Quantum-Chemical Insights into the Self-Assembly of Carbon-Based Supramolecular Complexes

Abstract

Understanding how molecular systems self-assemble to form well-organized superstructures governed by noncovalent interactions is essential in the field of supramolecular chemistry. In the nanoscience context, the self-assembly of different carbon-based nanoforms (fullerenes, carbon nanotubes and graphene) with, in general, electron-donor molecular systems, has received increasing attention as a means of generating potential candidates for technological applications. In these carbon-based systems, a deep characterization of the supramolecular organization is crucial to establish an intimate relation between supramolecular structure and functionality. Detailed structural information on the self-assembly of these carbon-based nanoforms is however not always accessible from experimental techniques. In this regard, quantum chemistry has demonstrated to be key to gain a deep insight into the supramolecular organization of molecular systems of high interest. In this review, we intend to highlight the fundamental role that quantum-chemical calculations can play to understand the supramolecular self-assembly of carbon-based nanoforms through a limited selection of supramolecular assemblies involving fullerene, fullerene fragments, nanotubes and graphene with several electron-rich π-conjugated systems.

Keywords: carbon-based supramolecular assemblies; noncovalent interactions; quantum chemistry.

Figure 1

Selected examples of supramolecular assemblies involving fullerene (a), nanotubes (b) and graphene (c) with different π-conjugated electron-donors. The carbon atoms of the electron-acceptor carbon-based systems have been highlighted in red whereas the carbon atoms of the electron-donor systems are colored in green. Sulfur, oxygen and hydrogen atoms in the electron-donor systems are colored in yellow, red and white, respectively.

Figure 2

Chemical structure of TTF (a) and exTTF (b). The curved shape of exTTF is also represented (c). Sulfur, carbon and hydrogen atoms are colored in yellow, green and white, respectively. Chemical structures of the supramolecular complexes MTW•C₆₀ (d) and PTW•C₆₀ (e) are also shown.

Figure 3

Complexes obtained from exTTF-based 1–6 and C₆₀. Reproduced from Reference [84] with permission from the Royal Society of Chemistry.

Figure 4

Minimum-energy embraced (a) and non-embraced (b) conformations calculated at the PM7 level for the 2•C₆₀ complex. The electron-acceptor C₆₀ is colored in red whereas the sulfur, carbon, oxygen and hydrogen atoms in the electron-donor system are colored in yellow, green, red and white, respectively.

Figure 5

B97-D/cc-pVDZ minimum-energy geometries calculated for the exTTF•C₆₀ and 1–6•C₆₀ complexes. The electron-acceptor C₆₀ is colored in red whereas the sulfur, carbon, oxygen and hydrogen atoms in the electron-donor system are colored in yellow, green, red and white, respectively.

Figure 6

Side view of the B97-D/cc-pVDZ-optimized geometries calculated for complexes 2•C₆₀ (a) and 5•C₆₀ (b) showing the different spatial arrangement of the crown and aza-crown ethers, respectively, along the C₆₀ guest. The electron-acceptor C₆₀ is colored in red whereas the sulfur, carbon, oxygen and hydrogen atoms in the electron-donor system are colored in yellow, green, red and white, respectively.

Figure 7

Chemical structure of the truxene and truxTTF compounds.

Figure 8

Minimum-energy structures of the truxTTF•C₆₀ complex calculated at the MPWB1K/6-31G** level. Top and side view of structures CC (a) and CS (b) are given. The electron-acceptor C₆₀ is colored in red whereas the sulfur, carbon and hydrogen atoms in the electron-donor system are colored in yellow, green and white, respectively.

Figure 9

Chemical structure of the methano[60] fullerene guest 7 (Left), the metalloporphyrin host 8-M (Center), and the host–guest supramolecular complex 8-M•7 (Right). M refers to either 2H, Co., Ni, Cu or Zn.

Figure 10

Minimum-energy geometries calculated for the 8-Cu•7 complex at the PM7 level. Side (Left) and front (Right) views are displayed. The different types of intermolecular contacts are denoted with labels a–d. Only relevant hydrogen atoms are displayed for clarity. Except for C₆₀ carbon atoms depicted in grey, the following color code is used: carbon in green, nitrogen in blue, oxygen in red and hydrogen in white.

Figure 11

Porphyrin•C₂H₄ model (MP•C₂H₄) used to understand the nature of the interaction between the porphyrin host 8 and the fullerene derivative guest 7. Except for the ethylene carbon atoms depicted in red, the following color code is used: carbon in green, nitrogen in blue and hydrogen in white.

Figure 12

Chemical structure of the ditopic porphyrin-based hosts 9 and 10.

Figure 13

Chemical structure (Left) and minimum-energy geometry calculated at the B97-D3/(6-31G**+LANL2DZ) level (Right) of the supramolecular assembly of ditopic host 9 with one and two molecules of guest 7. Except for C₆₀ carbon atoms depicted in grey, the following color code is used: carbon in green, nitrogen in blue, oxygen in red and hydrogen in white. Adapted with permission from [90]. Copyright 2014 American Chemical Society.

Figure 14

Chemical structure (left) and minimum-energy geometry calculated at the B97-D3/(6-31G**+LANL2DZ) level (right) for the supramolecular assembly of ditopic host 10 with one and two molecules of guest 7. Except for C₆₀ carbon atoms depicted in grey, the following color code is used: carbon in green, nitrogen in blue, oxygen in red and hydrogen in white. Adapted with permission from [90]. Copyright 2014 American Chemical Society.

