J. Phys. Chem. 1981, 85,914-917
914
stead of the assumed M, provided the estimate of = 6.5 kcal/mol given by Lee and Lister1*is correct. A value of poma2= 0.25 kcal/mol implies the following changes in the rate constants: k-1/400, k-z X 400, k-4 X 400, k 4 4 0 0 , and k-, X 4002, provided that all changes in equilibrium constants are attributed to the less “sensitive” rate constants. When these values of the rate constants are used, the lower transition point remains the same as with the original constants. The upper transition diverges, however, from the experimental points as [BrO,-], decreases. The same results are obtained if, instead of increasing k-, by a factor of 1.6 X lo5 = 4002, we multiply k-, by 400 and divide k7 by the same amount. In other words the regular rate constants given above (k4-k7) give better agreement with the experimental data than do the changed rate constants. Other changes in various rate constants conforming with the thermodynamic restrictions of eq 8 and 9, such as changes in k2 or k4, imply a single steady state only, contrary to experimental evidence. This is expected, since both rate constants are “sensitive” in the sense of Figure 6. The values of k l , k+ k-4, k,, and recently k-S were deduced from e~periment’~J’with certain assumptionslO regarding the activity coefficients of the various species. The present mechanism does not include the recent value of k+ As the above discussion shows, the recent new value of k-S implies such changes in k2 and k4 as to bring about a strong contradiction to experiment. poBd,-
(18) C. L. Lee and M. W. Lister, Can. J. Chem., 49, 2822 (1971).
We will return now to the “sensitive” rate constants, namely, those rate constants that influence the transition points most, i.e., k l , k2, and k4. Some small changes in these rate constants (changes of their reverse reactions are immaterial in our calculations) can be introduced without changing the calculated transition in any appreciable manner. For example, a change in the assumed activity coefficients of the ions involved in reactions 1, 2, and 4 , namely, bromate, bromide, and hydrogen ions, can be introduced. These activity coefficients were all assumed1° to be 0.7. Any change in their activity coefficients implies a change in k l , k2, and k4 in such a way as to have the change in k l equal the change in k z times the change in k4. A glance at Figure 6 shows that our freedom is rather limited. Detailed calculations show that the present rate constants are correct within a factor of 2 or even less. The sensitivity of the transition points to the rate constants depends, of course, on the set of constraints used, on the particular transition (whether I 11-lower or I1 I-upper) tested (asseen in Figure 6), and on the set of rate constants, and so we have limited our discussion to some of the most important points. We also confined our attention only to the [Br03-]o-[Br-]osubspace of constraints. It may be that another subspace will prove to be more “sensitive” and thus more practical in evaluating other rate constants. . A complete analysis needs a mathematical procedure to find those rate constants which will cause all of the experimental results to have a best fit with the hysteresis surface in the five-dimensional constraint space, i.e., a best fit with the face of the “football” mentioned above. Such a detailed analysis is planned for a subsequent publication.
-
-
Isotopic Fractionation Factor and Hydrogenic Potential in 2-Hydroxy-I ,I,I,5,5,5-hexafluoro-2-penten-4-one1 Maurice
M. Kreevoyl and Barbara A. Rid1
Laboratory for Chemical Dynamics, University of Minnesota, Minneapolis, Minnesota 55455 (Receive& August 18, 1980)
The title compound (enol-hexafluoroacetylacetone) has an isotopic fractionation factor of 0.6 f 0.1. This, and much other information about this compound, can be rationalized if the enolic hydrogen bridges between the two oxygens and is governed by a double minimum potential function with a central maximum of -3000 cm-’ (8 kcal/mol) (eq 10).
