Isotopes and Chemical Principles - ACS Publications

8 Isotope Effects and Reaction Mechanisms V. J. S H I N E R , JR.

Downloaded by CORNELL UNIV on May 26, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/bk-1975-0011.ch008

Department of Chemistry, Indiana University, Bloomington, Ind.

47401

Introduction T h e subject of t h i s c o n t r i b u t i o n i s so e x t e n s i v e , m a t u r e and w e l l - d e v e l o p e d that one c a n only hope i n the s p a c e a v a i l a b l e h e r e to g i v e the n o n - s p e c i a l i s t s o m e g e n e r a l knowledge of the u t i l i t y , the s c o p e and the l i m i t a t i o n s of the u s e of i s o t o p e r a t e effects i n the study of r e a c t i o n m e c h a n i s m s and an i n t r o d u c t i o n to the m o r e d e t a i l e d l i t e r a t u r e f o r those who m a y w i s h to d e l v e d e e p e r . It i s v e r y m u c h to be hoped that this t e c h n i q u e w i l l c o m e into o c c a s i o n a l , i f not r e g u l a r , u s e by a l l who u n d e r t a k e the i n v e s t i g a t i o n of r e a c t i o n m e c h a n i s m s and w i l l not be c o n s i d e r e d to lie m a i n l y i n the p r o v i n c e of those who m a k e i t a s p e c i a l t y . P r o b a b l y the m a i n barrier to m o r e g e n e r a l u s e of t h i s technique i s the s o m e what r e f i n e d a c c u r a c y g e n e r a l l y r e q u i r e d i n the m e a s u r e m e n t of r e a c t i o n r a t e s or i n the m e a s u r e m e n t of i s o t o p e r a t i o s if the competitive technique i s used. T h e s e experimental r e q u i r e m e n t s c a n be m a s t e r e d r e a s o n a b l y r e a d i l y w i t h the m o r e s o p h i s t i c a t e d c o m m e r c i a l i n s t r u m e n t s w h i c h a r e now g e n e r a l l y a v a i l able. I do not intend h e r e to d i s c u s s e x p e r i m e n t a l t e c h n i q u e s but r a t h e r the g e n e r a l f r a m e w o r k for the i n t e r p r e t a t i o n of r e s u l t s w h i c h has b e e n b u i l t up by m a n y i n v e s t i g a t o r s o v e r the c o u r s e of the l a s t t w e n t y - f i v e or so y e a r s . (1) T h e e a r l i e r c o n t r i b u t o r s to this s y m p o s i u m have outlined the b a s i c t h e o r y of the i n t e r p r e t a t i o n of the e f f e c t s of i s o t o p i c s u b s t i tution on r e a c t i o n r a t e s o r i g i n a l l y d e v e l o p e d i n d e p e n d e n t l y by B i g e l e i s e n and M a y e r (2) and M e l a n d e r . (3) T h e y showed that i t i s the g e o m e t r i c a l s t r u c t u r e , n u c l e a r m a s s e s and, m o s t i m p o r tantly, the v i b r a t i o n a l f o r c e f i e l d s of i n i t i a l and t r a n s i t i o n states that d e t e r m i n e the m a g n i t u d e of i s o t o p e effects on r e a c t i o n r a t e s . S i n c e t h e s e p r o p e r t i e s of the i n i t i a l state r e a e t a n t s a r e subj e c t to r e a s o n a b l y d i r e c t o b s e r v a t i o n or d e r i v a t i o n , the r e a c t i o n m e c h a n i s m s c h e m i s t uses experimentally m e a s u r e d isotope effects on r e a c t i o n r a t e s p r i n c i p a l l y as a p r o b e f o r f e a t u r e s of the t r a n s i t i o n state v i b r a t i o n a l f o r c e f i e l d . P r i m a r i l y t h r o u g h

163

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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the e f f o r t s of W o l f s b e r g and S t e r n (4,5,6) c o m p u t e r p r o g r a m s a r e a v a i l a b l e w h i c h a l l o w the c a l c u l a t i o n of expected i s o t o p e r a t e effects f r o m c o m p l e t e l y s p e c i f i e d s t r u c t u r e s and f o r c e f i e l d s of r e a c t a n t and t r a n s i t i o n states c o n t a i n i n g up to 30 a t o m s . This k i n d of d e t a i l e d m o d e l l i n g has been s e r i o u s l y i n v e s t i g a t e d f o r only a r e l a t i v e l y s m a l l n u m b e r of r e a l r e a c t i o n s . (7,8,9,10) S u c h a n a l y s e s a r e c r u c i a l to a g r e a t e r u n d e r s t a n d i n g of tEe~prec i s e d e t a i l s of r e a c t i o n s but p r e s e n t l y this a s p e c t of the subject i s s t i l l i n i t s i n f a n c y and v e r y m u c h i n the p r o v i n c e of s p e c i a l i s t s . R a t h e r than r e v i e w t h e s e quantitative r e s u l t s I w i l l h e r e t r y to i l l u s t r a t e s o m e of the g e n e r a l q u a l i t a t i v e f e a t u r e s of the t h e o r e t i c a l a n a l y s i s that can be u s e d by r e a c t i o n m e c h a n i s m s c h e m i s t s a l o n g w i t h other e l e m e n t s of t h e i r t r a d i t i o n a l a r m a m e n t a r i u m to d i s t i n g u i s h a m o n g a p r i o i m e c h a n i s t i c p o s s i b i l i t i e s . T h e t r a d i t i o n a l r e a c t i o n m e c h a n i s m s c h e m i s t i s at s o m e w h a t of a d i s a d v a n t a g e t h i n k i n g i n t e r m s of t r a n s i t i o n state f o r c e f i e l d s a n d / o r v i b r a t i o n f r e q u e n c i e s b e c a u s e m o s t other t e c h n i q u e s f a m i l i a r to h i m do not r e l a t e d i r e c t l y to f o r c e f i e l d s but to s u c h " e l e c t r o n i c " p r o p e r t i e s as total e n e r g y , e l e c t r o n d i s t r i b u t i o n , d i p o l e m o m e n t or g e o m e t r i c s t r u c t u r e . Of c o u r s e a l l of t h e s e things a r e r e l a t e d t h r o u g h f u n d a m e n t a l t h e o r y , but so f a r quan t u m m e c h a n i c a l c a l c u l a t i o n s have not y i e l d e d v e r y s u c c e s s f u l explanations of s u c h things as the effects of substituents on r e a c tion r a t e s of o r g a n i c c o m p o u n d s . N e i t h e r h a v e they yet p r o v i d e d v e r y a c c u r a t e f o r c e constants for h y p o t h e t i c a l t r a n s i t i o n states, but I think i t i s r e a s o n a b l e to hope f o r p r o g r e s s t o w a r d this g o a l and I would e n c o u r a g e t h e o r e t i c i a n s to give m o r e thought and effort to the c a l c u l a t i o n of m o l e c u l a r f o r c e constants. Success i n t h e s e e f f o r t s would g r e a t l y a s s i s t i n the m e c h a n i s t i c i n t e r p r e t a t i o n of i s o t o p e e f f e c t s . P r i m a r y Isotope E f f e c t s If we c o n s i d e r the d i s s o c i a t i o n of a d i a t o m i c m o l e c u l e , the e n e r g e t i c s of the s y s t e m can be q u a l i t a t i v e l y r e p r e s e n t e d as i n f i g u r e 1, w h e r e i n i t i s a s s u m e d for p u r p o s e s of s i m p l i c i t y that the t e m p e r a t u r e i s low enough so that a l l m o l e c u l e s a r e i n t h e i r l o w e s t v i b r a t i o n a l state and t h e r e f o r e contain the z e r o point v i b r a t i o n a l energy. S i n c e , by the B o r n - O p p e n h e i m e r a p p r o x i m a t i o n the m o l e c u l a r e n e r g y and t h e r e f o r e the i n t e r a t o m i c r e s t o r i n g f o r c e s depend only on n u c l e a r and e l e c t r o n i c c h a r g e s and not on the n u c l e a r m a s s e s , the v i b r a t i o n a l f o r c e constants w i l l be the s a m e f o r both i s o t o p i c m o l e c u l e s . H o w e v e r , the h e a v i e r m o l e c u l e , A - Β w i l l v i b r a t e m o r e slowly, as expected f r o m Hook's Law, than the l i g h t e r m o l e c u l e *A-B. S i n c e the z e r o point e n e r gy i s p r o p o r t i o n a l to the v i b r a t i o n f r e q u e n c y , A - B r e s t s l o w e r i n the p o t e n t i a l w e l l than *A-B and r e q u i r e s a h i g h e r " a c t i v a t i o n e n e r g y " to r a i s e i t to the d i s s o c i a t e d state. It t h e r e f o r e should on the a v e r a g e a t t a i n that state at a s l o w e r r a t e than the l i g h t e r m o l e c u l e and we expect a n o r m a l i s o t o p e r a t e effect, i . e. , the lighter molecule reacts faster. 2

