research communications
Structure of tetrakis(pentafluorophenoxido)bis(tetrahydrofuran)titanium(IV)
aDepartment of Chemistry, The Pennsylvania State University, Commonwealth College at Altoona, Altoona, Pennsylvania 16601, USA
*Correspondence e-mail: [email protected]
Titanium(IV) chloride was reacted with a slight excess of barium pentafluorophenoxide in tetrahydrofuran (THF) solution. After filtration and solvent evaporation, the resulting orange crystalline material was obtained. The product was recrystallized by preparing a concentrated solution in THF at room temperature, followed by cooling to 253 K. The supernatant solution was decanted using a pipet, and the crystals were dried by allowing the solvent to evaporate in the atmosphere of a glovebox. It was possible to obtain good-quality X-ray data at 100 K on a crystal, namely, tetrakis(pentafluorophenoxido-κO)bis(tetrahydrofuran-κO)titanium(IV), [Ti(C6F5O)4(C4H8O)2], having monoclinic (P21/n) symmetry. This compound adopts a solid-state structure in which the titanium(IV) ions have a distorted octahedral coordination environment with two coordinated THF molecules occupying cis positions.
Keywords: alkoxides; crystal structure; fluoroalkoxides; ionization isomer; coordinating solvent; Ziegler–Natta polymerization catalyst.
CCDC reference: 2570948
1. Chemical context
Early transition-metal have been of interest for applications ranging from organic synthesis and catalysis to the preparation of metal oxide materials via the sol-gel process (Bradley, 1959
; Bradley et al., 1978
; Bradley et al. 2001
). Earlier work by the author of this article assumed the use of fluorinated alkoxides would provide enhanced Lewis acidity, while maintaining steric and stereochemical control over Ziegler–Natta polymerization-type processes. These publications described the partial substitution of alkyl alkoxides by fluoroalkoxides in alcoholysis-type reactions (Campbell et al., 1994
; Fisher et al., 1993
).
In addition, the structure of an acetonitrile adduct of tetrakisfluoroalkoxide titanium(IV), Ti[OCH(CF3)2]4(N≡CCH3)2, was described, in which the coordinated solvent molecules act as Lewis bases in cis positions by way of nitrogen lone pairs. The coordination geometry of the titanium(IV) ion was best described as being a distorted octahedral structure. It was tempting to assume that this structure was typical for the disolvates of the tetrakisfluoralkoxide titanium(IV) complexes.
However, it was not possible to obtain suitable quality X-ray data for the analogous tetrahydrofuran (THF) adduct due to the significantly low melting point. However, the data that were obtained seemed to suggest that the THF adduct was an ionization isomer in the solid state comprised of a Ti(OPrf)2THF42+ cation and a Ti(OPrf)62− anion (OPrf is hexafluoroisopropoxide). Ionization isomers of metal complexes are known (Barbier et al., 1972
; Tebbe & Muetterties, 1967
; Kamata et al., 2012
; Giesbrecht et al., 2004
; Xie et al., 1996
; Niemeyer, 2001
), and it was assumed that the enhanced electron-withdrawing ability of the fluoroalkoxides as compared with the electron-donor properties of alkyl alkoxides would have a preference for such an ionization isomer in a polar solvent such as THF. Malinowski & Koteras (2026
) recently described the crystal structure of [Ti{OC(CF3)3}2(N≡CCH3)4][Al{OC(CF3)3}4], with the perfluoroalkoxide ligands coordinated to the titanium(III) cation exhibiting a significant amount of disorder.
Some recent efforts to obtain X-ray-quality crystals of the Ti[OCH(CF3)2]4THF2 complex, which was prepared by way of a metathesis reaction between titanium(IV) chloride and sodium hexafluoroisopropoxide in THF as a solvent, have been published (Van Der Sluys, 2024
), but were again not entirely successful. However, it was possible to obtain the structure of a slightly higher melting minor product, in which only three chlorides had been substituted by fluoroalkoxides, producing TiCl(OPrf)3THF2. In the present article, the X-ray crystal structure of the related pentafluorophenoxide complex, Ti(OC6F5)4THF2 (complex 1), is reported.
2. Structural commentary
The molecular structure of 1 shown in Fig. 1
emphasizes the nearly octahedral coordination geometry of the Ti atom, with the THF ligands adopting a cis configuration. Guzei & Winter (1997
) have presented arguments concerning the factors that affect the formation of cis versus trans isomers in TiCl4L2 complexes containing pyrazole ligands. Their arguments suggest that π-donor ligands greatly influence the stability of the cis versus trans isomers. Alkoxide ligands are generally considered better π-donor ligands than chloride ligands, but presumably the fluorophenoxide ligands somewhat attenuate these properties due to the electron-withdrawing nature of the F atoms and the potential delocalization of the oxygen lone pairs into the benzene π-ring system. Fractional coordinates and other crystallographic data can be found in the supporting information.
| Figure 1 The molecular structure of 1, showing the atom-numbering scheme used. Displacement ellipsoids are drawn at the 50% probability level. |
The coordination geometry of 1 is best described as distorted octahedral. The fluorophenoxide Ti—O bond lengths [average 1.8691 (19) Å] are comparable to those found in other fluorophenoxide compounds whose structures have been published previously (Campbell et al., 1994
; Fisher et al., 1993
). The Ti—O bond lengths for the coordinated THF ligands [average 2.1195 (18) Å] are significantly longer than the phenoxide bond lengths, comparable to those previously observed (Van Der Sluys, 2024
), and consistent with the weaker polar coordinate bonds associated with the neutral ether ligands as compared with the phenoxide ligands.