There has been considerable interest in the structure of enolized, hydrogen-bonded, P-diketones, such as malondialdehyde and the title compound (enol-hexafluoroacetylacetone, 1). Both e~perimental~-~ and theoreticalG9 (1)This work was supported by the National Science Foundation through grant CHE76-01181to the University of Minnesota. (2) Brown, R. S.;Tse, A.; Nakashima, T.; and Haddon, R. C. J. Am. Chem. SOC. 1979,101,3157-62. (3) Altman, L: J.; Laungani, D.; Gunnarsson, G.; Wennerstrom, H.; Forsgn, S. J. Am. Chem. SOC.1978,100,8264-6. (4) Egan, W.; Gunnarsson, G.; Bull, T. E.;Forsen, S.J . Am. Chem. SOC.1977,99,4568-72. (5) Rowe, W. F.; Duerst, R. W.; Wilson, E.B. J. Am. Chem. SOC. 1976, 98, 4021-3. (6)Karlstrom, G.; Jonsson, B.; Roos, B.; Wennerstrom, H.J. Am. Chem. SOC.1976,98, 6851-4.
studies have been reported. These studies establish that most compounds of this class are mixtures of degenerate tautomers, the mobile hydrogen oscillating between two equivalent sites. Another experimental parameter which can give information about the hydrogenic potential funct‘lon is the isotopic fractionation-factor, 4%; which is defined in eq 1 and 2.’0-12 This is particularly sensitive XH + D(L20) + XD + H(L20) (1) (7) Fluder, E. M.; de la Vega, J. R. J . Am. Chem. SOC. 1978,100, 5265-7. (8) Catalln, J.; YGiez, M.; Fernlndez-Alonso, J. I. J.Am. Chem. SOC. 1978,100,6917-9 (9)Haddon, R. C. J.Am. Chem. SOC.1980,102,1807-11; this paper contains many references to earlier work in the field.
0022-3654/81/2085-0914$01.25/00 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 7, 1987 915
Isotopic Fractionation Factor ~ X = L
[(XD)/(XH)I(H/D)L,O
(2)
to the magnitude of the central barrier.13J4 The isotopic fractionation factor for the mobile, hydroxylic hydrogen of 1, &, has now been measured, and a value of 0.6 f 0.1 has been obtained in acetonitrile solution. This suggests that V, the potential function for the hydrogen oscillating between the two oxygens, has a central barrier height of -3000 cm-l (8 kcal/mol). It is also consistent with a considerable body of other information that is available for such compounds. Experimental Section Materials. Hexafluoroacetylacetonewas purchased from PCR Research Chemicals, Inc., and purified by distillation: bp 63-64 “C (previously reported, 68 and 70 OC).16 tert-Butyl alcohol was purchased from Aldrich Chemical Co., with a specified minimum purity of 99.5%,and was not further purified. tert-Butyl alcohol-d was purchased from Aldrich Chemical Co. and used without further purification. It had a specification of at least 98% isotopic purity, and its actual OH content was redetermined as a part of each fractionation-factor determination. Acetonitrile was purchased from Aldrich Chemical Co., with a specified minimum purity of 99%. It was further purified by “procedure I” of Coetzee.16 Procedures. The spectra of tert-butyl alcohol containing acetonitrile solutions, in 0.1-cm cells, were scanned with a Beckman DK-2 spectrophotometer between 2650 and 3000 nm. A maximum was found at 2815 nm (3552 cm-l).17 The absorbance, A, at that wavelength was measured for eight tert-butyl alcohol solutions ranging in concentration from 0.035 to 0.164 M. A plot of A against the concentration of tert-butyl alcohol was linear and passed through the origin, giving a slope of 10.24, which leads to an extinction coefficient, cRoH%15, of 102.4 M-l cm-l. The average deviation of points from this line was 0.018, and the probable error of eRoHB15 was 0.2. Water was found to have an absorbtion maximum at 2740 nm (3650 cm-l)17in dilute solution in acetonitrile, with an extinction coefficient of 111 M-l cm-’. Each fractionation factor was determined from the concentrations of tert-butyl alcohol-L and 1-L1L2in solution and from nine measured absorbances: at 2740 and 2815 nm in acetonitrile without either reagent; at 2740 and 2815 nm with tert-butyl alcohol-d added but not 1; at 2815 nm with 1 added but not the tert-butyl alcohol; at 2815 nm with both reagents present; and at 3000 nm in the absence of either reagent, in the presence of 1 only, and in the presence of both reagents. The absorbance at 2740 nm is a measure of the adventitious water concentration. This was generally of the order of 0.01 M. Since the tert-butyl alcohol concentrations ranged from 0.1 to 0.25 M, the water was almost completely deuterated on addition
