Microwave spectroscopy and characterization of the helical conformer of perfluorohexane

The lowest energy conformer of perfluorohexane (C 6 F 14 ) is helical and its microwave rotational spectrum has been observed and assigned. The helicity along the carbon chain results in overall C 2 symmetry with the C 2 axis corresponding to the c-principal axis. The assignment of a c-type spectrum confirms the structure of C 6 F 14 to be helical. The rotational constants are A 824.9001(9) MHz, B 202.2195(8) MHz, and C 198.3355(10) MHz. The molecular parameters were characterized by scaling computed models by the square root of the ratio of the observed second moments to those computed. The scaled structures exactly reproduce the observed second moments. From this scaling approach, the exterior C 1 C 2 C 3 C 4 dihedral angle is 16.7 o and the interior C 2 C 3 C 4 C 5 dihedral angle is 18.0 o away from trans. Computed models at the PBE0/VTZ level of theory are in excellent agreement with the experimental results.


Introduction
The polymer polytetrafluoroethylene (PTFE) is well characterized and known to have a helical structure by X-ray diffraction studies on single fibers. 1 A helix can be described by either a helical perspective or a molecular perspective.In the helical perspective, the helix is defined by the following three parameters: the distance from each atom to the helical axis (the helical radius), ρ; the helical angle about the helical axis, θ; and the translation from one atom to the next (pitch) along the helical axis, d.In the molecular perspective, the helix is defined as follows: the C-C bond length, r; the CCC bond angle, φ; and the CCCC dihedral angle, τ.A visual representation of the two perspectives is displayed in Figure 1.The mathematical relationships for converting between the two perspectives are given in Equations 1 and 2. 2,3 For the low temperature (<19 o C) phase II form of PTFE, the helical angle is periodic and equal to 13.8 o . 4his corresponds to a CCCC dihedral angle of about 17 o away from trans.The helicity of PTFE is attributed to steric and dipole repulsions of F atoms on alternate carbons.A small helical twist along the carbon chain helps alleviate these repulsions (Figure 2).][7][8][9][10][11][12][13][14][15] The helical (trans), gauche, and ortho (τ ~ 90 o ) conformers of C4F10 were observed by nitrogen matrixisolated IR spectroscopy. 8Only the gauche form was observed in a microwave study, 16 with the }d ρ θ τ2345 φ r helical form apparently having too small a dipole moment to be observable and the ortho form relaxing to the lower energy gauche form. 178][9][10][11][12][13] cosθ = ½(-cosφ + cosτ -cosφ cosτ -1) (1) The microwave spectra of perfluoropentane (C5F12) and its three 13 C isotopomers have recently been assigned. 15The value of the dihedral angle was determined by scaling computed models to exactly reproduce the observed second moments.0][11][12][13][14] In the same study, the structure of perfluoropropane (C3F8) was found to be non-helical (C2v).Apparently, the steric and dipole interactions in the three carbon chain are not sufficient to cause a twist in the structure.
To continue characterization of short perfluoroalkanes, a microwave spectroscopic study on perfluorohexane (C6F14) was performed.The two CCCC dihedral angles in C6F14 are predicted to be about 16 o -18 o away from trans by various computational methods. 7,11,12,14C6F14, if helical, would have a dipole moment and, therefore, be observable by microwave spectroscopy.The microwave spectrum of the lowest energy helical conformer of C6F14 (Figures 2 and 3) has been observed and assigned and the molecular geometry analyzed.The lowest energy all trans conformer of n-hexane (C2h) lacks a dipole moment and is therefore spectroscopically unobservable.The lowest energy all trans structure of perfluoroalkanes, beginning with C4F10, is helical.A figure of the helical structure of C6F14, similar to Figure 3, given in reference 14 sparked our interest as this structure clearly has a dipole moment.The helicity of perfluoroalkanes results in structures with overall C2 symmetry.For an odd numbered chain, like C5F12, 15 the C2 axis corresponds to the b-axis and b-type transitions are observed.For an even numbered chain the C2 axis becomes the c-axis and, thus, c-type transitions are expected for C6F14.The observation and assignment of the microwave spectrum of C6F14 to c-type transitions (see Table 1 and Supplementary Table 1) unambiguously shows that the lowest energy structure of C6F14 is helical.The observation of c-type transitions requires that the molecule have a non-zero dipole moment along the c axis.If the molecule were non-helical, the structure would have C2h symmetry and no dipole moment along any principal axis.The structure of C3F8 was recently determined to be non-helical (C2v). 15The Pcc second moment is 134.338u Å 2 , or 44.78 u Å 2 per CF2/CF3 group.Assuming transferability, C6F14 would have a Pcc of 6 x 44.78 or 268.68 u Å 2 if it exhibited C2h symmetry.The observed Pcc is 281.857u Å 2 , or 46.98 u Å 2 per CF2/CF3 group.This increase in Pcc also confirms the helical structure of C6F14 because C atoms as well as F atoms lie outside the ab plane and contribute to Pcc.The Pcc second moment increases steadily as the C chain becomes longer.The Pcc per CF2/CF3 group for C3F8 15 is 44.78 u Å 2 and is predicted to be 45.16 u Å 2 for C4F10 (from PBE0/VTZ calculations).This value increases to 45.92 u Å 2 for C5F12 15 and to 46.98 u Å 2 for C6F14.The trend demonstrates that as the C chain length increases more mass is displaced outside the ab plane and contributes to Pcc due to the helicity of the structures.
The microwave data alone do not allow for an exact determination of the CCCC dihedral angles.To analyze the structural parameters of C6F14, the principal coordinates of the computed model were scaled by the square root of the ratio of the observed second moments to the computed second moments.This shifts the coordinates of each atom to exactly reproduce the observed second moments.Computations were performed at the PBE0/VTZ level of theory using the Gaussian 03 program. 18The PBE0 functional has been shown to accurately model perfluoroalkanes 13,15 and is again evident by the excellent agreement between the observed and computed spectroscopic constants for C6F14 (Table 2).The scale factors are 0.99996 for the acoordinates, 1.00167 for the b-coordinates, and 1.00288 for the c-coordinates.Since the scale factors are nearly equal to 1, the structural parameters do not change much from the computed model (Table 3).The overall C2 symmetry of C6F14 allows for two distinct dihedral angles.The exterior C1C2C3C4 dihedral angle (also equal to C3C4C5C6) is 16.7 o away from trans and the interior C2C3C4C5 dihedral angle is 18.0 o away from trans using this scaling approach.The exterior dihedral angle is in agreement with the single dihedral angle of about 17 o from trans determined in C5F12 using this same scaling approach. 15The interior dihedral angle is slightly larger than the exterior dihedral angle likely because the interior of the molecule is more sterically crowded.The scaled C6F14 structure was converted to helical parameters using Equations 1 and 2 above, averaging bond lengths, bond angles, and the dihedral angles.The helical radius ρ is 0.434 Å, the helical angle θ is 14.3 o , and the pitch d is 1.298 Å.These values are in reasonable agreement with the 0.42 Å helical radius, 13.8 o helical angle, and 1.292 Å pitch of the low temperature phase II form of PTFE. 3 By comparison, the determined helical parameters of C5F12 from a scaled MP2/VTZ model are 0.431 Å helical radius, 14.1 o helical angle, and 1.297 Å pitch. 15