3. Supramolecular features
Two of the fluorophenoxides in 1 have significantly more obtuse Ti—O—C bond angles and shorter Ti—O bond lengths than the other two fluorophenoxides. Specifically, the bond lengths and angles for the fluorophenoxides that are trans to the THF ligands are Ti1—O2 and Ti1—O3, which are 1.8777 (18) and 1.8370 (18) Å, respectively, while the Ti1—O2—C7 and Ti1—O3—C13 angles are 131.35 (17) and 158.45 (17)°, respectively. Alternatively, the fluorophenoxide ligands that are trans to each other, Ti1—O1 and Ti1—O4, have bond lengths of 1.8548 (19) and 1.9068 (19) Å, respectively, and Ti1—O1—C1 and Ti1—O4—C1 angles of 166.99 (17) and 129.21 (16)°, respectively. These bond angles do not seem to correlate well with anticipated trans-influence effects associated with phenoxide ligands being trans to a phenoxide versus a THF ligand. The larger Ti—O—C bond angles and shorter Ti—O bond lengths could be interpreted as resulting from more significant π bonding interactions of the oxygen lone-pair interactions with the empty t2g (dxy, dxz and dyz) set of d orbitals of the titanium(IV) ion in an octahedral which has a 3d0 These variations do not seem to correlate with significant changes in the C—O bond lengths, which might be anticipated from changes in the bonding delocalization interactions of the benzene and the oxygen lone pairs. These variations in bond angles and lengths may simply be a result of crystal packing forces that influence the orientations of the benzene rings, as shown in the unit-cell packing diagram in Fig. 2
.
| Figure 2 Packing diagram for the unit cell of 1. |
4. Synthesis and crystallization
The reaction of pentafluorophenol with various of titanium(IV) resulted in incomplete substitution of the alkyl alkoxide ligands (Campbell et al., 1994
). Mazdiyasni et al. (1971
) described the synthesis of a series of hexafluoroisopropoxide Group IV element compounds by way of a metathesis approach, in which the metal chlorides were reacted with four equivalents of the sodium fluoroalkoxides, with the corresponding liquid fluoroalcohols as the solvent. The desired compounds were obtained by fractional distillation and could be recrystallized from various organic solvents, including diethyl ether and THF. It was hoped that a similar metathesis approach could be used to prepare the corresponding titanium(IV) pentafluorophenoxide compounds, but since pentafluorophenol is a solid at room temperature, THF was used as the solvent. A potential complicating factor in the reaction with greater than four equivalents of alkoxide is the potential formation of anionic species, such as [Ti(OR)5]− (Boyle et al., 1999
; Chandler et al., 1993
) and [Ti(OR)6]2− (Day et al., 1995
), which have been shown to be useful in controlling sol-gel production of titanium oxide solid-state materials.
Reaction of titanium(IV) chloride with greater than two equivalents of barium pentafluorophenoxide, which was prepared in situ from barium metal and pentafluorophenol, resulted in the rapid formation of an orange solution and a white precipitate. The solution was stirred at room temperature for 12 h, after which the solution was filtered, and the volume of the solution was reduced in vacuo. Cooling the solution to 253 K resulted in the formation of orange crystals, which were characterized by SEM-XPS and IR spectroscopy (see supporting information). The crystalline product has been formulated as Ti(OC6F5)4THF2. It was somewhat disappointing that this reaction did not appear to produce a double alkoxide complex containing barium and titanium(IV) ions similar to the BaTi(OC6H5)6·2DMF compound (Day et al., 1995
), which was used to prepare barium titanate by way of the sol-gel process.
