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determined as 3.5; pK1 of benzimidazole was found as 5.4. Since at these pH values cyl for both is equal to 1.0, the increase of rate with p H results from CYZ mainly. The enhanced rates of the polymers vs. the monomers in these particular cases is therefore mainly due to a modified contribution of the anionic fractions of the polymers. 143th poly4(5)-vinylimidazole and the negatively charged substrate NABA the results were similar to those previously observed by Letsinger and Savereide12 for analogous systems. The protonated sites (an), which do not catalyze the hydrolysis of PNPA, serve as binding sites for NABA. As a result a bell-shaped pH-rate profile was observed (Fig. 2 ) with a strong maximum near p H 7 . 5 , At this point the catalytic rate of poly-4(5)-vinylimidazole is five times faster than t h a t of imidazole with NABA, and ca. 12 times the latter's rate with PNPA. On the other hand, while a t pH 8.0 the catalytic activity of poly-5(6)-vinylbenzimidazole with NABA was found comparable to t h a t of benzimidazole, a t pH 10.0 the polymer was found to be 50-fold faster than the monomer. Since at these pH values cy0 for t'his polymer is zero, the enhancement in this case can be only explained as for the neutral substrate. Acknowledgment.-The authors are indebted to Professor Herbert Morawetz for his stimulating and helpful advice. Financial support by the United States Chemical Corps is gratefully acknowledged.
mann distribution for the conformers leads to the following expression relating RoT to R a and R b
+ exp ( - A G " / N k T ) ] - '
4- Rb (1) Here N is Avogadro's number, k is Boltzmann's constant, and AGO is the standard Gibbs free energy change for the reaction a e b. The equilibrium constant K can be written as ROT
=
(Ra - R b ) [ l
K
=
( R , - RoT)/(RaT- Rb)
+
(2)
According to eq. 1, a plot of ROTvs.l,'[l exp (-AGO/ N k T ) ] should yield a straight line for the proper temperature-dependent values of AGO. If AGO is in fact a constant over the temperature range studied, then substitution of various trial values for AGO into eq. 1 yields a family of curves, only one of which (that for the proper AGO) is a straight l i r ~ e . ~From . ~ the slope and intercept of this line one can obtain the correct values for Ra and R b , which, when substituted into eq. 2, provide an explicit temperature-dependent expression for K in terms of the experimental Ro'. It is noteworthy that one obtains specific values for the rotational strengths (Ra and R b ) of the nonisolatable forms a and b. Without solvent corrections. these values refer to the apparent rotational strengths in solution, rather than to their values in vacz~o. HowI'ever, because K appears as a ratio of R-values, the equilibrium constant can be shown to be largely independent of these solvent corrections if the solvation (12) K . L. Letsinger and T. J . Savereide, J . A m . Chem. SOC.,84, 114, 3122 effects themselves are not markedly temperature de(1962); and also cf. H. Ladenheim, E. M . Loebl, and H . Morawetz, ibid., pendent, as often seems to be the case.8 Hence the 81, 20 (1959). K-value obtained is a reasonable reflection of the C . G. OVERBERCER T. ST.PIERRE population of conformers present Moreover, it folDEPARTMENT OF CHEMISTRY K. VORCHHEIMER lows as a corollary that once one obtains R a and R b POLYTECHSIC ISSTITUTE OF BROOKLYN S . YAROSLAVSKY values in one solvent, K can be found in any other BROOKLVN 1, SEW YORK RECEIVED AUGUST9, 1963 solvent a t any temperature T simply by measuring ROTfor that solvent. .-I facile meansfor obtaining K in a variety of solvents i s therefore available. Conformer Populations and Thermodynamic Data from By way of specific example, we consider the equilibTemperature Dependent Circular Dichroism rium I, e I, in (+)-trans-2-chloro-3-methylcyclohexanone in EPA.3 Some of the curves corresponding to Measurements', the plot of eq. 1 are indicated in Fig. 1. An optimized6 Sir: straight line is obtained for AGO = 1.72 kcal. 'mole, Recent measurements3 of circular dichroism (C.D.) with Ra = f 2 . 3 4 X c.g.s. and R b = -34.7 X curves over relatively large ranges of temperature open c.g.s. This value for AGO is good to +0.09 a new door to comparatively accurate information on kcal.imole. Since AGO is assumed to be temperaturethe population of conformers in flexible, optically active independent, AHo = AGO, and A S o = 0 for the molecules. Under favorable circumstances, AGO,A H o , equilibrium I e e I a . and A S o pertinent to the distribution of conformers may Conformer populations in various solvents a t 2.io, be derived from the C.D. data. I n addition, similar calculated from the preceding values of Ra and R b in information relating to solvation of an optically active conjunction with measured3 vaues of RoZg8, are given in species can sometimes be obtained. We confine Table I along ,with estimates obtained previously ourselves in the present note to a quantitative treatment from ultraviolet and optical rotatory dispersion data. of a two-conformer equilibrium, and adapt to our The three sets of percentages agree within the stated purposes a type of analysis used previously in connection error limits. with monochromatic rotations.4 For a particular absorption band, the observed total rotational strength R O T a t temperature T can be derived5 from the relevant C.D. curve. If R a and R b denote the rotational strengths associated with the lower energy conformer a and the higher energy conformer b , respectively, then assumption of a Boltz(1) Paper X C l I I in t h e Stanford series "Optical Rotatory Ilispersion Studies." For preceding article see C . Iljerassi, J . Burakevich. J W. Chamberlin, 1). Elad, .'l T o d a , a n d G Stork, J . A n . C h ~ m Snc., . in press. (2) Financial support from t h e Alfred P. Sloan Foundation (A.M.) and the National Science Foundation (Grant G-19905 t o Stanford University) is gratefully acknowledged. (8) K . M . Wellman, E. Bunnenberg, and C. Iljerassi. J . A m . C h e m S O C . . 8S, 1870 (1963). Some of t h e d a t a and representative C . D . curves used in the present analysis m a y be found here. (4) W. W. Wood, W. Fickett, and J . G. Kirkwood, J . C h e m P k y s . . 20, A61 (19.52) (.5) C. Djerassi, "Optical Rotatory Dispersion," McGraw-Hill Book Co., New York, K.Y . , 1960, p. 164.
