2.1 Synthesis

In order to get reproducible NMR spectra, the synthesis of a previously reported [33] titanium(IV) oxo-aryloxide (1) has been optimized:

First, a solution made from 15 ml of 1,4-dioxane and 5 ml of ethanol and containing 0.8 g (4.76 mmol) of 2,6-bis(hydroxymethyl)-p-cresol (H₃bhmpc, 4.76 mmol) and 0.021 mL (1.20 mmol) of water was prepared. After complete dissolution of the ligand, 0.5 ml (2.38 mmol) of Ti(OEt)₄ were added under a nitrogen atmosphere in a plastic bag. The resulting orange solution was magnetically stirred for 10 minutes and then left overnight leading to an abundant precipitation of orange-colored rod-shaped crystals. Fig. 1 (top left) shows that (1) is a centro-symmetric molecule built from a planar {Ti₄(μ₃-O)₂}assembly of four TiO₆ octahedra sharing edges and surrounded by three pairs of aromatic ligands. The overall shape of (1) may be described as a doubly fused calix[3]arene (Fig. 1, bottom left) where the organic joints have been replaced by Ti-atoms. Owing to the existence of these two divergent cavities and to the fact that aromatic ligands are found under three different protonation states (bhmpc, Hbhmpc and H₂bhmpc), solvent molecules (dioxane and ethanol) are found to be associated through hydrogen bonds to the complex (Fig. 1, right). The complete energetic characterization of both the intra- and intermolecular H-bonding scheme in this kind of complex has been studied elsewhere [1,33]. It is worth noticing that another structure may be obtained after recrystallization of (1) in CHCl₃, where CHCl₃ molecules are trapped instead of EtOH [33]. This structure exhibits two non-equivalent complexes per unit cell, differing essentially by their interactions with solvent molecules, but with the same molecular structure, identical to the molecular entity found in the as-synthesized compound. As explained above, the correlation between the electronic densities derived from the crystalline structure of (1) in the solid state and the NMR parameters measured when (1) in dissolved in CDCl₃ will also be studied. Thus, it was assumed that the presence of the interaction between the complex and EtOH (in the solid) or its absence (when the complex is surrounded by CDCl₃ molecules in solution) does not influence too much electronic densities at C-sites, so that calculations based on solid-state structures can be reasonably correlated to ¹³C parameters of the complex in solution. As will be discussed below, this rough assumption appears to be valid for the majority of the complex C sites, as few of them are under strong influence of the solvent molecules in any case.

Orange-colored crystalline powders may also be obtained by adding to a solution of 6 mL of Ti(OPrⁱ)₄ in 5 mL of isopropanol, a solution of 0.67 g of H₃bhmpc dissolved in 15 mL of 1,4-dioxane and 3.17 μL of water. The same protocol using 6 g of Ti(OBuⁿ)₄ in 5 mL of butanol-1 and 0.59 g of H₃bhmpc has also led to orange-colored crystalline powders. In all cases, these crystals were found to be too small for performing a structure determination through single-crystal X-ray diffraction.

2.2 U.V.-Vis. spectroscopy

Spectra of the free ligand and of the complex after dissolution in CHCl₃ have been recorded on a Varian Multicell Block for Cary 1/3 spectrophotometer at a concentration of 7·10⁻⁴ M.

2.3 IR and Raman spectroscopy

FT-IR spectra were recorded on KBr pellets between 400–4000 cm⁻¹ on a Perkin-Elmer 1600 spectrometer. Micro-Raman measurements have been made on a Renishaw microscope, Ramascope model, equipped with 200 mW Ar⁺ blue laser (λ = 488 nm). The best resolution (1 cm⁻¹) was obtained by recording four spectra (0–4000 cm⁻¹) using each time a 1000 cm⁻¹ range. Signals below 200 cm⁻¹ were filtered with the Rayleigh line and were not observed. Calibration of the microscope for the 0–1000 cm⁻¹ range was made on a silicon wafer (520.1 cm⁻¹ line). Microcrystalline powders were observed (×50 magnification) without any special preparation after deposition on a glass wafer. For each powder, acquisition of the spectra was made on at least four different crystallites with acquisition times within a 5–60 s range.

2.4 NMR

¹⁷O NMR spectra were recorded on a Bruker spectrometer operating at 400 MHz for ¹H and 44.2 MHz for ¹⁷O after dissolution of 26 mg of (1) in CDCl₃ (3.2 g). Owing to the low solubility of (1) in CDCl₃, the solution has been filtered before filling the 10 mm NMR tube preventing the computation of the real concentration. Acquisition time was 12 h for 221,694 scans using a 0.1 s repetition time.

¹H MAS and ¹³C{¹H} CPMAS NMR measurements were performed using a Bruker Avance-300 spectrometer, operating at 300.33 MHz for ¹H and 75.52 MHz for ¹³C (spectra 1 and 2 on Figs. 6 and 7), or a Bruker Avance-500 spectrometer, operating at 500.03 MHz for ¹H and 125.73 MHz for ¹³C (spectra 3 to 5 on Figs. 6 and 7), both equipped with 4 mm H-X probes. The samples were rotated at, respectively, ν_R = 10 kHz with corresponding CPMAS magnetization transfer conditions ν_RF(¹H) = 32.5 kHz and ν_RF(¹³C) = 42.5 kHz or rotated at 13 kHz with ν_RF(¹H) = 45.7 kHz and ν_RF(¹³C) = 32.7 kHz, using a 2.5 ms contact time in both cases. ¹H decoupling composite pulse sequences used were spinal64 for measurements performed on Avance-300 and tppm180 on Avance-500 spectrometers. Other acquisition parameters were typically eight scans using a 10 s repetition time for ¹H MAS and for ¹³C{¹H} CPMAS, 1024 to 2048 scans using a 5 s repetition time.

