JOURNAL O F T H E A M E R I C A N C H E M I C A L SOCIETY Reeirlered i n U.S. Patent Ofice.
@ Copyripkt
1974 b y the American Chemical Socirly
VOLUME96, NUMBER 12
JUNE12, 1974
Chlorine Kinetic Isotope Effect Models. 11.’ Vibrational Analysis and KIE Calculations of tert-Butyl Chloride Transition State Models Robert C. Williams and James W. Taylor”
Contribution f r o m the Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706. Received January 11, 1974 Abstract: A transition state model is advanced for the methanol solvolysis of tert-butyl chloride, and various transition state structures are evaluated in terms of their calculated chlorine kinetic isotope effects. The best model gives chlorine KIE values of 1.01087 and 1.00951 at 10 and 60°, respectively, us. the experimentally determined values of 1.01087 and 1.00953, and does not require large imaginary values of YL. The influence of transition state geometry on calculated KIE is appreciable; there is a good correlation between the transition state carbon-chlorine bond length and the difference in KIE values at 10 and 60”. The degree of planarity of the C(CH,), group correL , does the carbon-methyl group bond length. The lates well with the temperature-independent factor Y ~ L / Y ~ as most probablq transition state c9nfiguration in the methtnol solvolysis of tert-butyl chloride is estimated to be C-Cl = 1.89 A, C-CHa = 1.50 A, and Z(CHa) = -0.16 A, relative to the central carbon. The efiects of various transition state force constant assumptions are studied, and methods of estimating transition state force constants are enumerated.
H
eavy atom kinetic isotope effects (KIE) have shown promise as a useful tool both for studying fundamental chemical processes and for elucidating the transition state. 2-8 Unfortunately, this promise has only been partially fulfilled to date, and most of the information about transition state structures has been obtained by i n f e r e n ~ e . ~ - lIn ~ testing other techniques for im(1) Taken in part from the Ph.D. Dissertation of R. C. Williams, Universitv of Wisconsin. 1972. (2) L. Melander, “Isdtope Effects on Reaction Rates,” Ronald Press, New York, N. Y., 1960. (3) (a) M. Wolfsberg, Annu. Reo. Phys. Chem., 20, 449 (1969); (b) Accounts Chem. Res., 7.225 (1972). (4) W. A. van Hook in ‘‘Isotone Effects on Chemical Reactions.” C.‘J. Collins and N. S. Bowman,*Ed., Van Nostrand-Reinhold, New York, N. Y., 1970. ( 5 ) A. Fry in ref 4. (6) E. R. Thornton, ”Solvolysis Mechanisms,” Ronald Press, New York, N. Y., 1964, pp 194-229. (7) L. B. Sims, A. Fry, L. T. Netherton, J. C. Wilson, K. D. Reppond, and S. W. Cook, J . Amer. Chem. SOC.,94,1364 (1972). (8) C. R. Turnquist, J. W. Taylor, E. P. Grimsrud, and R. C. Williams, J. Amer. Chem. Soc., 95,4133 (1973). (9) J. C. Harris and J. L. Kurz, J . Amer. Chem. Soc., 92,349 (1970). (10) E. R. Thornton, J. Amer. Chem. Soc., 89,2915 (1967). (11) C. G.Swain and E. R. Thornton, J. Amer. Chem. SOC.,84, 817 (1962). (12) E. P. Grimsrud and J. W . Taylor, J. Amer. Chem. Soc., 92, 739 (1970). (13) E. P. Grimsrud, “Chlorine Kinetic Isotope Effects in Nucleophilic Displacement Reactions,” Ph.D. Dissertation, University of Wisconsin, 1970. (14) N. Pearson, “A Carbon-14 Kinetic Isotope Effect Study of Nucleophilic Substitution,” Ph.D. Dissertation, University of Arkansas, 1970.
proving this situation Wolfsberg and Stern have extensively studied the KIE temperature dependence of model systems resembling methyl halides but have cautioned against applying their generalized results to specific experimental systems. 15 Stern and coworke r ~ have ~ ~also, made ~ ~ a rather elegant study of the variation in temperature dependence of isotope equilibrium. Because these were equilibrium calculations, somewhat less information could be inferred about transition states. For intramolecular decarboxylation reactions Yankwich and coworkers have made a very complete model study of the temperature dependence and have derived conclusions about the transition state for this class of reactions. l * $l9 As a continuation of previous work from these laboratories where the ground state force constants and isotopic separations of the skeletal vibrational frequencies of tert-butyl chloride were considered using a methyl chloride type it was decided to attempt (15) M. Wolfsberg and M. J . Stern, Pure Appl. Chem., 8, 225, 325 (1964). (16) W. Spindel, M. J. Stern, and E. U. Monse, J. Chem. Phys., 52, 2022 (1970). (17) M. J. Stern, W. Spindel, and E. U. Monse, J . Chem. Phus., 45, 2618 (1966). (18) T . T. S. Huang, W. J. Kass, W. E. Buddenbaum, and P. E. Yankwich, J. Phys. Chem., 72,4431 (1968). (19) J. H. Keller and P. E. Yankwich, J. Amer. Chem. Soc., 95, 7968 ( 1 973). -,. \ - -
(20) Part I: R. C. Williams and J. W. Taylor, J . Amer. Chem. SoC., 95, 1710 (1973).