2


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Of course, translational and rotational partition functions are usually different for molecules differing in isotopic substitu tion and,in general,will change on activation,leading to effects on reaction rates. Kinetic isotope effects from these sources are, however, generally dominated by the vibrational zero-point ener gy effects which are the main focus of all general, qualitative discussions. This simply explains the occurrence of a primary isotope rate effect, "primary" referring to the fact that the rate deter mining step involves a bond to the isotopically substituted atom. However, many reactions which show large primary isotope ef fects do not involve dissociation into free particles but rather are displacement reactions wherein the isotopic atom is abstrac ted by an attacking agent. Since the isotopic atom is bound both in reactant and product and is bound also in the transition state, how can the occurrence of large isotope effects in such proces ses be explained? This can be seen with the aid of figure 2 wherein the zero point energy levels are depicted qualitatively for diatomic initial and final states and for the triatomic "abstraction" transition state. (The inclusion of bending modes for the transition state is necessary, of course, in a rigorous treatment but will be ignor ed for simplicity in the qualitative argument. ) The stretching motions of the triatomic transition state can be visualized in the same way that one would visualize the stretching modes for a stable molecule, except that, from tran sition state theory, we expect one of these modes to have no re storing force but rather to be replaced by a translation in one direction to give products and in the other direction to give re aetants. The arrows in the center of the figure represent the atomic movements expected for triatomic molecular stretching motions. The symmetrical stretch, ν , has a restoring force and is a normal vibrational mode of the transition state. One i n tuitively knows this because if there were no restoring force for this motion it would continue indefinitely with the resulting dis sociation of all three atoms giving a reaction which is not the ab straction process. The asymmetrical stretching mode expected for a normal molecule i s , for the triatomic abstraction transi tion sta^te, the reaction coordinate; in this motion in one direc tion, v^, the C A bond contracts while the A B bond stretches, there is no restoring force and the continuation of t h i | transla tion produces products; the reverse of this motion, ν , produces reaetants. It is important to note that i f the transition state is symmetrical with the force of attraction between A and Β equal to that between A and C and if the masses of Β and C are equal, the frequency of the symmetric stretching mode will be the same for both isotopes of A, since A will not move in this vibration. Even if the transition state is not quite symmetrical the motion of A in the symmetrical stretching vibration will be relatively ς


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166

Figure 2.

Abstraction reactions. C + *A — Β

—» C — *A + Β.


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unimportant and the zero point energy difference between the isotopic molecules will be small. Thus,for the symmetrical iso topic transition states in the abstraction reaction, there is no difference in zero point energies and one expects a large p r i mary isotope effect because the difference in zero point energies in the initial state contributes to make the activation energy for the lighter isotope smaller than that for the heavier isotope. This analysis has always appealed to me as one of the nicest ex perimental demonstrations of the major hypothesis of transition state theory. The primary isotope effect shows that the transi tion state has a translational degree of freedom which replaces a vibrational one expected in a normal molecule. Thus, whether the reaction involves a dissociation or a trans fer, a simple diatomic molecular model can give useful semi quantitative results indicative of the typical large primary iso tope effects which might be observed for a simple bond cleavage. Some values calculated in this way are shown in Table 1. (11) In most cases primary isotope effects about this size have been observed, and results of this magnitude are taken as prima facie evidence that the isotopically substituted bond is being broken in the rate-determining step. There is another obvious qualitative problem that immediate ly arises in examining any reasonably large collection of p r i mary isotope effect data, particularly results on isotope effects in hydrogen transfer reactions. This is that many isotope ef fects in abstraction reactions are much smaller than the expec ted maxima. One explanation, due to Westheimer (12) and to Melander, (13) as to how this can arise is illustrated qualitative ly in figure 3. In a very exergonic reaction, the reaction coordi nate involves a stretching type motion in which A and Β together move toward C. The stretching motion,ν , is perpendicular to the reaction coordinate, has a restoring ft>rce, and involves the motion of the isotopic atom; hence there is a zero point energy difference in the stretching mode in the transition state between the two isotopic molecules and an activation energy difference that is less than the maximum. In the extreme, one could look at this as a diffusion controlled reaction with the approach of C to the A-B unit as the reaction coordinate and the internal vibra tion of A-B in the transition state being unaffected by C. This analysis suggests that p r i m a r y isotope effects in a series of re lated reactions will vary with reactivity; the maximum effect being found for nearly thermoneutral reactions having transition states which are nearly symmetrical and increasingly smaller effects being exhibited by processes either increasingly endergonic or increasingly exergonic. Such behavior has apparently been found for both proton abstractions and for hydrogen atom abstractions. This would seemingly limit the utility of the p r i m a r y isotope effect as a criterion of mechanism, but in practice one usually knows when to expect the occurrence of such asym-


ISOTOPES

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a b T a b l e I.