All ¹H and ¹³C solution NMR measurements were performed at room temperature on a solution of (1) (5 mg) in CDCl₃ (0.6 mL) using a Bruker Avance-500 spectrometer, operating at 500.13 MHz for ¹H and 125.7 MHz for ¹³C, equipped with a ¹H/¹³C 5 mm gradient-probe. We used a gradient selected version (gs-) for each type of 1D and 2D pulse sequence except for ROESY. The solvent signal was taken as a secondary reference for ¹H and ¹³C chemical shift (7.26 ppm for C¹HCl₃ residue and 77 ppm for ¹³CDCl₃, relative to TMS). In addition to classical 1D ¹H and ¹³C {¹H} spectra, four types of 2D spectra were collected: a ¹H¹H scalar correlation spectrum, recorded using a gs-DQFCOSY pulse sequence, two scans, 2.5 s as repetition time, and 512 increments for indirect dimension; a ¹H¹H dipolar correlation spectrum, recorded with a ROESY pulse sequence, 16 scans, 2.5 s as repetition time, 512 increments for indirect dimension and a total mixing spin-lock duration of 300 ms suitable for the correlation time one can expect, considering the size of the molecular entity under study; a ¹H¹³C via ¹J_CH scalar correlation spectrum, acquired with a gs-HSQC pulse sequence, eight scans, 2 s as repetition time, 1024 increments in ¹³C dimension and a delay 1/4J = 1.56 ms corresponding to mean ¹J_CH = 160 Hz; a ¹H¹³C long range scalar correlation spectrum, obtained with a gs-HMBC pulse sequence, eight scans, 2 s as repetition time, 1024 increments in ¹³C dimension and a delay 1/2J = 3.12 ms corresponding to mean ¹J_CH = 160 Hz. ¹H and ¹³C {¹H} T₁ measurements involved a classical inversion-recovery sequence, with ¹H decoupling in the case of ¹³C. We adopted a 10 s repetition time with two scans for ¹H and 5 s with 1024 scans for ¹³C.

2.5 Electron density modeling

All calculations were made using the homemade PACHA software [34,35]. This software was designed for retrieving a partial charge distribution from the molecular or crystalline structure without the introduction of empirical parameters. Briefly stated, these charges are recovered after application of the electronegativity equalization principle that is known to have a firm quantum-mechanical basis and a deep thermodynamic significance as a measure of the electronic chemical potential. The transformation of a set of atomic coordinates into a partial charges distribution is performed using an atomic parameterization resting on two non-empirical parameters per atom: an electronic chemical potential measured by a spectroscopic electronegativity (Allen's scale) and an atomic radius measured by the most diffuse principal maxima in the radial distribution function r²ψ²(r), computed using relativistic wavefunction solutions of the Dirac equations. Interested readers should refer to the original papers for more details [34,35]. In the present case, the original CIF file cannot be used as such, owing to missing H-atom coordinates and to large uncertainties in the position of H-atoms and/or solvent molecules (here dioxane and ethanol). Consequently, in order to get electronic densities that reflects the averaged topology observed in solution and not the various metrical errors coming from the crystal structure determination in the solid state, the structure has been standardized in the following way.

All bonds involving H-atoms were first scaled to some standard values (see [36] for a compilation). In this study, OH, CarH, CH bonds in methylene and CH bonds in methyl groups have all been set equal to 97, 108, 109 and 106 pm respectively. Similarly all HCH bond angles in methylene and methyl groups have been set equal to their ideal tetrahedral value (110°). For methylene groups, standard torsion angles ±120° were assumed, whereas for the methyl group, one torsion angle was arbitrarily varied, the two other ones being fixed at ±120°. For the hydrogen bridge between Hbhmpc and H₂bhmpc ligands (see Fig. 2), the H41O3C7O6 torsion angle was fixed to 0° to avoid divergence in the charge distribution. For the three remaining hydrogen bonds the corresponding torsion angle was arbitrarily varied.

The atomic coordinates for dioxane and ethanol were recomputed starting from one oxygen atom (labeled O11 for dioxane and O13 for ethanol in the CIF file) using 143 and 153 pm for CO and CC bond lengths. Among the 10 and four angles needed to fix in space the dioxane and ethanol molecules, respectively, (3 + 3) were arbitrarily varied, the other ones (7 for dioxane and 1 for ethanol) being fixed at 110° (OCC and COC bond angles) and ±60° (torsion angles). This procedure allows one to conserve the overall “chair shape” identified for the dioxane molecule in the original X-ray data file and avoids the large metrical distortions observed in this CIF file.

After this parameterization, there remained 13 arbitrary angles associated to the mobile part of the complex that are CH₂OH and CH₃ groups or dioxane and ethanol orientation in the two divergent cavities. A reasonable structural model for describing the solution behavior is then derived by applying a two-step non-empirical energy minimization technique. In a first step involving the 13 variable angles, we have looked for the geometry corresponding to a minimum in steric energy by using short-range repulsive potentials derived from the Gordon–Kim electron gas model [37]. These non-empirical potentials are known to correlate extremely well with experimental van der Waals or non-bonded radii and were successfully used in a previous work [38]. In a second step, all H-atoms positions (7 arbitrary angles) were deduced after minimization of the electrostatic lattice energy using the non-empirical PACHA scheme [34,35,39]. It was found to be very close to the experimental one concerning the O-atom and C-atom coordinates and now contains all H-atoms in their most favorable position (both from a steric and electrostatic viewpoint) with ideal bond lengths and almost perfect tetrahedral bond angles.

2.6 Correlation of electron densities with NMR shifts

Previous studies have shown that the electron densities retrieved from the PACHA software were very useful for interpretation of chemical shifts variations [40–46]. Referring to an absolute scale (σ_ref = 185.4 ppm) [47], the chemical shift δ of a¹³C nucleus bearing a partial charge q and submitted to an average excitation energy ΔE with an electronic population unbalance in p-orbitals P_u may be expressed as [45,46]:

In this relationship, the diamagnetic contribution σ_dia(q) may be evaluated from Hartree–Fock–Slater wave functions using the procedure of Saxena and Narasimhan [48] while the effect of partial charge q on the electron–nucleus distance r averaged over 2p-orbitals may be modeled as < (a₀/r)³>_2p = R°·(1 − f·q), where R° = 1.23 a.u. is the value applying to a free neutral carbon atom [49] and f a dimensionless factor close to unity. Molecular orbital theory is usually applied for recovering the charge distribution and bond order matrix P_ij (i, j = x, y or z) governing the P_u-term [50,51] as well as the average excitation energy ΔE. These treatments, being in any case very approximate, we prefer to assume equal sharing of the electronic density among the three p-orbitals: P_xx = P_yy = P_zz = P, P_xy = P_yx = P_xz = P_zx = P_yz = P_xy = 0. With P_ss, the population of the carbon 2s-orbital charge conservation leads to P_ss + 3P = 4 – q, i.e. P = (1 – q/3) if P_ss ≈ 1, leading to P_u = 3/2(1 – q²/9). The average excitation energy ΔE was evaluated by inversion of Eq. (1) using an average chemical shift computed from a set of NMR resonances characterized by the same first coordination sphere and from the corresponding averaged partial charges and diamagnetic shifts. Values less than 1 eV or much larger than 20 eV usually indicate wrong scaling in the charge dependence of the < (a₀/r)³>_2p = R°·(1 − f·q) term.

