J. Phys. Chem. 1993,97, 5901-5904
5901
Ab Initio Study of Molecular Geometry and the Torsional Potential in Perfluoro(ethy1 methyl ether) C. L. Stanton,? H. L. Paige,'-t: and M. Schwartz'pt Department of Chemistry, University of North Texas, Denton, Texas 76203, and Materials Directorate, Wright Laboratory, Wright Patterson Air Force Base, Dayton, Ohio 45433-6533 Received: November 23, 1992
Molecular geometries, energies, and vibrational frequencies for equilibrium and transition-state conformations
of perfluoro(ethy1 methyl ether) have been calculated using ab initio molecular orbital theory. Geometries were optimized at the 6-3 1G(d) level, and single-point energies were also obtained with the 6-3 11G(d) basis set. MP2 correlation energies were calculated with both bases. Examination of the potential energy surface reveals that a distorted twist-trans structure is the lowest energy conformation. The gauche conformer has an unexpectedly narrow and high-energy minimum, separated from the twist-trans structure by a low torsional barrier. The published explanation for the helical structure of perfluorobutanel-* is supported by this work and is extended in order to explain the distortion in the gauchetrans transition-state angle. Vibrational frequencies are used to confirm saddle points and are reported for all conformers.
Introduction Insight into the structural features responsible for physical and chemical properties is of increasing importance to developers of new materials. The number and variety of pure compounds necessary to obtain meaningful structureproperty correlations make the experimental route to this information costly and timeconsuming. In addition, for some properties, the impact of low concentrations of impurities on experimentally challenging measurements is uncertain. For these reasons, there is substantial interest in computational alternatives to traditional quantitative structureproperty relation (QSPR) studies. The viscosity of a polymeric fluid is dependent in part on the rotational mobilities of the constituent polymer chains. The rotational mobility, in turn, is dependent on the torsional barriers within that chain. The geometric parameters and energies of the various conformationsof small molecules can be found with good accuracy from ab initio molecular orbital calculations. The energies permit calculation of the relative populations of the conformers and of the energy barriers separating them. The calculated torsional potentials can then be used to improve molecular dynamics parameters and, hence, the resulting simulations and estimations of viscosities (and other bulk properties) of the molecules of interest. Perfluoro(ethy1 methyl ether) (PFEME) is the smallest fluorocarbon ether exhibiting internal rotation about a C-0 bond. There have been two earlier computational investigations of the equilibrium (lowest energy) structure of PFEME.3,4 However, neither study addressed the second equilibrium or transitionstate geometries nor the torsional barrier to internal rotation. Perfluoropoly(alky1ethers) (PFPAE's) are finding increasing application as stable, effective lubricants over extended ranges of temperature. As part of our program designed to understand the determinants of the viscosity-temperature behavior of PFPAE's, we havecalculated the structures of all stationary point conformers and the internal rotation barriers of PFEME. The results are compared to those from earlier calculations on this m0lecule3~~ and to reported data on perfluorobutane'S2 (PFB) and ethyl methyl ether5 (EME). Calculations Ab initio molecular orbital calculations were performed on a Cray X-MP/216 computer using the Gaussian 90 programa6 +
University of North Texas. Patterson Air Force Base.
1 Wright
Equilibriumand saddle-pointgeometries were gradient-optimizd at the SCF level using the 6-31G(d)8,9basis set. Hartree-Fock energies were also obtained with the 6-31 lG(d)9JO basis, using the 6-3 1G(d) geometries. In addition, single-point second-order M~ller-Plesset~' (MP2) energy calculationswere performed with both basis sets. Vibrational frequencieswere calculated for all conformersusing the 6-3 1G(d) basis set. Transition-state geometries were confirmed by the presence of a single imaginary frequency. Results and Discussion
