Fluorescent Bis-Calix[4]arene-Carbazole Conjugates: Synthesis and Inclusion Complexation Studies with Fullerenes C60 and C70

Supramolecular chemistry has become a central theme in chemical and biological sciences over the last decades. Supramolecular structures are being increasingly used in biomedical applications, particularly in devices requiring specific stimuli-responsiveness. Fullerenes, and supramolecular assemblies thereof, have gained great visibility in biomedical sciences and engineering. Sensitive and selective methods are required for the study of their inclusion in complexes in various application fields. With this in mind, two new fluorescent bis-calix[4]arene-carbazole conjugates (4 and 5) have been designed. Herein, their synthesis and ability to behave as specific hosts for fullerenes C60 and C70 is described. The optical properties of the novel compounds and their complexes with C60 and C70 were thoroughly studied by UV-Vis and steady-state and time-resolved fluorescence spectroscopies. The association constants (Ka) for the complexation of C60 and C70 by 4 and 5 were determined by fluorescence techniques. A higher stability was found for the C70@4 supramolecule (Ka = 5.6 × 104 M−1; ΔG = −6.48 kcal/mol). Evidence for the formation of true inclusion complexes between the host 4 and C60/C70 was obtained from NMR spectroscopy performed at low temperatures. The experimental findings were fully corroborated by density functional theory (DFT) models performed on the host–guest assemblies (C60@4 and C70@4).


Introduction
Supramolecular chemistry represents one of the main topics of modern chemical sciences. Crossing traditional frontiers of organic, inorganic, and physical chemistry, supramolecular chemistry affords opportunities to create new supramolecules and nanostructures for applications as functional materials in chemistry, biology, and nanomedicine [1][2][3]. Reversible, usually weak, non-covalent host-guest interactions constitute the basis for the development of supramolecular architectures. The nature of such interactions ranges from electrostatic interactions, hydrogen bonding, cation-π, CH-π and π-π interactions, dispersion interactions (van der Waals interactions), and hydrophobic effects, resulting in a wide range of binding energies (around 0.5 kcal/mol for dispersion forces up to 70 kcal/mol for ion-ion interactions) [4].
It is also worth mentioning that the success of the coupling reaction is strongly dependent on the aryl halide used. When a bromo derivative was used instead of the iodinated compound 1, under a variety of experimental conditions -a large range of reaction temperatures and time, Pd(0) versus Pd(II) catalysts, and molar ratio of coupling partners -very complex reaction mixtures result and no useful yields of 4 or 5 could be retrieved.
Compounds 4 and 5 are freely soluble in CH2Cl2, CHCl3, THF, cyclohexane, and toluene. The novel calix [4]arene-carbazole conjugates 4 and 5 were fully characterized through FTIR, 1 H/ 13 C NMR, and 2D NMR spectroscopies, and combi MALDI-ESI highresolution mass spectrometry. All data are in excellent agreement with the proposed
It is also worth mentioning that the success of the coupling reaction is strongly dependent on the aryl halide used. When a bromo derivative was used instead of the iodinated compound 1, under a variety of experimental conditions -a large range of reaction temperatures and time, Pd(0) versus Pd(II) catalysts, and molar ratio of coupling partners -very complex reaction mixtures result and no useful yields of 4 or 5 could be retrieved.
It is also worth mentioning that the success of the coupling reaction is strongly dependent on the aryl halide used. When a bromo derivative was used instead of the iodinated compound 1, under a variety of experimental conditions-a large range of reaction temperatures and time, Pd(0) versus Pd(II) catalysts, and molar ratio of coupling partners-very complex reaction mixtures result and no useful yields of 4 or 5 could be retrieved.
Compounds 4 and 5 are freely soluble in CH 2 Cl 2 , CHCl 3 , THF, cyclohexane, and toluene. The novel calix [4]arene-carbazole conjugates 4 and 5 were fully characterized through FTIR, 1 H/ 13 C NMR, and 2D NMR spectroscopies, and combi MALDI-ESI high-resolution mass spectrometry. All data are in excellent agreement with the proposed structures.
Through extensive NMR analysis, using COSY, 13 C DEPT 135, 13 C-1 H HSQC, 13 C-1 H HMBC, and NOESY techniques, a comprehensive H/C assignment has been made (cf. Experimental section and SM for details; numbering of H and aryl rings may be found in the insets of 1 H NMR spectra).