2.7 Thermodynamic modelization

In addition of bringing considerable help in the spectroscopic characterization of sol–gel precursors and in the quantification of ionic characters for any kind of molecular interactions, the PACHA approach may also be used to discuss chemical reactions from a thermodynamic viewpoint. This was already the case with the original partial charge model developed in collaboration with J. Livage [20–23], but with the ability of taking now into account the detailed molecular structures of the precursors it is now possible to perform a fully quantitative treatment of both enthalpic and entropic contributions. As far as enthalpy is concerned, PACHA relies onto the Hellman–Feynman theorem allowing one to introduce a unique partition of the molecular internal energy into a SE-term accounting for inter-atomic contributions, and a F-term accounting for intra-atomic electronic contributions independent of nuclear coordinates (see [35] for a rigorous quantum-mechanical treatment). Assuming that the variations of the F-term are well accounted by the choice of the Allen's absolute electronegativity scale used to derive equilibrium partial charges distributions and using the spherical charge approximation, it is possible to identify the SE-term with the internal energy U of the system. Using the common assumption that U ≈ H for condensed phases, it comes that the enthalpy variation ΔH should scale like the ΔSE variation.

Concerning entropy variations PACHA is able to estimate rotational entropies S_rot at temperature T for a given molecular structure by computing its three principal moments of inertia (I_A, I_B, I_C) and assuming that all rotational energetic levels are accessible at room temperature, leading to [52]:

In this relation, k_B is Boltzman's, e is Neper's constant, ℏ is reduced Planck's constant, R is the ideal gas constant and σ is the number of indistinguishable orientations of the molecule (symmetry number equal to the order of the rotational sub-group of the molecular point-group). If such an approximation is obviously not justified for very small molecules, it should work quite well for sol–gel precursors that are precisely not small molecules. It is worth stressing that (2) applies only to rigid rotators having no flexible parts. For molecules having flexible parts, such as freely rotating methyl groups, for instance, an additional contribution of about 15 J.mol⁻¹.K⁻¹ per methyl group should be added to (2) [53]. Besides free rotation around its three principal inertia axes, PACHA also consider the experimental IR and Raman frequencies ν_i associated to the 3N-5 (linear molecule) or 3N-6 (non-linear molecules) vibration modes using the following computational scheme [53]:

Finally, besides this internal entropy S_int = S_rot + S_vib, PACHA also computes a standard partial molar entropy (molar scale, SI units) S° using a classical partition function derived by Powell and Latimer [54]:

In this relation, S_int = S_rot + S_vib is the internal contribution, V_S is the molar volume of the solvent expressed in L.mol⁻¹, M is the molar weight of the solute expressed in g.mol⁻¹, N_A is Avogadro's number, h is the Planck's constant while e, R and k_B have the same meaning as in Eq. (2). The rotational entropy of (1) and H₃bhmpc have thus been estimated from the knowledge of their crystalline structure ([33] and CSD code MUGNAD respectively) assuming free rotation of the methyl group and from the IR/Raman data given in Tables 1 and 2. Two geometries were considered for H₃bhmpc: one with two intramolecular H-bonds after SE-minimization and one with intermolecular H-bonds observed in the solid-state structure. Vibrational entropy of H₃bhmpc has been computed using the experimental IR and Raman spectra available on Sigma–Aldrich's web site. Structural models for other compounds have been generated by minimization of repulsive energy using short-range repulsive potentials derived from the Gordon–Kim electron gas model [37] and assuming perfectly tetrahedral bond angles with CC distances of 153 pm, CO distances of 142 pm, CH distances of 108 pm and OH distances of 97 pm. Ideal structural models have been thus generated using the above standard structural parameters for 1,4-dioxane (V_S = 0.0853 L.mol⁻¹), EtOH and ⁱPrOH with free rotation of methyl groups, while the best ab initio molecular geometry [55] has been considered for the water molecule. Vibrational entropies of 1,4-dioxane, EtOH and ⁱPrOH have been computed using the experimental IR and Raman spectra available at the SDBS database [56]. Concerning titanium alkoxides precursors, the {Ti₄O₁₆} core of [Ti₄(OMe)₁₆] [57] has been used for building a molecular model of tetrameric [Ti₄(OEt)₁₆] known to exist in the solid state [58], while XANES/EXAFS data [59] have been used for trimeric [Ti₃(OEt)₁₂]. Owing to the unknown status of free rotation of the methyl groups in these structures, they were all considered as rigid rotators with no flexible parts. For monomeric [Ti(OPrⁱ)₄], it was found that the SE-energy was highly sensitive to the choice of the TiO distance. Using the 1.77 Å TiO distance measured on pure titanium isopropoxide [59] leads to SE = −4548 kJ.mol⁻¹, a much too low value leading to abnormally highly endothermic reactions even with water. Using the 1.82 ± 0.02 Å TiO distance measured also by EXAFS on titanium isopropoxide dissolved in toluene [60] leads to SE = −3732 ± 234 kJ.mol⁻¹, a value more compatible with known Ti(OPrⁱ)₄ chemistry. For this study performed in dioxane/alcohol mixtures where H-bonding may readily occur, the upper uncertainty limit (TiO = 1.84 Å) has been selected accounting for a possible additional extension due to H-bonding interactions that are absent in toluene. As in the case of titanium ethoxide, Ti(OPrⁱ)₄ has been considered as a rigid rotator with no flexible parts (fully hindered rotation of methyl groups). Vibrational entropies for these titanium(IV) alkoxides have been computed using their experimental IR and Raman spectra available on Sigma–Aldrich's web site [61] (Table 3).