of the deuterated alcohol and the 2740 absorbance almost completely eliminated. The 2815 absorbance in solutions containing only the alcohol was due to the adventitious OH content of the alcohol, plus tert-butyl alcohol-h produced by exchange with the water. The original H 2 0 concentration of the solvent and the tert-butyl alcohol-h concentration of the solution could, therefore, be obtained by simultaneous solution of eq 3 and 4. The extinction (-4’2740
- A2,4J/leHa02740 = (H2O)o[l - (ROH)i/(ROL)I (3) (4)
coefficient of HDO at 2740 nm is assumed, in these equations, to be half that of H20. The distribution of deuterium among OL groups is assumed to be statistical. Quantities in parentheses are concentrations. R is the tert-butyl group. The water content of the solvent before the addition of other reagents is (H20),. A, 1, and e have their usual significance. The subscript, 1, here and below, identifies a concentration prevailing in a solution containing the alcohol but not 1. When both tert-butyl alcohol and 1 were present ABls and Am were both measured; ABl6 was used as a measure of (ROH). Since 1-HlH2has a nonzero absorbance at 2815 nm, the base line had to be obtained from a solution containing 1, but no tert-butyl alcohol. For this solution, A was measured at 2815 nm and also at 3000 nm. With both reagents present, A3000was below that with 1 alone; the decrease was assumed to be due to 0-deuteration of 1. The fractional decrease at 3000 nm was assumed to be also applicable to the base line at 2815 nm. The validity of this correction was not proved, but it is reasonable, and the correction itself was not large, typically between 0.01 and 0.02 units of absorbance. Thus (ROH) was obtained from eq 5. Since the total (ROL) was known, (ROD) could (ROW =
(A2816 - Aozsis-4sooo/A03m)/zcRoH28is
be evaluated by difference. On the time scale of these experiments, there are two exchangeable hydrogens in 1: L1, the hydrogen on carbon, and La, the hydrogen of interest, on oxygen. The local environment of L1 is -c
II -CL1
=c-
I
By analogy with the aromatic hydrogens of trimethoxybenzene, qh1 was assumed to be 0.86.18 Very similar 4 values have been obtained for the structurally similar carbon-bound protons of fumarate (0.86) and diphosphopyridine nucleotide (0.83).19 Equation 6 then gives the (l-DiL2)/(1-HlL2) = 0.86(ROD)/(ROH)
(10) Gold, V. Trans. Faraday SOC. 1960,56, 255-61. (11) Kresge, A. J. Pure Appl. Chem. 1964,8, 243-58. (12) The symbol, L, is used for an atom which may be either H or D. The symbol D(L20) indicates that the deuterium which enters the equilibrium is taken from liquid water which contains both isotopes, preferably in approximately equal amounts; H(L20) has the analogous significance for hydrogen. (13) Kreevoy, M. M.; Liang, T. M.; Chang, K-C. J. Am. Chem. SOC. 1977, 99, 5207-9. (14) Kreevoy, M. M.; Liang, T. M. J. Am. Chem. SOC.1980, 102, 3615-22. (15) Boit, H.-G. “Beilstein’s Handbuch der Organischen Chemie”; 4th Supplement; Springer Verlag: Berlin, 1974; Vol. 1, part 5, p 3681. (16) Coetzee, J. F. Prog. Phys. Org. Chem. 1967,4,45-92. (17) The instrument was not recently calibrated in this region of the spectrum, so the absolute reliability of wavelengths given is uncertain; however, they were reproducible, h2-3 nm.
(5)
(6)
H content of position 1. Since the total (1-L1L2)was known, (1-H1L2)and (1-D1L2)could both be evaluated. Similar equations give the H and D content of the adventitious water. The fractionation factor of interest, 42, was then evaluated from eq 7-9. (7)
(18) Kresge, A. J.; Chiang, Y. J. Chem. Phys. 1968,49, 1439-40. (19) Cleland, W. W., private communication.