A brief description of H assignments is highlighted below. The establishment of a cone conformation for the calixarene units was first undertaken, as they can adopt other plausible spatial arrangements through the flipping of aryl rings, in particular partial cone conformations.  8 Hz) and an unresolved multiplet between 4.34-4.49 ppm for equatorial and axial bridged methylene protons, respectively. In compound 4, the multiplets at 6.32-6.45 (8H) and 6.46-6.56 ppm (4H) are assigned to protons on rings B and C, the triplet at 6.98 ppm (2H), and a doublet at 7.18 ppm (4H) to the resonances on ring D, and the multiplet at 7.35-7.46 ppm (4H) to those protons on ring A, which are overlapped with aryl protons (H 1 and H 8 ) of carbazole. Similar assignments for compound 5 may be found in the Experimental section. The complete set of NMR spectra of 4 and 5 are shown in Figures S1-S11 (SM).
The MALDI-ESI-HRMS spectra of compounds 4 and 5 are depicted in Figures S12 and S13.

Photophysical Properties
The photophysical properties of bis-calixarenes 4 and 5 were studied by UV-Vis and steady-state and time-resolved fluorescence spectroscopies. Figure 1 depicts the groundstate absorption, excitation, and emission spectra of 4 and 5 in toluene solution, showing structured absorption and emission. UV-Vis ( Figure S14) and steady-state emission ( Figure S15) spectra of the compounds in various solvents (CH 2 Cl 2 , CHCl 3 , THF, cyclohexane, and toluene) are reported in SM. No significant solvatochromism was observed on any of these solvents either at ground-or excited-state, meaning that 4 and 5 are not very sensitive to solvent polarity.
Molecules 2021, 26, x FOR PEER REVIEW 4 of 20 13 C-1 H HMBC, and NOESY techniques, a comprehensive H/C assignment has been made (cf. Experimental section and SM for details; numbering of H and aryl rings may be found in the insets of 1 H NMR spectra). A brief description of H assignments is highlighted below. The establishment of a cone conformation for the calixarene units was first undertaken, as they can adopt other plausible spatial arrangements through the flipping of aryl rings, in particular partial cone conformations. Compound 4 in CDCl3 displayed two sets of resonances for the bridged methylene groups in the calixarene skeleton: one at 3.  8 Hz) and an unresolved multiplet between 4.34-4.49 ppm for equatorial and axial bridged methylene protons, respectively. In compound 4, the multiplets at 6.32-6.45 (8H) and 6.46-6.56 ppm (4H) are assigned to protons on rings B and C, the triplet at 6.98 ppm (2H), and a doublet at 7.18 ppm (4H) to the resonances on ring D, and the multiplet at 7.35-7.46 ppm (4H) to those protons on ring A, which are overlapped with aryl protons (H1 and H8) of carbazole. Similar assignments for compound 5 may be found in the Experimental section. The complete set of NMR spectra of 4 and 5 are shown in Figures S1-S11 (SM).
The MALDI-ESI-HRMS spectra of compounds 4 and 5 are depicted in Figures S12 and S13.

Photophysical Properties
The photophysical properties of bis-calixarenes 4 and 5 were studied by UV-Vis and steady-state and time-resolved fluorescence spectroscopies. Figure 1 depicts the groundstate absorption, excitation, and emission spectra of 4 and 5 in toluene solution, showing structured absorption and emission. UV-Vis ( Figure S14) and steady-state emission (Figure S15) spectra of the compounds in various solvents (CH2Cl2, CHCl3, THF, cyclohexane, and toluene) are reported in SM. No significant solvatochromism was observed on any of these solvents either at ground-or excited-state, meaning that 4 and 5 are not very sensitive to solvent polarity.  The bis-calixarene-3,6-CBZ 4 exhibits several electronic transitions in the 270-380 nm region, being its absorption maximum around 319 nm, bearing a lower energy shoulder near 343 nm. The 2,7-CBZ isomer 5 displays the main absorption band peaking at 358 nm, accompanied by a shoulder at 377 nm. The extended π electron delocalization involving the bis-2,7-phenyleneethynylene-carbazole moiety in 5 is responsible for the observed red shifts (ca. 40 nm) of the main absorption band. The optical HOMO-LUMO energy gaps (E g ), calculated from the low energy onset of the absorption bands of 4 and 5 (E g(4) = 3.37 eV; E g(5) = 3.08 eV) quantify the above observation (Table 1).  1 All data was collected using toluene as solvent; 2 optical energy gaps (E g ) were calculated from the low energy onset of the absorption bands; 3 Stokes shifts were calculated from λ F,max (0-0) − λ A,max ; 4 fluorescence quantum yields were determined using 9,10-diphenylanthracene as reference in air-equilibrated conditions at λ exc = 340 nm.