3.1 U.V.-vis. spectroscopy

One of the most remarkable features of the complex is its deep orange color, a not so common situation for Ti^IV-based complexes. Fig. 2 compares the U.V.-Vis. spectra of the complex with that of the free ligand. The high energy band of the free ligand assigned to π→π^* transitions within the aromatic ring is characterized by λ_max = 238 nm (ɛ = 1200) and undergoes a slight hypsochromic shift, λ_max = 234 nm, associated to a significant intensity increase (ɛ = 18700) after binding to Ti(IV)-centers. The low energy band of the free ligand assigned to n→π^* transitions between O-atom lone pairs and the anti-bonding orbitals of the aromatic ring is characterized by λ_max = 286 nm (ɛ = 2300) and undergoes a large bathochromic shift, λ_max = 344 nm, with a significant intensity increase (ɛ = 8000) after binding to Ti(IV)-centers. This last band is responsible for the orange-color of the complex owing to its considerable width (ca. 100 nm at half-height) that may be assigned to charge transfers between the lone pairs of phenolic O-atoms and the empty 3d-orbitals on Ti-atoms.

3.2 IR spectroscopy

Attribution of the spectrum (Fig. 3) has been made (Table 1) by comparison with the IR spectra of the free ligand H₃bhmpc [61] and of 1,4-dioxane [62]. Upon complexation, the three ν_OH bands found in the H₃bhmpc ligand are replaced by a single large band centered at 3440 cm⁻¹ (Δν_1/2 = 400 cm⁻¹). It is thus not possible to differentiate between the three kinds of intramolecular H-bonds existing in the crystal. Complexation has also the effect of rendering visible ν^ar_CH and ν^ar_CC vibrations that are not observed in the free H₃bhmpc ligand. For the other bands, the global effect of complexation is an increase in frequency of at most 30 cm⁻¹ except for δ^a_CH3, δ_CH2, δ_COH vibrations and one π_PhH component showing a decrease in frequency of at most –12 cm⁻¹. A few bands ν^a_CH2, δ^S_CH3, δ_PhH, ν_PhC are also observed at the same frequency in the free ligand or in the complex. On the other hand, it is observed that encapsulation of 1,4-dioxane within the two cavities has the global effect of decreasing vibrations frequencies by at most –16 cm⁻¹ except for δ_CH2(C), π_CH2(O), ρ^w_CH2 and one type of ring breathing vibrations showing small increase in frequency except for the π_CH2(O) vibration that appears to be strongly affected. This detailed attribution has allowed detection of the vibration bands associated to the formation of TiO bonds. The frequency found for the ν_CO(Ti) band is within the expected 1000–1170 cm⁻¹ range for TiOC bonds while that proposed for the μ₃-oxo bridge are close to what is observed in the rutile structure showing similar bridges: 811 cm⁻¹ (A_2u, longitudinal), 806 cm⁻¹ (A_2u, longitudinal), 500 cm⁻¹ (E_u, transverse) and 458 cm⁻¹ (E_u, longitudinal) [63]. The assignment of the 703 cm⁻¹ band with δ_TiOC is tentative and should not be considered as firmly established.

3.3 Raman spectroscopy

Attribution of the spectrum (Fig. 4) has been made (Table 2) by comparison with the Raman spectra of the free ligand H₃bhmpc [61] and of 1,4-dioxane [64]. The spectrum is dominated by the aromatic doublet at (1644, 1504) cm⁻¹ and by the breathing of the dioxane ring at 835 cm⁻¹. As already observed in the IR spectrum, the global effect of complexation is an increase in frequency of at most 26 cm⁻¹ except for δ^a_CH3, δ^S_CH3, ρ^w_CH2, π_CH2 vibrations and one ν_CC component showing rather a decrease in frequency of at most –22 cm⁻¹. It is also again observed that encapsulation of 1,4-dioxane within the two cavities has the global effect of decreasing vibration frequencies of at most –8 cm⁻¹ except for one δ_CC component showing a slight increase in frequency and two vibrations (ring breathing and δ_CC) being unaffected. This detailed attribution has allowed detection of vibration bands associated to the formation of TiO bonds. The frequency found for the ν_CO(Ti) band is slightly higher than the 1160–1180 cm⁻¹ range for observed for aliphatic TiOC bonds [65]. This increase in frequency may well reflect the fact that we are dealing here with an aryloxide and not with an alkoxide. The attribution proposed for the ν_TiO and μ₃-oxo bonds is in agreement with what is observed in the rutile structure showing similar bridges: 826 cm⁻¹ (B_2g), 612 cm⁻¹ (A_1g) and 447 cm⁻¹ (E_g) [63] or in the Raman spectra of titanium alkoxides [65].

3.4 ¹⁷O NMR spectroscopy

Fig. 5 shows the 44.2 MHz ¹⁷O NMR spectrum of complex (1) dissolved in CDCl₃. As expected, only one signal is observed at 455 ppm falling within the 450–650 ppm range expected for μ₃-OTi₃ bridges [31–32].