Geometries. Selected geometric parameters for all equilibrium and transition-state conformers of PFEME are displayed in Table I. In the table and following discussion, the atoms are numbered as shown in Figure 1. The most striking result for the optimized geometries is that the skeletal dihedral angle, ~ ( C I C ~ O C of~the ) ,equilibrium trans conformer is twisted from 180' by approximately 17'. The perfluoromethoxy group in this rotamer is similarly twisted [4(FjAC30C2)= 162'1 from a purely trans configuration, giving an overall helical structure to the molecule;this rotamer is labeled as "twist-trans", TT, in Table I. Similarly, the stable gauche conformer is labeled G, and the three transition states were (T)* [4 = 180'1, (GT)* [180° < 4 < 60'1, and (GG')* [4 = O O ] . Dixon1,2and Van Catledgel have earlier reported that the structure of the trans conformationof PFB is helical,characterized by a twist of the carbon skeleton, 4(CCCC) = 164.6',2 and rotation of the fluorines about both terminal CC bonds, t$(FCCC) = 170.2°.2 They have suggested that the calculated helicity in PFB, and in other perfluoroalkanes,may result from a tendency to lower the repulsiveinteractionsbetween CFdipoles on alternate carbons, which are precisely parallel in the perfectly trans structure. Most significantly, while fluorines on the perfluoromethoxy carbon of PFEME are twisted from 180' in theTT rotamer (vide supra), there is virtually no rotation of the fluorines on the C1 carbonabouttheCIC2axis[ ~ ( F ~ A C I C = ZO 179.1'1. ) Thisresult provides supportingevidencefor Dixon's explanationof the helicity in perfluoroalkanesbecause, as seen clearly in Figure 1, CF bond dipole repulsions on alternate atoms are removed by the substitution of oxygen for the CF2 group (in PFB) in PFEME. Pacansky et al.3 have reported the geometry of the TT rotamer of PFEME determined with the 3-21G12 basis set. Their CC bond length is shorter (by 0.03 A) and their calculated CO and
0022-365419312097-5901%04.00/0 0 1993 American Chemical Societv
5902 The Journal of Physical Chemistry, Vol. 97, No. 22, 1993
TABLE I: Conformation Dependence of Selected Geometric Parameter@ parameter
TT
1.529 NCiC2) R(C2O) 1.358 R(C3O) 1.358 R(Ci FIA) 1.311 R(CIFI B) 1.310 R(CI FIc) 1.310 R(C2h) 1.319 1.320 R(czF2~) R(C~F~A) 1.301 R(C3Fie) 1.309 R(C3F3c) 1.307 107.9 L(ClC20) L(c2oc3) 121.4 109.1 L(C~CIFII\) 107.1 L(oc3F3~) &(C2C2OC3) 162.8 &(FIACIC~O) 179.1 ~ ( F ~ A C ~ O 162.3 C~)
(T)*
(GT)*
G
(GG')*
1.530 1.358 1.359 1.311 1.310 1.310 1.320 1.319 1.301 1.308 1.308 107.5 122.5 109.0 106.6 180.0 180.1 180.0
1.537 1.365 1.355 1.311 1.310 1.311 1.314 1.318 1.301 1.307 1.310 114.4 125.7 108.9 106.5 76.8 165.8 172.8
1.535 1.364 1.355 1.310 1.310 1.310 1.314 1.319 1.308 1.313 1.301 115.1 125.2 109.0 106.9 61.7 171.1 160.4
1.543 1.363 1.351 1.310 1.312 1.309 1.320 1.318 1.301 1.309 1.308 119.8 130.3 107.9 106.6 0.0 169.2 166.1
Bond lengths are in angstroms and angles in degrees. See Figure 1 for atom numbering.
Figure 1. Structure and atom numbering in PFEME.
CF bonds are longer (by 0.01-0.02 and 0.01-0.03 A, respectively) than those found here. Bond angles agree to within 1-2' on average. The calculated twist of the skeleton using the smaller basis was similar to that obtained here, with ~ ( C I C Z O C=~ ) 164.6', but the rotation of the perfluoromethoxy group was substantially higher [+(F3AC3OCZ) = 147.6'1 .3 Smart and Dixon4 have also calculated the geometry of the TT equilibriumconformer using a DZ+D, basis set, which is a double-S basis with polarization functions on carbon. Their results agree even more closely with those obtained here, particularly for thedihedal angles [#(CIC20C3)= 160.9' and 4(F3AC30C2)= 161.2'1. The observed differences, which are relatively small, are expected when comparing geometries calculated with and without polarization functions on the various atoms. Not surprisingly, since the (T)* energy barrier is quite low (vide infra), the geometric parameters of the TT equilibrium conformer and the (T)* saddle point agree closely (Table I), with the exception of the dihedral angles, which are all 180' in the transition state. From the table, it is observed that both the COC and CCO angles vary in the order (T)* = TT < (GT)* = G < (GG')*, reflecting the increased 1,4 atomic repulsions with decreasing CCOC dihedral angle. Similarly, R(ClC2) and R(C20) exhibit modest increases with diminishing dihedral angle; this trend is not, however, observed for R(C30),which is slightly longer in the TT and (T*) rotamers. Significantly, it may be seen in the last column of the table that, unlike in PFB,IJ the terminal fluorines remain twisted from 180' in the (GG' ) * conformation of PFEME. This may reflect greater F-F repulsions in the syn conformation of the ether, resulting from the shorter CO bond lengths. It is of interest to compare the geometry of PFEME with that reported earlier for EME,Susing the same [6-31G(d)] basis set. Both of the CO bond lengths in the fluorinated ether are substantially shorter than in EME, in which R(C2O) = 1.417 A and R(C30) = 1.390 A in the trans conformer; in contrast, the CC bond lengths are approximately the same [R(CIC2) = 1.516
Stanton et al.