The emission spectra of both compounds showed different shapes, being both dominated by 0-0 transitions (λ max at 404 and 394 nm for 4 and 5, respectively). Vibronic progressions appear in both spectra at 424 and 414 nm for 4 and 5, respectively, being highly noticeable for compound 5 (Figure 1b). Fluorescence quantum yields (Φ F ) determined for compound 4 have shown to be strongly correlated with the solvent nature. Indeed, a deceptively low quantum yield (Φ F = 0.028) was retrieved when CHCl 3 was used as solvent; fortunately, the quantum yield raised significantly in other solvents (CH 2 Cl 2 , Φ F = 0.13; THF, Φ F = 0.18; cyclohexane, Φ F = 0.20 and toluene, Φ F = 0.17). No single correlation with the solvent polarity was found. As the selected solvent for inclusion studies with fullerenes was toluene, all the photophysical data involving 4 and 5 are presented in this solvent (Table 1), except where noted otherwise. It is of note that a much higher quantum yield was retrieved for 5 (Φ F = 0.40).
The time-resolved fluorescence measurements were conducted by a single-photon timing method with laser excitation and microchannel plate detection under 340 nm excitation. The lifetime decay of 4 was best fitted by a sum of two exponentials (τ 1 = 7.46 ns (99.1%) and τ 2 = 1.63 ns (0.9%)), yielding an average lifetime (τ ave ) of 7.40 ns in toluene solution ( Figure 2). A great stability toward photodegradation was observed for 4 and 5 ( Figure S16a,b, respectively), under conditions of continuous irradiation (20 min) in toluene, ensuring a good starting point for fluorescence titration assays. A great stability toward photodegradation was observed for 4 and 5 ( Figure S16a,b, respectively), under conditions of continuous irradiation (20 min) in toluene, ensuring a good starting point for fluorescence titration assays.

Complexation Studies with Fullerenes
The design of the new bis-calixarene-carbazole conjugates 4 and 5 was directed toward the evaluation of their ability to form inclusion complexes with the fullerenes C 60 and C 70 in solution, in a sensitive and selective manner. The existence of any host-guest interactions was first assessed through fluorometric titrations in toluene. The experiments were performed with the guests in a concentration range of 2.04 × 10 −6 -2.21 × 10 −5 M, while keeping that of the fluorophore constant (6.0 × 10 −7 M) (Figures 3 and 4). As is immediately perceived from the titration curves, a very strong quenching of the emission of the hosts 4 and 5 occur upon addition of C 60 and C 70 . Plotting the ratio of the fluorescence intensities against the fullerene concentrations, curves showing an upward curvature are obtained. While this behavior can be associated with several quenching mechanismsnamely, a combined dynamic and static quenching mechanism and/or the existence of a sphere of effective quenching (i.e., a dynamic quenching within the sphere of action) [40] the high positive deviations from the linear Stern-Volmer (SV) equation are largely, in this case, simply due to hetero-inner-filter effects (h-IFEs). A great stability toward photodegradation was observed for 4 and 5 ( Figure S16a,b, respectively), under conditions of continuous irradiation (20 min) in toluene, ensuring a good starting point for fluorescence titration assays.

