (organic light-emitting diodes) and other optoelectronic devices.² The conjugated polymers and carbon nanotubes with a one-dimensional (1D) assembly now dominate the field of organic electronics.

At the same time, two-dimensional (2D) materials such as graphene³ and graphene-like⁴ compounds are also attracting great attention in organic electronics, especially in connection with various edge modifications⁵ and patternization with regular pores in the graphene sheets.⁶ However, the vanishing band gap between the valence and conduction zones in graphene provides a great shortcoming⁷ for most optoelectronic device applications of this fantastic material.

Thus, the proper manipulation of the structural arrangement of the 2D aggregates is very important for practical applications.⁸ A manipulation with the regular pores⁶ arrangement has recently been achieved in a graphene sheet; this success can open not only the energy band gap but also other possibilities, which provides methods for introducing atoms, molecules, and functional groups into the regular pores for further functionalization.^6a

Any production of the 2D graphene-like structures starting from macro solids of a graphite type material can be classified as an assembly “from the top”.⁹ In the past decade, self-assembly on surfaces by supramolecular coordination has provided an approach for the “bottom-up” fabrication of 2D nanostructures.¹⁰

A large network is difficult to create by traditional chemical synthesis, and especially it is not easy to deposit it on a surface while remaining intact,^10a since such an assembly is typically very reactive and unstable.⁵ It is known that a scanning tunneling microscope (STM) can be used to create covalent bonds between single molecules on a surface,^1c but this method is not suitable for applications in molecular electronics where a large number of molecules need to be connected in a desired device architecture.^1b,10a Nowadays, many laboratories try to use the ability of molecules to form supramolecular structures on noble surfaces under a high vacuum by self-assembly and create tailor-made organic materials for molecular electronics.¹⁰

Great progress in organic chemistry on surfaces has lead to the synthesis of planar 2D polymers.^8,10d,e During the last few years, self-assembly on noble surfaces by supramolecular coordination has provided an efficient approach for the “bottom-up” fabrication of two-dimensional nanostructures (Fig. 1b–e).¹⁰ Li et al.¹¹ have recently studied the coordination self-assembly and metalation reaction of copper with 5,10,15,20-tetra(4-pyridyl)porphyrin (2HTPyP, Fig. 1c) on a Au(111) surface. The porphyrin 2HTPyP is found to interact with copper through both the peripheral pyridyl groups and the porphyrin core. The first, most easy polymerization occurs at room temperature when pairs of pyridyl groups from the neighboring molecules coordinate Cu(0) atoms; this leads to formation of a supramolecular metal–organic coordination network.¹¹ Annealing activates the intramolecular redox reaction, by which the coordinated copper atoms are oxidized to Cu(II) ions and the complex Cu(II)TPyP is formed.¹¹ Above 520 K, the network degrades and the Cu(0) atoms in the linking positions leave, while the Cu(II)TPyP complexes produce a close-packed structure that is stabilized by the weak intermolecular interactions forming the two-dimensional coordination network.¹¹ Another way to produce the 2D porphyrin networks was recently realized by the stepwise polymerization of tetraphenylporphyrin (TPP) monomers with different halogen-phenyl side groups (this process is known as “hierarchical growth”).^{4a,8c,10a,b,12} The structure of the produced polymers is very sensitive to the number and type of the halogen moieties.^10a As an example, the monohalogen substituted tetraphenylporphyrins can grow only in a single direction producing the corresponding dimers. Doubly halogenated TPPs are susceptible to an aligned coupling, resulting in a 1D polymer (Fig. 1a). Finally, the tetrahalogen substituted TPPs are successfully extended into the second dimension, producing the 2D networks (Fig. 2b).

Fig. 1 Some examples of the 1D and 2D polymers containing porphyrin (a–d), phthalocyanine (e) and tetraoxa[8]circulene (f and g) monomers.

Fig. 2 The structure of the tetraoxa[8]circulene sheets (n denotes the total numbers of tetraoxa[8]circulene units, whereas indicates the size of the corresponding square sheets, except rectangle compound 4 for which n = 4 and 16 in horizontal and vertical directions, i.e. ).

