Supercomputer Research in Chemistry and Chemical Engineering

Chapter 12

Computational Investigations of Organic Reaction Mechanisms 1

William L. Jorgensen, James F. Blake, Jeffry D. Madura , and Scott D. Wierschke

Downloaded by GEORGETOWN UNIV on August 22, 2015 | http://pubs.acs.org Publication Date: October 22, 1987 | doi: 10.1021/bk-1987-0353.ch012

Department of Chemistry, Purdue University, West Lafayette, IN 47907

Ab initio molecular orbital calculations are being used to study the reactions of anionic nucleophiles with carbonyl compounds in the gas phase. A rich variety of energy surfaces is found as shown here for reactions of hydroxide ion with methyl formate and formaldehyde, chloride ion with formyl and acetyl chloride, and fluoride ion with formyl fluoride. Extension of these investigations to determine the influence of solvation on the energy profiles is also underway; the statistical mechanics approach is outlined and illustrated by results from Monte Carlo simulations for the addition of hydroxide ion to formaldehyde in water. The i m p o r t a n c e o f d i s p l a c e m e n t r e a c t i o n s on c a r b o n y l compounds i n c h e m i s t r y and b i o c h e m i s t r y has r e s u l t e d i n numerous m e c h a n i s t i c studies. In solution, there is general acceptance of the f o l l o w i n g mechanism f o r a d d i t i o n o f a n i o n i c n u c l e o p h i l e s which features a tetrahedral intermediate, 1, and i s d e s i g n a t e d B 2 (1). However, r e c e n t e x p e r i m e n t a l (2-10) and t h e o r e t i c a l (11-17) A C

X"

+

R—C

studies have found the situation in the gas phase to be intriguingly complex w i t h the possibility of the tetrahedral s p e c i e s as a t r a n s i t i o n s t a t e , the i n t e r v e n t i o n o f i o n - d i p o l e c o m p l e x e s , 2, as i n t e r m e d i a t e s , and energy p r o f i l e s f e a t u r i n g one, 1Current address: Department of Chemistry, University of Houston, Houston, TX 77004

0097-6156/87/0353-0200506.00/0 © 1987 American Chemical Society

In Supercomputer Research in Chemistry and Chemical Engineering; Jensen, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

12.

J O R G E N S E N ET A L .

Organic Reaction

X"