Complexation Studies with Fullerenes
The design of the new bis-calixarene-carbazole conjugates 4 and 5 was directed toward the evaluation of their ability to form inclusion complexes with the fullerenes C60 and C70 in solution, in a sensitive and selective manner. The existence of any host-guest interactions was first assessed through fluorometric titrations in toluene. The experiments were performed with the guests in a concentration range of 2.04 × 10 −6 -2.21 × 10 −5 M, while keeping that of the fluorophore constant (6.0 × 10 −7 M) (Figures 3 and 4). As is immediately perceived from the titration curves, a very strong quenching of the emission of the hosts 4 and 5 occur upon addition of C60 and C70. Plotting the ratio of the fluorescence intensities against the fullerene concentrations, curves showing an upward curvature are obtained. While this behavior can be associated with several quenching mechanisms -namely, a combined dynamic and static quenching mechanism and/or the existence of a sphere of effective quenching (i.e., a dynamic quenching within the sphere of action) [40] the high positive deviations from the linear Stern-Volmer (SV) equation are largely, in this case, simply due to hetero-inner-filter effects (h-IFEs).  Indeed, since both guests display, even at the low concentration range used, strong absorption of radiation at the excitation (357 nm) and emission wavelengths (404 nm for 4 and 394 nm for 5) (see fullerenes absorption spectra in Figure S17), correction for h-IFEs is mandatory. Otherwise, huge errors may occur when calculating Stern-Volmer and/or association constants by fluorescence spectroscopy. Unfortunately, in many articles, Indeed, since both guests display, even at the low concentration range used, strong absorption of radiation at the excitation (357 nm) and emission wavelengths (404 nm for 4 and 394 nm for 5) (see fullerenes absorption spectra in Figure S17), correction for h-IFEs is mandatory. Otherwise, huge errors may occur when calculating Stern-Volmer and/or association constants by fluorescence spectroscopy. Unfortunately, in many articles, including some related to the detection of fullerenes by fluorometric titration [41], no mention is given of this issue. The mathematical correction of fluorescence intensities was done according to ref. [42] (see Experimental section for details). The association constants (K a ) of the supramolecular complexation (association or binding constants will be used interchangeably throughout the text) were calculated by a non-linear fitting approach (refer to Experimental section for calculation details) because no previous assumptions need to be made before applying it (for example, the existence, or not, of a non-fluorescent ground-state complex, or that the concentration of added guest is equal to the free guest), contrary to what occurs with the derived SV equation for static quenching or linearized forms of it (e.g., double reciprocal plots) [43,44]. The calculation of K a by this methodology implies that dynamic quenching of the host fluorescence is absent or negligible. To verify this, time-resolved fluorescence assays were conducted with compound 4. It is known that, in a static or in a sphere of effective quenching mechanism, the lifetimes of the fluorophores do not change upon increasing the concentration of the guests [40].
As may be clearly seen from Figure 5, a dynamic mechanism can be safely excluded in the quenching of 4 fluorescence by fullerenes C 60 and C 70 , since τ 0 /τ remains constant over the entire guest concentration range. A similar behavior was assumed to take place with 5. With this information at hand, the host-guest association constants were determined. The binding isotherms calculated for each host-guest pair using the non-linear regression are shown in Figure 6a-d together with the upper and lower confidence intervals (CI) for fitted data (cf. Experimental section). With this information at hand, the host-guest association constants were determined. The binding isotherms calculated for each host-guest pair using the non-linear regression are shown in Figure 6a-d together with the upper and lower confidence intervals (CI) for fitted data (cf. Experimental section). Table 2 gathers the corresponding association constants and the estimated free energy of complexation (∆G) associated with the binding event. With this information at hand, the host-guest association constants were determined. The binding isotherms calculated for each host-guest pair using the non-linear regression are shown in Figure 6a-d together with the upper and lower confidence intervals (CI) for fitted data (cf. Experimental section).  Table 2 gathers the corresponding association constants and the estimated free energy of complexation (G) associated with the binding event. The excellent goodness of fit of the data by the non-linear approach assures that a 1:1 host-guest stoichiometry was attained in all cases. The continuous variation method (Job's method) was additionally used to establish the stoichiometry of the complexes (see Experimental section for details). Figure 7 shows the Job plots of 4 with C60 and C70 (for 5, see Figure S18). In either case, a maximum of the relative complex concentration is found at a mole fraction of 0.5 pointing to the formation of a 1:1 complex.  The excellent goodness of fit of the data by the non-linear approach assures that a 1:1 host-guest stoichiometry was attained in all cases. The continuous variation method (Job's method) was additionally used to establish the stoichiometry of the complexes (see Experimental section for details). Figure 7 shows the Job plots of 4 with C 60 and C 70 (for 5, see Figure S18). In either case, a maximum of the relative complex concentration is found at a mole fraction of 0.5 pointing to the formation of a 1:1 complex.
The excellent goodness of fit of the data by the non-linear approach assures that a 1:1 host-guest stoichiometry was attained in all cases. The continuous variation method (Job's method) was additionally used to establish the stoichiometry of the complexes (see Experimental section for details). Figure 7 shows the Job plots of 4 with C60 and C70 (for 5, see Figure S18). In either case, a maximum of the relative complex concentration is found at a mole fraction of 0.5 pointing to the formation of a 1:1 complex.