Isotopic m o l e c u l e s 1


v

V 2

for Diatomic M o l e c u l a r

V

il/ 2L

^Α (25°) 2

VM200'

2

C-*H

2

C- H

3015

2212

1.36

6.93

3. 39

c-

1 2

c

c-

1 3

c

1129

1107

1. 020

1. 055

1.036

c-

1 2

c

c-

1 4

c

1129

1088

1.038

1. 109

1.069

1134

1116

1. 016

1. 044

1. 029

1113

1086

1. 025

1. 068

1. 045

915

908

1. 008

1. 018

1.013

804

798

1. 007

1. 014

1.010

14

C- N c-

1 6

15

C- N

o

3 2

c-

3 5

1 8

c-

C- S

a

1

C a l c u l a t e d Isotope E f f e c t s Dissociation Model

o

C-^S

ci

c-

3 7

ci

T h e s e results have been calculated using the equation (11) * ^

k /k = s in h x

s

2

„, •„ . Α. hCv Tin

=

A

>

Τ

Έ

Γ

2~Pr

n n

'

^ measured in c m s

-1

and

0. 71929V T

T h e s e c a l c u l a t i o n s a r e e s p e c i a l l y e a s y to p e r f o r m with one of the new " e l e c t r o n i c s l i d e r u l e " pocket c a l c u l a t o r s i f it has a " h y p e r b o l i c s i n e " key. F o r s u c h an a p p r o x i m a t i o n one only needs to know the i s o t o p i c m a s s e s and the a p p r o x i m a t e v i b r a t i o n f r e q u e n c y for one of the i s o t o p i c m o l e c u l e s ; the f r e q u e n c y f o r the second i s o t o p i c m o l e c u l e can be c a l c u l a t e d f r o m that for the f i r s t and the r e d u c e d m a s s r e l a t i o n s h i p , e. g. :

*CD - - C H

f(m , ^(m

C

c

+m ) / m , +m ) / m D

H

w

" m C

\ 1/2

5

c

· rr^ /

"

/14. l 2 « l \ l / 2 777T:) = v U2-2-13/ 1 / 2

H

« 0. 73380

S i n c e the r e d u c e d m a s s r e l a t i o n s h i p a s s u r e s that the r a t i o of f r e q u e n c i e s f o r heavy and light m o l e c u l e s w i l l be v e r y n e a r l y c o r r e c t , any e r r o r i n the e s t i m a t e d f r e q u e n c y w i l l i n g e n e r a l c a u s e only an a p p r o x i m a t e l y p r o p o r t i o n a l e r r o r i n the l o g a r i t h m of the c a l c u l a t e d i s o t o p e effect so that the f r e q u e n c y does not have to be e s t i m a t e d with high p r e c i s i o n to get r e a s o n a b l e ans wers. T h e e x a m p l e s c i t e d a s s u m e that the a t o m s a r e held together by a s i n g l e bond; c a l c u l a t i o n s for e x a m p l e s with m u l t i p l e bonds could be c a r r i e d out u s i n g the a p p r o p r i a t e f r e q u e n c i e s .



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Isotope Effects and

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Reaction Mechanisms

169

m e t r i c a l t r a n s i t i o n states as, for example, i n the t r a n s f e r of a p r o t o n between b a s e s of s t r o n g l y u n e q u a l b a s i c i t y . In addition, this effect c o u l d be u s e d , f o r e x a m p l e , to d e t e r m i n e the e f f e c t i v e b a s i c i t y of a p r o t o n a b s t r a c t i n g site i n a r e a c t i o n and to d i s t i n g u i s h t h e r e b y between a l t e r n a t i v e t r a n s i t i o n state m o d e l s . B e l l (14) has pointed out that a plot of h y d r o g e n k i n e t i c i s o t o p e effects for a v a r i e t y of p r o t o n t r a n s f e r r e a c t i o n s vs. the d i f f e r ence i n pK between the two b a s e s shows a c e n t r a l m a x i m u m n e a r ΔρΚ = 0. 0 and d e c r e a s i n g l i m b s f o r ΔρΚ < 0 or > 0. An e x a m p l e o f this i s shown i n f i g u r e 4 f r o m B e l l and Cox (14). P r y o r and K n e i f f (15) have shown that a s i m i l a r r e l a t i o n s h i p holds f o r a s e r i e s of r a d i c a l s r e a c t i n g with t h i o l s i f the i s o t o p e effects a r e plotted vs. the heats of r e a c t i o n s . S i m s and c o w o r k e r s (16) have r e c e n t l y pointed out that c a r bon t r a n s f e r p r o c e s s e s , s u c h as S 2 r e a c t i o n s , should a l s o show s i m i l a r i s o t o p e effect b e h a v i o r . O r i g i n a l l y i t was b e l i e v e d that c a r b o n i s o t o p e effects i n S^2 d i s p l a c e m e n t s on c a r b o n m i g h t be s m a l l b e c a u s e bonding about c a r b o n i s q u a l i t a t i v e l y " p r e s e r v e d " i n the t r a n s i t i o n state. T h e e s s e n c e of t h i s , as of any s y n c h o nous d i s p l a c e m e n t p r o c e s s , i s that the e n e r g y b i l l to be paid for b r e a k i n g the " o l d " bond i s p a r t i a l l y r e d u c e d by the e n e r g y gained i n f o r m i n g the "new" bond. H o w e v e r , the a n a l y s i s w h i c h we have m a d e h e r e s u g g e s t s that, for n e a r l y s y m m e t r i c a l t r a n s i t i o n states, c a r b o n m o t i o n should be s t r o n g l y i n v o l v e d a l o n g the r e a c t i o n c o o r d i n a t e and c a r b o n i s o t o p e r a t e effects should be l a r g e . T h e m o d e l c a l c u l a t i o n s of S i m s et a l . (16) i n d i c a t e how the effect should v a r y as the t r a n s i t i o n state bonding v a r i e s . T h i s i s shown i n f i g u r e 5 f o r the i n c o m i n g n u c l e o p h i l i c a t o m s oxygen, c h l o r i n e or s u l f u r d i s p l a c i n g c h l o r i d e i o n f r o m b e n z y l c h l o r i d e . T h e u p p e r c u r v e s d i s p l a y the C / C effect and the l o w e r c u r v e the C l / C l l e a v i n g g r o u p effects as a function of bond o r d e r (n ) of the f o r m i n g bond, a s s u m i n g that the b r e a k i n g bond has bond order, n e q u a l to ( l - n ) . A l t h o u g h this g e n e r a l kind of b e h a v i o r i s c e r t a i n l y to be expected, no a v a i l a b l e e x p e r i m e n t a l e v i d e n c e s u p p o r t s the e x i s t e n c e of a c u r v e w i t h a m i x i m u m . M a n y c o m m o n S 2 r e a c t i o n s a r e p r o b a b l y not m a n y k i l o c a l o r i e s p e r m o l e away i r o m t h e r m o n e u t r a l i t y s ο the c o m m o n o b s e r v a t i o n of C / C effects i n the r a n g e of 8-12% ( l 7) s e e m s to c o n f i r m the e x i s t e n c e of n e a r m a x i m a l i s o t o p e effects i n the c e n t r a l r e g i o n of the plot, but t h e r e i s as yet no e v i d e n c e s u p p o r t i n g the s y s t e m a t i c f a l l - o f f w i t h n > 0. 5 or < 0. 5. One of the p r o b l e m s i n i n t e r p r e t i n g a wide v a r i e t y of data on this c l a s s of r e a c t i o n s i s that b i g c h a n g e s i n n u c l e o p h i l i c i t y u s u a l l y a r e a c c o m p a n i e d by c h a n g e s i n a t t a c k i n g atom. T h i s u s u a l l y c a u s e s b i g changes both i n bonding strength, as r e f l e c t e d i n the f o r c e constants f o r n o r m a l s i n g l e bonds, and i n m a s s , w h i c h of c o u r s e has i t s own effect on t r a n s i t i o n state s y m m e t r y independent of the f o r c e constant s i t uation. T h u s one needs a c a r e f u l l y d e s i g n e d set of e x p e r i m e n t s and a c o m p a n i o n set of t h e o r e t i c a l c a l c u l a t i o n s to a p p r o p r i a t e l y i n v e s t i g a t e the phenomenon. No doubt we w i l l see r e s u l t s of e f f o r t s t o w a r d t h i s end i n the next few y e a r s . M