Liquid TiCl4 and solid TiCl4THF2 were purchased from Aldrich and used as received. All synthetic procedures were carried out using standard Schlenk techniques or in a purified nitrogen atmosphere using a Braun UNIlab glovebox. Solvents were purified by distillation from a sodium benzophenone ketal solution and stored in glass containers with solvent seal fittings. IR spectra were recorded as KBr pellets, by grinding small portions of the sample with dried potassium bromide using an agate mortar and pestle in the glovebox. Fourier transform IR (FT–IR) spectra (Fig. S1 in the supporting information) were recorded on a ThermoScientific Nicolet iS10 FT–IR spectrometer. Residual gaseous carbon dioxide asymmetric vibrations were sometimes observed in the 2400 cm−1 region, due to incomplete background subtraction, and calibration was checked regularly using a film of polystyrene. Scanning electron micrograph (SEM) images and (XPS) for compositional analysis (Fig. S2) were obtained by the Materials Characterization Lab of the Materials Research Institute at the PSU University Park campus.
5. Refinement
Crystal data collection and structure details are summarized in Table 1
. The positions of the H atoms were initially determined by geometry and were refined using a riding model. Non-H atoms were refined with anisotropic displacement parameters. H-atom displacement parameters were set at 1.2 times the isotropic equivalent displacement parameters of the bonded atoms.
|
Supporting information
CCDC reference: 2570948
contains datablock I. DOI: https://doi.org/10.1107/S2056989026007024/oi2040sup1.cif
Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989026007024/oi2040Isup2.hkl
Fig. S1: IR spectrum of compound 1. DOI: https://doi.org/10.1107/S2056989026007024/oi2040sup3.jpg
Fig. S2: An SEM image (top) and XPS (bottom) of a sample of compound 1. DOI: https://doi.org/10.1107/S2056989026007024/oi2040sup4.jpg
Supporting information file. DOI: https://doi.org/10.1107/S2056989026007024/oi2040Isup5.mol
| [Ti(C6F5O)4(C4H8O)2] | F(000) = 1832 |
| Mr = 924.35 | Dx = 1.788 Mg m−3 |
| Monoclinic, P21/n | Mo Kα radiation, λ = 0.71073 Å |
| a = 10.7678 (3) Å | Cell parameters from 8410 reflections |
| b = 18.6224 (5) Å | θ = 2.4–30.4° |
| c = 17.1245 (5) Å | µ = 0.40 mm−1 |
| β = 90.204 (2)° | T = 100 K |
| V = 3433.82 (17) Å3 | Block, orange |
| Z = 4 | 0.14 × 0.14 × 0.09 mm |
| Bruker APEX CCD diffractometer | 4550 reflections with I > 2σ(I) |
| φ and ω scans | Rint = 0.068 |
| Absorption correction: multi-scan (SADABS2016; Krause et al., 2015) | θmax = 25.0°, θmin = 2.2° |
| Tmin = 0.623, Tmax = 0.695 | h = −12→12 |
| 41654 measured reflections | k = −22→22 |
| 6043 independent reflections | l = −19→20 |
| Refinement on F2 | 0 restraints |
| Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
| R[F2 > 2σ(F2)] = 0.039 | H-atom parameters constrained |
| wR(F2) = 0.097 | w = 1/[σ2(Fo2) + (0.0415P)2 + 2.4623P] where P = (Fo2 + 2Fc2)/3 |
| S = 1.00 | (Δ/σ)max = 0.001 |
| 6043 reflections | Δρmax = 0.34 e Å−3 |
| 532 parameters | Δρmin = −0.46 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
| x | y | z | Uiso*/Ueq | ||
| Ti1 | 0.54379 (4) | 0.21700 (2) | 0.65158 (3) | 0.01836 (13) | |
| F2 | 0.48061 (15) | 0.07750 (8) | 0.46061 (9) | 0.0275 (4) | |
| F3 | 0.46785 (16) | 0.08295 (9) | 0.30352 (10) | 0.0361 (4) | |
| F4 | 0.52382 (17) | 0.20695 (10) | 0.22618 (9) | 0.0392 (4) | |
| F5 | 0.58924 (15) | 0.32564 (9) | 0.30822 (10) | 0.0330 (4) | |
| F6 | 0.60174 (15) | 0.32125 (8) | 0.46622 (9) | 0.0285 (4) | |
| F8 | 0.30266 (16) | 0.27450 (9) | 0.50221 (10) | 0.0389 (5) | |
| F9 | 0.27079 (18) | 0.39576 (11) | 0.41814 (11) | 0.0532 (6) | |
| F10 | 0.33334 (18) | 0.52580 (10) | 0.48005 (12) | 0.0534 (6) | |
| F11 | 0.42690 (17) | 0.53281 (9) | 0.62739 (12) | 0.0439 (5) | |
| F12 | 0.45684 (16) | 0.41232 (8) | 0.71255 (10) | 0.0311 (4) | |
| F14 | 0.82314 (16) | 0.23242 (8) | 0.53812 (11) | 0.0375 (4) | |
| F15 | 1.02058 (17) | 0.30959 (10) | 0.48959 (12) | 0.0504 (5) | |
| F16 | 1.06352 (16) | 0.44323 (9) | 0.54877 (11) | 0.0417 (5) | |
| F17 | 0.90700 (15) | 0.49807 (8) | 0.65763 (10) | 0.0350 (4) | |
| F18 | 0.71103 (16) | 0.42083 (8) | 0.70748 (10) | 0.0344 (4) | |