3.5 ¹³C solid state CPMAS NMR

Fig. 6 shows the different ¹³C CPMAS NMR spectra recorded at 75 or 125 MHz for different crystals obtained after mixing in 1,4-dioxane, H₃bhmpc and Ti(OR)₄ using R = Et (spectra 1-4) or R = Prⁱ, Buⁿ (spectrum 5). According to the two single-crystal X-ray structures available for the R = Et compounds [33], three signals corresponding to bhmpc, Hbhmpc and H₂bhmpc ligands are expected for phenolic CO(Ti) and PhCH₃ sites in the as synthesized crystals, while six signals should be obtained after recrystallization in CHCl₃ owing to the existence of two non-equivalents complexes in the unit-cell of this last compound. Spectra 1, 2 and 4 are in good agreement with this analysis. The two spectra recorded on samples 1 and 2 illustrate the effect of drying the crystals at room temperature under ambient atmosphere. In the phenolic CO(Ti) region (left of Fig. 6), drying essentially affects the chemical shift of the central resonance which moves from 157.0 ppm (sample 1) to 156.5 ppm (sample 2), the two outer resonances at 159.4 and 153.7 ppm being almost unaffected (159.6 et 153.7 ppm in sample 2). In the methyl region (right of Fig. 6), the number of signals changes from 4 to 3 with a change in chemical shifts for all resonances, reflecting the fact that ethanol molecules are no more present in the structure (while dioxane is still trapped as can be seen on Fig. 7). The spectrum of sample 3 in Fig. 6 points out the existence of at least two polymorphs in the as synthesized crystalline powders of the R = Et system. A pure single phase (1) is usually produced but, in spite of identical working conditions, obtaining a mixture similar to sample 3 is not rare. As will be discussed below, this mixture appears to contain two polymorphs. Spectrum 3 can actually be fitted as a sum of a spectrum identical to 1 (major component) and a second spectrum which appears to be identical to 5. Spectrum 5 is the reproducible signature of orange crystalline powders obtained when either Ti(OPrⁱ)₄ or Ti(OBuⁿ)₄ are used as sources of titanium instead of Ti(OEt)₄. In these cases, no alcohol or alkoxy signals are present on spectra that are the same for both sources of titanium, but in each case 1,4-dioxane molecules are detected. In the phenolic CO(Ti) region of the spectrum, six components can be identified at 159.7, 159.5, 157.1, 156.9, 153.0 and 152.7 ppm. This can be compared to the case of sample 4, obtained by recrystallization in CHCl₃ for which six signals are also found, shifted, at 159.7, 159.4, 159.0, 158.4, 153.5 and 153.0 ppm. This similarity suggests a single-phase composition for samples giving rise to spectrum #5, corresponding to a polymorph with two non-equivalent molecules in the unit-cell as was observed with the recrystallized sample 4. Unfortunately all attempts to determine this new crystalline structure suggested by ¹³C CPMAS measurements have failed owing to the very small size of the crystals, not suitable for a single-crystal X-ray study. Fig. 7 shows the two other regions of interest in these ¹³C CPMAS spectra that are either too complex to be analyzed in details (aromatic carbons zone at the left) or sometimes showing a bad resolution (methylene zone at the right for spectra 3 to 5). Despite this lack of resolution, it is worth noticing the absence of ethanol signals in samples 2, 4 and 5 in good agreement with the above discussion. It is also worth noting that 1,4-dioxane is detected in all cases as a large signal at 66–67 ppm. For sample 4, identifying the signal due to included CHCl₃ molecules on the ¹³C CPMAS spectrum is not straightforward because of superimposed large signals but the presence of these molecules could be clearly evidenced by comparison with ¹³C{¹H} MAS spectrum and on the ¹H MAS spectrum (not shown).

3.6 ¹H and ¹³C solution NMR spectroscopy

It was observed that all samples studied by ¹³C CPMAS NMR gave rise to exactly the same ¹H or ¹³C spectra after dissolution in CDCl₃. This shows that if the nature of the R group used for the synthesis has a subtle effect upon the stacking of such molecules in the solid state, it plays absolutely no role in the building of the molecular unit in solution. Consequently, three different kinds of signals coming from aromatic ligands: bhmpc, Hbhmpc and H₂bhmpc are expected if the centro-symmetric structure of the complex is conserved upon dissolution. For discussion we have labeled each peak on ¹H and ¹³C spectra starting from low frequencies and ignoring solvent molecules. Fig. 8 shows the numbering scheme derived from X-ray crystallography, while Fig. 9 gives the final ¹H and ¹³C NMR assignment.

Fig. 10 shows the ¹H spectrum of a sample of (1) dissolved in CDCl₃, (5 mg/0.6 mL). Dioxane and ethanol are readily identified by a singlet at 3.66 ppm (OCH₂CH₂O), a quadruplet at 3.61 ppm (CH₃CH₂OH) and a triplet at 1.15 ppm (CH₃CH₂OH) respectively. Some free H₃bhmpc is also detected by the occurrence of three signals at 6.62 ppm (aromatic CH), 4.45 ppm (OCH₂Ar) and 2.19 ppm (ArCH₃). Other signals may be attributed to the three different kinds of ligands. No signal is detected from any hydroxy proton, clearly due to exchange processes. The methyl groups of the cresol moiety lead to three well-resolved signals (1:1:1) between 2.1 and 2.3 ppm. Between 4 and 6 ppm, 12 doublets of equal integral are observed showing the existence of six inequivalent methylene groups, each bearing two inequivalent protons. Four measured ²J values are significantly different (11.1, 11.8, 13.55, 14.5 Hz) and lead to pair some signals corresponding to different CH₂ groups, respectively, (H5,H6), (H4,H10), (H13,H14) and (H9,H12). ²J values measured for the doublets H7, H8, H11 and H15 are too close and distributed (13.33, 13.38, 13.31, 13.25) to show pairs unambiguously. According to the second order coupling figures, one can nevertheless pair ¹H signals the following way: (H11,H7 or H8) and (H15, H7 or H8). Finally, between 6.7 and 7 ppm, six doublets (⁴J∼1.6 Hz) of equal integral are observed corresponding to the two aromatic protons of the three kind of ligands. Detailed ¹H chemical shift values can be found Table 1.

Fig. 11 shows the ¹³C {¹H} spectrum on the same sample. As before, dioxane and ethanol are detected by three signals at 67.1 ppm (OCH₂CH₂O), 58.4 ppm (CH₃CH₂OH) and 18.3 ppm (CH₃CH₂OH). Signals attributed to the complex are: three signals observed at 20–21 ppm (ArCH₃), six signals at 60–75 ppm (OCH₂Ar), 14 signals at 123–131 ppm for 15 aromatic C-atoms, two signals being superimposed as demonstrated by the HMBC experiment, see Fig. 14a and three signals at 152–159 ppm (phenolic COTi). Detailed ¹³C chemical shift values can be found Table 4. One may thus safely conclude that the structure observed in the solid state is conserved in solution and that the complex is rigid enough to keep the quite low P-1 symmetry of the crystal. These well-resolved spectra (21 ¹H and 26 ¹³C signals) also call for an attribution linking each NMR signal to its corresponding crystallographic site in the structure. Thus, a set of 2D NMR experiments was performed in order to identify on ¹H and ¹³C spectra three groups of labels corresponding to the three ligand forms: bhmpc, Hbhmpc and H₂bhmpc.