1 2

3 5

1 4

3 7

2

l9

2

N

1 2

1 4

2



ISOTOPES

Figure 3.

AND CHEMICAL

PRINCIPLES

Very exergonic abstraction reaction.

C + *A - Β -> C - Ά + B.

1.08

X OXYGEN IE CHLORINE m SULFUR

1.07

1.06

1.05

1.04

1.03

1.02

1.01

ι

00 ' υ υ

1

00

0.2

Q4

1

1

OS

06

I - n, « n

1 1.0

2

Chemical Reviews Figure 4. Relations between the primary iso tope effect (k /k ) and the pK difference be tween the reacting bases in proton transfer H

D



8.

SHINER

Isotope Effects and Reaction Mechanisms

i f o'

10r

171

.·5

ν % ν 4·\

.ο ·7 pQ

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08 \

\ \

06

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-15

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0

Journal of the Chemical Society, Part Β Figure 5. Calculated carbon-14 (upper curves) and chlorine-37 (lower curves) iso tope effects for displacement on benzyl chlorine by oxygen, chlorine, and sulfur as a function of bond order


ISOTOPES

172

AND

CHEMICAL

PRINCIPLES


Secondary Isotope Effects Having, thus far, given a very brief survey of the general shape of the theory and results on p r i m a r y isotope effects in thermal reactions, I would like next to turn to secondary isotope effects. Here,for the sake of simplicity and brevity,I will con fine my examples to the isotopes of hydrogen,since secondary isotope effects are usually so small that their reliable observa tion is difficult and they have been reported for isotopes other than those of hydrogen in only a few instances. It is convenient to divide secondary isotope effects into at least two kinds (one of which could be further subdivided): 1* a-effects. The isotopic atom is bound to an atom under going bond rupture and/or formation through its other valences. One can readily imagine several possible "sources" of an isotope rate effect in this situation: a. The breaking bond causes a reduction in bending force constant to the a-substituted isotopic atom. b. A forming bond at the reaction center introduces a new bending force constant to the a-substituted isotopic atom. c. Rehybridization of the reaction center causes a change in bond strength and therefore a change in bond force constant to the α-substituted isotopic atom. d. Changes in electron density at the reaction center change the bond strength and bond force constant at the α-substituted isotopic center. e. A change in steric hindrance at the reaction center changes the force constants at the isotopic atom. 2. The second general kind of secondary isotope effects are those caused by isotopic substitution at positions in the molecule more remote from the reaction center. There are two general possible causes for such effects. a. Electronic or steric intramolecular interactions be tween isotopic center and reaction center cause force constant differences between initial and transition states. b. "No force constant change" effects could be caused by changes in moments of inertia, or masses or in me chanical coupling of vibrations. Wolfsberg and Stern (4) have shown that these effects generally are expect ed to amount to no more than a few percent per D atom (replacing H) for example. Many isotope effects due to substitution of deuterium for hy drogen at positions β- or more remote from the reaction center have been observed. (18) There is only space here to refer the reader to more detailed"summaries or to the original literature and to comment that each of the "big three" mechanisms of intra molecular interaction between reaction and isotopic centers has been shown in one case or another to cause isotope effects: 1) Hyperconjugative electron release from a C-H bond causes normal


8.

Isotope Effects and Reaction

SHINER

Mechanisms

173


deuterium isotope effects of the order of krr/k-Q =1.30 or less per D atom and the effect is qualitatively proportional to the ex pected change in hyperconjugative demand. 2) Inductive electron acceptance by a C-H bond causes small normal isotope effects (D compound reacting slower than H compound) of a few percent per D or less depending on demand. (19) 3) Increased crowding causes inverse isotope effects, the lar~gest so far observed being around 1 0 % per D. (20) Of course,effects in directions opposite to those enumeratecTabove give the opposite kind of isotope effect i . e. , inductive electron release by C-H causes an inverse iso tope effect. The interaction effects referred to in each case are those in the transition states relative to the respective initial states. I would like to take the rest of the space available to discuss some general qualitative theory about α-d rate effects and some results obtained from the application of this technique to nucleophilic solvolytic substitution reactions. an

We can represent the dissociation reaction of a bond having α-d substituent as follows:

H

H \ a

a

\

C—X

—X

4

c

Λ

+

X

Ct-Effect: Dissociation Reaction The example involves a reacting carbon atom with the attach ments to the two other valences unspecified; qualitatively this makes no difference in principle and the same general arguments should hold for other kinds of reacting atoms. A s Wolfsberg and Stern (4) have argued, the partial breaking of the C-X bond in the reaction transition state should cause the bending force constant, *HCX' * ^ t ^ to be less than that of the initial state, fjjçx* Thus the zero point energy differences between H and D compounds should be smaller in the transition state (assuming no big changes in the other force constants constraining the H) and the activation energy for the reaction of the H compound should be smaller than that for the reaction of the D compound and a normal isotope effect should result. If we consider a series of related transition states having greater and greater degrees of C-X bond extension we would expect the isotope rate effect to increase with bond extension but to a smaller and smaller degree until a point is reached where the X group no longer has any influence on the transition state vibrations of the a-H. Thus for reactions of this type the secondary isotope effect nt

ie

r

a

n

s

o

n

s t a t e


ISOTOPES

174

A N D CHEMICAL

PRINCIPLES

s h o u l d be a m e a s u r e of the extent of C - X bond b r e a k i n g i n the t r a n s i t i o n state, a s y m p t o t i c a l l y a p p r o a c h i n g s o m e m a x i m u m v a l u e c o r r e s p o n d i n g to c o m p l e t e bond c l e a v a g e . O f c o u r se,the m a x i m u m effect o b t a i n a b l e would depend on the n a t u r e of X and the s t r e n g t h of i t s bond to C, p a r t i c u l a r l y as r e f l e c t e d i n the i n i t i a l state b e n d i n g f o r c e constant. F o r a c o n c e r t e d d i s p l a c e m e n t the s i t u a t i o n i s s i m i l a r except that a new bond to the e n t e r i n g group,Y, has been p a r t i a l l y f o r m ed i n the t r a n s i t i o n state,

H


Ήα Y

+

a

\

X-X

Y---C---X

γ

-

ν

χ

\

a -Effect: Concerted Displacement Reaction In the t r a n s i t i o n state the f o r c e constant, f j ^ c y , f o r the new bond p a r t i a l l y , at l e a s t , c o m p e n s a t e s f o r the r e d u c t i o n i n the i n i t i a l state f o r c e constant, ^jq-^* that one expects the α-d i s o t o p e effect to be s i g n i f i c a n u y l o w e r than that f o r a s i m p l e d i s sociation. s

o

In the w o r k f r o m m y own l a b o r a t o r y o v e r the l a s t ten y e a r s or s o we have u s e d a c o m b i n a t i o n of e x p e r i m e n t a l m e a s u r e m e n t s on s e l e c t e d r e a e t a n t s and m o d e l c a l c u l a t i o n s r e l a t i n g to α-deu t e r i u m effects on the r a t e s of s o l v o l y t i c n u c l e o p h i l i c d i s p l a c e m e n t s on c a r b o n to t r y to c o r r e l a t e a l l known r e s u l t s on s u c h r e a c t i o n s i n t e r m s of S c h e m e I. T h i s i s a g e n e r a l i z e d s c h e m e i n c o r p o r a t i n g the S-,1 and S-,2 m e c h a n i s m s of H u g h e s and Ingold w i t h the i d e a s of "Winstein and c o w o r k e r s and o t h e r s on the e x i s t e n c e of i o n p a i r i n t e r m e d i a t e s in r e a c t i o n s h a v i n g c a r b o n i u m i o n c h a r a c t e r . T h e c o v a l e n t sub s t r a t e h a v i n g a bond between the e l e c t r o n e g a t i v e l e a v i n g g r o u p X and c a r b o n i s r e p r e s e n t e d b y RX; the c o m p o u n d having the op p o s i t e c o n f i g u r a t i o n at c a r b o n i s r e p r e s e n t e d b y X R . T h e S.^2 r e a c t i o n with a p r o t i c s o l v e n t n u c l e o p h i l e , S H , i s r e p r e s e n t e d b y the a r r o w i n d e n t i f i e d w i t h r a t e constant 1^. T h e other p r o d u c t s ^ Η and X a r e o m i t t e d f o r s i m p l i c i t y but a r e u n d e r s t o o d to be f o r m e d i n this p r o c e s s as w e l l as b y the p r o c e s s e s w i t h r a t e c o n s t a n t s kg, k and k T h e s o l v o l y t i c s u b s t i t u t i o n p r o d u c t SR i s r e p r e s e n t e d a s b e i n g f o r m e d i n the S 2 r e a c t i o n f r o m r e a c t ?

6

r


SHINER



8.


175

ISOTOPES A N D

176

CHEMICAL

PRINCIPLES

ant of the o p p o s i t e c o n f i g u r a t i o n R X . R X c a n a l s o i o n i z e w i t h a f i r s t o r d e r r a t e constant k to p r o d u c e the tight i o n p a i r , R X", v i s u a l i z e d a s two i o n s i n d i r e c t contact- T h i s i n t e r m e d i a t e c a n (1) " r e t u r n " with a f i r s t o r d e r r a t e constant k_j to c o v a l e n t R X or (2) f u r t h e r s e p a r a t e w i t h a ra|e constant k to the s e c o n d c a r b o n i u m i o n type i n t e r m e d i a t e , R βχ~, the s o l v e n t separated i o n p a i r , where* // r e p r e s e n t s a s o l v e n t m o l e c u l e between R and X ~ or (3) b y R r o t a t i n g r e l a t i v e to X " p r o d u c e X " R , the tight i o n p a i r of c o n f i g u r a t i o n o p p o s i t e the o r i g i n a l tight i o n p a i r or (4) u n d e r g o n u c l e o p h i l i c a t t a c k b y s o l v e n t to p r o d u c e s u b s t i t u t i o n p r o d u c t expected to b e of o p p o s i t e c o n f i g u r a t i o n to R X * b e c a u s e the f r o n t s i d e i s s t i l l " p r o t e c t e d " f r o m n u c l e o p h i l i c attac^. by the c l o s e p r o x i m i t y of^C". T h e s o l v e n t s e p a r a t e d i o n pair,R / ^ " , c a n (1) r e t u r n to R X", (2) i n v e r t i t s con figuration^ to X " / R , (3) d i s s o c i a t e c o m p l e t e l y to k i n e t i c a l l y independent R and X " o r (4) c o l l a p s e b y n u c l e o p h i l i c s o l v e n t a t t a c k at front o r r e a r to g i v e both SR ar^d RS, p r o b a b l y i n u n e q u a l amounts. T h e f r e e c a r b o n i u m i o n R c a n ( l ) r e t u r n to R / X ~ o r X ~ / R w i t h equal f a c i l i t y by a s s o c i a t i n g w i t h a k i n e t i c a l l y f r e e a n i o n X " o r (2) f o r m SR and R S i n equal a m o u n t s by n u c l e o p h i l i c a t t a c k b y s o l v e n t . In this s c h e m e i t i s a s s u m e d that a s o l v e n t m o l e c u l e i s always r e a s o n a b l y c l o s e l y p o s i t i o n e d to R on f r o n t o r b a c k o r both s i d e s i f X " does not o c c u p y one o r the other of t h e s e s i t e s . T h e effects of added s a l t s , o r added n o n s o l v e n t n u c l e o p h i l i e s , the i n c u r s i o n of e l i m i n a t i o n o r r e a r r a n g e m e n t a r e not i n c l u d e d but c o u l d r e a d i l y b e s o b y obvious e l a b o r a t i o n s of the s c h e m e . x