| F19 | 0.31651 (14) | 0.25946 (9) | 0.80634 (10) | 0.0299 (4) | |
| F20 | 0.29102 (14) | 0.36793 (8) | 0.91024 (9) | 0.0286 (4) | |
| F21 | 0.49437 (15) | 0.42573 (8) | 0.98074 (9) | 0.0289 (4) | |
| F22 | 0.72545 (14) | 0.37964 (8) | 0.93880 (9) | 0.0283 (4) | |
| F23 | 0.75251 (14) | 0.27640 (8) | 0.83031 (9) | 0.0265 (4) | |
| O1 | 0.54289 (18) | 0.19743 (9) | 0.54538 (11) | 0.0239 (4) | |
| O2 | 0.40712 (17) | 0.27960 (9) | 0.64940 (11) | 0.0240 (4) | |
| O3 | 0.66287 (17) | 0.28759 (9) | 0.64923 (11) | 0.0254 (4) | |
| O4 | 0.54803 (16) | 0.21227 (9) | 0.76279 (10) | 0.0210 (4) | |
| O5 | 0.67766 (17) | 0.13425 (9) | 0.66137 (10) | 0.0217 (4) | |
| O6 | 0.41500 (17) | 0.13131 (9) | 0.66251 (11) | 0.0232 (4) | |
| C1 | 0.5398 (2) | 0.19959 (13) | 0.46761 (15) | 0.0179 (6) | |
| C2 | 0.5075 (2) | 0.13973 (14) | 0.42396 (16) | 0.0209 (6) | |
| C3 | 0.5019 (2) | 0.14218 (15) | 0.34369 (17) | 0.0241 (6) | |
| C4 | 0.5293 (3) | 0.20430 (15) | 0.30475 (16) | 0.0244 (6) | |
| C5 | 0.5616 (2) | 0.26442 (14) | 0.34650 (16) | 0.0216 (6) | |
| C6 | 0.5680 (2) | 0.26185 (13) | 0.42646 (16) | 0.0202 (6) | |
| C7 | 0.3861 (2) | 0.33975 (14) | 0.60855 (16) | 0.0233 (6) | |
| C8 | 0.3355 (3) | 0.33817 (16) | 0.53372 (18) | 0.0293 (7) | |
| C9 | 0.3184 (3) | 0.39969 (18) | 0.49046 (18) | 0.0361 (8) | |
| C10 | 0.3496 (3) | 0.46504 (17) | 0.52192 (19) | 0.0359 (8) | |
| C11 | 0.3969 (3) | 0.46866 (15) | 0.59653 (19) | 0.0315 (7) | |
| C12 | 0.4132 (3) | 0.40705 (15) | 0.63897 (17) | 0.0256 (6) | |
| C13 | 0.7608 (2) | 0.32487 (13) | 0.62373 (15) | 0.0203 (6) | |
| C14 | 0.8424 (3) | 0.29829 (14) | 0.56797 (17) | 0.0257 (6) | |
| C15 | 0.9432 (3) | 0.33737 (16) | 0.54330 (17) | 0.0299 (7) | |
| C16 | 0.9649 (3) | 0.40483 (15) | 0.57279 (17) | 0.0270 (7) | |
| C17 | 0.8863 (3) | 0.43218 (14) | 0.62814 (17) | 0.0243 (6) | |
| C18 | 0.7862 (2) | 0.39280 (14) | 0.65310 (16) | 0.0218 (6) | |
| C19 | 0.5350 (2) | 0.26492 (13) | 0.81489 (15) | 0.0174 (6) | |
| C20 | 0.6369 (2) | 0.29737 (13) | 0.85021 (16) | 0.0193 (6) | |
| C21 | 0.6242 (2) | 0.35047 (13) | 0.90531 (16) | 0.0205 (6) | |
| C22 | 0.5080 (3) | 0.37395 (13) | 0.92656 (15) | 0.0207 (6) | |
| C23 | 0.4055 (2) | 0.34380 (14) | 0.89140 (16) | 0.0204 (6) | |
| C24 | 0.4187 (2) | 0.28991 (14) | 0.83767 (15) | 0.0195 (6) | |
| C25 | 0.7764 (3) | 0.13369 (16) | 0.72070 (17) | 0.0303 (7) | |
| H25A | 0.746264 | 0.112362 | 0.770084 | 0.036* | |
| H25B | 0.806424 | 0.182994 | 0.731279 | 0.036* | |
| C26 | 0.8780 (3) | 0.08829 (16) | 0.68563 (19) | 0.0332 (7) | |
| H26A | 0.927828 | 0.064229 | 0.726705 | 0.040* | |
| H26B | 0.933751 | 0.117468 | 0.652470 | 0.040* | |
| C27 | 0.8055 (3) | 0.03401 (14) | 0.63716 (17) | 0.0293 (7) | |
| H27A | 0.858044 | 0.012813 | 0.595813 | 0.035* | |
| H27B | 0.772060 | −0.004972 | 0.670294 | 0.035* | |
| C28 | 0.7021 (3) | 0.07884 (14) | 0.60249 (16) | 0.0247 (6) | |
| H28A | 0.728349 | 0.100807 | 0.552551 | 0.030* | |
| H28B | 0.627176 | 0.049252 | 0.593037 | 0.030* | |
| C29 | 0.4092 (3) | 0.07952 (15) | 0.72628 (18) | 0.0347 (8) | |
| H29A | 0.406771 | 0.104471 | 0.777298 | 0.042* | |
| H29B | 0.482501 | 0.047409 | 0.725375 | 0.042* | |
| C30 | 0.2905 (3) | 0.03692 (16) | 0.7130 (2) | 0.0380 (8) | |
| H30A | 0.304888 | −0.015034 | 0.721297 | 0.046* | |
| H30B | 0.223958 | 0.053268 | 0.748501 | 0.046* | |
| C31 | 0.2572 (3) | 0.05210 (18) | 0.6292 (2) | 0.0456 (9) | |
| H31A | 0.301009 | 0.018998 | 0.593386 | 0.055* | |
| H31B | 0.166589 | 0.047790 | 0.620419 | 0.055* | |
| C32 | 0.3000 (3) | 0.12791 (16) | 0.61809 (19) | 0.0322 (7) | |
| H32A | 0.314747 | 0.138376 | 0.562205 | 0.039* | |
| H32B | 0.238228 | 0.162378 | 0.638617 | 0.039* |
| U11 | U22 | U33 | U12 | U13 | U23 | |
| Ti1 | 0.0195 (3) | 0.0161 (2) | 0.0194 (3) | −0.00047 (19) | 0.0011 (2) | −0.0020 (2) |
| F2 | 0.0306 (9) | 0.0192 (8) | 0.0327 (10) | −0.0024 (7) | −0.0023 (7) | 0.0027 (7) |
| F3 | 0.0415 (11) | 0.0354 (9) | 0.0313 (10) | −0.0037 (8) | −0.0082 (8) | −0.0142 (8) |
