Electron Diffraction Study of Perfluoro-fert-butyl Alcohol
155
An Electron Diffraction Study of Perfluoro-teert- butyl Alcohol. Large Amplitude Motions and Structure A. Yokoreki and S. H. Bauer* Department of Chemistry and the Material Science Center of Cornell University, Ithaca, New York 14850 (Received July 8, 1974)
A least-squares analysis of electron diffraction intensities for (CF3)3COH [gas phase] gave the following structural parameters: r,(C-C) = 1.566 f 0.009 8; r,(C-F) = 1.335 f 0.004 8; rg(C-0) = 1.41 f 0.02 A; LCCF = 110.6 f 0.4’; and LCCO = 108.5 f 0.8’, wheqe the angles are in terms of ra, and the uncertainties were set at 2 . 5 ~( u is the least-squares standard deviation) plus estimated systematic errors, due to inaccuracies in the nozzle-to-plate distances and the accelerating voltage. The (long) C-C and (short) C-0 distances are not in harmony with the general trend observed for corresponding distances in tert- butyl compounds, (CH3)SC-X, indicating the presence of a substitution effect of CF3 for CH3 on the tert- butyl group. The contribution of the torsional motions of the three coupled CF3 rotors to the diffraction pattern were computed by means of a Monte Carlo integration routine. The potential function for these motions is characterized by a “flat minimum” at the staggered position for each CF3 group. The classical turning point for CF3 torsion occurs at about 23.0’, and its root mean square amplitude (at room temperature) is about 14.2’. The flat minimum potential can be rationalized in terms of a balance between nonbonded interactions of F F, C * F, and 0 F pairs.
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..
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Introduction Perfluorinated tert- butyl alcohol, (CF3)3COH, is almost as strong an acid as is acetic acid (pK, = 5),l whereas the acidity of tert- butyl alcohol is weaker than that of methyl alcohol (pK, = 19 us. pK, = 16-18).2 Such a large difference in acidity due to substitution of CF3 for CH3 is probably associated with changes in structural parameters. This question is of special interest to us as part of a broad program of study of F for H or CF3 for CH3 substitution effects on molecular ~ t r u c t u r e . ~ Another more specific problem introduced by this compound concerns the development of an efficient routine for calculating the effects of large amplitude intramolecular motions due to librations of three CF3 and one OH rotors; see Figure 1. In order to analyze diffraction data for correlated motions of multiple rotors, a practical and general procedure was developed based on a Monte Carlo integration program which has been applied successfully to many problems in statistical physi~s.~-6 Without introducing sophisticated and intractable analytical expression for multiple rotor^,^ this approach has the advantage of being a simple and practical reduction of diffraction data for all kinds of potential functions to which rotors are subjected. In the present study, large-amplitude motions of the coupled CF3 groups have been treated, while the rotation of the OH group was not explored because of its small contribution to the diffraction intensity. Experimental Section Data Reduction. A sample of perfluoro-tert- butyl alcohol was obtained from Penninsular ChemResearch and used in the present study, after purification by vacuum distillation. Electron diffraction patterns were taken with the reservoir at room temperature, at two nozzle-to-plate distances (291.50 f 1.7 mm (LVL) and 128.73 f 0.35 mm (HVS)), on Kodak Electron Image plates. The accelerating voltages were 41 (LVL) and 57 (HVS) kV, the electron beam currents were 0.28 (LVL) and 0.42 (HVS) MA,and the
W
Flgure 1. Perfluoro-tert-butyl alcohol, (CF&COH.
exposure times were 15 (LVL) and 10 sec (HVS), respectively. To determine the scale factor, diffraction patterns of MgO powder and C02 were taken concurrently with those for the sample. Optical densities (0.05-0.25 for the LVL plates and 0.17-0.21 for the HVS plates) were recorded with a modified Jarrell-Ash densitometer.8 Least-squares analyses of the above COP data gave -a scale factor of -0.14% for distances, relative to determination of L (nozzle-to-plate distance) from MgO patterns, and a correction of -7.6% for mean amplitudes of vibrations. The indices of resolutions for both C02 and (CF3)3COH were about 0.8. Typical intensity and background curves of the sample are given in Figure 2. The experimental radial distribution curves, f (r ), and molecular intensity curves, qM ( q ) were derived following our usual procedureg (Figures 3 and 4). Most of these data reduction steps were performed on the DEC PDP-9 computer. Additional details of the routine are given in previous p u b l i c a t i o n ~ . ~ J ~ The Journal of Physical Chemistry, Vol. 79,
No. 2, 1975
156
A. Yokozeki and S. H. Bauer
0.204 0.198 0.192
0.186 0.180
0.174 0.168
0.162
0.156
q (k') Flgure 2. Photographic density for (CFs)&OH, plotted as a function of the scattering variable 9. The refined background is also shown.