Conclusions
The helical structure of C6F14 has been observed by assignment of its c-type rotational spectrum, consistent with overall C2 symmetry.The structure was characterized by scaling a PBE0/VTZ computed model to exactly reproduce the observed second moments.The scaled structure has a C1C2C3C4 exterior dihedral angle of 16.7 o from trans and a C2C3C4C5 interior dihedral angle of 18.0 o from trans.In terms of helical parameters C6F14 has a helical angle of about 14 o , in good agreement with the 13.8 o helical angle of the low temperature phase II form of PTFE.

Experimental Section
General.C6F14 was purchased from Synquest Laboratories and studied directly.Vapor of the sample was transferred to a 7 L stainless steel tank to a pressure of 0.04 atm.6.5 atm He was added to produce a 0.6% sample mixture.Pulses of the sample mixture at 1.75 atm were admitted at 5 Hz into the pulsed-jet Fourier transform microwave spectrometer 19 of the Southern New England Microwave Consortium. 20Five microwave pulses were observed per gas pulse and rotational transitions were measured in the 6-11 GHz range, although the complete spectrum was not scanned.Transitions were observed as Doppler doublets with estimated uncertainties to be about 2 kHz.The rotational temperature of the expanded gas is estimated to be about 5 K. Three observed transitions at 7624.38 MHz, 8024.94MHz, and 8425.50MHz were tentatively assigned to the 550-440/551-441, 651-541/652-542, and 752-642/753-643 degenerate pairs, respectively.This tentative assignment predicted the 853-743/854-744 degenerate transitions to be around 8826 MHz.The assignment proved to be correct as a line was observed at 8826.05 MHz, and several more of these degenerate pairs were measured.Since the transitions are doubly degenerate, B and C are not distinguishable.A host of non-degenerate lines were predicted from the new assignment and were measured to distinguish B and C. The transitions were fit using rotational constants and one quartic centrifugal distortion constant using Watson's S reduction 21 to an rmsd of 1.8 kHz.The use of only one centrifugal distortion constant that is quite small indicates that C6F14 is very rigid.The observed spectroscopic constants are displayed in Table 1 and the 46 assigned transitions are listed in Supplementary Table 1.

Figure 1 .
Figure 1.Helical (left) and molecular (right) perspectives for describing a helix.The dashed line represents the helical axis and the green circles represent CF2 groups.

Figure 3 .
Figure 3.The C2h structure of C6H14 with dihedral angles of 180 o (left) and the C2 structure of C6F14 with dihedral angles of ~17 o from trans (right).

Table 2 .
Comparison of observed spectroscopic constants to the computed and scaled models

Table 3 .
Selected structural parameters from the computed and scaled models