| F4 | 0.0424 (11) | 0.0569 (12) | 0.0184 (10) | −0.0050 (9) | −0.0027 (8) | 0.0001 (8) |
| F5 | 0.0330 (10) | 0.0343 (9) | 0.0316 (10) | −0.0014 (8) | 0.0022 (8) | 0.0128 (8) |
| F6 | 0.0367 (10) | 0.0187 (8) | 0.0303 (10) | −0.0020 (7) | 0.0008 (7) | −0.0030 (7) |
| F8 | 0.0360 (10) | 0.0458 (11) | 0.0348 (11) | 0.0117 (8) | −0.0100 (8) | −0.0138 (9) |
| F9 | 0.0499 (13) | 0.0814 (15) | 0.0280 (11) | 0.0230 (11) | −0.0068 (9) | 0.0092 (10) |
| F10 | 0.0467 (12) | 0.0537 (12) | 0.0598 (14) | 0.0116 (10) | 0.0023 (10) | 0.0352 (10) |
| F11 | 0.0465 (12) | 0.0229 (9) | 0.0623 (13) | 0.0021 (8) | 0.0018 (10) | 0.0067 (8) |
| F12 | 0.0384 (10) | 0.0241 (8) | 0.0307 (10) | 0.0034 (7) | −0.0037 (8) | −0.0005 (7) |
| F14 | 0.0363 (10) | 0.0299 (9) | 0.0465 (12) | −0.0084 (8) | 0.0153 (8) | −0.0211 (8) |
| F15 | 0.0387 (11) | 0.0573 (12) | 0.0554 (13) | −0.0122 (9) | 0.0263 (10) | −0.0242 (10) |
| F16 | 0.0271 (10) | 0.0412 (10) | 0.0568 (13) | −0.0143 (8) | 0.0083 (9) | 0.0010 (9) |
| F17 | 0.0348 (10) | 0.0201 (8) | 0.0502 (12) | −0.0078 (7) | −0.0045 (8) | −0.0067 (8) |
| F18 | 0.0341 (10) | 0.0291 (9) | 0.0399 (11) | −0.0026 (7) | 0.0113 (8) | −0.0162 (8) |
| F19 | 0.0159 (8) | 0.0402 (9) | 0.0338 (10) | −0.0069 (7) | 0.0026 (7) | −0.0108 (8) |
| F20 | 0.0178 (8) | 0.0334 (9) | 0.0348 (10) | 0.0041 (7) | 0.0089 (7) | −0.0058 (7) |
| F21 | 0.0349 (10) | 0.0222 (8) | 0.0296 (10) | −0.0008 (7) | 0.0060 (7) | −0.0105 (7) |
| F22 | 0.0232 (9) | 0.0294 (8) | 0.0322 (10) | −0.0030 (7) | −0.0082 (7) | −0.0069 (7) |
| F23 | 0.0149 (8) | 0.0322 (8) | 0.0322 (10) | 0.0025 (7) | −0.0008 (7) | −0.0070 (7) |
| O1 | 0.0301 (11) | 0.0221 (9) | 0.0194 (11) | 0.0002 (8) | 0.0005 (8) | −0.0005 (8) |
| O2 | 0.0245 (11) | 0.0215 (9) | 0.0260 (11) | 0.0037 (8) | 0.0010 (8) | 0.0003 (8) |
| O3 | 0.0251 (11) | 0.0225 (10) | 0.0287 (12) | −0.0041 (8) | 0.0059 (9) | −0.0035 (8) |
| O4 | 0.0208 (10) | 0.0203 (9) | 0.0219 (11) | 0.0003 (8) | 0.0022 (8) | −0.0045 (8) |
| O5 | 0.0220 (10) | 0.0222 (9) | 0.0210 (11) | 0.0030 (8) | −0.0011 (8) | −0.0050 (8) |
| O6 | 0.0241 (10) | 0.0219 (9) | 0.0236 (11) | −0.0040 (8) | −0.0036 (8) | 0.0027 (8) |
| C1 | 0.0176 (14) | 0.0216 (13) | 0.0145 (14) | 0.0029 (11) | −0.0013 (11) | −0.0001 (11) |
| C2 | 0.0179 (14) | 0.0209 (13) | 0.0240 (16) | −0.0005 (11) | −0.0008 (11) | −0.0010 (12) |
| C3 | 0.0162 (14) | 0.0291 (15) | 0.0271 (17) | 0.0000 (12) | −0.0039 (12) | −0.0091 (13) |
| C4 | 0.0176 (14) | 0.0400 (17) | 0.0157 (15) | 0.0009 (12) | −0.0016 (11) | −0.0015 (13) |
| C5 | 0.0157 (14) | 0.0265 (14) | 0.0225 (16) | −0.0015 (11) | 0.0013 (11) | 0.0067 (12) |
| C6 | 0.0162 (14) | 0.0207 (13) | 0.0235 (16) | 0.0024 (11) | −0.0013 (11) | −0.0050 (11) |
| C7 | 0.0193 (14) | 0.0252 (14) | 0.0253 (16) | 0.0067 (12) | 0.0022 (12) | 0.0021 (12) |
| C8 | 0.0220 (15) | 0.0346 (16) | 0.0314 (18) | 0.0092 (13) | 0.0027 (13) | −0.0060 (14) |
| C9 | 0.0294 (17) | 0.054 (2) | 0.0251 (18) | 0.0159 (15) | −0.0012 (14) | 0.0071 (15) |
| C10 | 0.0275 (17) | 0.0403 (18) | 0.040 (2) | 0.0107 (14) | 0.0079 (15) | 0.0216 (16) |
| C11 | 0.0272 (17) | 0.0250 (15) | 0.042 (2) | 0.0025 (13) | 0.0059 (14) | 0.0064 (14) |
| C12 | 0.0218 (15) | 0.0297 (15) | 0.0253 (16) | 0.0031 (12) | 0.0023 (12) | 0.0030 (13) |
| C13 | 0.0205 (14) | 0.0216 (13) | 0.0187 (15) | −0.0029 (11) | 0.0007 (11) | −0.0008 (11) |
| C14 | 0.0284 (16) | 0.0200 (14) | 0.0287 (17) | −0.0033 (12) | −0.0006 (13) | −0.0064 (12) |
| C15 | 0.0260 (16) | 0.0349 (16) | 0.0288 (18) | −0.0008 (13) | 0.0075 (13) | −0.0072 (13) |
| C16 | 0.0194 (15) | 0.0304 (15) | 0.0313 (18) | −0.0059 (12) | 0.0016 (13) | 0.0017 (13) |
| C17 | 0.0269 (16) | 0.0168 (13) | 0.0293 (17) | −0.0014 (12) | −0.0086 (13) | −0.0009 (12) |
| C18 | 0.0202 (14) | 0.0221 (14) | 0.0232 (16) | 0.0029 (11) | 0.0013 (12) | −0.0047 (12) |
| C19 | 0.0200 (14) | 0.0166 (12) | 0.0156 (14) | −0.0003 (11) | 0.0019 (11) | 0.0009 (11) |
| C20 | 0.0128 (13) | 0.0220 (13) | 0.0231 (15) | 0.0032 (11) | 0.0039 (11) | 0.0018 (11) |