The well-ordered organometallic sheets consisting of two-dimensional polymeric phthalocyanine moieties (Fig. 1e) represent another type of 2D polymer synthesized from the initial benzene-1,2,4,5-tetracarbonitrile according to the “bottom-up” principle.¹³ Spitler and Dichtel¹⁴ proposed another way to obtain the phthalocyanine covalent organic frameworks by the BF₃·OEt₂-catalysed 1,4-phenylenebis(boronic acid) esterification with the phthalocyanine tetra(acetonide). The synthetic availability, structural precision and robust nature of these materials make them perspective candidates for organic photovoltaic devices.

One more chemical route to create 2D π-conjugated materials by the “bottom-up” strategy is the direct meso–meso coupling of porphyrin subunits.¹⁵ This reaction provides the formation of a non-planar cyclic porphyrin tetramer, which is transformed into the planar porphyrin sheet (Fig. 1d) upon a subsequent oxidation process. By the same principle linear 1D fused triple porphyrins were synthesized with the aim to create potential photonic wires.¹⁶ These compounds demonstrate the particular spectral and electrochemical properties associated with the presence of strongly delocalized π-electronic systems as a consequence of their planar structure.

In this way the porphyrin and phthalocyanine molecules are found to be the most promising building blocks to synthesize the novel 1D and 2D semiconducting materials (Fig. 1a–e). In the present paper we want to propose another π-conjugated macrocyclic species, tetraoxa[8]circulene (TOC),¹⁷ as a perfect candidate for 1D and 2D assembly (Fig. 1f and g). This is because the TOC molecules are stable enough and synthetically available, being susceptible to peripheral functionality in both dimensions¹⁸ due to the “square-planar” D_4h symmetry point group (like the metal porphyrins and phthalocyanines).

Computational methods

To investigate the structure, UV-visible absorption spectra and charge carrier mobilities of the new TOC-based materials, a series of model compounds was designed. One-dimensional oligomers (Fig. 1f) were constructed as n-repeating units along the 1D direction (n = 2–4, 9 and 16). The 2D sheets 1–3 were built as the square compounds sized by (n = 4, 9, 16 for compounds 1, 2, 3, respectively, Fig. 2). Another 2D sheet 4 was built asymmetrically in the form of a rectangle containing eight TOC units (Fig. 2). The terminal carbon atoms for all the model compounds were closed with hydrogen. This building principle lead to the planar π-extended 2D sheets of the repeated monomers with four nearest neighbours each (Fig. 1g, excepting the terminal edge units).

The equilibrium structural parameters of the studied molecules were optimized at the B3LYP/6-21G(d) level of the density functional theory (DFT)¹⁹ with control of the possible symmetry constraints, using the Gaussian 09 software package²⁰ (there is no significant difference observed between the structural parameters, HOMO–LUMO gaps and charge carrier reorganization energies calculated with the 6-21G(d) and extended 6-31G(d)^19d basis sets for the low-mass oligomers containing up to nine TOC units). We also calculated the Hessians for the 1D oligomers (n = 1–4) and for the simplest 2D square sheet structure containing four TOC units (2 × 2, Fig. 2) with the same B3LYP/6-21G(d) method to determine vibrational frequencies and the true minimum of the total energy. All the vibrational wavenumbers were found to be real, which indicates the location of the true minimum on the hypersurface of the total energy of the molecule. The electronic absorption spectra of all the studied molecules were calculated by the time dependent (TD) DFT method²¹ in gas phase using the same B3LYP functional and 3-21G basis set.

The reorganization energy values for the electron (λ₋) and hole (λ₊) carriers were calculated using the following equation, widely used for the estimation of the charge transport nature (n- or p-type conductivity) of organic materials:²²

λ_−/+ = (E^*_−/+ − E_−/+) + (E^**_−/+ − E₀), (1)

where E₀ is the optimized ground state energy of the neutral molecule, E_−/+ is the optimized energy of the anionic/cationic molecule, E^**_−/+ is the energy of the neutral molecule at the anionic/cationic geometry and E^*_−/+ is the energy of the anionic/cationic molecule at the optimized geometry of the neutral species.