(a) (b)  Comments on the above results are in order. First, all the binding constants are of significant magnitude (>3.7 × 10 4 M −1 ), being the strongest binding observed between bis-calixarene-3,6-CBZ conjugate (4) and fullerene C 70 . This finding is in accordance with what was expected based on preliminary molecular mechanics force field (MMFF94) calculations [45] performed on the best supramolecular conformers of the hostguest pairs 4: C 60 /C 70 , where a higher interaction energy was foreseen for C 70 over C 60 (∆∆E = −1.41 kcal/mol). These results were later fully corroborated by density functional theory (DFT) calculations (see below). Secondly, the considerable high association constants retrieved for compound 5 were somewhat surprising. The cavity of its structure, with a distance between the closest carbon atoms on the two D rings of 17.61 Å (comparing with 9.84 Å in 4), seems to be too large to accommodate fullerene C 60 (diameter of 7.05 Å) or C 70 (7.94 Å across the larger axis of the ellipsoid) in a way that moderate to strong CH-π, π-π, and van der Walls interactions could be developed between the partners. One possibility to explain such results is to consider that unspecific π-π interactions between the electron rich phenyleneethynylene-derived carbazole unit and the electron-accepting fullerenes species, not related to the host-guest structural complementarity and, thus, not a true inclusion phenomenon, dominate the observed fluorescence quenching event. In other words, an apparent static quenching mechanism (sphere of effective quenching) may be in action. It is worth mentioning in this context that several PPEs devoid of molecular receptors in their structures were also able to sense C 60 (K SV~1 × 10 4 M −1 ), having the π-π interactions between the polymer backbone and C 60 put forward to explain the results [33]. A 5,5 -bis-p-tert-butyl-calix [4]arene incorporating a phenyleneethynylene moiety, or its simple π-conjugated model, 4,4'-bis(phenylethynyl)-1,1'-biphenyl, showed even higher SV constants (K SV~2 -3 × 10 4 M −1 ) for C 70 [37]; in this case, as the authors stated, no evidence was found for inclusion complexation.
From the above, we hypothesized that two types of quenching mechanisms may be involved on the fluorescence quenching of compound 4 with the fullerenes. One resulting from a sphere of effective quenching, resembling that observed with 5, and the other a true static quenching mechanism stemming from the inclusion of C 60 /C 70 in the host cavity. Heeger et al. have proposed a combination of static and sphere of action quenching mechanisms to explain the luminescence quenching of poly(phenylenevinylene) polyelectrolytes by methyl viologen [46].
Our attention was then turned to find experimental evidence for the existence of true inclusion complexes of 4 with C 60 /C 70 and their possible spatial arrangements. For that, NMR experiments in toluene-d 8 were undertaken. At room temperature (25 • C), the complexation-induced changes in the chemical shift (CIS) observed upon mixing equimolar amounts of 4 and C 60 or C 70 were very small. As the complex strength should increase at lower temperatures, variable-temperature (VT) NMR was performed for the host and for equimolar host-guest mixtures up to −80 • C ( Figures S19-S21, supplementary materials), hoping that, in this way, enhanced CIS would result. The selected temperature for the observation of CIS was −10 • C since, at this temperature, a reasonable peak resolution is maintained. The CIS are, in general, of small magnitude (Table 3) but the reproducible downfield shifts observed for all the protons (calixarene and carbazole aryl protons) spatially closer to the fullerenes, which experience higher ring current effects, are consistent with the formation of inclusion complexes. Moreover, the AB sets of equatorial and axial protons at methylene bridges in 4 suffer a change in their shapes as a result of a conformational change upon complexation. Partial NMR spectra of representative regions are displayed in Figure S22. The foregoing experimental findings were very well corroborated by DFT calculations (for details see Experimental section) [45,47]. The two calixarene units in 4 adopt a pinched cone conformation, with the A and D rings almost parallel to each other and the rings B and C tilted outwards ( Figure 8a); after inclusion of C 60 /C 70 in the pocket of 4, an almost symmetrical cone conformer results (Figure 8b,c). In the pinched cone, the O-O distance between distal rings A and D is 5.28 Å, and that of B and C rings is 4.21 Å (average distance in the two calixarene units); these turn, respectively, into 4.39 Å and 4.20 Å for C 60 @4 and 4.43 Å and 4.29 Å for C 70 @4. One of the consequences would be the formation of stronger H-bonds as the average (two calixarene units) OH . . . OPr distance changes from 1.80 Å to 1.745 Å (both on C 60 and C 70 ); this probably reflects the significant downfield shifts observed for the phenolic protons in C 60 (∆δ = 0.0099) and C 70 (∆δ = 0.0178) assemblies, and the concomitant upfield shifts of O-methylenic protons on the propyl group of rings B, C, and D.
