4404
smaller volumes near the downstream end of the experimental section than did the products of low-temperature runs. Since quantities of product with significantly different reaction times were closest together following high-temperature runs, the lowering of calculated rate constants due to mixing would be largest for these runs, even if the extent of mixing were the same for all runs. From the pressure histories it seems likely that the extent of mixing, if any, would have increased with increasing reflected shock temperature: this would increase the error at the high end of the temperature range. We cannot assess the magnitude of mixing except to note that it was not extensive enough to introduce detectable amounts of driver gas into the product samples. However, as mixing should have no significant effect on the comparative rate analysis, this could explain the small divergence between comparative and absolute rate results in the 1100-1175" region and the resulting difference in activation energy values.
From our data and the arguments discussed above, we feel that the activation energy for tert-butyl alcohol decomposition to isobutene and water lies somewhere between 63.0 and 66.2 kcalimol. Because the 66.2-kcali mol value results in the best internal consistency among the many comparative rate experiments discussed in this report and leads to deduced parameters for a number of reactions that agree well with extrapolations of low-temperature work,10z11'26 h e favor the higher end of the acceptable range. Acknowledgment. We would like to thank the Sloan Foundation, the Carter-Wallace Foundation, and the Colgate University Research Council for financial support. The shock tube was donated to us by the Cabot Corporation. We would also like to thank Dr. Wing Tsang for suggesting the cyclohexene decyclization as the standard reaction for this comparative rate study.
Boron- 1 1 Nuclear Magnetic Resonance Chemical Shift Assignments for Monohalogenated Decaborane( 14) Isomers Richard F. Sprecher," la Brian E. Aufderheide,'" George W. Luther III,lb and James C. Carterlb
Contribution f r o m the Departments of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, and University of Pittsburgh, Pittsburgh, Pennsylvania 15213. Received December 18, 1973 Abstract: Boron-11 nmr chemical shifts have been assigned for all possible isomers of monochloro-, monobromo-, and monoiododecaborane(14) using the llB-llB double resonance technique. The properties of 5-chlorodecaborane(l4) and 6-iododecaborane(l4)were reported for the first time. Chemical shifts are found to depend on the halogen and the site of substitution in a regular manner. All shift trends are dominated by the influence of the 2p orbita! size on the paramagnetic shielding term (up). It was suggested that a small up accounts for the shielding of B2and Bqrelative to the rest of the cage. heories of the origin of the nmr chemical shift have been proposed by Saika and Slichter, 2a Karplus and Das,2band P ~ p l e . In ~ all of those treatments, the shielding at a particular atom was found to be separable into a diamagnetic atomic term, a paramagnetic atomic term, and a term due to neighboring atoms. Applications of these theories to chemical shifts by Karplus and P ~ p l e Pople,j ,~ and Cheney and Grant,6 to "B chemical shifts by Boer, et u I . , ~to I4N chemical shifts by Kent and Wagner,8 to I7O chemical shifts by Moniz and Poranski,g and to 19Fchemical shifts by Saika and SlichterZaand Karplus and DasZbhas resulted in confirmation of the theory and explanation of many em-
T
( 1 ) (a) Carnegie-Mellon University; (b) University of Pittsburgh. (2) (a) A . Saika and C. P. Slichter, J . Cheni. Pbj.s., 22, 26 (1954); ( b ) M. Karplus and T. P. Das, ibid.,34, 1683 (1961). (3) J. A . Pople, J . Chem. Phys., 37, 53 (1962). (4) M. Karplus and J. A. Pople, J . Chem. Phys., 38,2803 (1963). (5) J. A . Pople, Mol. Pbys., 7,301 (1964). (6) B. V. Cheney and D. &I. Grant, J . Amer. Chem. SOC.,89, 5319 ( 1967). (7) F. P. Boer, R. A. Hegstrom, M. D. Xewton, J. A . Potenza, and W. N. Lipscomb, J. Amcr. Chem. Soc., 88, 5340 (1966). (8) J. Kent and E . Wagner, J . Chem. Phys., 44, 3530 (1966). (9) W. B. Moniz and C. F. Poranski, Jr., J . .Wag!?. Resonunre, 11, 62(1973).