I
L
v
*-
-
I
iiti 2
4 5 3 r (A) Figure 3. The radial distribution curve, f ( r ) , for (CF3)3COH: dots, experimental: solid curve, theoretical ((peff = 15'); see text.
0.5
dlff \
v
I
The elastic scattering factors and Born phase shifts of Schafer, Yates, and Bonhamll were used for the following analysis, while the inelastic scattering factors were taken from Tavard's12 tables. Analysis. Structure. With the assumptions that each C-CF3 group and the carbon skeleton (0-CC3) have local CsU symmetry, 11 independent parameters are needed to define the geometry: four bond distances (C-C, C-0, C-F, and 0-H), three bond angles (LCCF, LCCO, and K O H ) , three rotational angles for CF3 groups around the corresponding C-C bonds (PI,e,and ( ~ 3 ) ; and one rotational angle for the 0-H group around the C-0 bond (e). The di..),-,.,"," p hedral angles, p ~ m, , and (03, were measured from the staggered positions relative to the C-C and C-0 bonds; for instance, vhen the three CF3 groups eclipse the carbon skeleton, p1 = cpz = (p3 = f60'. The 0 parameter was defined to be zero, when the 0-H and C-C bonds are staggered. T o make the initial stages of analysis tractable, a single
The Journal of Physical Chemistry, Vol. 79, No. 2, 1975
Electron Diffraction Study of Perfluoro-fert-butylAlcohol effective rotational angle, cpeff, for the CF3 groups (ca,ff = p1 = (p2 = cpj) was used; this constraint was released in the subsequent study of large amplitude motions. Trial-anderror resolution of the experimental radial distribution curves indicated that the position of the hydrogen was quite uncertain, and that imposing a constraint on the hydrogen parameters had practically no effect on the other structural parameters. When all the contributions of H - - X (X = C, 0, F) pairs to the total molecular intensity and radial distribution curves were calculated using several different sets of the hydrogen parameters, their total contribution was of the order of magnitude of the random noise in the experimental curves. Concerning the hydrogen position, therefore, the following additional assumptions were introduced: 0-H = 0.96 A, LCOH = 108.5', and 0 = Oo, or f120° (staggered); these values were taken from the corresponding magnitudes for the COH group in methyl alcoh01.I~ Preliminary structural parameters were then derived by least-squares reductions of radial distribution and intensity curves: C-C = 1.56 A, C-0 = 1.42 A, C-F = 1.33 A, LCCF = l l O o , LCCO = 108O, and peff = 7-16', These analyses showed that the derived magnitude of peffstrongly depends on some of the inserted mean amplitudes of vibration; large lij's with respect to CF3 torsional motions, qualitatively, resulted in small values for cpeff. This indicated (as was anticipated) that the CF3 groups undergo large amplitude torsional oscillations. In order to examine quantitatively the dependence of the mean amplitudes on peff,and to refine the structural parameters obtained above, the following normal mode analysis was carried out. Calculation of Mean Amplitudes. Root mean square amplitudes and shrinkage corrections for this molecule were computed by a conventional normal coordinate analysis. In this calculation, the molecule was assilmed to have C, point group symmetry, and the structural parameters derived from the previous section were used. Since none of the force constants for this compound was available, simple Urey-Bradley force fields were estimated from analogous compounds. Then the force constants were adjusted to reproduce the ir and Raman frequencies observed by Murto, et al. l 4 The adopted force constants and the calculated normal frequencies are listed in Tables I and 11, respectively. In the latter the calculated values are compared with the observed frequencies. The agreement between them is only fair; both the assignments and the force fields are incomplete. Of immediate concern to this study are the lowest frequencies, which correspond to librations of the CF3 groups around C-C bonds. In order to examine these motions, the corresponding torsional force constant, Y, (V(torsion) 3 ( Y / 2 )ZC3cpi2)was systematically varied in the calculation of mean amplitudes: Y = 0.08 (set I), 0.14 (set 11),and 0.20 (set 111) mdyn A. These led to calculated torsional frequencies of 40-48, 50-58, and 63-68 cm-l, respectively; the observed value is my70 cm-l. If a threefold potential barrier, V3, about the C-C bond is assumed for each CF3 group, the above force constants (set I, 11,and 111) correspond to barrier heights of 2.5, 4.5, and 6.5 kcal/mol, respectively, and the corresponding root mean square amplitudes for the angles, ( % are about 13, 10, and 8 O at room temperature: ( pL2) = kT/Y and Y = 9v3/2. In addition, mean amplitudes for the frame vibrations [Y = m (set IV)] were calculated. The results are summarized in Table 111. Refinement of Structural Parameters. Preliminary
157
TABLE I: Force Constants K(C-C) K(C-F)
K(C-0) K(O-H)
H(C-C-C) F(C-**C) H(C-C-F) F(C F)
2 .o 3.75 2.8 7.19 0.78 0.34 0.15 1.30
H(F-C-F) F(F.4.F) H(C-C-0) F(C*.*O) H(C-0-H)
0.15 1.35 0.28 0.60 0.29 0.60 0.20 0.038
F(C0a.H) Y(C-Cb Y(C-0) a See text. Units mdyrl/18, for K, H, and F, mdyn A for Y.