To estimate the magnetic properties of the designed materials the nucleus-independent chemical shift (NICS)²³ indexes were calculated for the most simple sheet 1 by the B3LYP/6-311++G(d,p) method (starting from the B3LYP/6-31G(d) optimized geometry) with the gauge-independent atomic orbital (GIAO) approximation.

All the calculations were performed at the PDC supercomputers of the Royal Institute of Technology (Stockholm).

Results and discussion

Structural features

All the designed compounds, including the linear 1D oligomers and 2D sheets represent completely planar nanoscaled species. The square sheets 1–3 and the initial tetraoxa[8]circulene molecule correspond to the D_4h symmetry point group,²⁴ whereas the linear oligomers and compound 4 were assigned D_2h symmetry. In the following discussion we shall focus on the structural features of the 2D compounds 1–4, which are the primary objects of the paper. The general size parameters (length, width and total area) of the designed sheets 1–4 (Fig. 2 and 3) and ribbons (Fig. 1g) are presented in Table 1. As one can notice from Table 1, the direct fusion of the TOC monomers along both dimensions provides a decreasing size of the constructed sheets compared with the total size of the free initial TOC units. This is explained by the CH bonds disappearing upon condensation. (The data can be checked by the STM nano-size measurements and mass-spectra detection.)

Fig. 3 The optimized structure of the tetraoxa[8]circulene sheet 3 and nanotube 5 both constructed from 16 basic TOC monomers (total side area of compound 5 is equal to 12.0 nm²).

Table 1 Length (a), width (b) and total area (S) parameters for the TOC-based sheets 1–4 and 1D ribbons (n = 2–4, 9, 16)

Compound	a, nm	b, nm	S, nm^2	M, g mol^−1
1 (C88H16O16)	1.86	1.86	3.46	1329.07
2 (C192H24O36)	2.70	2.70	7.29	2906.27
3 (C336H32O64)	3.54	3.54	12.53	5091.89
4 (C172H24O32)	1.86	3.54	6.58	2602.05
1D ribbons (C46H12O8–C354H68O64)	1.02	1.86–13.6	1.90–13.87	692.59–5344.37
TOC (C24H8O4)	1.02	1.02	1.04	360.32

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Now, we shall analyze the structure of the simplest TOC-based sheet 1 in more detail, including the T₁ exited state characterisation. One should note that compound 1 remains planar in the triplet excited state and corresponds to the D_4h symmetry point group, like the ground singlet state. The T₁ state is higher in energy than the ground S₀ state by 2.11 eV, but the structure of the triplet sheet 1 is not significantly distorted compared with the ground singlet state (Fig. S1†). In both states, the central cyclooctatetraene ring consists of the alternative short and long C–C bonds, but the average alternation difference (ΔR̄‡) between two neighbouring C–C bonds is much higher for the S₁ state (ΔR̄ = 0.027 Å) than for the T₁ excited state (ΔR̄ = 0.017 Å). Such an alternation parameter for both the T₁ and S₀ states seems to be very weak in comparison with the hypothetical free planar cyclooctatetraene (ΔR̄ = 0.121 Å).²⁵ This fact qualitatively proves the very weak antiaromatic character of the inner eight-membered ring in the 1–4 sheets compared with the strongly antiaromatic free planar cyclooctatetraene.²⁵

A distinctive feature of the rectangular 2D sheets is that they become flexible and susceptible to out-of plane bending upon gradual growth. This phenomenon is well known as the “cochlea” model, proposed by Kroto and McKay to describe the mechanism of fullerene formation from curved graphene sheets.²⁶ This model was also recently approved for some other fused TOC ribbons containing one intermediate benzene ring between each of the TOC fragments.¹⁸ In this way we have predicted that the rectangular 2D sheets, like compound 4, can grow and spiralize enough to close the edge vacancies. As a result, the new 1D materials are produced in the form of the single-wall nanotubes (Fig. 3, compound 5). The diameter and length of such nanotubes depend on the size parameters a and b of the initial sheet. Another way to modify the size of TOC-based nanotubes is the insertion of additional benzene rings, which enter the naphthalene-substituted tetraoxa[8]circulene species.^17,24