Journal of the American Chemical Society
pirical correlations. The theory has been extended to include the effects of bonding through d orbitals by Jameson and Gutowsky, l o who also discussed periodicities in the ranges of chemical shifts in terms of an explicit dependence of the paramagnetic term on the nuclear charge. A recent study of decaborane( 14) by Laws, et al.,ll gives a detailed picture of the electronic structure of the molecule but unfortunately does not give much attention to the problem of IlB chemical shifts. I. Discussion We have assigned all IlB nmr chemical shifts for all of the monochloro-, monobromo-, and monoiqdodecaboranes, using a double resonance technique,I2 and have compared the shifts with those of the parent compound. In order to explain the trends we see, one must assume that the contribution of the paramagnetic part of the (10) C. J. Jameson and H. S. Gutowsky, J . Chem. Phys., 40, i714 (1964). (11) E. A. Laws, R. M. Stevens, and W. N. Lipscomb, J. Amer. Chem. SOC.,94,4467 (1972). (12) R. F. Sprecher and J. C. Carter, J . Amer. Chem. Soc., 95, 2369 (1973).
1 96:14 1 July IO, 1974
4405 Table I. llB Chemical Shifts for Halogen-Substituted Decaborane(l4) Isomers as 0.1 M Solutions in CHzClz Referenced by External Replacement to 0.1 M TMB in CHsClz
Decaborane( 14) 1-Chlorodecaborane(l4) 2-Chlorodecaborane(14) 1-Bromodecaborane( 14) 2-Bromodecaborane( 14) 1-Iododecaborane(14) 2-Iododecaborane(l4) 5-Chlorodecaborane(14) 6-Chlorodecaborane(14) 5-Bromodecaborane( 14) 6-Bromodecaborane( 14) 5-Iododecaborane(14) 6-Iododecaborane( 14)
B,
B?
Bt
B4
B5
B6
B7
B8
Bs
Bio
6.2 -4.8 5.3 2.0 4.8 17.8 4.2 6.1 9.8 5.1 8.5 3.4 6.9
54.2 52.9 38.3 52.2 45.6 51.7 64.0 52.8 51.2 52.4 51.3 51.5 51.4
6.2 4.6 5.3 4.6 4.8 5.3 4.2 5.3 9.8 5.1 8.5 4.7 6.9
54.2 52.9 54.6 52.2 53.8 51.7 53.1 54.7 58.0 54.4 56.8 53.6 55.1
17.7 18.6 17.1 18.4 16.8 18.6 16.7 7.1 21.4 15.0 19.3 31.9 16.1
7.8 10.3 8.5 9.4 7.9 8.7 7.6 10.2 0.3 8.6 7.7 6.9 24.1
17.7 15.8 17.1 15.6 16.8 16.3 16.7 22.4 21.4 21.0 19.3 18.3 16.1
17.7 15.8 18.6 15.6 17.9 16.3 17.5 19.2 16.8 18.8 17.1 17.6 17.8
7.8 10.3 11.9 9.4 10.4 8.7 8.9 7.0 8.8 7.3 8.5 7.3 7.0
17.7 18.6 18.6 18.4 17.9 18.6 17.5 14.1 16.8 14.3 17.1 13.6 17.8
-.-
~~
BORON BONDED TO HALOGEN
5.01 4.0
1 -HALODECABORANES
2-HALODECABORANES
5-HALODECAB0RANES
6-HALOOECABORANES
4
5,7-
1,3-
9
8,lO
-2 -4.0 -
Figure 2. The chemical shift of the nonsubstituted borons relative to the shift of the equivalent boron in decaborane(l4). Positive A corresponds to an upfield shift.