· · · ·

201

Mechanisms

R— Y 2

two o r t h r e e minima. The gas-phase d i s p l a c e m e n t r e a c t i o n s may also be accompanied by competing proton transfer and SJJ2 (bimolecular s u b s t i t u t i o n ) processes that are not observed i n solution. These r e s u l t s have, i n t u r n , l e d t o doubts about the u n i v e r s a l i t y o f the t r a d i t i o n a l B 2 mechanism i n condensed phases and have r a i s e d many q u e s t i o n s c o n c e r n i n g the e n e r g y s u r f a c e s f o r the r e a c t i o n s i n the gas phase, i n s o l u t i o n , and i n b i o m o l e c u l a r environments (12). The c o n t r i b u t i o n o f modern t h e o r e t i c a l methods t o e l u c i d a t i n g organic r e a c t i o n mechanisms i n c l u d e s the a b i l i t y o f ab initio molecular orbital calculations to provide quantitative c h a r a c t e r i z a t i o n o f the gas-phase energy s u r f a c e s and of the s t r u c t u r e s o f any i n t e r m e d i a t e s and t r a n s i t i o n s t a t e s . For the reactions o f c a r b o n y l compounds w i t h a n i o n s , the s i z e o f the systems, t h e i r a n i o n i c n a t u r e , and the need f o r e x t e n s i v e geometry optimizations make reliable calculations taxing on computer resources. N e v e r t h e l e s s , the a v a i l a b i l i t y o f supercomputers s u c h as the Cyber 2 0 5 a t Purdue and s u p e r m i n i c o m p u t e r s such as the G o u l d 3 2 / 8 7 5 0 i n our l a b o r a t o r y now a l l o w s i g n i f i c a n t p r o g r e s s i n t h i s area. Some r e c e n t r e s u l t s a r e r e v i e w e d h e r e t h a t show the u t i l i t y o f the methodology as w e l l as the v a r i e t y o f energy s u r f a c e s and r e a c t i o n p a t h s t h a t may o c c u r f o r even r e l a t i v e l y s i m p l e systems; s p e c i f i c a l l y , the r e a c t i o n s t h a t a r e c o n s i d e r e d are f o r hydroxide i o n w i t h methyl formate and formaldehyde, c h l o r i d e i o n w i t h f o r m y l and a c e t y l c h l o r i d e , and f l u o r i d e i o n with formyl f l u o r i d e . I n a d d i t i o n , the e f f e c t o f s o l v a t i o n on the gas-phase e n e r g y s u r f a c e s i s b e g i n n i n g to be s t u d i e d v i a Monte C a r l o s t a t i s t i c a l mechanics and m o l e c u l a r dynamics c a l c u l a t i o n s for the reacting system surrounded by hundreds of solvent molecules ( 1 8 ) . Our i n i t i a l e f f o r t s a l o n g t h e s e l i n e s on the SJJ2 r e a c t i o n o f C i " + C ^ C i were o n l y made p r a c t i c a l by the advent o f the Cyber 2 0 5 a t Purdue i n 1 9 8 3 ( 1 9 ) . More r e c e n t r e s u l t s ( 1 1 ) on the r e a c t i o n o f OH" + H2C-O i n w a t e r a r e a l s o summarized i n the f o l l o w i n g and i l l u s t r a t e the d e t a i l s t h a t a r e now accessible on the v a r i a t i o n o f s o l v a t i o n a l o n g r e a c t i o n p a t h s , the o r i g i n o f solvent-induced activation barriers, and the location of t r a n s i t i o n states i n solution.


A C

Energy S u r f a c e s from the Ab

Initio

Calculations

(a) OH" 4- HCOOCH3. The r e a c t i o n s o f h y d r o x i d e i o n w i t h m e t h y l f o r m a t e have b e e n s t u d i e d by s e v e r a l groups i n the gas phase and nicely illustrate the variety of available reaction paths (2,9,10). F l o w i n g a f t e r g l o w e x p e r i m e n t s f o u n d the f o l l o w i n g B ^2, SJJ2, and p r o t o n t r a n s f e r pathways to account for 34%, 5% and 61% of the product distribution, respectively (9). These interesting results leave open numerous q u e s t i o n s about the c o r r e s p o n d i n g e n e r g y s u r f a c e s t h a t we s e t out t o e x p l o r e w i t h ab i n i t i o molecular o r b i t a l c a l c u l a t i o n s . A


202

SUPERCOMPUTER

li5

18,OH"

HC0 0-

+

CH3OH

HCOO"

+

CH

RESEARCH

(1)

SM2

HCOOCH3

1 8 3

OH

(2)

p.t. _

CO + C H 0 - · · Η

1 8


3

ΟΗ

(3)