3721
3722
to describe the transition state in terms of the transition Using these boundaries, a set of models was generated state geometry, the transition state force field, and the as shown in Table I where one or more of these paramcalculated temuerature deDendence of the kinetic isotope effect for. this m o d i . Particular emphasis was Table I. Initial Transition State Models placed on determining the effect that each of several ----Bond distances, A---geometric parameters (C-C1 transition state bond Model (C-Cl) (C-CHI) Z(CH3P MMlb length, degree of nonplanarity, and carbon-carbon 1.80 1.53 transition state bond length) has on the temperature -0.473 1 . 0000 1.80 1.46 16 0.0 1.0025 dependence and final KIE value. The influence of off1.98 1.46 17 1.001 I 0.0 diagonal (interaction) force constants and bending vibra1.89 1.53 18 0.0 1 ,0026 tions was also of special interest. It was expected that 1.89 1.50 19 1.0023 0.0 in the studies with the transition state models, it would 1.89 1.46 20 1.0018 0.0 1.89 21 1.42 1.0014 0.0 also be possible to evaluate several commonly used ap1.89 1.50 22 -0.01 1 ,0022 proximations and determine their accuracy relative to 1.89 23 1.50 -0.16 1.0012 the more rigorous calculations involving the complete 1.89 24 1.50 -0.32 1.0001 partition functions. 1.89 1.50 25 -0.473 0.9991 26 I .80 1.50 1.0030 0.0 Selection of Transition State Models. As in the 1.98 1.50 27 0.0 1.0015 ground state case, methyl groups were assumed to be 2.16 1.50 28 0.0 1.0002 point masses, the skeletal vibrations were assumed to be 29 2.70 1.50 0.9972 0.0 separable from hydrogen modes, and the hydrogen 30 4.50 1.50 0.9927 0.0 vibrations were assumed to be negligibly affected by 1.89 31 1.0017 1.50 -0.08 1.89 1.50 32 1.0007 -0.24 chlorine substitution on the central carbon. The 1.80 33 1.0019 1.50 -0.16 choice of a transition state geometry is more complicated 34 I .98 1 ,0005 1.50 -0.16 than in the previously discussed ground state case20 be35 1.89 1.53 -0.16 1.0015 cause no vibrations can be measured directly. The 36 1.89 1.46 1.0007 -0. I 6 approach must essentially be that of choosing extremes, The axis Z lies colinear with the C-Cl bond and is centered which encompass all reasonable transition state geomeabout the central carbon. * [(13;*/137 *)/(Z~;/13j)]”,[(M,-,i/ tries, then working within these extremes. The three M3i* ) / ( M 3 j / M 3 7 ) ] 3 / ~Ground . state configuration. geometric parameters, which together completely describe the molecule and whose extremes must be determined, eters was varied. The MMI (mass times moment of are the carbon-chlorine distance, the carbon-methyl of inertia) term ratios are fixed by the geometry,’j and distance, and the 2 coordinate of the methyl groups relathese are also listed as part of Table 1. In order to tive to the central carbon, where the carbon-chlorine probe the importance of each parameter and its inbond lies colinear with the Z axis. One might reasonfluence on the KIE calculations, model 19 was chosen ably expect these extremes to be represented by the as the primary planar model and model 23 was chosen reactant and product cation geometries. Olah and coas the nonplanar model. Other models were generated workersz1have shown that the carbon skeleton of tertby variation of one or two parameters from these basic butyl cation is planar by correlation of its infrared specconfigurations. These choices were made on the basis trum with that of trimethylboron, a molecule with which of preliminary calculations initiated from the expectait is isoelectronic. However, the central carbontion (Hammond postulatezG)that the transition state for methyl distanceois not well known. Olah, et a1.,**used the S N ~reaction should more closely resemble the proda value of 1.50 A for their normal coordinate analysis of uct than the reactant. On this basis, the most reasonthe catioa, but other workers have used values as small a_ble central carbon-methyl distance was taken to be 1.50 as 1.42 A, which is the measured (nonaromatic) interA, in carbon distance for the crystalline trimethyl c a t i ~ n . * ~ ~ ~ ~ accordance with Olah’s work. Similarly, the C(CH,), fragment was expected to be planar or near A conservative assignment for the tert-butyl Shloride planar. In choosing the C-Cl bond length, qualitacase might be between the bounds 1.42 and 1.53 A. For tive aides such as Pauling’sz7 and Badger’szsrules indithe carbon-chlorine {istance preliminary calculationsz5 cate that even small displacements from ground state have shown that 4.5 A (2.5 times the ground state C-C1 equilibrium cause drastic changes in force constants. distance) could be taken as the extreme. Finally, the This could be expected to be even more severe in solumethyl Z coordinate which represents the degree of tion, where solvent shielding is possible. In other calplanarity, or nonplanarity, of the $(CH3), portion might culations when changes in bond length have been be expected to have a value of 0 A if completely planar. made,7qi4,15 the maximum changes seem to be no more Values of 2 betweeathe planar extreme and the ground than 2 5 x of the ground state bond distance, and most state value (-0.47 A) were chosen for this parameter. of the changes are on the order of a few per cent. Both Models l 9 a n d 23 increase the c-cl distance Only (21) G. A. Olah, J. R . DeMember, A . Commeyras, and J. L . Bribes, J . Amer. Chem. Soc., 93,459 (1971). over the ground state value. (22) G. A. O W E. B. Baker, J. C. Evans, W. S. Tolgyesi, J. S. Selection of the Transition State Force Field and McIntyre, and I. J. Bastien, J. Amer. Chem. SOC.,86, 1360 (1964). (23) A. J. I