I
I 3.0 2.8 2.5 _.ELECTRONEGATIVITY OF HALOGEN SUBSTITUENT I
Figure 1. The chemical shift of the halogen-substituted boron in the halodecaboranes relative to the shift of the equivalent boron in decaborane( 14). Positive A corresponds to a n upfield shift.
shielding tensor dominates the trends. The detailed shift data and assignments are presented in Table I. Chemical shifts relative to equivalent atoms in decaborane(l4) are presented in Figures l and 2. For want of a simple correlation, the data are presented as functions of the electronegativity of the halogen. Shielding of the Substituted Boron. Inspection of Figure 1 immediately reveals a trend of increasing shielding of the substituted atom in the order a(B-C1) < a(B-Br) < a(B-I). This trend should be explicable in terms of the anisotropic susceptibility of the halogen atom and an induced paramagnetic shielding at the substituted boron atom. Pople13 has calculated the principal components of the susceptibility tensor for 19F. From his equations and values of ( r 3 given ) by Jameson and Gutowskylo for the other halogens, one can readily infer that the anisotropies of the atomic susceptibilities (Ax) will be in the order Ax(F) > Ax(C1) > Ax(Br) > Ax(]), if we assume that the contribution from (13) J. A. Pople, J . Chem. Phys., 37,60 (1962).
the filled d and f orbitals is small. Because Ax(X) is in the sense of excess diamagnetism along the B-X bond axis, we must expect shielding at boron in the ordzr o(B-F) > a(B-Cl) > a(B-Br) > a(B-I). Such is not the case and we look to the induced paramagnetic term for an explanation. As noted by Karplus and P ~ p l e , ~ an electronegative substituent can contribute to a paramagnetic shielding (a,"") through the polarity parameterI4 and through changes in the dimension of the 2p orbital on the atom induced by changes in the orbital population. While the first effect is expected to be small4and yields the trend laPAA(B-Cl)I< ~ u , " ~ ( B - B ~ ) ~ < Iqp""(B-I)l, the second effect can be expected to be significant. The influence of ( ~ - changes 9 ~ ~ on 13C shifts is well d o c ~ m e n t e d . ~ -While ~ llB shifts should be less sensitive to orbital population changes because of the smaller effective 2 for llB, the term must still be important. The effect of the electronegativity of the halogen on ( ~ - ~ ) leads 2 ~ to paramagnetic terms in the > lapAA(B-Br)/> lupAA(B-I~), which order /aPAA(B-Cl)~ agrees with the observed trend. Substitution of I for H leads to shielding of the substituted boron and is readily explained by the observation that Ax(H) must be zero.I3 Thus, B-X must be shielded relative to B-H. Part of this shielding is canceled by apAA and the superposition of the opposing trends leads to a roughly linear correlation of A6 with electronegativity as seen in Figure (14) C. A. Coulson, "Valence," Oxford University Press, New York, N. Y., 1952.
Sprecher, et al. / Boron-I1 Chemical Shifts of Halogenated Decaboranes
4406
hydrogen at Bg or Bg would seem to be reflecting the electron deficient nature of that part of the cage. However, interaction between the halogen n orbitals and open three-center boron bonds should be stronger than the corresponding interaction with closed three-center bonds. In addition, ( r 3 ) a P is more sensitive to change in orbital population when that population is small. Because all of these effects are expected to yield the same trends, we decline to single out one of them without detailed calculations. The regular decrease in k , on going through the series C1, Br, and I is as we expect on Figure 3. Numbering scheme and topological representation for the basis of decreasing overlap between the halogen n decaborane(l4) (B = B-H). orbitals and the cage. The relative insensitivity to substitution at BI coupled with a strong correlation of 1. The smaller dependence on the site of substitution that with the Hammett CJ leads us to suspect an inparallels a trend in the variance of A6 for the unsubductive component to the trends but we would not exstituted atoms. As we will show later, this may relate pect it to be a long-range effect,fiand it is certainly