A in EME]. Also, the COC bond angle is markedly greater in PFEME [L(C2OC3) = 114.2' in trans EME], whereas the CCO bondanglesareapproximatelyequalin the two species [L(C~C~O) = 108.6' in EME]. The shortening of the CO bond lengths and increase in the COC angle in the fluoro ether may be explained on the basis of relative bond polarities. The calculated difference between the Mulliken charges on carbon and oxygen [q(C) - q(O)] is 1.7-2.1 in PFEME,13 whereas it is only 0.6-0.8 in EME.I4 Therefore, one expects a more ionic and, hence, shorter CO bond in the fluorinated compound. Consequently,the COC bond angle should increase to moderate the otherwise enhanced electrostatic and/ or van der Waal's interactions between fluorines on CZand C3 in Figure 1. The same trends in bond lengths and angles and in Mulliken charges are found in calculations on dimethyl ether and its fluorinated analogue.15 Energies. The total HF and MP2 energies (in au) of the five equilibrium and saddle-point conformations of PFEME, calculated with the two basis sets (using the 6-3 1G(d) geometries), are presented in Table IIA. The energies (in kcal/mol) relative to the TT rotamer are given in Table IIB. For comparision, relative conformationalenergies for EMESand PFB2J6are also contained in Table IIB. One sees from the table that the (T)* transition state is only slightly higher in energy than the TT minimum, with AI3 = 0.30.4 kcal/mol at the SCF level and hE = 0 . 5 4 6 cal/mol with correlation energy corrections. One observes, also, that relative energies of the G, (GT)*, and (GG' )* conformations are all lower at the MP2 level than the HF level, within a given basis set. This trend may be explained by analysis of Table IIA, from which it is found that, with the 6-31G(d) basis, for example, the correlation energy correction (in kcal/mol) varies in the order (T)* [-1190.21 < TT [-1190.41 C (GT)* [-1191.01 C G [-1191.41 < (GG')* [-1191.51. It is reasonable that inclusion of the electron correlation will preferentiallystabilizethe more structurally congested conformations [lower I$(CCOC)] in which the electronicrepulsionsare greatest. The principal effect of increasing the size of the basis is to increase the relative energies of the G, (GT)*, and (GG') conformations. Again, this trend arises from analysis of Table IIA, where it is found that the larger basis sets preferentially stabilize the TT and (T)* states in comparison to the above conformations. Thus, the effects of increasing basis size and introducing electron correlation tend to offset one another. A principal focus of this investigationis to perform a comparison of the torsional potential for rotation about the central bond in PFEME to those obtained earlier in the fluoroalkane and in the nonfluorinated ether. The three energy curves, calculated at the HF/6-3 1G(d) level for PFEME and EME and at the equivalent HF/DZ+P16 level for PFB, are shown superposed (displaced from one another for clarity) in Figure 2. As noted, the SCF and MP2 energies of the stationary-state conformers of the latter two molecules are also tabulated at the bottom of Table IIB. One observes from both Figure 2 and Table I1that the rotational potential of PFEME is markedly different from that of either of the other molecules in the vicinity of the G and (GT)* conformations. Most striking is that the dihedral angle of the (GT)* barrier is shifted by over 40' below the nominal angle of 120' (see also Table I). In order to verify this highly unusual behavior, we have performed additional HF/6-3 1G(d) optimizations at various fixed values of 4(C1CflC3) ranging from 70 to 120' The resultant energies, plotted also in Figure 2, confirm the position of the (GT)* transition state. A possible explanation for the large shift in the torsional angle of this transition state may be found by examination of the structure of PFEME at 4(CIC20C3) = 120' (Figure 3). One observes from the figure that, at this angle, the C 3 0 and one of the CZFbond dipoles are precisely antiparallel, which would lead I
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5903
Study of Perfluoro(ethy1 methyl ether) TABLE 11: Calculated Conformational Energiesa TT
method
-984.007 -984.268 -985.904 -986.470
A. Total Energies (hartrees) -984.002 -984.006 8 12 -984.267 804 -984.262 -985.903 717 -985.900 -986.469 558 -986.465 B. Relative Energies (kcal/mol) +0.34 +3.19 +0.41 +3.61 +0.52 +2.59 +0.57 +3.16 0.00 +2.56 +O. 15 +2.35 0.00 +2.67 +0.38 +2.41
346 45 1 547 460
0.00 0.00 0.00 0.00
PFEME/HF/6-3 1G(d) PFEME/HF/6-311G(d) PFEME/MP2/6-3 1G(d) PFEME/MP2/6-311G(d) EME/HF/6-31G(d)b PFB/HF/DZ+Pr EME/MP2/6-3 lG(d)b PFB/MP2/DZ+Pc
(GT)*
IT\*
0.00 0.00
IGG' I*
G
264 704 419 422
-984.002 -984.263 -985.901 -986.466
692 112 509 529
-983.995 -984.255 -985.894 -986.458
+2.92 +3.35 +1.91 +2.47 +1.67 +1.47 +1.40 +1.48
404 622 362 868
+7.49 +8.05 +6.39 +7.27 +6.84 +8.30 +7.00 +8.02
All energies were calculated using the HF/6-31G(d) geometries. From ref 3. From ref 2.