On the COSY spectrum (Fig. 12), correlation peaks among the methylene signals (HCH correlation part, not shown) confirm and complete the pairing started, relying on J values on the 1D spectrum: (H4,H10), (H5,H6), (H9,H12), (H13,H14), (H11,H8) and (H15,H7). This information is also available on the C H₂ correlation part of the HSQC spectrum, Fig. 13a, where ¹H and ¹³C signals of directly bonded C and H atoms of the six non equivalent CH₂ groups are identified: (C4,H4,H10), (C5,H5,H6), (C6,H8,H11), (C7,H9,H12), (C8,H13,H14) and (C9,H7,H15).

The CHCH₃ correlation part of the COSY spectrum given in Fig. 12a evidences three subsets of ¹H signals corresponding to aromatic CH and CH₃ groups on each of the three ligand types: (H1,H16,H18), (H2,H19,H20) and (H3,H17,H21). Then HSQC CH and C H₃ correlation parts Fig. 13b and c respectively lead to group CH₃ and CH ¹³C and ¹H signals the following way : (C1,H1; C13,H16; C17,H18), (C2,H3; C21,H17; C18,H21), (C3,H2; C16,H19; C23,H20).

The CH₂CH correlation part of the COSY spectrum (not shown) does not help to identify CH and CH₂ neighbors readily because of long range couplings ⁶J between distant CH and CH₂ in addition to ⁴J couplings between close CH and CH₂ on the same ligand. Running a ROESY experiment allows one to investigate ¹H¹H dipolar interactions and correlates the following pairs of signals: (H4,H20), (H5,H17), (H7,H18), (H8,H17), (H9,H16), (H13,H21), see Fig. 12b. This leads to assign NMR signal labels to CH₃, CH₂ and CH neighbors on the three different ligands. Furthermore each H site of one given CH₂ group can be labeled according to its distance to the neighboring CH given by XRD, see Figs. 8 and 9, making the assumption that the molecular structure is rigid enough, due to intra-molecular H-bonds, to compare that way atoms proximity in solution and in the solid state.

We are then left with the assignment of C-atoms bearing no protons, for which the HMBC spectrum, showing long-range CH J couplings, has been recorded, see Fig. 14. Among CH₃C and CH₃CCH correlation peaks, Fig. 14c, (H1,C22), (H2,C23), (H3,C21) peaks identify the signals corresponding to the C atoms of each CH₃C fragment. The CHCC OTi correlation peaks, Fig. 14b, allows one to label phenolic COTi sites, showing (H16,H18,C24), (H17,H21,C25), (H19,H20,C26) vicinities. Finally, from the CH₂C and CH₂CCH correlation part, Fig. 14a, we get (H6,C10), (H8,H11,C11), (H9,H12,C12), (H13,H14,C14), (H4,H7,H10,H15,C15,C15’) associations, where the last one can be expressed as (H7,H15,C15), (H4,H10,C15’), according to the known assignment for the CH₂ protons.

We have thus defined three unambiguous sets of labels for three different ligands:

[C1,H1; C22; (C13,H16; C12; C7,H9,H12); (C17,H18; C15; C9,H7,H15); C24]

[C2,H3; C19; (C21,H17; C10; C5,H5,H6); (C18,H21; C14; C8,H13,H14); C25]

[C3,H2; C20; (C16,H19; C11; C6,H8,H11); (C23,H20; C15’; C4,H4,H10); C26].

At this point, no conclusion has been drawn about the assignment of each of these sets to one specific type of ligand, three protonation states being possible: bhmpc, Hbhmpc and H₂bhmpc. For that, we can first propose an assignment based on chemical shift arguments and start by considering the six ¹³C signals corresponding to the methylene moieties (labeled C4 to C9 on Fig. 9). From the chemical shift of these moieties in the free ligand H₃bhmpc dissolved in CDCl₃ (1 mg / 0.6 mL, spectrum not shown), δ = 63.65 ppm, we propose to assign the two low frequency peaks (δ_C4 = 60.68 ppm and δ_C5 = 63.00 ppm) to arms that are not coordinated to Ti-atoms. Then it follows that the two sets containing C4 and C5 should correspond to either Hbhmpc or H₂bhpmc, leaving the last set containing C7 and C9 for bhmpc. Yet another assignment for the bhmpc ligand is possible by looking at the three ¹³C signals in the phenolic region (labeled C24, C25 and C26 on Fig. 9) where one signal (C24) appears to be clearly separated from the two other (C26 and C27). Referring to the molecular structure of the complex, it appears that the phenolic O-atoms are in the chelating position for Hbhmpc and H₂bhmpc ligands and in the bridging position for bhmpc. This strongly suggests to assign C24 to bhmpc, leading to assign the same set of signals as before to this ligand : [C1,H1; C22; (C13,H16; C12; C7,H9,H12); (C17,H18; C15; C9,H7,H15); C24]. Assuming this attribution is correct, an oriented assignment has to be proposed for this bhmpc ligand. One can notice that one of its OCH₂ arm is engaged into an intramolecular hydrogen bond with a HOCH₂ arm of a H₂bhmpc ligand (Fig. 8). If we look for the available protons around this H-bonded arm in the molecular structure, we found at a distance less than 320 pm one OH bond and three CH bonds. The situation is completely different for the other arm where it comes six CH bonds (four from CH groups and two from CH₂ groups). Noticing the broadness of the C9 signal compared to the C7 one particularly, it is tempting to assign C9 to the H-bonded arm, for which H-bond might well lead to chemical shift distribution and/or shorter transversal relaxation time T₂, and C7 to the non H-bonded one. A complete assignment is then proposed for the bhmpc ligand.

The two remaining sets are still to be assigned either to Hbhmpc or H₂bhmpc. The Ti-bonded OCH₂ zone in the ¹³C NMR spectrum shows three rather close peaks (C7,C8, C9), separated from a single peak (C6). In the molecular structure, two situations also appear: three similar TiOCH₂Ar arms (two in bhmpc, one in H₂bhmpc) and the (Ti)₂OCH₂Ar arm belonging to the Hbhmpc form. Then, C6 can be assigned to the Hbhmpc form, leaving C8 for the H₂bhmpc one, as C7 and C9 are already supposed to belong to bhmpc. Considering the identified sets of signals, it follows that C4 belongs to the free arm of Hbhmpc and C5 to the free arm of H₂bhmpc. Then we have reached a complete assignment of the ¹³C NMR spectra, inducing a complete assignment of the ¹H NMR spectra as well.