not to interactions between the nonbonding orbitals on the a dominant one in the Ba-, Bj-, and Be-substituted halogen and the bonding orbitals in the cage. series. Shielding of the Unsubstituted Borons. In the average Examination of Figure 2 reveals a regular pattern in excitation energy approximation, one generally assumes the direction of the shifts relative to decaborane( 14). the mean excitation energy does not vary in the series Atoms directly attached to the substituted site tend to be under consideration. We feel this approximation is deshielded and those with one atom intervening tend to justified here, for although decaborane(l4) has lowbe shielded. Long-range effects are also obvious with lying nonbonding orbitals, the electron-deficient the most striking being the behavior of Bg on C1 subnature of the bonding results in 16 unoccupied levels stitution at B?. A full explanation of these datamust L’S. 8 occupied levels in a minimum basis set calculation. await a detailed quantum mechanical treatment. Thus perturbation of a few unoccupied levels is not Shielding in Decaborane(l4). We feel that enough likely to affect KE strongly. Of greater consequence qualitative trends are available to allow us to suggest an could be the perturbation of an occupied bonding level. origin for the decaborane( 14) shifts. Calculations by We assume that such a perturbation could arise from Lipscomb’j and Laws, et show a charge density in interactions between the nonbonding orbitals on the the algebraic order 2, 4 Br > I because the overlap between the 2s,p orbitrest of the cage. Accordingly, B1 and B3 are slightly deals on B and the ns,p orbitals on X decreases with inshielded relative to our expectations. This can be and ) iapAAl rationalized in terms of a small paramagnetic contribucreasing n. The result is an increase of ( r 3 with increasing n. We expect then to see a general tion at B1 and B3from local circulation on B, and BI. shielding in the order u(C1) > u(Br) > u(1). Such a 11. Results trend is seen in the mean shift values (G) for substitution at a particular site as shown in Table 11. The Syntheses. Decaborane( 14) has Cz, symmetry and shifts also show a variation in the sensitivity to the site of can be topologically1; represented by the diagram in substitution and the halogen substituent as indicated by Figure 3. Four different monosubstituted decaborane the variance (k2)of the shift from the mean value. isomers are possible if one of the nonbridged hydrogens The sensitivity toward substitution of chlorine for is replaced by some functional group. There are three halogenation reactions known, each of which produces varying mixtures of the four possible monohalo isomers. Table 11. Mean IIB Shifts Relative to Equivalent Atoms An uncatalyzed reaction of iodine with decaborane( 14) in Decaborane(l4). produces a mixture of 1- and 2-monoiodinated species. l 6 Site C1[0.37Ib Br[0.39] I[O. 351 An A1CI3-catalyzed reaction between decaborane( 14) I -0.13 ( 3 . 3 9 ) ~ -0.58 (2.81) -0.57 (2.20) and bromine or chlorine produces corresponding mix2 0.44 (2.46) -0.21 (1.52) -0.73 (0.96) tures of 1- and 2-brominated or 1- and 2-chlorinated 5 0 26(5.77) -0.28 (3.69) -1 .40 (2.29) decaboranes. l7 A mixture of decaborane isomers 6 1 .62 (6.96) 0.78 (3.33) -0.48 (1.67) halogenated at the 5 and 6 borons is obtained from the The shift of the substituted boron is not included in the calcureaction of the anhydrous hydrogen halide with a decalation. * Hammett u for halogens from J. Hine, “Physical Organic borane dialkyl sulfide diligand, BloHl2(SR?)9.ls The Chemistry,” McGraw-Hill, New York, N. Y , 1962, p 87. kr
a
~
~~
(variance as defined by E. S . Keeping, “Introduction to Statistical Inference,” Van Nostrand, Princeton, N. J.. 1962, p 36). (15) W. N. Lipscomb, “Boron Hydrides,” W. A. Benjamin, New York, N. Y . , 1963.
Journul of the American Chemical Society
1 96: I4
July IO, 1974
(16) M.Hillman, J . A m e r . Chem. Soc., 82, 1096 (1960). (17) L. Zakharkin and V. Kalinin, Zh. Obshch. Khinz., 36, 2160 (1966). (18) B. Stibr, J. PleSrk, and S . Heiminek, Collect. Czech. Chem. Commun., 34,194 (1969).