918
The Journal of Physical Chemistry, Vol. 85, No. 7, 1981
Kreevoy and Rid1
(1-LlDZ) = (ROW - (ROW1 - (1-DiL2) + [D(LzO)Ii - [D(LzO)I (8)
[D(LzO)I/2(HzO)o = (ROD)/(ROL)
(9)
[D(L20)I1was evaluated by an equation exactly analogous to eq 9. The whole calculation of was programmed for and carried out on a Texas Instruments T-56 calculator.
Results Using the methods described above, we obtained 15 values of 42for reagent concentrations ranging from 0.10 to 0.25. The derived values ranged from 0.32 to 1.12, with an average value of 0.63 and an average deviation from the mean of 0.22; the probable error of the mean was 0.06. No systematic variation of 42with either reagent concentration was discernible. The magnitude of the scatter is regretable but not unreasonable. The principle spectroscopically determined quantities, through which error enters, are (ROH) and (ROH)l. Other spectroscopically determined quantities are less important to the final result, and quantities obtained by weighing are relatively secure. A typical fractional uncertainty in (ROH) was taken to be 0.02, by analogy with the deviations of points from the linear re~~~~ lation used to define CRoH2815 and past e ~ p e r i e n c e . ’For (ROH)l, the fractional uncertainty, obtained in the same way, was -0.1. The fractional uncertainty in (ROH)l was larger because the concentration itself was smaller. If these errors are propagated through eq 6-9 and the conservation equations in the usual way,2O they result in an anticipated fractional error of 0.4 in &, marginally worse than was actually observed. This tends to confirm the randomness of the scatter and support the idea that the uncertainty could be reduced to reasonable proportions by repetition of the measurement. In addition to these random errors, the fractional probable error of 0.002 in CRoH2815 would introduce a further, systematic fractional error of 0.04, and, if we impute an uncertainty of 0.01 or 0.02 to &, that also will carry over into @z as a systematic error. Considering all these sources of random and systematic error, it seems reasonable to cite 4z as 0.6 f 0.1. For comparison with conventional fractionation factors,214z should be multiplied by the fractionation factor of tert-butyl alcohol in acetonitrile solution. However this should be within a few percent of unity,21~22 so that the failure to include such a correction does not introduce further significant error.
Figure 1. A plausible one-dimenslonal potential function for the bridging hydrogen In 1. The oxygens are assumed to be of infinite mass. The lowest four allowed energy levels for H are shown on the right, and those for D, on the left. The two lowest levels of D are combined In the figure because they are separated by only 10 cm-’. The units of Vand all of the energy levels are lo3 cm-’. The width of the barrier is in A.
by linear interpolation between the values given by Laane.23 Equation 11gives a value of 0.53 for $2. The 4D hc 4 = -QH eXp-(ZPEH kT - ZPED - ZPEH,L20 ZPED,L20)
+
(11)
is expressed in cm-l. The eigenvalues for protium or deuterium atoms governed by this function were obtained
required zero-point energies (ZPE) are the lowest eigenvalues of V, expressed in cm-l. The other symbols have cm at their usual significance, and hc/(kT) is 4.84 X 25 “C. The required zero-point energies for H and D in liquid water were assumed to be 1750 and 1237 cm-l, res p e ~ t i v e l y .Equation ~ ~ ~ ~ ~ 11differs from eq 8 of ref 14 by the preexponential ratio of one-dimensional partition functions, qD/qH. They are each given by Cexp[E,/(kT)], where the E, values are the allowed vibrational energy levels, measured up from the lowest allowed level in each case. Only the first two terms make significant contributions to the sum. The ratio of q’s was omitted in ref 14, because, in the cases considered there, it never differed from unity by more than a few percent, but, in the present case, it is 1.23. Equation 11and the chosen V give 0.53 for &. The calculated value is expected to be somewhat below the experimental because of the neglected bending vibrations. The 0-0distance in 1 can be estimated by adding twice the 0-H bond length to the interminimum distance in V, although such an estimate should be higher than the experimental distance, since the hydrogen probably lies off the 0-0 axis! There is also some uncertainty in the best 0-H distance to use. The 0-H bond length in alcohols is 0.97 Asz4 The actual 0-H distance in strongly hydroen-bonded substances with an off-center hydrogen is 1.1 The former is too short because hydrogen bonding
(20) Livingston, R. M. “Physic0 Chemical Experiments”;Macmillan: New York, 1957; pp 22-30. (21) Schowen, R. L. Prog. Phys. Org. Chem. 1972,9, 275-332. (22) Mata-Segreda, J. F.; Wirt, S.; Schowen, R. L. J.Am. Chem. SOC. 1974, 96, 5608-9.