Analysis of the induced shifts reported in Table 3 clearly evidence that the protons of carbazole nucleus residing at positions 4,5 and 2,7 and those belonging to aryl calixarene units, particularly at the meta positions of bridged rings, suffer the highest deshielding effects by the presence of the fullerenes. This fact is more evident for C 70 @4, where the CIS are consistently higher than C 60 . Within the bis-calixarene-3,6-CBZ (4) pocket, closer contacts are expected between C 70 and aryl protons, owing to its larger molecular size, as compared to C 60 , and the size of the (somewhat fixed) constructed cavity. This is supported by theoretical analysis (DFT) of host-guest distances. For C 70 , the average distance (in all cases, the two calixarene units are considered) of aryl protons (meta to CH 2 bridges) on ring D to the closest carbon atom on the fullerene is 3.05 Å, where the same located proton on B/C rings is 3.28 Å; the average distance for the 4,5 protons on the carbazole is 3.165 Å. These values are comparable with 3.11 Å, 3.38 Å, and 3.105 Å reached by the same atoms on inclusion of C 60 . Fullerene-arene distances in various supramolecules are found in the range 3.0-3.5 Å [24]. The electronic binding energies of compound 4 and its inclusion complexes with C60 and C70 were calculated by high level DFT (see Experimental section for details of the methods) using recommended state-of-the-art procedures [48][49][50]. Dispersion-corrected functionals D3(BJ)-B3LYP and B97M-V were used in conjunction with an extended basis set (6-311+G(2df,2p)). The gas phase equilibrium binding energies (E) were determined by the supramolecular approach using the equation: E = Ecomplex − (Ehost + Eguest), where E corresponds to the total electronic energy of the species. The electronic binding energies of the complexes are presented in Table 4. The results show that, in gas phase at 0 K, the supramolecule C70@4 has a higher equilibrium electronic binding energy than C60@4, whatever the quantum mechanical The higher binding interactions of 4 with fullerene C 70 observed in the NMR experiments are in qualitative agreement with the relative magnitudes of the association constants of 4 with C 60 /C 70 obtained from fluorescence spectroscopy ( Table 2).
The electronic binding energies of compound 4 and its inclusion complexes with C 60 and C 70 were calculated by high level DFT (see Experimental section for details of the methods) using recommended state-of-the-art procedures [48][49][50]. Dispersion-corrected functionals D3(BJ)-B3LYP and B97M-V were used in conjunction with an extended basis set (6- 311+G(2df,2p)). The gas phase equilibrium binding energies (∆E) were determined by the supramolecular approach using the equation: ∆E = E complex − (E host + E guest ), where E corresponds to the total electronic energy of the species. The electronic binding energies of the complexes are presented in Table 4. The results show that, in gas phase at 0 K, the supramolecule C70@4 has a higher equilibrium electronic binding energy than C60@4, whatever the quantum mechanical model used in the calculations. These theoretical results (∆E) are in line with those retrieved experimentally (∆G; Table 2). For a direct comparison with the experimental results obtained in solution, the theoretical free energies of association (∆G th-sol ) in solution at, for example, 298 K, need to be calculated. The usual approach [48,49] is to consider it as a sum of three energy components: ∆G th-sol = ∆E + ∆G RRHO + ∆∆G solv , where ∆E is the electronic binding energies in the gas phase, ∆G RRHO is the gas phase free energy of the complex calculated in the rigid-rotor-harmonic oscillator approximation (sum of zero-point vibrational energy, temperature correction of enthalpy and entropy for each species in gas phase), and ∆∆G solv is the change in the free energy of solvation upon complexation (∆∆G solv = ∆G solv-complex − (∆G solv-host + ∆G solv-guest )). Owing to the large size of our molecular species, ∆G RRHO was calculated by the dispersion-corrected PM6-D3H4 semiempirical method [51] as implemented in MOPAC 2016 [52] (see Experimental section for details). While the solvation free energy has been calculated for smaller systems using several advanced solvation models [53,54], not without criticism [29], huge computational resources and well-validated solvation models are needed for systems such as the ones treated here.