The computations were c a r r i e d o u t w i t h t h e GAUSSIAN/82 program (20) and t h e split-valence 4-31+G b a s i s s e t which i n c l u d e s a s e t o f d i f f u s e s and ρ o r b i t a l s on a l l atoms e x c e p t hydrogen (21). D i f f u s e f u n c t i o n s a r e well-known t o be i m p o r t a n t for describing the e l e c t r o n i c s t r u c t u r e o f anions c o n t a i n i n g f i r s t - r o w elements (21-23). The 4-31+G b a s i s s e t was a l s o chosen b e c a u s e i t has been f o u n d t o y i e l d e x c e l l e n t p r o t o n a f f i n i t i e s f o r o r g a n i c a n i o n s ( 2 1 ) . Furthermore, t h e computed e n e r g e t i c s f o r t h e three r e a c t i o n channels are i n acceptable accord with experimental data. Specifically, t h e 4-31+G AE's f o r r e a c t i o n s 1 and 3 a r e -43.3 a n d -19.1 k c a l / m o l , w h i l e t h e e x p e r i m e n t a l e n t h a l p y changes a r e -44.0 and -27.6 k c a l / m o l (10,24). F o r comparison, t h e ΔΕ f o r r e a c t i o n 1 computed w i t h t h e 4-31G b a s i s s e t i s -62.9 kcal/mol (16). Clearly, the d i f f u s e functions p r e f e r e n t i a l l y improve t h e d e s c r i p t i o n o f t h e charge l o c a l i z e d h y d r o x i d e i o n . I t may a l s o be n o t e d t h a t t h e 4-31+G d i s s o c i a t i o n energy f o r t h e methoxide-water complex from t h e R i v e r o s r e a c t i o n (3) i s 28.4 k c a l / m o l which compares w e l l w i t h t h e l a t e s t e x p e r i m e n t a l Δ Η o f 23.9 k c a l / m o l ( 2 4 ) . The r e l a t i v e l y g r e a t e r importance o f t h e d i f f u s e atomic o r b i t a l s t h a n c o r r e l a t i o n energy o r z e r o - p o i n t e f f e c t s i n t h i s c o n t e x t h a s b e e n d i s c u s s e d elsewhere ( 2 2 ) . The key s t r u c t u r a l and e n e r g e t i c r e s u l t s f o r the three r e a c t i o n s a r e summarized i n F i g u r e s 1-3. F o r t h e B ^ 2 p r o c e s s , the t e t r a h e d r a l s p e c i e s , 3, i n F i g u r e 1 was f o u n d t o b e a n energy minimum w i t h no symmetry c o n s t r a i n t s . The i l l u s t r a t e d conformer with t h e h y d r o x y l hydrogen e c l i p s i n g the alkoxy oxygen was p r e v i o u s l y shown t o be t h e l o w e s t energy form a t t h e 4-31G l e v e l (16). W i t h t h e 4-31+G c a l c u l a t i o n s , i t i s 31.1 k c a l / m o l lower i n energy t h a n t h e r e a c t a n t s . T h i s s p e c i e s may r e a r r a n g e t o t h e formate-methanol complex, 6, shown a t t h e bottom o f F i g u r e 2 which i s 30.1 k c a l / m o l lower i n energy t h a n 3 a n d 17.8 k c a l / m o l below the s e p a r a t e d p r o d u c t s , HCOO' + CH3OH. The hydrogen-bond e n t h a l p y for t h e formate-methanol complex has a l s o been determined e x p e r i m e n t a l l y a s 17.6 k c a l / m o l (24). Though a n i o n - d i p o l e complex l i k e 2 was sought p r e c e d i n g 3, none was f o u n d as a n energy minimum w i t h t h e 4-31+G c a l c u l a t i o n s . However, a t r a n s i t i o n s t a t e was l o c a t e d b y g r a d i e n t methods f o r t h e e l i m i n a t i o n o f methanol from 3 on t h e way t o 6; i t i s l a b e l l e d TS i n F i g u r e 1 a n d i s 10.4 k c a l / m o l h i g h e r i n energy t h a n 3. The h y d r o x y l h y d r o g e n h a s r o t a t e d i n t h i s s t r u c t u r e t o h e l p form t h e i n c i p i e n t 0-H bond o f methanol and t h e C-OCH3 bond h a s l e n g t h e n e d from 1.48 t o 2.00 À . Thus, t h e r e a c t i o n p r o f i l e f o r t h e B ^ 2 r e a c t i o n 1 h a s a doublewell form with 3 and 6 as i n t e r m e d i a t e s s e p a r a t e d b y t h e t r a n s i t i o n state f o r the elimination. The e x i s t e n c e o f 3 as a n energy minimum i s c o n s i s t e n t w i t h l o w e r - l e v e l t h e o r e t i c a l r e s u l t s (15,16) a n d r e c e n t o b s e r v a t i o n s o f p r o t o n exchange i n such A

A



JORGENSEN ET AL.

Organic Reaction

203

Mechanisms

F i g u r e 1. 4-31+G r e s u l t s f o r r e a c t i o n 1. k c a l / m o l and l e n g t h s i n angstroms t h r o u g h o u t .