TABLE 11: Normal Frequencies (C,) (cm-1) A'
A"
Calcda
Obsdb
Calcd
Obsd
3650 1431 1330 1203 1131 1107 1092 1039 993 761 684 590 534 501 466 369 354 334 286
3630 1381 1313 1270 1260 1155
1382 1159 1116 1105 996 686 536 503 501 372 356 355 322 251 161
1288 1209
958 955 771 650 540 488 440 328
63
979 729 572 535 357 316 273 252 165 -70
285 242
161 176)
195
68
-70
Calculated using the force constants in Table 1. b Observed values taken from ref 14. a
structural parameters derived in the earlier section were then refined by a least-squares analysis of the molecular intensities, using the calculated mean amplitudes and shrinkage corrections (set I through IV). The converged values for cpeff strongly correlated with the torsional amplitudes; sets I, 11,111,and IV gave the peffvaluesof 7.5 f 3.5O, 12.3 f 2', 15.3 f lo,and 17.1 f l o ,respectively. However, none of the other parameters changed beyond their standard deviations (for the various sets of mean amplitudes listed in Table 111).The results of peff us. ( pi2)112 are plotted in Figure 5: ( (pi2 )112 = (kT/Y)I12,where Y = 0.08,0.14,0.20, and m mdyn A, for sets I, 11, 111, and IV, respectively. On the basis of Figure 5, one may describe the CF3 motions within the above one dimensional harmonic approximation. Extrapolation of the curve in Figure 5 cpeff 0 &e., the staggered conformation) gives ( %2)1/2 = 17.4O, which implies a classical turning point for the motions, pt = 24.6'; pt = ~ ' (2 The structural parameters obtained from the above analyses are given in Table IV. The uncertainties listed were estimated to be [ ( 2 . 5 ~ + ) ~ A2I1l2, where CT is the calculated standard deviation (least squares), and A is an estimated systematic error due to the uncertainty in the scale factor
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The Journal of Physical Chemistry, Vol. 79, No. 2, 1975
A. Yokozeki and S. H. Bauer
158
TABLE 111: Mean Amplitudes ( & j ) and Shrinkage Corrections (Si,) ( X 10-4
Cl CO CO Ci CO C1
470 635 521 685 512 720 611 699
Fil
F11
C1 C2 0 0
Fil
F12
H
0
320 92 28 24 54 45 584 756
470 63 5 52 1 685 512 720 611 699
214 141 22
7 43 34 359 752
8)"for (293°K)
470 635 521 685 512 720 611 699
156 92
35 27 9 -8 26 12 35 744
1113 1108 733 1032 704 1689 1681 1247 1137 1125 786 = ra - r,.