An important observation is that all the tetraoxa[8]circulene sheets 1–4 and nanotubes, like 5, contain the 16-crown-4 system²⁷ (blue square in Fig. 3) which is active in respect to the metal ions extraction²⁷ (the distance between two opposite oxygen atoms equals 4.09 Å). It is possible to compare the 16-crown-4 system with the tetraoxaporphyrin molecule which exists in a dicationic form and represents the isoelectronic analogue of diprotonated porphyrin.²⁸ In this context the studied TOC-based sheets and nanotubes can be compared with the porphyrin sheets (Fig. 1d) described in ref. 15; the meso–meso fusion of the four porphyrin molecules produces the central tetraaza[8]circulene core. Similarly, the four tetraoxaporphyrin units surround each TOC unit in the corresponding 2D sheets (Fig. 3). This fact demonstrates the fundamental likeness between the TOC-based and porphyrin-based two-dimensional sheets.

Electronic absorption spectra

Experimental and calculated electronic absorption spectra of the initial tetraoxa[8]circulene compound were previously published and are well described.^24a,c In particular, the absence of a visible absorption in the observed and calculated UV-vis spectra of the free TOC molecules was highlighted. Surprisingly, we have found that the tetraoxa[8]circulene sheets 1–4 and nanotube 5 can strongly absorb light in the visible region (around 560 nm, Fig. 4, Table 2) in great contrast to the free TOC monomer and other π-extended tetraoxa[8]circulenes^17g,h which demonstrate only a weak light absorption near the blue edge of the visible region (below 410 nm).

Fig. 4 The calculated electronic absorption spectra (left side) for the compounds 1–5 (the right scale denotes molecular notations corresponding to the absorption peaks) and selected π-MO (right side) for compound 1 illustrating the dibenzofuran chromophore contribution.

Table 2 Selected vertical transitions for compounds 1–5

Compound	State	Transition	λ, nm	Mxy^a, a.u	μz^b, β	f
a Mxy – electric-dipole transition moment in the xy molecular plane.b β – Bohr magneton.
1	S1	X^1A1g → 1^1A2g	519	0	6.22	0.000
	S2(3)	X^1A1g → 1^1Eu	482	3.40	0	0.730
	S11(12)	X^1A1g → 3^1Eu	382	1.66	0	0.219
2	S1	X^1A1g → 1^1A2g	592	0	10.69	0.000
	S2(3)	X^1A1g → 1^1Eu	561	0.89	0	1.158
3	S1	X^1A1g → 1^1A2g	635	0	15.62	0.000
	S2(3)	X^1A1g → 1^1Eu	610	5.69	0	1.605
	S5(6)	X^1A1g → 2^1Eu	576	3.87	0	0.788
4	S1	X^1Ag → 1^1B1u	562	6.52	0	2.296
	S6	X^1Ag → 2^1B2u	500	3.47	0	0.732
	S11	X^1Ag → 2^1B2u	459	2.48	0	0.407
	S16	X^1Ag → 4^1B1u	435	2.52	0	0.443
	S17	X^1Ag → 5^1B1u	430	0.39	0	0.150
	S25	X^1Ag → 8^1B1u	408	1.90	0	0.270
	S28	X^1Ag → 9^1B1u	400	2.57	0	0.501
5	S1	X^1A1g → 1^1A2g	641	0	15.61	0.000
	S2(3)	X^1A1g → 1^1E2u	569	5.73	0	1.757

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In the calculated absorption spectra of the 1–3,5 species the first electronic transition X¹A_1g → 1¹A_2g is symmetry forbidden in the electric-dipole approximation (M_xy = 0), but exhibits a large magnetic–dipole transition moment μ_z (Table 2) which increases simultaneously with the total area growth (Table 1). In contrast, the doubly degenerated X¹A_1g → ¹E_u electronic transitions (Table 2) are completely allowed in the electric-dipole approximation. These transitions are characterized by huge oscillator strength values f (Table 2) and determine a strong absorption in the visible region (Fig. 4). It should be noted that the oscillator strength values are size-dependent and correlate qualitatively with the total area parameter (Table 1) of the compounds 1–5 (Table 1). This fact suggests the key role of the π-conjugation effect defining the rise of the absorption intensity with the sheet growth. A similar, size-dependent phenomenon is highly reproduced for the 1D TOC ribbons (Fig. 5) presented in Fig. 1f.