2

In c l a s s i f y i n g a m e c h a n i s m a c c o r d i n g to this g e n e r a l s c h e m e it i s f i r s t i m p o r t a n t to e s t a b l i s h w h i c h of the s e v e r a l p o s s i b l e steps i s the r a t e d e t e r m i n i n g one and i n w h i c h step the c o v a l e n t bond to the i n c o m i n g n u c l e o p h i l e i s f o r m e d ("product f o r m i n g step"). F o r e x a m p l e ,if the Reaction goes i n the s e q u e n c e of steps through the tight i o n p a i r (R X " ) to the solverjt s e p a r a t e d i o n p a i r (R / X " ) and then b y n u c l e o p h i l i c attack on R to p r o d u c t , the r a t e d e t e r m i n i n g step c o u l d be a n y of the t h r e e l a b e l e d with r a t e constant k ^ k o r k . T h e step with r a t e constant kj w i l l b e r a t e d e t e r m i n i n g i f k 2> k . T h e step w i t h r a t e constant k w i l l be r a t e d e t e r m i n i n g i f k « k , and 1^ :» k_ . T h e step with r a t e constant w i l l be r a t e d e t e r m i n i n g i f k » k and k_ » k^. 2

6

2

e l

2

2

e l

2

-]L

2

2

F r o m the point of v i e w of the α - i s o t o p e effect, one c a n i d e n tify t h r e e g e n e r a l c l a s s e s into w h i c h a l l r e a c t i o n s of this m e c h a n i s t i c s c h e m e w i l l f a l l : ( l ) the one r e a c t i o n i n w h i c h the t r a n s i t i o n state has two p a r t i a l c o v a l e n t bonds to c a r b o n , i . e. , the S^2 r e a c t i o n l a b e l e d with r a t e constant 1%. T h e α - e f f e c t i n this type of r e a c t i o n s h o u l d be l o w (see above). (2) R e a c t i o n s i n w h i c h the t r a n s i t i o n state has one p a r t i a l c o v a l e n t bond to carbon. T h e s e i n c l u d e those r e a c t i o n s with r a t e d e t e r m i n i n g steps l a b e l ed w i t h k kg, k£ and k . T h e α - i s o t o p e effect i n t h e s e types of r e a c t i o n s should be l a r g e but not at the m a x i m u m . (3) R e a c t i o n s i n w h i c h the t r a n s i t i o n state has no p a r t i a l c o v a l e n t bonds to c a r 1 }

7


8.

Isotope Effects and

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Reaction Mechanisms

177

bon. T h e s e i n c l u d e the r e a c t i o n s w i t h r a t e d e t e r m i n i n g steps l a b e l e d k , k , and k^. T h e i s o t o p e effects i n a l l of these type r e a c t i o n s should be at the m a x i m u m . 2

8

It i s f u r t h e r i m p o r t a n t to r e a l i z e that the m a x i m u m i s o t o p e effect w i l l depend on the n a t u r e of the l e a v i n g g r o u p X and that the r e a c t i o n s i n c l a s s e s 1 and 2 above w i l l show i s o t o p e effects that w i l l , to s o m e extent, depend on r e a c t i v i t y and (except f o r c a s e s w h e r e the step l a b e l e d kj i s r a t e d e t e r m i n i n g ) on the n a t u r e of the i n c o m i n g n u c l e o p h i l e . Of c o u r s e , it i s to be expected that m a n y r e a c t i o n s w i l l not c l e a r l y have one step as c o m p l e t e l y r a t e d e t e r m i n i n g but might, f o r e x a m p l e , i f k_j — k have k and k both p a r t l y r a t e - d e t e r m i n i n g . Downloaded by CORNELL UNIV on May 26, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/bk-1975-0011.ch008

2

x

2

In our e f f o r t s to c l a s s i f y a v a r i e t y of r e a c t i o n s by the above s c h e m e and to d e t e r m i n e what r a n g e of α-d effects apply for d i f f e r e n t m e c h a n i s m s we have studied (18) e x a m p l e s i n c l u d i n g s i m ple a l k y l , α - p h e n y l e t h y l , b e n z y l and"~propargyl c o m p o u n d s hav i n g h a l i d e and sulfonate l e a v i n g g r o u p s i n s o l v e n t s ethanol-water, t r i f l u o r o e t h a n o l - w a t e r and m o r e r e c e n t l y t r i f l u o r o a c e t i c a c i d water. In T a b l e 2 a r e shown the m a x i m u m v a l u e s f o r the α-d e f f e c t s w h i c h we b e l i e v e a p p l y f o r the d i f f e r e n t l e a v i n g g r o u p s studied. F o r e a c h of t h e s e l e a v i n g g r o u p s , e f f e c t s of the s i z e i n d i c a t e d have been o b s e r v e d i n one or m o r e r e a c t i o n s w h i c h show a l l of the c h a r a c t e r i s t i c s of the Ingold S 1 or the W i n s t e i n L i m c l a s sification. M

T a b l e 2. A p p r o x i m a t e M a x i m u m α - d e u t e r i u m B a t e E f f e c t s f o r D i f f e r e n t L e a v i n g G r o u p s A t t a c h e d to Saturated Carbon.

Leaving Groups

V oD k

-OS0 R

-CI

-Br

1. 23

1. 16

1. 12

2

-I 1. 09

A l l of the r e a c t i o n s so f a r studied w h i c h show t h e s e m a x i m a have been c l a s s i f i e d as i n v o l v i n g r a t e d e t e r m i n i n g f o r m a t i o n of the solvent s e p a r a t e d i o n p a i r f o l l o w e d by n u c l e o p h i l i c attack. R e a c t i o n s going v i a f r e e c a r b o n i u m i o n s a r e m u c h r a r e r , and although they undoubtedly e x i s t , we have not m e a s u r e d α-d ef fects f o r any of them. We have a l s o studied r e a c t i o n s c l a s s i f i e d as h a v i n g the step labeled with h or the step l a b e l e d w i t h kc, r a t e d e t e r m i n i n g . T h e s e r e a c t i o n s show α-d effects about 2/3 r d s or 3/4 ths of the l i s t e d m a x i m u m v a l u e s . In a d d i t i o n , a n u m b e r of r e a c t i o n s w h i c h we have e x a m i n e d s e e m to c l e a r l y i n v o l v e S^2 attack by solvent, , and to show i s o t o p e effects between 0. 96 and 1. 06 w i t h r e a c tions i n v o l v i n g the i o d i d e l e a v i n g g r o u p f a l l i n g i n the l o w e r end of the r a n g e and those w i t h a sulfonate g r o u p i n the u p p e r end. lf