Figure 15

Chemical structure of the hemifullerene C₃₀H₁₂ buckybowl (a); Structure of the dimers formed by C₃₀H₁₂ (carbon atoms in red) in its trigonal (b) and orthorhombic (c) crystal polymorphs, respectively; (d) Dimers formed by truxTTF in the crystal. For C₃₀H₁₂, the carbon atoms are depicted in red and hydrogen atoms in white. For truxTTF, the sulfur, carbon and hydrogen atoms are colored in yellow, green and white, respectively.

Figure 16

Minimum-energy structures (A1–4) computed for the truxTTF•C₃₀H₁₂ heterodimer at the revPBE0-D3/cc-pVTZ level. For C₃₀H₁₂, the carbon and hydrogen atoms are depicted in red and white, respectively. For truxTTF, the sulfur, carbon and hydrogen atoms are colored in yellow, green and white, respectively.

Figure 17

Selected intermolecular distances computed for structures A1–A4 at the revPBE0-D3/cc-pVTZ level. For C₃₀H₁₂, the carbon and hydrogen atoms are depicted in red and white, respectively. For truxTTF, the sulfur, carbon and hydrogen atoms are colored in yellow, green and white, respectively. Adapted with permission from [18]. Copyright 2014 WILEY-VCH Verlag GmbH & Co. KGaA.

Figure 17

Selected intermolecular distances computed for structures A1–A4 at the revPBE0-D3/cc-pVTZ level. For C₃₀H₁₂, the carbon and hydrogen atoms are depicted in red and white, respectively. For truxTTF, the sulfur, carbon and hydrogen atoms are colored in yellow, green and white, respectively. Adapted with permission from [18]. Copyright 2014 WILEY-VCH Verlag GmbH & Co. KGaA.

Figure 18

(a) Experimental UV–Vis spectra, as obtained during the titration of truxTTF (1.7 × 10⁻⁴ M) with C₃₀H₁₂ (0.8 × 10⁻³ M) in CHCl₃ at room temperature; (b) TD-DFT simulation of the absorption spectrum of truxTTF as the ratio of truxTTF•C₃₀H₁₂ increases from 0 to 100% (B3LYP/cc-pVDZ calculations including CHCl₃ as solvent for structure A4). Adapted with permission from [18]. Copyright 2014 WILEY-VCH Verlag GmbH & Co. KGaA.

Figure 19

Isovalue contours (±0.03 a.u.) and energies calculated for the HOMOs and LUMOs of structure A4 at the revPBE0-D3/cc-pVTZ level. H and L denote HOMO and LUMO, respectively. Adapted with permission from [18]. Copyright 2014 WILEY-VCH Verlag GmbH & Co. KGaA.

Figure 20

Chemical structure of corannulene-based C₃₂H₁₂ and C₃₈H₁₄ buckybowls. The corannulene skeleton is highlighted in red.

Figure 21

Minimum-energy structures and computed at the revPBE0-D3/cc-pVTZ level for the most stable conformations of the heterodimers formed by the C₃₂H₁₂ (B1–4) and C₃₈H₁₄ (C1–6) fullerene fragments with truxTTF (truxTT•C₃₂H₁₂ and truxTT•C₃₈H₁₄). Except for the carbon atoms of the C₃₂H₁₂ and C₃₈H₁₄ buckybowls depicted in red, the following color code is used: carbon in green, sulfur in yellow and hydrogen in white. Adapted with permission from Reference [19]. Copyright 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 22

Chemical structure of a SWNT model and the hosts used to supramolecularly interact with SWNTs and test the experimental association constant protocol.

Figure 23

Minimum-energy geometries of parallel 11•SWNT assemblies and the perpendicular 11•C₂₀₀H₂₀ calculated at the PBE0-D3/6-31G** level from a semi-rigid optimization with fixed intramolecular parameters (see the original Reference [117] for further details). Carbon atoms of SWNTs are highlighted in red whereas the carbon atoms of pyrene are in green. Hydrogen atoms are depicted in white. Reproduced from Reference [117] with permission from the Royal Society of Chemistry.

Figure 24

Minimum-energy geometry for the supramolecular assemblies formed by hosts 11–15 vs. SWNTs calculated at the PBE0-D3/6-31G** level of theory. Reproduced from [117] with permission from the Royal Society of Chemistry.

Figure 25

Side view of the supramolecular complex formed by 11 and two types of SWNTs. Carbon atoms of SWNTs are highlighted in red whereas the carbon atoms of pyrene are in green. Hydrogen atoms are depicted in white. Reproduced from [117] with permission from the Royal Society of Chemistry.

Figure 26

Plot of lnK_a vs. −E_bind, comparing the experimental and calculated data.

Figure 27

Minimum-energy structures computed for the exTTF-graphene models (G1–G5) at the revPBE0-D3/cc-pVDZ level. Carbon atoms of exTTF are depicted in green, sulfur in yellow and hydrogen in white. Carbon atoms of the graphene sheet are depicted in red and hydrogen atoms have been omitted for clarity. Adapted with permission from [120]. Copyright 2013 WILEY-VCH Verlag GmbH & Co. KGaA.

Figure 28

(a) Top and side views of the minimum-energy geometry computed for anthracene-graphene (G6) at the revPBE0-D3/cc-pVDZ level. The intermolecular interacting regions of anthracene and graphene are colored in red; (b) Magnification of the interacting region emphasizing the most representative intermolecular distances collected in the table. Adapted with permission from [120]. Copyright 2013 WILEY-VCH Verlag GmbH & Co. KGaA.