TABLE IIk Vibrational Frequencies in PFEME.96
., . , . , . , . , . 0
60
120
. , .,., . . 180
240
. . .
300
360
4 Figure 2. The torsional potential in (A) PFEME (circles), (B) EME (squares) (fromref 5),and (C) PFB (triangles) (fromref2). Thepotential curves for EME and PFB are displaced upward by 8 and 16 kcal/mol, respectively, for clarity of presentation.
vib no.
TT
(T)'
(GT)*
G
(GG')*
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
35 54 83 122 202 215 30 1 327 343 364 419 507 515 542 587 612 644 669 745 837 905 1119 1224 1244 1280 1288 1291 1302 1343 1463
25i 57 109 117 21 1 218 301 323 344 364 420 515 515 54 1 588 614 649 667 745 834 905 1121 1225 1240 1281 1288 1290 1301 1342 1463
28i 41 113 174 189 22 1 308 335 344 363 440 457 514 546 585 606 650 706 724 793 929 1113 1232 1259 1271 1288 1290 1301 1349 1434
41 53 102 158 197 213 312 332 342 365 434 458 516 547 585 608 647 709 718 789 932 1114 1231 1261 1269 1284 1291 1305 1345 1437
741 48 89 148 199 218 318 338 346 366 42 1 489 509 539 590 615 617 682 717 776 941 1120 1238 1251 1262 1268 1292 1306 1332 1430
Frequencies are in units of cm-I. Calculated frequencies have been scaled by the factor 0.9.
Figure 3. Structure of the (GT)* transition state in PFEME.
to a stabilization of this configuration, not expected in either PFB or EME, and thus result in a shift of the position of the energy maximum. An additional feature of the potential energy surface of PFEME is that the relativeenergy of its G equilibrium conformer is greater than that in either of the two other molecules. The explanation for this difference may reside in the closer approach distance between terminal fluorine atoms, resulting from the shorter CO and greater CF (compared to CH) bond lengths, which would destabilize the gauche conformation in PFEME. As seen clearly in Figure 2, the overall effect of the displaced position of the (GT)* transition state and the high energy of the G conformer is to result in a very shallow,narrow energy minimum for the gauche conformation of PFEME. From Table 11, the energy barrier, E[(GT)*] - E[G], varies from only 0.26 to 0.69 kcal/mol, dependent upon the level and method of calculation. Vibrational frequencies for all five stationary states of PFEME were calculated using the 6-31G(d) basis set and are displayed,
TABLE IV Thermodynamic Correction Factors. quantity TT (T)* (GT)* G ZPVE H( T ) - H(O) A[ZPVE] A[H(T)-H(0)] net corr
29.42 7.14 0.00 0.00 0.00
29.43 6.85b 0.01 -0.29 -0.28
29.41 6.28b -0.01 -0.32 -0.33
29.44 7.08 0.02 -0.06 -0.04
(GG')* 29.25 6.87b -0.17 -0.27 -0.44
a Quantities are given at 298.15 K in units of kilocalories per mole. The torsional motion at the barriers was treated as free rotation.