Nonetheless, an attempt was made to calculate the solvation contribution in our systems using the simpler Conductor-like Screening Model (COSMO) solvation model, also implemented in MOPAC (see Experimental section for details). The results are gathered in Table 5. There is a reasonable agreement between the experimentally found binding free energies for the fullerenes encapsulation by 4 and those obtained by the theoretical approaches. The theoretical results should, however, be taken with caution, since the methods used for the calculation of ∆G RRHO and ∆∆G solv , in particular the last contribution, contain errors. Further investigations are still needed to fully validate those results.  [45,47]; 2 calculated with PM6-D3H4 semi-empirical method at 298 K [47]; 3 the free energy ∆G 1M for the standard state in solution (1M) is obtained from free energy ∆G g for the standard state in gas phase (1 atm) (∆G g = ∆E + ∆G RRHO ) by subtracting the amount RTln(RT/P) [55], which equals + 1.902 kcal/mol at 298 K; 4 calculated by COSMO solvation model using toluene as solvent [52].
High-resolution mass spectra were obtained at the Structural, Proteomic, and Xenomic Determination Services of Universidad de Vigo (C.A.C.T.I.) on a Solaris XR (FT-ICR) mass spectrometer (Bruker Daltonics, Billerica, MA, USA) equipped with a 7-Tesla actively shielded magnet. Ions were generated using a Combi MALDI-electrospray ionization (ESI) source. Ionization was achieved by electrospray, using a voltage of 4500 V applied to the needle, and a counter voltage of 300 V applied to the capillary. Samples were either prepared by adding a spray solution of 50:50 (v/v) Toluene/Acetone to a solution of the sample in toluene or a spray solution of 50:50 (v/v) CH 3 OH/Acetonitrile saturated with NaCl to a solution of the sample in CH 2 Cl 2 , at a v/v ratio of 1 to 5% to obtain the best signal-to-noise ratio. Data acquisition was performed using FtmsControl software version 2.2.0, and data processing was performed using DataAnalysis software, version 5.0, both from Bruker Daltonics.
UV-Vis spectra were recorded on a VWR UV 3100PC (VWR International bvba, Leuven, Belgium) or on a Jasco J-815 spectrophotometer (Jasco Inc., Tokyo, Japan) using 1 cm quartz cells at 25 • C.
Steady-state fluorescence spectra were collected on a PerkinElmer LS45 fluorimeter (PerkinElmer, Waltham, MA, USA) using a 1-cm quartz cuvette with right angle (RA) geometry at 25 • C in air-equilibrated conditions.
Fluorescence quantum yields were measured using 9,10-diphenylanthracene as fluorescence reference standard (Φ = 0.72, EtOH, air-equilibrated conditions, RA geometry) [57]. The quantum yields were determined by the slope method [58], keeping the optical densities of the sample and reference below 0.05 at the excitation wavelength to prevent inner filter effects.
Fluorimetric solution experiments were carried out by titration of diluted solutions (6 × 10 −7 M) of fluorophores in toluene with known amounts of the analytes (fullerenes C 60 and C 70 ) using RA geometry. For each determination, at least three replicates were used. Correction of fluorescence intensities was done by the expression: η = Ax 0 Ay 0 (1 − 10 −Axi )(1 −10 −Ay i )/Ax i Ay i (1 − 10 −Ax 0 )(1 − 10 −Ay 0 ), where Ax 0 and Ay 0 are the fluorophore absorbances and Ax i = Ax 0 + ∆Ax i and Ay i = Ay 0 + ∆Ay i are the total absorbances of the fluorophore and the quencher (∆Ax i and ∆Ay i ) at the excitation and emission wavelengths, respectively [42]. On applying this correction, it is assumed that the fluorescence intensity comes exactly from the center of a centrally illuminated cuvette under RA observation.
The association constant (K a ) for the formation of a supramolecular complex (HG) between the host (H) and the guest (G), from the 1:  Reactions under microwave irradiation were performed by using a mono-mode microwave reactor (CEM, Discover), and pressure-rated reaction vials with poly(tetrafluoroethylene) -silicon caps.