ISOTOPES


178

ANDCHEMICAL

PRINCIPLES

Classically, on of the most interesting problems in solvolysis mechanisms relates to the reactions of secondary alkyl sul fonates. Therefore, I will choose three examples from this group of compounds to illustrate the kinds of conclusions which we derive from the study of α-deuterium isotope rate effects. The esters are those of the isopropyl, pinacolyl (3, 3-dimethyl2-butyl) and 2-adamantyl groups; to obtain convenient reaction rates in the range of solvents involved we have used p-toluenesolfonate, p- br omob en ζ en e sulfonate and 2, 2 , 2-trifluoroethanesulfonate esters. We have shown, in at least one of the solvents involved, that a change among these three leaving groups causes only a few tenths of a percent of less, change in the isotope effect. CH* I CH* —CH—CH* CHa-C-*—CH-CH* Ο CH, Ο S 0 - C H4~ C H isopropyl p-toluenesulfonate 2

6

3

SO - C H — Br pinacolyl p-bromobenzenesulfonate z

6

4

Η

0-S0 -CH -CF 2

2

3

2-adamantyl trifluoroethanesulfonate The rates of solvolysis of one or more of the three sulfonate esters of each of these three alkyl groups have been measured in ethanol-water, 2, 2, 2-trifluoroethanol-water and trifluoacetic acid-water solvents. In addition, the corresponding a-deuteroesters have been synthesized and their solvolysis rates mea sured under identical conditions. F o r ethanol-water and t r i fluoroethanol water mixtures the rates were measured conductimetrically and the first order rate constants obtained with an electronic computer using a doubly weighted non-linear least squares routine. (21) The reactions were followed for about two half-lives starting at about ΙΟ- M initial concentration and tak ing a total of about 150 readings for each reaction. The stand ard e r r o r s in the rate constants and the reproducibility are both of the order of 0. 1%. The rates of solvolysis in trifluoroacetic acid were measured using a C a r y 118 ultraviolet spectrophoto meter and following the reduction in the ester absorbance around 270 nm. from about 1. 2 o. d. to about 0. 7 o. d. at an initial con centration about 3 χ 10" molar. (22) A computer program s i m i lar to that mentioned above was useH to obtain the first order rate constants from around 200 readings per reaction. Standard e r r o r s and reproducibility in trifluoroacetic acid are only around 1%. apparently because the reactions are not precisely first order. In Table 3 are given the isotope effects expressed as the ratio of the first order rate constants for hydrogen and deuterium 3

3


8.

SHINER


Table 3.

α-d Effects and Relative Rates of Solvolyses at 25°

Solvent

Isopropyl Pinacolyl Sulfonates , Sulfonates k / k , k/k . d k/k , H ad pm ' ad 1


179

2-Adamantyl Sulfonates ,

k/k H ad a

k 1

Apm·

-

-

0. 714

1. 159

1. 225

0.0315

1.16

0. 026

1. 153

1. 228

0.0595

1. 22

0.0041

1. 16

1. 22

0. 207

90E

1. 08

3. 35

50E

1.11

97TFE 99TFA

a

-

F r o m references 22, 23, and 24. 9 0 E is 90 vol. % ethanol, 10 vol. % water; 50E is 50 vol. % ethanol, 50 vol. % water; 9 7 T F E is 97 wt. % 2, 2, 2-trifluoroethanol, 3 wt. % water; 9 9 T F A is 99 vol. % trifluoroacetic acid, 1 vol. % water. °The sulfonate esters used were: in 90E the p-bromobenzenesulfonate; in 50E and 9 7 T F E isopropyl-p-bromobenzenesulfonate and 2,2,2trifluoroethanesulfonate, pinacolyl p-bromobenzenesulfonate and 2-adamantyl 2, 2 , 2-trifluoroethanesulfonate; in 99TFA, isopropyl and p-bromobenzenesulfonate, pinacolyl p-toluenesulfonate and g-adamantyl p-toluenesulfonate and p-bromobenzenesulfonate. Rate relative to that of the corresponding pinacolyl ester. compounds in four different solvents, and, for isopropyl and ada mant y 1 esters, the ratio of their solvolysis rates to the c o r r e s ponding faster solvolyzing pinacolyl esters. The results in the four solvents are interesting to compare because on progression through the series, 90 vol. % ethanol, 50 vol. % ethanol, 97 wt. % trifluoroethanol, 99 vol. % trifluoroacetic acid, the tendency towards slower nucleophilic reactions and more facile carbonium ion forming reactions becomes more and more pronounced. Adding water to ethanol affects the reaction p r i m a r i l y through increasing the solvent dielectric constant and its ability to ionize covalent bonds. Trifluorethanol is about 1000 times less basic than ethanol or water (and therefore less nucleophilic) but it is nevertheless a good ionizing solvent because of its abilitv to sta bilize anions by hydrogen bonding. (25) In trifluoroacetic acid these trends are extended considerably further. (26) Despite this wide range of nucleophilicity and ionizing ability we find that pinacolyl esters show almost the same α-d effect on the solvoly sis rate in each solvent! We have argued (23) that the esters of this alcohol all react by the same mechanism in each of these solvents and that this involves rate-determining formation of the tight ion pair; this tight ion pair does not return but rather r e arranges rapidly by methyl migration to form the tertiary c a r bonium ion pair:


ISOTOPES

180

CH ROBs

CH

3

3

—• C — i

CH

3

AND

+

CHEMICAL

CH

+

CH — __

CH

CH

3

3

—

OBs

PRINCIPLES

3

C — CH — ι _ CH OBs

CH

3

3

I


products The tetiary carbonium ion is so much more stable than the secondary ion that it does not return but forms products. Es sentially all of the products found are those of rearranged car bon skeletal structure. Return to the secondary structure seems highly improbable since all reactions which are expected to go through the pinacolyl cation structure never give significant yields of pinacolyl derivatives but always yield products of re arranged carbon skeletal structure. The only question which seems arguable about this mechanism is whether or not rear rangement is concerted with ionization; if so, it is expected to accelerate ionization but relative rate comparisons in several solvents (see below) do not suggest accelerated rates. Also, the Y-d derivative does not show an appreciable isotope effect. (23) If a CD group were migrating in the rate-determining step 9