| C21 | 0.0181 (14) | 0.0208 (13) | 0.0226 (15) | −0.0049 (11) | −0.0040 (11) | 0.0003 (11) |
| C22 | 0.0250 (15) | 0.0178 (13) | 0.0192 (15) | 0.0005 (11) | 0.0039 (12) | −0.0012 (11) |
| C23 | 0.0151 (14) | 0.0241 (14) | 0.0219 (15) | 0.0024 (11) | 0.0068 (11) | 0.0031 (11) |
| C24 | 0.0174 (14) | 0.0243 (13) | 0.0170 (14) | −0.0045 (11) | 0.0008 (11) | 0.0016 (11) |
| C25 | 0.0263 (16) | 0.0374 (16) | 0.0273 (17) | 0.0060 (13) | −0.0067 (13) | −0.0071 (13) |
| C26 | 0.0270 (17) | 0.0330 (16) | 0.0396 (19) | 0.0090 (13) | −0.0019 (14) | −0.0047 (14) |
| C27 | 0.0400 (18) | 0.0218 (14) | 0.0261 (17) | 0.0073 (13) | 0.0064 (14) | 0.0023 (12) |
| C28 | 0.0321 (17) | 0.0191 (13) | 0.0227 (16) | 0.0017 (12) | 0.0054 (12) | −0.0063 (12) |
| C29 | 0.046 (2) | 0.0271 (15) | 0.0309 (18) | −0.0110 (14) | −0.0019 (15) | 0.0081 (13) |
| C30 | 0.0323 (18) | 0.0322 (16) | 0.049 (2) | −0.0087 (14) | 0.0087 (16) | 0.0071 (15) |
| C31 | 0.037 (2) | 0.0425 (19) | 0.058 (2) | −0.0156 (16) | −0.0047 (17) | −0.0011 (17) |
| C32 | 0.0236 (16) | 0.0362 (17) | 0.0369 (19) | −0.0074 (13) | −0.0096 (14) | 0.0041 (14) |
| Ti1—O1 | 1.8548 (19) | C7—C8 | 1.391 (4) |
| Ti1—O2 | 1.8777 (18) | C7—C12 | 1.388 (4) |
| Ti1—O3 | 1.8370 (18) | C8—C9 | 1.376 (4) |
| Ti1—O4 | 1.9068 (19) | C9—C10 | 1.372 (5) |
| Ti1—O5 | 2.1163 (18) | C10—C11 | 1.375 (4) |
| Ti1—O6 | 2.1227 (18) | C11—C12 | 1.369 (4) |
| F2—C2 | 1.350 (3) | C13—C14 | 1.391 (4) |
| F3—C3 | 1.350 (3) | C13—C18 | 1.388 (4) |
| F4—C4 | 1.347 (3) | C14—C15 | 1.375 (4) |
| F5—C5 | 1.349 (3) | C15—C16 | 1.374 (4) |
| F6—C6 | 1.348 (3) | C16—C17 | 1.371 (4) |
| F8—C8 | 1.349 (3) | C17—C18 | 1.374 (4) |
| F9—C9 | 1.341 (3) | C19—C20 | 1.390 (4) |
| F10—C10 | 1.351 (3) | C19—C24 | 1.392 (4) |
| F11—C11 | 1.345 (3) | C20—C21 | 1.374 (4) |
| F12—C12 | 1.347 (3) | C21—C22 | 1.376 (4) |
| F14—C14 | 1.345 (3) | C22—C23 | 1.375 (4) |
| F15—C15 | 1.347 (3) | C23—C24 | 1.369 (4) |
| F16—C16 | 1.346 (3) | C25—H25A | 0.9900 |
| F17—C17 | 1.345 (3) | C25—H25B | 0.9900 |
| F18—C18 | 1.341 (3) | C25—C26 | 1.509 (4) |
| F19—C24 | 1.348 (3) | C26—H26A | 0.9900 |
| F20—C23 | 1.352 (3) | C26—H26B | 0.9900 |
| F21—C22 | 1.347 (3) | C26—C27 | 1.522 (4) |
| F22—C21 | 1.344 (3) | C27—H27A | 0.9900 |
| F23—C20 | 1.350 (3) | C27—H27B | 0.9900 |
| O1—C1 | 1.333 (3) | C27—C28 | 1.511 (4) |
| O2—C7 | 1.340 (3) | C28—H28A | 0.9900 |
| O3—C13 | 1.337 (3) | C28—H28B | 0.9900 |
| O4—C19 | 1.333 (3) | C29—H29A | 0.9900 |
| O5—C25 | 1.468 (3) | C29—H29B | 0.9900 |
| O5—C28 | 1.467 (3) | C29—C30 | 1.521 (4) |
| O6—C29 | 1.458 (3) | C30—H30A | 0.9900 |
| O6—C32 | 1.452 (3) | C30—H30B | 0.9900 |
| C1—C2 | 1.386 (4) | C30—C31 | 1.505 (5) |
| C1—C6 | 1.391 (4) | C31—H31A | 0.9900 |
| C2—C3 | 1.376 (4) | C31—H31B | 0.9900 |
| C3—C4 | 1.368 (4) | C31—C32 | 1.497 (4) |
| C4—C5 | 1.373 (4) | C32—H32A | 0.9900 |
| C5—C6 | 1.371 (4) | C32—H32B | 0.9900 |
| O1—Ti1—O2 | 95.80 (8) | F17—C17—C16 | 119.8 (2) |
| O1—Ti1—O4 | 165.98 (8) | F17—C17—C18 | 119.9 (3) |
| O1—Ti1—O5 | 86.32 (8) | C18—C17—C16 | 120.3 (2) |
| O1—Ti1—O6 | 86.42 (8) | F18—C18—C13 | 119.2 (2) |
| O2—Ti1—O4 | 93.70 (8) | F18—C18—C17 | 119.0 (2) |
| O2—Ti1—O5 | 170.82 (8) | C17—C18—C13 | 121.8 (2) |
| O2—Ti1—O6 | 87.49 (8) | O4—C19—C20 | 121.7 (2) |
| O3—Ti1—O1 | 96.91 (8) | O4—C19—C24 | 122.0 (2) |
| O3—Ti1—O2 | 95.87 (8) | C20—C19—C24 | 116.2 (2) |
| O3—Ti1—O4 | 92.33 (8) | F23—C20—C19 | 119.5 (2) |
| O3—Ti1—O5 | 92.73 (8) | F23—C20—C21 | 118.4 (2) |
| O3—Ti1—O6 | 174.99 (8) | C21—C20—C19 | 122.1 (2) |
| O4—Ti1—O5 | 82.73 (7) | F22—C21—C20 | 120.1 (2) |
| O4—Ti1—O6 | 83.72 (7) | F22—C21—C22 | 119.7 (2) |
| O5—Ti1—O6 | 83.72 (7) | C20—C21—C22 | 120.2 (2) |
| C1—O1—Ti1 | 166.88 (17) | F21—C22—C21 | 120.7 (2) |
| C7—O2—Ti1 | 131.35 (17) | F21—C22—C23 | 120.3 (2) |
| C13—O3—Ti1 | 158.45 (17) | C23—C22—C21 | 118.9 (2) |
| C19—O4—Ti1 | 129.21 (16) | F20—C23—C22 | 119.4 (2) |
| C25—O5—Ti1 | 123.46 (15) | F20—C23—C24 | 120.1 (2) |
| C25—O5—C28 | 109.84 (19) | C24—C23—C22 | 120.5 (2) |