In order to validate these assignments, we have also measured the longitudinal relaxation times T₁ of both ¹H and ¹³C nuclei in our complex. For the ¹³C nuclei, we found that relaxation times were ruled by the first coordination sphere as all values for a given type of chemical group are very similar (standard deviation is given in brackets): T₁(CH₂) = 0.135(14) s, T₁(CC₂H) = 0.22(3) s, T₁(CH₃) = 0.81(7) s, T₁(CC₃) = 0.83(13) s and T₁(CC₂O) = 1.24(17) s, with no significant differences observed among the three protonation states. The situation was very similar concerning ¹H relaxation times of methyl T₁(CH₃) = 0.822(6) s or aromatic CH groups T₁(CH) = 1.34(6) s, but not with methylene groups where significant differences were observed T₁(CH₂) = 0.401(34) s, see Table 5. Two protons belonging to the same methylene group are expected to reveal similar T₁ values if mobility allows them to explore a same mean environment. On the contrary, if their mobility is restrained, different sensed environments will lead to significantly different relaxation times. When comparing the two relaxation times measured for each proton belonging to the same methylene group (identified below by its C atom NMR label), three cases may be encountered:

• • almost no differentiation: ΔT₁(C5) = 1 ms and ΔT₁(C7) = 8 ms;
• • moderate differentiation: ΔT₁(C4) = 37 ms and ΔT₁(C8) = 57 ms;
• • strong differentiation: ΔT₁(C9) = 94 ms and ΔT₁(C6) = 112 ms.

A large ΔT₁ being associated to a high rigidity of the CH₂ arm, we can assign the largest ΔT₁ (protons on C6) to the most constrained μ₂-CH₂OTi₂ bridge occurring in the Hbhmpc ligand. This single observation is enough to validate in an independent way the previously derived assignment. It also explains the satisfactory correlation shown in Fig. 15 concerning the relationship between observed ¹H T₁-values and (Σ 1/r⁶)⁻¹ values computed according to the proposed NMR assignment using the available structural data (H-atoms neighbors at less than r = 300 pm distance).

3.7 Assignment directly from crystal structures

The above results show how it was possible to establish on a purely experimental basis a link between the solid-state molecular structure of a sol–gel precursor and its associated high-resolution ¹H and ¹³C NMR solution spectra. The problem is that such a full assignment is quite expensive in terms of NMR-recording time and the question is now asked if such an assignment could be made directly from available crystalline data. The principal motivation for such a theoretical analysis is the high-quality partial charges derived from the PACHA algorithm [34] and the fact that two crystal structures are available for the same structural motif differing only by the kind of solvent molecules filling the holes in the lattice [33]. Through the aid of Eq. (1), it becomes then possible to quantify in terms of chemical shifts the effect of replacing ethanol by chloroform, thereby allowing diving more deeply into the origin of these ¹³C chemical shifts.

As explained in the theoretical section, the first job is to fix reasonable values for the two critical parameters of the model, the f-factor ruling the charge dependence of the inverse electron–nucleus cubed distance r averaged over 2p-orbitals < (a₀/r)³>_2p = R°·(1 − f·q) and average excitation energy ΔE. As the partial charges given by the PACHA software are of ab initio quality [34], we have set f = 1 as suggested by computations based on Hartree–Fock–Slater-type orbitals [48,66]. The only adjustable parameter in the modeling was thus the average excitation energy, whose value is generally ruled by the nature of the first coordination sphere of the ¹³C nucleus. In the present case, the experimentally observed ¹³C resonances have been grouped into five (free ligand) and six (tetranuclear complex) different sets differing by the nature and number of atoms within the first coordination sphere of the carbon-atom (Table 6). For each set, an average chemical shift was computed, leading after inversion of equation (1) to an associated ΔE-value also indicated in Table 6. Furthermore, a comparison between the ΔE-values deduced from the structure of the free ligand (H₃bhmpc, MUGNAD code in the Cambridge Structural Database) and that of the two complexes shows, as expected, a pretty good constancy for all C-sites not linked to oxygen atoms. For the two carbon sites linked to OTi moieties, a significant ΔE-decrease is observed relative to the ligand, responsible for the observed deshielding of the associated resonances in the NMR spectrum. Another point of interest of this table lies in the easy identification of the phenolic “CCO” groups as the least affected set of resonances by the substitution EtOH → CHCl3, owing to the perfect invariance of the corresponding ΔE-values. With Table 6, it is now possible by direct application of Eq. (1) to transform the partial charges given by the PACHA algorithm into ¹³C NMR chemical shifts.