(23) Laane, J. Appl. Spectrosc. 1970, 24, 73-80. (24) Gordon, A. J.; Ford, R. A. “The Chemist’s Companion”;Wiley: New York, 1972; p 107. (25) Speakman, J. C. Struct. Bonding (Berlin)1972,12,141-99. (26) Ichikawa, M. Acta Crystallogr., Sect. B 1978, 34, 2074-80.
Discussion This fractionation factor, and a number of other observations on 1 and related substances, can be rationalized if the motion of the bridging hydrogen, Lz, is governed by a double minimum potential function with a barrier of several thousand wavenumbers, measured up from the minima. A single minimum function approaching a simple harmonic could also mimic &, but ample other evidence excludes it.2-5 Figure 1and eq 10 show a plausible function.13J4Energy 171103 = 453x4 - 7 2 . w
(10)
w
-
.25iz6
Isotoplc Fractionation Factor
undoubtedly shifts the minimum energy distance toward longer values. The latter is too long because the most probably O-H distance in a system like the present one is sure to be longer than the minimum energy distance. The interminimum distance, shown in Figure 1, is 0.56 A. If the former value of the O-H bond distance is used, the estimated 0-0distance is 2.50 A; if the latter is used, it is 2.8 A. The experimental value is 2.55 A.27 The general agreement is very satisfactory. Equation 10 is the type of potential function suggested by Fors6n3to account for the isotopic changes in the NMR chemical shift for the mobile proton in 1. The barrier provided by V, 8.2 kcal mol-l, is a little lower than the 10 kcal mol-l which appears to be the best calculation of the barrier in enol-malonaldehyde.6 Correspondingly, the tunneling frequency provided by V is 110 cm-l for H and 10 cm-l for D, while 16 f 14 has been experimentally estimated for H in enol-malonaldehyde, While these differences are not large, considering the many uncertainties, they appear to be real. A potential function which would give a tunneling frequency of 44 cm-l for H and 4 cm-’ for D gives a 42 of 0.67. Since the one-dimensional model seriously underestimates (because of the neglected bending frequencies),14this 42value is clearly too large, and the corresponding tunneling frequencies are too small. It seems likely that the hydrogen bond in 1 is marginally stronger and the 0-0 distance shorter than that in enol-malonaldehyde. The tunneling frequencies suggest that some doubling of bands might be observed in the fingerprint region of the (27)Andreassen, A. L.;Zebelman, D.; Bauer, S. H. J.Am. Chem. SOC. 1971,93,1148-52.
The Journal of Physical Chemistry, Vol. 85, No. 7, 1981 917
IR spectrum of 1-D1D2, but not in that of 1-H1HP2* No such doubling is actually observable in the spectrum of 1-D1D2,29 possibly because of the coupled rotations of the trifluoromethyl group^.^ However such doubling has been observed in naphthazarin, 2, which has the same 0-0
/H (f’
‘0
2
u
distance and a local geometry around the functional group very similar to that of 1.3l It has been interpreted in just this way.31 V is very similar to a potential function which has recently been suggested for the bridging proton in 9hydroxyphenalenone, on the basis of its fluorescence and fluorescence excitation spectra.32 (28)Wood, J. L. J. Mol. Struct. 1972,13,141-53. (29) Ogoshi,H.; Nakamoto, K. J. Chern. Phys. 1966,46,3113. (30)Busch, J. H.; Fluder, E. M.; de la Vega, J. R. J. Am. Chern. SOC. 1980,102,4000. (31)Bratan, S.;Strohbursch, F. J.Mol. Struct. 1980,61, 409-14. (32)Rossetti, R.;Haddon, R. C.; Brus, L. E. J. Am. Chem. SOC.,in press.