Energies

in


SUPERCOMPUTER RESEARCH


204

F i g u r e 2.

4-31+G r e s u l t s f o r r e a c t i o n

2.


12.

JORGENSEN ET AL.

Organic Reaction

Mechanisms


Proton T r a n s f e r

.950 F i g u r e 3.

4-31+G r e s u l t s f o r r e a c t i o n 3.


205

206

SUPERCOMPUTER

RESEARCH

i n t e r m e d i a t e s ( 2 5 ) , though i t c o n t r a s t s the i n t e r p r e t a t i o n o f some e a r l i e r experimental findings (2c). The Sfl2 r e a c t i o n was s t u d i e d i n C symmetry and f o u n d t o have the double-well form typical of gas-phase S^2 reactions (12,25,27), as summarized i n F i g u r e 2. The i n i t i a l i o n - d i p o l e complex 4 i s 17.5 k c a l / m o l below the energy o f the r e a c t a n t s . The t r a n s i t i o n s t a t e 5 was l o c a t e d w i t h g r a d i e n t methods, 8.1 k c a l / m o l above 4, but still 9.4 kcal/mol below the reactants. Rearrangement o f 5 t o the e x i t complex, 6, i s t h e n accompanied by r e l e a s e o f 51.8 k c a l / m o l . S e p a r a t i o n t o the p r o d u c t s , HCOO" + CH3OH, r e q u i r e s 17.8 k c a l / m o l , as d i s c u s s e d above, and y i e l d s the o v e r a l l 4-31+G ΔΕ o f -43.3 k c a l / m o l . These e n e r g e t i c r e s u l t s a r e all similar t o our p r e v i o u s ab i n i t i o f i n d i n g s f o r the S2 r e a c t i o n o f HO" + C ^ C i (22); however, the b e n t arrangement o f the n u c l e o p h i l i c , e l e c t r o p h i l i c and l e a v i n g atoms i n 4 i s u n u s u a l .


s

N

The p r o t o n t r a n s f e r p r o c e s s was a l s o s t u d i e d i n C symmetry as summarized i n Figure 3. The proton transfer occurred s p o n t a n e o u s l y as the geometry o p t i m i z a t i o n b r o u g h t the r e a c t a n t s t o g e t h e r t o y i e l d the w a t e r - a c y l a n i o n complex, 7. Upon f l i p p i n g the f a r h y d r o g e n o f water, f u r t h e r o p t i m i z a t i o n y i e l d e d 8 w h i c h may be c a l l e d the " R i v e r o s complex" and i s 26.6 k c a l / m o l lower i n energy t h a n the r e a c t a n t s . The complex may be v i e w e d as h y d r a t e d methoxide i o n c o o r d i n a t e d w i t h c a r b o n monoxide. L o s s o f CO t o y i e l d C ^ O ' ^ ' ^ O r e q u i r e s o n l y 7.5 k c a l / m o l , whereas l o s s o f water t o g i v e the methyl f o r m y l a n i o n r e q u i r e s 19.9 kcal/mol. O v e r a l l , t h e s e r e s u l t s s u g g e s t t h a t the R i v e r o s r e a c t i o n (3) has a s i n g l e - w e l l energy s u r f a c e w i t h the i n t e r e s t i n g s t r u c t u r e 8 as the only intermediate. In summary, the 4-31+G c a l c u l a t i o n s f i n d the energy s u r f a c e s for the t h r e e o b s e r v e d r e a c t i o n s t o a l l c o n t a i n s i g n i f i c a n t l y s t a b i l i z e d i n t e r m e d i a t e s whose s t r u c t u r e s and r e l a t i v e e n e r g i e s have b e e n c h a r a c t e r i z e d . The formate-methanol complex 6 i s the g l o b a l energy minimum, 61 k c a l / m o l lower i n energy t h a n the reactants. I t i s a c c e s s i b l e t h r o u g h b o t h the S 2 and B 2 channels. The t r a n s i t i o n s t a t e s f o r t h e s e p r o c e s s e s have a l s o b e e n l o c a t e d and a r e s i g n i f i c a n t l y lower i n energy than the reactants. Thus, none o f the r e a c t i o n s has a n e t p o s i t i v e a c t i v a t i o n energy which i s c o n s i s t e n t w i t h t h e i r o b s e r v e d f a c i l i t y (2,9,10). (b) C i " + HCOCi and C l " + CH3COCI. A s u b i o j o and Brauman made the p r o v o c a t i v e p r o p o s a l t h a t the gas-phase displacement reactions of nucleophiles i n c l u d i n g h a l i d e ions with a c y l h a l i d e s have d o u b l e - w e l l energy s u r f a c e s ; the i n t e r m e d i a t e s were s u g g e s t e d to be i o n - d i p o l e complexes and the t e t r a h e d r a l s p e c i e s was l i k e l y to be a t r a n s i t i o n s t a t e ( 4 ) . In order to address t h i s p r o p o s a l , we expanded our s t u d y o f s u b s t i t u t i o n r e a c t i o n s t o the d e g e n e r a t e exchange reactions of chloride ion with formyl and acetyl c h l o r i d e , and o f f l u o r i d e i o n w i t h f o r m y l f l u o r i d e ( 1 2 ) . Key i s s u e s a r e the number o f minima on the energy s u r f a c e s and the s t r u c t u r e s o f any i n t e r m e d i a t e s and t r a n s i t i o n s t a t e s . Han and Brauman a l s o r e c e n t l y extended t h e i r ICR i n v e s t i g a t i o n s o f C i " w i t h CF3C0Ci and C H 0 C 0 C i ( 5 ) . They were a b l e t o show t h r o u g h l a b e l i n g s t u d i e s t h a t the two c h l o r i n e s i n the adducts a r e none q u i v a l e n t w h i c h s u p p o r t s the d o u b l e - w e l l p i c t u r e and the p r o b a b l e s