Fig. 5 The calculated electronic absorption spectra for the 1D TOC ribbons (the right scale denotes the ribbon length corresponding to the absorption peaks).

The unusually strong light absorption of the compounds 1–5 can be assigned to the formation of cyclic acene chromophores containing naphthalene moieties conjugated with the furan rings. Such an acene chromophore can be observed in Fig. 4 (right side) containing selected molecular orbitals which form the 1¹E_u excited state of compound 1. The key role of the acene (anthracene) chromophore and its clear manifestation in the absorption spectra were previously demonstrated for related TOC sheets which contain intermediate epenthetic benzene cores.¹⁸ The MO diagrams and Tables S1 and S2 presented in the ESI(†) additionally describe the absorption spectra of the 1–5 compounds.

The calculated energy (in the vertical approximation) of the first excited triplet state for compounds 1–5 is about 1.8–2.2 eV, which corresponds to the predicted phosphorescence in the range 570–670 nm (calculated energy of the T₁ exited state monotonously deceases when the molecular size increases). The T₁ → S₀ phosphorescence is forbidden by the orbital symmetry selection rule (even accounting for the spin–orbit coupling effect) and can be induced only by a spin–vibronic perturbation. With this background, a very weak and long-lived phosphorescence of the studied compound can be predicted.

The HOMO–LUMO gap engineering and charge carrier motilities

The concept of HOMO–LUMO gap (HLG) engineering is very interesting in the context of the principal differences between 1D and 2D materials. This fact opens up new opportunities to create novel, fundamentally different polymers (like the TOC sheets and ribbons) based on the same monomers.

The unique electronic coupling in the 1D and 2D TOC-based compounds results in a very strong electronic conjugation, leading to relatively small HLG values. As one can see from Fig. 6 the HLG evolves as a function of the oligomer size (1/n) for both the 1D and 2D conjugated structures. It is indicative that the HLG value is contracted by ∼1.2 eV in the 1D polymer and by ∼2.0 eV in the 2D polymer (n → ∞), compared with the initial TOC unit (1/n = 1). In this way, the principal difference between the 1D and 2D TOC-based conjugated polymers is abundantly clear: at an increasing n number, the HLG-1/n dependence quenches quickly in the 1D polymers, whereas in the 2D polymers it shows a much more rapid contraction.

Fig. 6 The size dependence behaviour of the HOMO–LUMO gap (HLG) for the TOC-based 1D and 2D oligomers/polymers.

One can conclude that the TOC-based 2D sheets are predicted to possess a very low HLG (∼1.66 eV at the boundary condition point 1/n = 0) compared with most of the known 2D-conjugated polymers.^8b The 1D tetraoxa[8]circulene ribbons are also characterized by the significantly low HLG values among the related structures like phenylene-, tetrathienoanthracene-, triphenylamine-based oligomers and polymers.^8b

The π-extended TOC-based 2D frameworks 1–4, 1D ribbons and nanotubes are also predicted to be good electron donors/acceptors, which is a general feature of the ambipolar semiconductors.²² This conclusion has been quantitatively proved on the ground of electron/hole reorganization energies (λ₋/λ₊) calculations by eqn (1) (Table 3). One should stress that the λ₋ and λ₊ values show a much more rapid decrease with the rise in the n number for the linear 1D oligomers, compared with the corresponding sheets 1–3 (Table 3). This fact demonstrates once again the fundamental size-dependent difference between the 1D and 2D oligomers containing the same number of n-repeating monomers.