| C28—O5—Ti1 | 125.56 (15) | F19—C24—C19 | 118.8 (2) |
| C29—O6—Ti1 | 126.34 (16) | F19—C24—C23 | 119.3 (2) |
| C32—O6—Ti1 | 122.87 (15) | C23—C24—C19 | 122.0 (2) |
| C32—O6—C29 | 109.0 (2) | O5—C25—H25A | 110.8 |
| O1—C1—C2 | 121.3 (2) | O5—C25—H25B | 110.8 |
| O1—C1—C6 | 121.8 (2) | O5—C25—C26 | 104.7 (2) |
| C2—C1—C6 | 116.9 (2) | H25A—C25—H25B | 108.9 |
| F2—C2—C1 | 119.6 (2) | C26—C25—H25A | 110.8 |
| F2—C2—C3 | 119.0 (2) | C26—C25—H25B | 110.8 |
| C3—C2—C1 | 121.5 (2) | C25—C26—H26A | 111.3 |
| F3—C3—C2 | 119.5 (2) | C25—C26—H26B | 111.3 |
| F3—C3—C4 | 120.1 (3) | C25—C26—C27 | 102.6 (2) |
| C4—C3—C2 | 120.4 (2) | H26A—C26—H26B | 109.2 |
| F4—C4—C3 | 120.6 (2) | C27—C26—H26A | 111.3 |
| F4—C4—C5 | 120.0 (2) | C27—C26—H26B | 111.3 |
| C3—C4—C5 | 119.4 (3) | C26—C27—H27A | 111.2 |
| F5—C5—C4 | 119.5 (2) | C26—C27—H27B | 111.2 |
| F5—C5—C6 | 120.3 (2) | H27A—C27—H27B | 109.1 |
| C4—C5—C6 | 120.2 (2) | C28—C27—C26 | 102.9 (2) |
| F6—C6—C1 | 119.1 (2) | C28—C27—H27A | 111.2 |
| F6—C6—C5 | 119.2 (2) | C28—C27—H27B | 111.2 |
| C5—C6—C1 | 121.6 (2) | O5—C28—C27 | 104.6 (2) |
| O2—C7—C8 | 121.9 (2) | O5—C28—H28A | 110.8 |
| O2—C7—C12 | 121.6 (3) | O5—C28—H28B | 110.8 |
| C12—C7—C8 | 116.5 (3) | C27—C28—H28A | 110.8 |
| F8—C8—C7 | 119.2 (3) | C27—C28—H28B | 110.8 |
| F8—C8—C9 | 118.8 (3) | H28A—C28—H28B | 108.9 |
| C9—C8—C7 | 122.0 (3) | O6—C29—H29A | 110.6 |
| F9—C9—C8 | 120.1 (3) | O6—C29—H29B | 110.6 |
| F9—C9—C10 | 120.2 (3) | O6—C29—C30 | 105.7 (2) |
| C10—C9—C8 | 119.6 (3) | H29A—C29—H29B | 108.7 |
| F10—C10—C9 | 120.2 (3) | C30—C29—H29A | 110.6 |
| F10—C10—C11 | 119.9 (3) | C30—C29—H29B | 110.6 |
| C9—C10—C11 | 119.8 (3) | C29—C30—H30A | 111.0 |
| F11—C11—C10 | 119.7 (3) | C29—C30—H30B | 111.0 |
| F11—C11—C12 | 120.4 (3) | H30A—C30—H30B | 109.0 |
| C12—C11—C10 | 119.9 (3) | C31—C30—C29 | 104.0 (2) |
| F12—C12—C7 | 119.3 (2) | C31—C30—H30A | 111.0 |
| F12—C12—C11 | 118.6 (3) | C31—C30—H30B | 111.0 |
| C11—C12—C7 | 122.1 (3) | C30—C31—H31A | 111.2 |
| O3—C13—C14 | 122.7 (2) | C30—C31—H31B | 111.2 |
| O3—C13—C18 | 120.6 (2) | H31A—C31—H31B | 109.1 |
| C14—C13—C18 | 116.7 (2) | C32—C31—C30 | 103.0 (3) |
| F14—C14—C13 | 119.3 (2) | C32—C31—H31A | 111.2 |
| F14—C14—C15 | 119.1 (3) | C32—C31—H31B | 111.2 |
| C15—C14—C13 | 121.6 (2) | O6—C32—C31 | 103.7 (2) |
| F15—C15—C14 | 119.8 (3) | O6—C32—H32A | 111.0 |
| F15—C15—C16 | 119.8 (3) | O6—C32—H32B | 111.0 |
| C14—C15—C16 | 120.3 (3) | C31—C32—H32A | 111.0 |
| F16—C16—C15 | 120.5 (3) | C31—C32—H32B | 111.0 |
| F16—C16—C17 | 120.2 (3) | H32A—C32—H32B | 109.0 |
| C17—C16—C15 | 119.3 (3) | ||
| Ti1—O1—C1—C2 | −159.0 (7) | O4—C19—C20—C21 | −178.4 (2) |
| Ti1—O1—C1—C6 | 20.6 (9) | O4—C19—C24—F19 | 0.5 (4) |
| Ti1—O2—C7—C8 | 86.4 (3) | O4—C19—C24—C23 | 179.7 (2) |
| Ti1—O2—C7—C12 | −93.8 (3) | O5—Ti1—O1—C1 | −141.9 (8) |
| Ti1—O3—C13—C14 | −14.4 (7) | O5—Ti1—O3—C13 | 61.0 (5) |
| Ti1—O3—C13—C18 | 166.3 (4) | O5—C25—C26—C27 | −32.4 (3) |
| Ti1—O4—C19—C20 | −98.6 (3) | O6—Ti1—O1—C1 | 134.1 (8) |
| Ti1—O4—C19—C24 | 82.2 (3) | O6—Ti1—O2—C7 | −142.4 (2) |
| Ti1—O5—C25—C26 | −155.01 (18) | O6—C29—C30—C31 | 17.0 (3) |
| Ti1—O5—C28—C27 | 179.54 (16) | C1—C2—C3—F3 | −178.8 (2) |
| Ti1—O6—C29—C30 | 171.78 (18) | C1—C2—C3—C4 | 0.4 (4) |
| Ti1—O6—C32—C31 | 166.3 (2) | C2—C1—C6—F6 | −179.0 (2) |
| F2—C2—C3—F3 | 1.1 (4) | C2—C1—C6—C5 | 1.3 (4) |
| F2—C2—C3—C4 | −179.6 (2) | C2—C3—C4—F4 | −179.9 (2) |
| F3—C3—C4—F4 | −0.7 (4) | C2—C3—C4—C5 | −0.4 (4) |
| F3—C3—C4—C5 | 178.9 (2) | C3—C4—C5—F5 | 179.7 (2) |
| F4—C4—C5—F5 | −0.8 (4) | C3—C4—C5—C6 | 0.9 (4) |
| F4—C4—C5—C6 | −179.6 (2) | C4—C5—C6—F6 | 179.0 (2) |
| F5—C5—C6—F6 | 0.2 (4) | C4—C5—C6—C1 | −1.3 (4) |
| F5—C5—C6—C1 | 179.9 (2) | C6—C1—C2—F2 | 179.2 (2) |
| F8—C8—C9—F9 | −0.6 (4) | C6—C1—C2—C3 | −0.9 (4) |
| F8—C8—C9—C10 | 179.1 (3) | C7—C8—C9—F9 | 179.2 (3) |
| F9—C9—C10—F10 | −0.4 (5) | C7—C8—C9—C10 | −1.2 (5) |
| F9—C9—C10—C11 | 179.2 (3) | C8—C7—C12—F12 | 176.9 (2) |
| F10—C10—C11—F11 | −0.1 (4) | C8—C7—C12—C11 | −3.0 (4) |
| F10—C10—C11—C12 | 179.9 (3) | C8—C9—C10—F10 | 180.0 (3) |