Synthesis
Compound 4: To an argon degassed solution containing 120 mg (177.0 µmol) of 1 [38] in freshly distilled NEt 3 (7.1 mL) were added PdCl 2 (PPh 3 ) 2 (8.9 mg, 12.4 µmol) and CuI (2.41 mg, 12.4 µmol). The yellow suspension was degassed, the flask sealed, and the contents stirred in a pre-heated bath at 35 • C. A second solution of 3,6-carbazole monomer 2 (21.7 mg, 85.0 µmol) [39] in dry and degassed toluene (7.1 mL) was added dropwise to the calixarene solution for 4 h and allowed to react for an additional hour. The mixture acquired a yellow color that gradually turned red-orangish with turbidity. The reaction was followed by TLC [AcOEt:Hexane (1:8)], which, after 5 h, revealed the consumption of 1. Solvents were removed by evaporation and the residue taken in CH 2 Cl 2 and washed successively with aqueous solutions of 2% HCl, 0.1M NaHSO 3 , 10% NH 4 SCN, and water. The organic extract was dried and evaporated to dryness. After flash chromatograph [AcOEt:Hexane (1:8)], compound 4 was isolated as a light-yellow solid in 37% (42.6 mg). The procedure using microwave-assisted synthesis was carried out at 35 •   All quantum mechanics calculations were performed by Q-Chem 5.1 [47] running on Spartan'18 molecular modelling software [45] using default integration grids (SG0/SG-1 for B3LYP and (75, 302) for B97M-V) and convergence criteria, in vacuum. The selection of the functionals for the study was based on the well-documented behavior of their performance in systems associated with non-covalent interactions [50].
The dispersion-corrected PM6-D3H4 semi-empirical method [51], as implemented in MOPAC 2016 version: 21.002W [52], was used for the calculation of thermodynamic parameters used in ∆G RRHO calculations, and solvation energies. Input geometries from B3LYP/6-31G(d) were fully optimized using the L-BFGS geometry optimizer and PRECISE keyword (see MOPAC manual for details at http://openmopac.net/manual/index.html). The thermodynamic quantities were obtained with the THERMO keyword at default temperature (298 K). No corrections were applied to the anharmonicities associated with the thermal contributions from the low-frequency vibrational modes (< 100 cm −1 ) during the ∆G RRHO calculations. The COSMO solvation energies were calculated by the MOPAC formalism, using a dielectric constant of 2.38 correspondent to toluene.

Conclusions
Based on simple principles of host-guest chemistry, two new fluorescent bis-calix [4]arenecarbazole conjugates 4 and 5 were designed to function as hosts for fullerenes C 60 and C 70 . The syntheses of 4 and 5 were accomplished in a one-pot double cross-coupling Sonogashira-Hagihara reaction, with 4 having been isolated in synthetic useful yields. The oxidative coupling of 3,6-diethynyl-9-propyl-9H-carbazole, or its 2,7-diethynyl isomer, leading to oligomeric/polymeric structures, is the major competitive reaction. Full structural characterization of 4 and 5 was undertaken ( 1 H/ 13 C NMR, 2D NMR, and ESI-HRMS), and their photophysical properties thoroughly evaluated (UV-Vis, and steady-state/timeresolved fluorescence spectroscopies).
The complexation of C 60 and C 70 by 4 and 5 was followed by fluorometric titrations in toluene solution. A great level of fluorescence quenching was observed for both hosts. Time-resolved fluorescence titrations with compound 4 and both fullerenes have indicated that dynamic quenching (occurring during the lifetime of excited host) was absent. This allowed the calculation of the association constants of the binding events by a non-linear fitting approach. It was found that, in toluene, 4 binds preferentially with C 70 over C 60 in a 1:1 stoichiometry, yielding, in either case, stable complexes (∆G = −6.48 and −6.31 kcal/mol, respectively). Surprisingly, high association constants were also obtained for 5 on interaction with C 60 /C 70 . The observed quenching was interpreted, in this case, as being largely a result of a sphere of effective quenching mechanism, since structural complementarity between 5 and the fullerenes barely exist, considering the geometrical mismatch between the dimension of the nanocavity of 5 and the size of the guests. In the case of host 4, evidence for the formation of true inclusion complexes (C 60 @4 and C 70 @4) came from low-temperature NMR assays. Theoretical calculations performed on the complexes at DFT level are in excellent agreement with the experimental findings.
The bis-calix [4]arene-carbazole conjugates 4 and 5 here disclosed are now being investigated as hosts for the construction of other supramolecular systems.