Table 3 The cation and anion reorganization energies for the TOC-based oligomers

Compound	n	λ+, eV	λ−, eV
1	4	0.045	0.066
2	9	0.042	0.041
3	16	0.032	0.035
4	8	0.055	0.049
1D ribbons	2	0.155	0.115
	3	0.107	0.081
	4	0.066	0.068
	9	0.033	0.032
	16	0.019	0.020
TOC	1	0.203	0.196

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The origin of the small cation/anion reorganization energies in the TOC-based oligomers can be understood on the basis of the strong delocalization of unpaired π-electron when the one-electron oxidation/reduction takes place. Moreover, the cationic and anionic oligomers retain a high symmetry without a significant deformation of the molecular skeleton upon the oxidation/reduction impact. In this way all the terms of eqn (1) are very similar to each other. This fact provides the small λ₊/λ₋ values for the TOC-based materials (Table 3).

Aromaticity of tetraoxa[8]circulene sheets

It is well known that all hetero[8]circulenes (‡) demonstrate unusual aromatic properties, which are well described by the NICS criterion.^15b,24d,29 The sheets 1–4 are not an exception. The significantly negative NICS(0) and NICS(1) values at the center of the benzene and furan rings for compound 1 (Fig. 7) indicate the presence of an induced diatropic ring current, i.e. the aromatic character of these rings.

Fig. 7 The NICS(0) (bold type) and NICS(1) (italic type) indexes for the square TOC-based sheet 1.

The positive NICS(0) and NICS(1) values for the inner cyclooctatetraene and tetraoxaporphyrin cores (Fig. 7) correspond to the presence of the paratropic ring currents, i.e. indicate the antiaromaticity of these cores. In this way, all the studied TOC-based sheets and ribbons are predicted to be non-aromatic compounds, because of paratropic and diatropic ring-currents are completely cancelled, yielding an almost zero net current, analogous to the well known saturated cyclic hydrocarbons and fullerene C₆₀.³⁰ In contrast, the dianionic compound 1 is predicted to be a completely aromatic species because of the inner cyclooctatetraene, tetraoxaporphyrin cores and all the surrounding benzene and furan rings are strongly aromatic (the corresponding NICS indexes are significantly negative, Fig. S8, ESI(†)). The dicationic compound 1 is predicted to possess a non-aromatic cyclooctatetraene core, but the other benzene, furan rings and tetraoxaporphyrin core support an aromatic character (Fig. S8†). Thus, we have predicted that the dicationic sheet 1 in total represents the predominantly aromatic species because of the prevailing diatropic ring currents presence.

Possible routes to synthesize the tetraoxa[8]circulene sheets

The synthesis of the TOC-based sheets and linear oligomers is an extremely important task which would open up new perspectives to create novel graphene-like semiconducting materials with the non-zero band-gap. In the present work, we have predicted two possible chemical routes to obtain the 2D oligomers 1–4 in accordance with the “bottom-up” principle (from the initial tetraoxa[8]circulene to the objective sheet). The first possible route represents the intermolecular dehydrohalogenation (IDHH) process of the corresponding dibromo dehydrohelicenes (§) (Scheme 1a). Such reactions are widely used for the C–H bond functionalization of heteroarenes (these reactions are metal-catalyzed in general).³¹

Scheme 1 The intermolecular dehydrohalogenation process as a possible route to synthesize the TOC-based sheet 1.

The calculated enthalpy and the free Gibbs energy for the IDHH Scheme 1a and b are found to be significantly negative. This fact indicates the principal possibility of these reactions from the thermodynamic point of view, though the proposed schemes are hypothetical. The main purpose of Scheme 1 is to demonstrate the high thermodynamic stability of the TOC-based sheets relative to the initial monomeric units. Indeed, the fusion of the four initial molecules (Scheme 1) provides the formation of the strongly π-conjugated sheet 1 in which the fused bonds (marked by the blue colour in Scheme 1) are implicated into the aromatic system of the local naphthalene moiety.