Table 7 shows the NMR shifts predicted for the ethanol solvate structure while Table 8 refers to the chloroform solvate structure. Owing to the quite low polarities of these highly covalent bonds (−0.18 < q_C < +0.05), the population unbalance contribution P_u is clearly not the dominant factor for explaining the observed chemical shift variations. For the same reason, the diamagnetic contribution σ_dia, remains stuck around 284 ppm (absolute shielding scale). It may thus be concluded, in agreement with more sophisticated approaches, that the dominant contribution to the ¹³C chemical shifts is due to the variation of the paramagnetic term either through the average excitation energy for C-sites differing in their first coordination sphere or through the inverse electron–nucleus cubed distance r averaged over 2p-orbitals < (a₀/r)³>_2p for C-sites sharing the same first coordination sphere. The high quality of our charge modeling is again well reflected by looking at the predicted values for C₂CO sites deduced from the crystal data concerning ethanol and chloroform solvates. In both cases, the observed experimental ordering δ(H-bhmpc) > δ(H₂bhpmc) >> δ(bhmpc) is quantitatively reproduced with less than 0.3 ppm and 0.7 ppm errors for the ethanol and chloroform cases, respectively. This right assignment based on two different crystal data rules completely out the possibility of a by-chance result. Obviously, such an agreement with solution NMR data for these C₂CO sites comes from the fact that they are deeply buried in the most rigid part of the complex and are thus not under the influence of moving solvent molecules. Consequently, the next step is to look at aromatic C₂CC sites that are also expected to be least affected by the presence of solvent molecules. The observed experimental ordering δ(bhmpc) > δ(Hbhpmc) > δ(H₂bhmpc) for the three H₃CPh sites (C22, C20 and C19 resonances) is here also quantitatively reproduced with errors less than 0.5 ppm for C20 (Hbhmpc) and C22 resonance (bhmpc) in the ethanol and chloroform cases, respectively. Interestingly enough, the least rigid H₂bhmpc ligand (C19 resonance) is characterized by a larger error (1.6 ppm) in EtOH than in CDCl₃ (1.0 ppm). This slightly larger error does not affect the predicted assignment, nor the fact that the H₃CPh resonances should all be deshielded relative to PhCCH₂O resonances. For these last signals, the agreement between calculated and experimental positions is found to be acceptable (errors less than 1.5 ppm) for C11, C12, C14, C15 resonances (Table 7) in the case of the ethanol solvate and for C12, C15, C15’ resonances (Table 8) in the case of the chloroform solvate. Most interesting is the large 3 ppm error in the position of the C15’ resonance, experimentally assigned to the PhCCH₂(OH)…H arm of a Hbhmpc ligand, in the ethanol solvate case that is reduced down to 0.4 ppm in the chloroform solvate case. It may then be deduced that the H-bonded structure in which the ethanol molecule is engaged in the ethanol solvate is most probably broken after dissolution of the crystals in CDCl₃. It is worth noticing that for the other coordinated PhCCH₂(OTi₂) arm of this Hbhmpc ligand (C11 resonance), the error is lower in the ethanol solvate case (0.5 ppm) relative to the chloroform case (1.4 ppm). This would suggest that we have not a complete ethanol-chloroform substitution upon dissolution, but just a significant rearrangement of the H-bond pattern in order to accommodate both ethanol and chloroform around the structure. As expected, the prediction for the C15 and C12 resonances assigned respectively to PhCCH₂(OTi)…H and PhCCH₂(OTi) arms of a bhmpc ligand are quite good in both cases (errors less than 1 ppm) while that concerning the C10 and C14 resonances assigned to the two arms of H₂bhmpc ligands are the worst ones with errors larger than 1 ppm. For the C10 resonance associated to the uncoordinated PhCCH₂(OH)…H arm, a large error is systematically observed. It is, however, logically smaller for the CDCl₃ case (4.4 ppm) relative to the EtOH case (6.6 ppm). As already observed in the Hbhmpc case, errors are reversed concerning the other coordinated PhCCH₂(OH)Ti arm (C14 resonance) with a better agreement (about 1 ppm error) for the ethanol solvate compared to the chloroform solvate (about 3 ppm error). Here also, a rearrangement of the H-bond pattern around the H₂bhmpc ligands specific to the solution is probably responsible for the difficulty to reproduce the observed chemical shifts using crystalline data alone.

Up to now, focus has been put on C-atoms bearing no protons because these atomic sites were expected to be the least affected by dissolving the crystals in CDCl₃, whereas protonated sites such as methine, methylene and methyl groups are expected to be in direct van der Waals contact with solvent molecules. For these groups, there is thus no a priori reason to expect a correlation between NMR data recorded in solution and structural data derived from single-crystal X-ray diffraction. Nevertheless, if such correlations are observed for some selected sites of the molecule, it could be concluded that the solvent is very probably excluded from the considered region. Obvious reasons for such an exclusion could be either an unfavourable steric interaction or even an entropic factor linked to the existence of very particular H-bonding scheme involving several kinds of small molecules. This is precisely the case here, with ethanol, dioxane and chloroform competing for the solvatation of the same double-calix shaped complex. The aromatic methine groups being the most buried sites, it is thus not surprising to find that using the ethanol solvate structure (Table 7), the relative positions of four resonances (C13, C16, C17, C18) among six possibilities are correctly predicted with less than 1 ppm error. Interestingly enough, these four sites are precisely those having in ortho position a Ti-coordinated arm: C13(bhmpc) = HCPhCH₂OTi, C16(Hbhmpc) = HCPhCH₂OTi₂, C17(bhmpc) = HCPhCH₂(OTi)…H and C18(H₂bhmpc) = HCPhCH₂(OH)Ti. Comparison with the chloroform solvate case (Table 8) then shows that the position of only two resonances (C16 and C18) are predicted with less than 1 ppm error. In this case, the two methine resonances associated to the bhmpc ligand (C13 and C17) are strongly affected (error of 2.7 and 2.3 ppm respectively). It may thus be concluded that, in solution, chloroform molecules are most probably excluded from the neighborhood of the bhmpc ligand, interacting more selectively with the less rigid Hbhmpc and H₂bhmpc regions. Large errors (more than 2 ppm) are observed in both solvates for the two other sites, C21(H₂bhmpc) and C23(Hbhmpc), having in ortho position an uncoordinated HCPhCH₂(OH)…H arm, evidencing as before a specific reorganisation of the intramolecular H-bond pattern in solution. In strong contrast with methine groups, errors larger than 1 ppm are systematically observed (Table 7) for the six resonances of the methylene groups using ethanol solvate crystal data. On the other hand, three very good predictions with errors less than 0.5 ppm can be observed: C7(bhmpc) = PhCH₂(OTi), C5(H₂bhmpc) = PhCH₂(OH)…O and C4(Hbhmpc) = PhCH₂(OH)…O, for the chloroform solvate case (Table 8). This observation strongly suggests that chloroform molecules should have a good affinity for such sites and is in perfect coherence with the errors larger than 1 ppm observed for the three other methylene sites that are much more crowded and thus less accessible to CDCl₃: C9(bhmpc) = PhCH₂(OTi)…H, C8(H₂bhmpc) = PhCH₂(OH)Ti…O and C6(Hbhmpc) = PhCH₂(OTi₂). At last, it was possible to predict with an error less than 0.5 ppm, the relative positions of the three resonances arising from the H₃CPh sites, using the ethanol solvate crystal data. Corresponding errors being one order of magnitude larger using the chloroform solvate data, it may be safely concluded that ethanol molecules are most probably selectively located in the neighbourhood of these methyl groups, thus preventing the approach of the solvent molecules.