for reference, in Table 111; these values have been multiplied by the normal 0.90 scalefactor to account for the effects of vibrational anharmonicity and electron correlation. The scaled frequencies and molecular structures have been used with the standard formulael7 to calculate the zero-point vibrational energies (ZPVE) and thermal contributions to the enthalpy, H(T ) - H(O), for each of the stationary states. The results are shown in Table IV, together with deviations from values for the TT equilibrium rotamer, A[ZPVE] and A[H(T) - H(O)]. The net corrections, A[ZPVE] + A[H(T) - H(O)]; to
5904 The Journal of Physical Chemistry, Vol. 97, No. 22. 1993
the relative energies, due to vibrational and thermal motions, are given in the last row of the table. The effects of these relatively small corrections are 2-fold. First, the very low (T)* barrier to interconversion of the two TT equilibrium conformers is reduced still further. There is also a reduction in the comparatively low (GT)* - G energy difference (vide supra). Summary and Conclusions
Molecular geometries and energies of all equilibrium and transition-state conformations of perfluoro(ethy1 methyl ether) were determined by ab initio molecular orbital calculations using the 6-31G(d) basis set. The CCOC skeleton in the "trans" conformer is twisted by 17O from 180°. There is a similar rotation of the perfluoromethoxy fluorines about the terminal CO bond (by 18O), but no twisting of fluorines on the other terminus of the molecule. These results are easily explained by dipolar repulsionsbetween CF bonds on Cz and C3 (Figure 1) and clearly support the proposed explanation for the helical structure of perfluorobutane.* The energy of the gauche conformers of PFEME (relative to the twisted trans structure) is substantially higher than reported earlier for either perfluorobutane or ethyl methyl ether. In addition, the dihedral angle of the transition-state conformation separating the gauche and trans conformers is markedly lower (by 40') than the nominal value of 120O. The large differences in the torsional potential energy curve in PFEME compared to either PFB or EME indicate that one could expect that the properties which depend upon molecular conformational mobility should be significantly different in liquid perfluoropoly(alky1 ethers) relative to those found in either perfluoroalkanes or alkyl ethers. Acknowledgment. This research was sponsored in part by the Air Force Office of Scientific Research/AFSC, United States Air Force, under Contract F49620-90-(2-0076. M.S. acknowl-
Stanton et al. edges the Robert A. Welch Foundation (Grant B-657) for partial support of this project. References and Notes (1) Dixon, D. A.; Van Catledge, F. A. Inr. J . Supercomput. Appl. 1988, 2, 52. (2) Dixon, D. A. J . Phys. Chem. 1992, 96,3698. (3) Pacansky, J.; Miller, M.; Hatton, W.; Liu, B.; Scheiner, A. J . Am. Chem. SOC.1991, 113, 329. (4) Smart, B. E.; Dixon, D. A. J. Fluorine Chem. 1992, 57, 251. (5) Tsuzuki, S.; Tanabe, K. J . Chem. Sot., Faraday Trans. 1991, 87, 3207. (6) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.;Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius. C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Pople, J. A.; Gaussian 90, Revision F; Gaussian, Inc.: Pittsburgh, PA, 1990. (7) Pulay, P. In Applications of Electronic Structure Theory; Schaefer, H. F.; 111, Ed.; Plenum Press: New York, 1977; p 153. (8) (a) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1982, 56,2257. (b) Hariharan, P. C.;Pople, J. A. Theor. Chim. Acta 1973,28,213. (9) Frisch, M. J.; Pople, J. A.; Binkley, J. S.J . Chem. Phys. 1984, 80, 3265. (10) (a) Krishnan, R.; Binkley, J. S.; Seeger. R.; Pople. J. A. J . Chem. Phys. 1980, 72, 650. (b) McLean, A. D.; Chandler, G . S.Ibid. 1980, 72, 5639. (11) Mdler, C.; Plesset, M. S.Phys. Rev. 1934, 46, 618. (12) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; Defrees, D. J.; Pople, J. A.; Binkley,J. S.J . Am. Chem.SOC.1982,104,5039 and references contained therein. (13) Calculated Mulliken charges on the skeletal atoms of PFEME (the TTconformation)areq(C,) = +l.OS,q(C*) = +l.OO,q(O) =-0.70randq(CJ = +1.36. (14) Calculated Mullikenchargeson theskeletal atomsof EMEareq(C,) = -0.49, q(C2) = 0.02, q ( 0 ) = -0.60, and q(C3) = -0.16. Stanton, C. L.; Marshall, P.; Schwartz, M. Unpublished results. (15) Stanton, C. L.; Paige, H. L.; Schwartz, M. Unpublished results. (16) Conformational energies for PFB, taken from ref 2 and contained in Table IIB, were obtained by single-point calculations (using DZ+D, geometries) with a DZ+P basis set, which is a double-f basis with polarization functions on all atoms. (17) Hill, T. L. An Introduction toSratisrical Thermodynamics; AddisonWesley, Reading, MA, 1960, p 167.