The second possible route represents an Ullman-type polymerization through the tetrabromo dehydrohelicenes (Fig. S8†) similar to those presented in Scheme 1. Such a route seems to be very reliable because most of the presently known 1D and 2D polymers are synthesized through an Ullman-type polymerization.^1c,10c,32 It should be noted that the Ullman polymerization opens up new routes to synthesize the planar TOC-based 2D frameworks, which contain additional four-membered “links” between the coupled monomers (Fig. S8†). Such compounds also provide interest for future investigation.

Conclusions

Nanoscaled 1D ribbons, 2D sheets and single-wall nanotubes containing directly fused tetraoxa[8]circulene monomers have been designed and described in the present work for the first time. The constructed tetraoxa[8]circulene sheets are found to be absolutely planar compounds which exhibit a trend to the bending ability for rectangular sheets with a subsequent spiralization and closure into the single-wall nanotube. The designed 1D and 2D compounds are characterized by the strong size-dependent visible absorption, because of the specific π-conjugation producing cyclic dibenzofuran chromophore.

Our calculations indicate that the HOMO–LUMO gap of the designed 2D sheets is significantly smaller than that of their linear 1D counterparts at large n values. This fact demonstrates novel possibilities in “band-gap engineering” activities, which is popular nowadays in order to create new materials for molecular organic electronics. Indeed, all the designed compounds (except the initial tetraoxa[8]circulene monomer) are predicted to be ambipolar organic semiconductors. This prediction is supported by the very small values of the electron/hole reorganization energies.

In the present work, we have additionally predicted possible ways for the experimental synthesis of the designed compounds. Among all the considered reaction schemes, only two routes seem to be the most reliable from the thermodynamic point of view: (i) the intermolecular metal-catalyzed dehydrohalogenation and (ii) the Ullman-type polymerization widely used nowadays for the synthesis of new 1D and 2D π-conjugated materials.

The calculations with the small and large basis sets for the smallest square molecule 1 justify the reliable accuracy level of the methods used and all the conclusions remain. For instance, the deviations in the bond lengths calculated with the two different basis sets 6-21G(d) and 6-31G(d) are negligibly small and do not exceed 0.004 Å. The estimated HGL values are equal to 2.69 and 2.72 eV, respectively, which also indicates the close similarity of both approaches. As a general tendency,^8b the combination of the B3LYP functional and the 6-31G(d) basis set (which similarly predicts the structure, λ₊/λ₋ and HLG values compared with the 6-21G(d) basis set) is a reasonable approach to predict the HLG of organic polymers³⁵ and seems to circumnavigate the frequently encountered underestimation of the band gap for 3D metals and semiconductors.³⁶

Acknowledgements

All the computations were performed with the resources provided by the Swedish National Infrastructure for Computing (SNIC) at the Parallel Computer Center (PDC) through the project “Multiphysics Modeling of Molecular Materials”, SNIC 020/11-23. This research was also supported by the Ministry of Education and Science of Ukraine (project number 0113U001694).

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available: Bond lengths for S₀ and T₁ states of compound 1, optimized Cartesian coordinates for compounds 1–5 and linear oligomers (n = 2–4, 9, 16), MOs energy diagrams for compounds 1–5, NICS calculations for the dicationic and dianionic compound 1, chemical schemes of the Ullman-type polymerization for the synthesis of compound 1. See DOI: 10.1039/c4ra02693d

‡ The hetero[8]circulenes family includes already synthesized tetraoxa[8]circulenes, azaoxa[8]circulenes, thio[8]circulenes and numerous theoretically predicted hetero[8]circulenes, containing different types of heteroatoms and groups (B, N, P, As, BF₂, AlF₂, GaF₂ etc.).^29a,b,d,33

§ Compounds (such as the reagents in Scheme 1a) in which the two helical termini of a helicene are connected by a σ-bond are called dehydrohelicenes. The sulfuric dehydrohelicenes were synthesized and comprehensively studied by Wynberg and colleagues.³⁴ The proposed oxygen-containing dibromo dehydrohelicenes are not yet synthesized, whereas they are closely similar to the sulfuric analogs and related polythioles.³⁴

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