| F11—C11—C12—F12 | 1.6 (4) | C8—C9—C10—C11 | −0.5 (5) |
| F11—C11—C12—C7 | −178.5 (3) | C9—C10—C11—F11 | −179.7 (3) |
| F14—C14—C15—F15 | 0.4 (4) | C9—C10—C11—C12 | 0.4 (5) |
| F14—C14—C15—C16 | 179.9 (3) | C10—C11—C12—F12 | −178.4 (3) |
| F15—C15—C16—F16 | −0.4 (4) | C10—C11—C12—C7 | 1.5 (4) |
| F15—C15—C16—C17 | −179.2 (3) | C12—C7—C8—F8 | −177.4 (2) |
| F16—C16—C17—F17 | 1.0 (4) | C12—C7—C8—C9 | 2.8 (4) |
| F16—C16—C17—C18 | −179.5 (3) | C13—C14—C15—F15 | 179.5 (3) |
| F17—C17—C18—F18 | −0.7 (4) | C13—C14—C15—C16 | −0.9 (5) |
| F17—C17—C18—C13 | 179.4 (2) | C14—C13—C18—F18 | −179.5 (2) |
| F20—C23—C24—F19 | −2.6 (4) | C14—C13—C18—C17 | 0.4 (4) |
| F20—C23—C24—C19 | 178.1 (2) | C14—C15—C16—F16 | 180.0 (3) |
| F21—C22—C23—F20 | 1.7 (4) | C14—C15—C16—C17 | 1.2 (5) |
| F21—C22—C23—C24 | −178.4 (2) | C15—C16—C17—F17 | 179.8 (3) |
| F22—C21—C22—F21 | −0.2 (4) | C15—C16—C17—C18 | −0.7 (4) |
| F22—C21—C22—C23 | 179.6 (2) | C16—C17—C18—F18 | 179.8 (2) |
| F23—C20—C21—F22 | −0.9 (4) | C16—C17—C18—C13 | −0.1 (4) |
| F23—C20—C21—C22 | 179.2 (2) | C18—C13—C14—F14 | 179.3 (2) |
| O1—Ti1—O2—C7 | −56.3 (2) | C18—C13—C14—C15 | 0.1 (4) |
| O1—Ti1—O3—C13 | −25.6 (5) | C19—C20—C21—F22 | 179.0 (2) |
| O1—C1—C2—F2 | −1.2 (4) | C19—C20—C21—C22 | −0.9 (4) |
| O1—C1—C2—C3 | 178.7 (2) | C20—C19—C24—F19 | −178.8 (2) |
| O1—C1—C6—F6 | 1.3 (4) | C20—C19—C24—C23 | 0.5 (4) |
| O1—C1—C6—C5 | −178.3 (2) | C20—C21—C22—F21 | 179.7 (2) |
| O2—Ti1—O1—C1 | 47.0 (8) | C20—C21—C22—C23 | −0.5 (4) |
| O2—Ti1—O3—C13 | −122.2 (5) | C21—C22—C23—F20 | −178.1 (2) |
| O2—C7—C8—F8 | 2.3 (4) | C21—C22—C23—C24 | 1.8 (4) |
| O2—C7—C8—C9 | −177.4 (3) | C22—C23—C24—F19 | 177.5 (2) |
| O2—C7—C12—F12 | −2.9 (4) | C22—C23—C24—C19 | −1.8 (4) |
| O2—C7—C12—C11 | 177.2 (3) | C24—C19—C20—F23 | −179.3 (2) |
| O3—Ti1—O1—C1 | −49.6 (8) | C24—C19—C20—C21 | 0.8 (4) |
| O3—Ti1—O2—C7 | 41.3 (2) | C25—O5—C28—C27 | 11.5 (3) |
| O3—C13—C14—F14 | −0.1 (4) | C25—C26—C27—C28 | 39.3 (3) |
| O3—C13—C14—C15 | −179.3 (3) | C26—C27—C28—O5 | −31.4 (3) |
| O3—C13—C18—F18 | −0.1 (4) | C28—O5—C25—C26 | 13.4 (3) |
| O3—C13—C18—C17 | 179.8 (3) | C29—O6—C32—C31 | −28.2 (3) |
| O4—Ti1—O1—C1 | 179.5 (7) | C29—C30—C31—C32 | −33.7 (3) |
| O4—Ti1—O2—C7 | 134.1 (2) | C30—C31—C32—O6 | 38.1 (3) |
| O4—Ti1—O3—C13 | 143.8 (5) | C32—O6—C29—C30 | 7.0 (3) |
| O4—C19—C20—F23 | 1.5 (4) |
| D—H···A | D—H | H···A | D···A | D—H···A |
| C25—H25A···F9i | 0.99 | 2.55 | 3.426 (4) | 147 |
| C25—H25B···F23 | 0.99 | 2.50 | 3.264 (3) | 134 |
| C27—H27A···F21ii | 0.99 | 2.62 | 3.580 (3) | 162 |
| C27—H27B···F18ii | 0.99 | 2.51 | 3.399 (3) | 149 |
| C28—H28A···F20iii | 0.99 | 2.60 | 3.572 (3) | 168 |
| C29—H29B···F3iv | 0.99 | 2.53 | 3.342 (4) | 139 |
| C29—H29B···F17ii | 0.99 | 2.50 | 3.184 (4) | 126 |
| C32—H32A···F22v | 0.99 | 2.34 | 3.174 (3) | 141 |
| Symmetry codes: (i) x+1/2, −y+1/2, z+1/2; (ii) −x+3/2, y−1/2, −z+3/2; (iii) x+1/2, −y+1/2, z−1/2; (iv) −x+1, −y, −z+1; (v) x−1/2, −y+1/2, z−1/2. |
Acknowledgements
The author would like to thank the Pennsylvania State University, Altoona, Office of Research and Sponsored Programs, for their support through a Research and Development (RDG) grant. The author thanks Doug Powell, Department of Chemistry and Biochemistry, The University of Oklahoma, Norman, Oklahoma, USA (https://orcid.org/0000-0001-7133-468X), for his assistance in collecting the X-ray data. The author also thanks Professor Nan Xu (PSU, Altoona) for allowing the use of his inert atmosphere glovebox and Dr Hemant Yennawar (PSU, University Park) for helpful discussions and analysis of the crystallographic data based on reviewers comments.
Conflict of interest
The author declares no competing financial interest.
Funding information
Funding for this research was provided by: National Science Foundation, Directorate for Mathematical and Physical Sciences (grant No. CHE-0130835); Pennsylvania State University, Commonwealth Campus at Altoona.
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