4407
ligand is made by direct combination of decaborane( 14) and the dialkyl sulfide. In most cases, these halogenation reactions also produce small amounts of other monohalogenated and dihalogenated products. Shift Assignments. Boron- 11 nuclear magnetic resonance shift assignments have been made for decaborane(l4) through a series of iodination1g and deuteration20 studies. Tentative shift assignments have also been made for some of the monohalogenated decaboranes. 21--2 Recently, l ’B double resonance experiments were used to obtain chemical shift assignments for 6-methyldecaborane( 14). l 2 We have used the same technique to obtain complete *lB shift assignments for the 12 possible chlorinated, brominated, and iodinated decaboranes. The lB-l lB double resonance experiment is similar to the transitory selective irradiation experiment described by Hoffman and Forsin,*j except that the observing field ( H I ) is not swept through the transition under examination but rather remains on that transition throughout the experiment. The perturbing field ( H 2 ) is swept through the remainder of the spectrum repeatedly and the response to HI is accumulated as a function of the frequency of H?. We follow Hoffman and Forse‘n in the analysis of the intensity perturbations to be expected in the experiment. For simplicity we will consider two coupled spin 3/2 nuclei in the limit of 6 >> J . The product functions are then the eigenfunctions and the energy level diagram is that given by Sprecher and CarterI2and is reproduced in Figure 4. The spectrum is seen to be composed of two sets of four triply degenerate lines. In the hightemperature limit the equilibrium population of a state is given by
P
=
a=+$
g.-9
outermost lines of the connected multiplet. The directions of the intensity changes will reverse if the high-field side rather than the low-field side of the resonance is monitored. In order to attain an adiabatic fast passage of H2, the sweep rate and Hz must satisfy the relationship
Ti-’
(19) R. Schaeffer, J. N. Shoolery, and R. Jones, J . Amer. Chem. 79.4606 (1957). (20) R . E. Williams and I. Shapiro, J . Chem. Phys., 29,677 (1958). (21) R. Schaeffer, J. N. Shoolery, andR. Jones, J . Amer. Chem. SOC., 80.2670 (1958). (22) R‘. E. Williams and T, P. Onak, J . Amer. Chem. Soc., 86, 3159 (1964). (23) R. E. Williams and E. Pier, Inorg. Chem., 4, 1357 (1965). (24) P. Sedmera, F. Hanousek, and Z. Samek, Collect. Czech. Chem. Commun., 33,2169 (1968). (25) R. A. Hoffman and S . Forsen, “Progress in Nuclear Magnetic Resonance Spectroscopy,” Vol. 1, Pergammon Press, Oxford, 1966.
p+&y . - l
Figure 4. Energy levels and transitions for two coupled spin nuclei.
No(1 - (F&o/kT))
where No is the average population, F, is the total spin in units of h/2a, and vo is the mean precession frequency. If we let NohvolkTbe represented by K and discuss populations relative to No, then the equilibrium population of state 66 is 3K, that of states 6y and y6 is 2K, and so on. To first order the sum of the equilibrium intensities of transitions 1, 3, and 7 is 3K. After an adiabatic fast passage of H2 through the degenerate transitions 2, 6, and 12, the populations of states 66 and a8 will be interchanged, as will those of states y6 and PS. The sum of intensities of transitions I, 3, and 7 will be OK after the passage and the change will be -3K. Similar reasoning leads to a change of OK on passage through 4, 10, 14 and 8, 16, 20 and a change of 3K on passage through 18, 22, 24. The same considerations lead to changes in the intensity of 5, 9, 17 of -K, 0, 0, and K on passage through 2, 6, 12; 4, 10, 14; 8, 16, 20; and 18, 22, 24. Thus, we expect H2 to have the largest effect on the outermost lines of the monitored multiplet and then only when H2 passes through the Soc..
ENERGY LEVELS AND TRANSITIONS F O R TWO COUPLED SPIN $ NUCLEI