(6) A minimal least-squares fit to a straight line can be used t o obtain a better value for A G O than can be achieved visually from the plot. In the example of 1rniis-2-chlor1i-.i-methylc~~clr,hexanone ( I ) discussed later, we used such a least-squares procedurc. In this case, the eye could distinguish easily to better t h a n 0.05 kcal. mole (7) Equations of t h e mathematical forms 1 and 2 appear in connection with a variety of kinetic and spectroscopic measurements [see Iz I , Izliel, J . C h e m . Edzrc , 37, 126 (1960)l Ilata from such meaiuren~entsare amenable t o the present method of analysis so long a s the quantities analoaous t o R, and RI,(~.g.,n . m . r chemical shifts for pure conforiners) are temperature independent. and the other stated assumptions are met. ( 8 ) Calculation of Rn' from the raw txperimental d a t a must take accnunt of the concentration changes accompanying the volume variation with temperature, which also produce changes in the index o t refraction of the 2) 3 1,orentz-type correction facmedium. According t o the simple ( i i p tor, this implies a further correction for RUT. However, in those steroids studied so far which one may expect t o be rigid, the differences between RoT a t 2.5' and - 192' generally represent changes of less t h a n 4 % , and these differences have been both positive and negative. Hence, in the absence of further information, we have ignored a n y corrections due t o chanRes i n the index of refraction with temperature.
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The evidence cited includes the "small" low-field shifts of the proton resonances in hexamethyldisiloxane' and tris(trimethylsilyl)amine2 as against tetramethylsilane; the smaller low-field shifts with increasing n in the series (CHa)4-,,lZC1, and (CHa)a-I,lIHCl,, when hl is Si than when M is C s , r ; the decrease in shielding along the series (CH3);,SiX,X = F, C1. Rr, I s ; and the increase in J(I3CH3) in (1RCH3)SiX(12CH:,), and in J(2gSiH)in (12CEI:ij32ySiX along the series CH3 < F < C1 < Br < I . 5 W'e have recently studied several substituted methylsilanes and related alkanes; from the results, taken with published work, we conclude t h a t many of the so-called anomalies in the spectra of silicon compounds are also to be found in the spectra of similar derivatives of carbon, and t h a t it is a t present unjustified to use these effects as evidence in favor of the occurrence of n-bonding in silicon conipounds. The 0-proton shieldings in the series of compounds / I CH3SiH2Xdecrease along the series X = H . N , 0, F (which is consistent with increasing inductive deshielding), but increase along the series X = I , Br, 080 OBI 0.90 0.95 1.00 I/[ I eip(-AG./NkTi] C1, F6; a similar effect is observed both in the dimethylsilyl' and t r i m e t h y l ~ i l y l halides, ~ and has been exFig. 1. -Plot o f eq. 1 for various trial values of AGO (kcal./mole). plained for the last named derivatives in terms of A variation of Iioz with temperature can also be increasing (p d ) n-bonding between silicon and the found in situations where rigidity of the molecular halogen atoms in the order I < Br < C1 < F. The same framework would seem to preclude the possibility of effect, however, has been observed in e t h ~ l , iso~,~ radical conformational changes. For example, we have propyl,y,g and cyclohexyl'" halides. presobserved such temperature variations for ROTin camphor ent there is no satisfactory explanation for this, b u t and norcainphor. In these cases, no temperaturesince it occurs in compounds in which the a-atom is independent value for AGO would yield a straight line carbon, i t is unlikely to be caused by (p + d ) r-bonding. It is now clearly established that SiHXYZ resonance TABLE I chemical shifts are less sensitive than are C H X U Z ----Yc Diequatorial