-1 8 -1 6 7 -1
11 6 38 22 249 749
85 1606 34 1308 27 1706 71 1599 30 1334 21 1736 F22 741 106 741 66 741 45 1469 64 1337 36 1705 100 Fli 137 704 96 7 04 66 F13 7 04 169 2500 28 2017 35 F2i 2673 123 2487 19 2077 2743 15 F13 F23 -195 2788 -120 2317 -83 Fi3 F21 3415 130 1568 67 1303 48 Fl2 F22 1658 118 1538 63 1316 43 1665 F13 F22 148 788 59 91 787 Fii F22 790 a Upper section, yi-independent pairs; lower section, cp&-dependent pairs, where hydrogen pairs are not listed. 611 sets I-IV. C1 Ci C1 0 0 Fiz
458 633 519 685 510 720 611 699
F21
F23
25 -84 -76 -1 0 -1 0 -9 4 See text for
TABLE IV: Structural Parametersa
4
C-C C-F C-O L CCF
1.566 kO.009 1.335k0.004 A 1.414 k0.022 A 110.6 kO.4" L cco 108.5 k0.8" L CCCb 110.4 lt0.8" LFCF~ 108.3 kO.4" a Distances ( r g ) ;angles (ra);see text for comments on estimated errors. * Calculated values from the independent parameters.
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0, a random number 9 [0,1] is chosen, and then if < exp(-AVIkT), the point is moved to its new position. If 9 I exp(-AV/ kT), it is returned to its old position. In the latter case, however, the old position must be regarded as a “new” position for the purpose of computing the canonical average ( F ) . Then, the entire procedure is repeated for the new configuration. After many such steps the weighted average ( F ) in the eq 1is simply given by
vFF2= A,
x
E
2 1 ~ / 3 ; yI
‘pi; ‘ p i f
Cp,j;
‘pj
(4)
* 2~/3
(i,j) = (1,2), (2,3), ( 3 , l ) yCF2=
x
Bo + B, sin x - B, cos x
*‘pi;
* q i f 21r/3 =
(5)
i = 1,2,3
co + ci cos x
(6)
i = 1,2,3 x 1 ‘ p i ; ‘pi k 2n/3 With the above equations the p-dependent distances for F F, C F, and 0 F pairs can be directly generated. The appropriate constants are listed in Table VI; these were calculated from the structural parameters in Table IV. It is very complicated to derive rigorous analytic expressions for the rms amplitudes of frame vibrations for the desired range of ((pl,a,(p3) values. Indeed, it is even trouble-
- -. - - -
-
~-
TABLE VI: Constantsa ~
_
~~
_
-~
~
A0 Ai A2 A3
14.3105 BO 10.3910 4.7681 Bi 3.2152 1.7806 B2 1.7670 2.7849 CO 9.5471 ff 0.5025 C1 3.3572 P 1.2578 =The coefficients for the eq 4-6; see text. A,, B,, and Ct in a and p in radians.
where F, is the value of the property F for the system after the j th move. To facilitate the computation of F,, which can be regarded as a function of r ( pi) and 1 f ( pi), analytical expressions of the cpi- dependent distances, r ( pi), were derived; in this case the contributions of hydrogen pairs to Fj were ignored, as justified above.
+ A , s i n (x - a) - A, s i n (y + a ) + A, sin (x + a ) sin y - A, cos (x + 0) COS y
ccco
‘Poi f
0.0011 -0.0021 0.0010 0.0014 -0.0009 0.0011 0.0012 0.0004 -0.0048 -0.0022 0.0046 0.0084 -0.26 0.0022 0.0016 0.0008 0.0085 -0.0050 0.13 0.30 -0.54 0.05 -0.59 0.0049 part of table.) b Dimensionless (lower left part of table).
the three rotors in the molecule are regarded as the motion of a representative point in a three dimensional space, wherein the point is subjected to a potential V(pl,(p2,(p3). The point is placed a t any location (e.g., c p ~= (p2 = (p3 = 0). Then, it is moved, successively, according to the following prescription: ‘pi
LCCF
I
I
I
3.5
4.0
4.5
A2.
5.0
r (A) Figure 6. Root mean square amplitudes of frame vibrations for eq 7-9; see also set IV in Table 111.
some to find empirical expressions which reproduce the numerical values computed at various configurations (pl,cpz,cp3). The following procedure was adopted. First lf,,,,(O,O,O) were calculated, as in the previous section (set IV in Table IV); the results were plotted (Figure 6) us. the corresponding distances. Then, to permit rapid computations, l f ( ( p ~ , ( ~ z was , ~ ) assumed to be a linear function of the various distances, expressed by the following equations (units A): Z~.(YFF) =
- 0 . 0 5 5 0 ~ F F+ 0.1247
YFF
- 0 . 0 1 5 1 ~ F F+ 0.1137
3.39
- 0 . 0 5 5 4 ~+~ 0.3416 ~
yFF 2
5