3

CD CD

3

—

3

C — I CD 3

CH ι OBs

CH

3

the HCC bending force constants should be lower in the transition state and an isotope effect should be observed. In any event, the extent of participation by methyl during ionization should be quite small, if not entirely absent. The α-d rate effect on pina colyl sulfonate solvolyses are seen to be constant at 1.15 - 1.16 for all four solvents listed in Table 3. 2-Adamantyl sulfonates on the other hand, do not rearrange appreciably during solvoly sis, apparently because to do so would introduce significant ring strain into the relatively strainless structure. They are also not readily subject to nucleophilic attack because the compact t r i cyclic structure hinders nucleophilic approach from the rear. Thus we believe that 2-adamantyl sulfonate esters undergo ioni zation to the tight ion pair and return,with rate determining for mation of the solvent separated ion-pair which is nucleophilically attacked to form product. The α-d effects for 2-adamantyl sulfonates in the solvents shown in Table 3 are all in the range 1. 22 - 1. 23 (24) It is interesting to note that the 2-adamantyl sulfonates react from five to 32 times slower than corresponding pinacolyl esters. One would expect the adamantyl esters to ionize somewhat faster because the adamantyl structure has four carbon atoms in the gamma position relative to the reaction cen ter (two on each side) while pinacolyl has only three. The cor responding difference in inductive effect on ionization should



8.

SHINER

Isotope Effects and

Reaction Mechanisms

181

contribute a factor of around two to the ionization rate ratio lead ing to estimated ratios of internal return to solvolysis for the 2adamantyl derivatives of — 10 in 9 9 % trifluoroacetic acid, — 34 in 97% trifluoroethanol and —65 in 5 0 % ethanol. If pinacolyl solvolyses were accelerated by rearrangement these factors would be even smaller; the factor of — 10 in T F A certainly could not be much smaller without causing kj to be partly rate deter mining for 2-adamantyl and causing the α-d effect to be lower than 1.22. Thus, the idea that rearrangement acceleration in pinacolyl ionization is small is reinforced. Return from 2-ada mantyl tight ion pairs is probably less in T F A than in T F E and still less in ethanol because Η-bonding of the more acidic solvent reduces the nucleop^hilicity of the leaving group and slows i|s re combination with R relative to the further separation to R /Χ~· The situation with the isopropyl sulfonates is especially interest ing: a very low α-d effect, 1.08, is observed in 90%> ethanol. This can only mean that an S^2 reaction is largely, but probably not completely, the reaction pathway. It is significant that in this solvent isopropyl sulfonates react about three times faster than the corresponding pinacolyl esters. Since the isopropyl ester must ionize slower than the pinacolyl ester due to the dif ference in inductive effects of the substituents, this faster obser ved rate can only be caused by an S ^ process. In 50% ethanol the isopropyl esters solvolyze at rates comparable to the cor responding pinacolyl esters and show increased α-d effects. This must be due to the formation and reaction of tight ion pairs in addition to some fraction of S 2 reaction. In 97%> trifluorethanol the pinacolyl esters react about forty times faster than the corresponding isopropyl esters and the α-d isotope effect for the isopropyl esters rises to 1. 16. In this solvent the reaction must be going almost exclusively through tight ion pairs and the only way that the isopropyl compounds can be reacting so much slower is for the ion pairs to be undergoing return about four times more rapidly than they are nucleophilically attacked. In trifluoroacetic acid the very low nucleophilicity of the solvent reduces the rate of nucleophilic attack on the tight ion pairs of the isopropyl sulfonate esters so much that the rate of ester sol volysis is now 244 times slower than the rate of solvolysis of the corresponding pinacolyl esters, suggesting that internal return takes place about twenty times faster than solvolysis. In addition, in this solvent, attack on the tight ion pair is so slow that the rate determining step is now separation of the isopropyl sulfon ate tight ion pair to the solvent separated ion-pair and the α-d effect is 1.22, the same as observed for 2-adamantyl sulfonates in all three solvents! Thus isopropyl sulfonate solvolyses are truly "borderline" in character and can shift over a range of me chanisms with different solvents. There are many other obser vations which buttress these interpretations but no need or space to go into more detail here. It is hoped that these illustrations will show, in part at least, how secondary deuterium isotope


182

ISOTOPES

AND

CHEMICAL

PRINCIPLES


rate effects can be used in the intricate process of sorting out reaction mechanistic pathways. Because isotopic substitution involves a minimal perturbation of the reacting system and because of the solid basic theory underlying our understanding of these effects they allow us an unparalleled tool with which to attack mechanistic problems. I hope that this brief review has conveyed some flavor of the intellectual adventure and satisfaction which can be involved in such studies. A c kn owl ed gm en t The preparation of this paper and the new results reported here were supported in part by grant G P 32854 from the National Science Foundation. The author wishes to thank Dr. W. E. Buddenbaum and Mr. Richard Seib for reading the manuscript before publication and for valuable discussion and suggestions. Thanks are also due to The Chemical Society, London for permission to reproduce figure 4.


8.

SHINER

183


Literature Cited 1. F o r a more detailed discussion of theory and the interpre tation of results from a variety of reactions see: "Isotope Effects in Chemical Reactions", C. J. Collins and N. S. Bow man, eds., Van Nostrand Reinhold, New York, 1970 and references cited therein. 2. Bigeleisen, J. and Mayer, M. G., J. Chem. Phys., (1947), 15, 261.


3. Melander, L. Arkiv. Kemi., (1950), 2, 211. 4. Wolfsberg, M. and Stern, M. J., Pure Appl. Chem., (1964), 8, 225. 5.

Wolfsberg. M. and Stern, M. J., Pure Appl. Chem., (1964), 8, 325.

6. Wolfsberg, M. and Stern. M. J., J. Pharm. S c i . , (1965), 54, 849. 7. Bigeleisen, J., Can. J. Chem., (1952), 30, 443. 8. Willi, Α. V., Can. J. Chem., (1966), 44, 1889. 9· Katz, A. M. and Saunders, W. Η., J r . , J. Amer. Chem. Soc., (1969), 91, 4469. 10. Williams, R. C., and Taylor, J. W., (1974), 96, 3721.

J. Amer. Chem. Soc.,

11. Melander, L a r s , "Isotope Effects on Reaction Rates," pg. 12, Ronald Press, New York, 1960. The approxima tions involved are also discussed on pg 35. See also ref. 6, pg. 850, equation 6: k /k 1

2

=

x (VP) x (EXC)x( Z P E )

For the diatomic model (VP) = (ν /ν ) Therefore, k /k = (EXC) x (ZPE) = sinh l/2 u ÷sinh l/2 u , where u = hν/ kT. 2L

1

2

12. Westheimer, F. Η., Chem. Rev.,

1

1L

2

(1961), 61, 265.

13. Melander, L. "Isotope Effects on Reaction Rates," pps. 24-32, Ronald Press, New York, 1960. 14. Bell, R.P. and Cox, B. G., J. Chem. Soc., Β, (l971), 783.


Isotopes and Chemical Principles - ACS Publications

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