conformer-shifts to changes in the rest of the molecule6,'; this is Present UltraSolvent Ro2BR X lO*O C.L, d a t a violet" O.R.IXa true not only when the substituents are potentially Methanol + 1 40 97 f 2 100 99 strongly a-bonding groups, such as --OK or -C1. but Dioxane +0 .80 96 3~ 2 88 100 also for others (like -I, -Br, and -SR) which are unEI'A +0 42 95 f 2 likely to be involved in strong n-bonds. It is therefore CCI, -1 21 90 f 3 not surprising that CH3SiXYZ resonances are less Isooctane - 1 87 89 f 3 82 82 sensitive than CH3CXUZ resonances to changes in From J , Allingcr, S . L. Allinger, L . E. Geller, arid C . Djerassi, X, U,and 2 . Substitution of -I (or -Br) for (Si)H in J . O i g . Chcni., 26, 3321 (1961). These authors indicate an acthe three methylsilanes, for instance, shifts the curacy of about i10' I p-proton resonance 0.7 (or 0.5) p.p.m. to low field, while in alkanes the analogous substitution shifts are in the plot suggested for eq. 1, and these results are about 0.9 and 0.7 p.p.m., r e ~ p e c t i v e l y . ~For polar, indicative of nonnegligible A S o values, such as one might expect in the case of asymmetric s o l ~ a t i o n . ~ potentially strongly a-bonding groups, the shifts follow the same pattern : -F or -OR substitution shifts The analysis of these data in terms of this hypothesis in the methylsilanes are about 0.15 and 0.05 p.p.m. and the problems posed by a multiplicity of conformers to low field, respectively,'j as against substitution shifts will be treated in a later paper. for the same substituents in alkanes of some 0.3 and 0.1 ( Y ) A. hloscowitz. K . M. Wellman, and C. I)jerassi, Pvoc. iVoil. Acad. S c i . L ' S . . 60 ( N o v . , 1963). p,p,m,g There is no reason to conclude from these ( I O ) 1 7 e I l w of the Alfred P Sloan Foundation. data that there is any unusual bonding in the silicon ( I 1 ) National Institutes of Health Postdoctriral Fellow, 19li2-1903. compounds. ALBERTM O S C O W I T Z ~ ~ 1) EPART41 E S T 0 F c H E M ISTRY Rather more convincing evidence indicating (p d) UXIVERSITY OF MISSESOTA n-bonding conies from the high-field shifts of the SiH M I N T E APOLI s 14, M I N s E SOT A proton resonances of fluorosilane (0.05 p.p.m.),l 1 DEPARTSIEST OF CHEMISTRY KEITHWELL MAN^^ difluorosilane (0.20)," and methylfluorosilane (0.0:3)7; STANFORI) USIVERSITY CARLDJERASSI and of the P-proton resonances of methylfluorosilane STASFORD, CALIFORNIA RECEIVED AUGUST 30, 1963 (0.05)7 and dimethylfluorosilane (0.02)' on substitution of one of the (Si)H atoms by -F. Even this, however, is by no means decisive. I t is very dangerous Nuclear Magnetic Resonance Spectroscopy and to draw conclusions from changes in S i H chemical (p d) a-Bonding in Silicon Compounds (3) M ,P. Brown and I ) . E Webster, J . P h y s . Chem., 64, 658 (1900) 20
/
,
I 1
-+
-+
-
Sir: In several studies of the n.m.r. spectra of substituted methylsilanes, it has been concluded t h a t the results can best be explained in terms of (p --t d ) a-bonding between silicon and electronegative atoms or groups. l P 5 [ I ) H Schmidbaur a n d 51. Schmidt, J .4m C h e n t . Soc., 84, 10G5 (1962). ( 2 ) H Schmidbaur a n d M Schmidt, A n g e w . Chem. Inlerit E d . Etigl , 1, 327 (19(i2)
( 4 ) D . E. Webster, .I. Chem Soc., ,5132 (1900). S o c . , 86, 2331 (1903). (a) E . A . V . Ebsworth and S . G . Frankiss, T r a n s F a r a d a r Soc., 6 9 , 1.518 (1903) 17) E . A . V. Ebsworth a n d S.G Frankiss, unpublished observations ( 8 ) A . A . Bothner-By a n d S C S a a r - C o l i n , J . A m . Chem. Sor , 8 0 , 1728 (19.58). (9) J . R . Cavanaugh and B. P. Dailey, J C h e m . P h y s , 3 4 , IO99 ( I O i i l ) (10) W C . Neikam and B . P. Dailey, ibid., 38, 445 (1903) (11) E . A , V . Ebsworth and J . J . Turner, J. P h y s . Chem , 6'7, 805 ( 1 9 6 3 )
(a) H. Schmidbaur, J A m C h e m .