N

3


A C

12.


Organic Reaction

Mechanisms

207


e x i s t e n c e o f a t e t r a v a l e n t s p e c i e s as a t r a n s i t i o n s t a t e ( 5 ) . At the same time, Howard and K o l l m a n have c a r r i e d out a r e l a t e d ab initio s t u d y o f the r e a c t i o n o f HS" and formamide ( 1 4 ) . In c o n t r a s t t o t h e i r r e s u l t s f o r HO" w i t h formamide (13), an i o n d i p o l e complex r a t h e r t h a n the t e t r a h e d r a l a d d u c t was f o u n d as an e n e r g y minimum. The geometry optimizations for reactions 4 and 5 were p r i m a r i l y c a r r i e d out w i t h the 3-21+G b a s i s s e t (23). This alternative typically g i v e s r e s u l t s s i m i l a r t o 4-31+G, b u t i t i s Ci"

+

HCOCi

>

HC0Ci "

Ci"

+

CH C0Ci

>

CH COCi "

3

(4)

2

3

2

(5)

n o t a b l y f a s t e r f o r the g r a d i e n t c a l c u l a t i o n s w h i c h i s p a r t i c u l a r l y desirable given the five non-hydrogen atoms i n reaction 5. N e v e r t h e l e s s , the e f f e c t o f b a s i s s e t e x t e n s i o n f o r the s t a t i o n a r y p o i n t s i n r e a c t i o n 4 was shown t o be s l i g h t t h r o u g h o p t i m i z a t i o n s w i t h the 6-31+G(d) b a s i s s e t ( 1 2 ) . The 3-21+G r e s u l t s t u r n e d out t o be f a s c i n a t i n g . The energy s u r f a c e s f o r r e a c t i o n s 4 and 5 i n d e e d have the d o u b l e - w e l l form. The i o n - d i p o l e complex, 9, shown i n F i g u r e 4 i s the o n l y minimum f o r r e a c t i o n 4 and the t e t r a h e d r a l adduct, 10, i s a t r a n s i t i o n state. Computation o f the v i b r a t i o n a l f r e q u e n c i e s f o r 9 and 10 u n e q u i v o c a l l y e s t a b l i s h e d these designations. As shown i n F i g u r e 5, 9 and 10 a r e c a l c u l a t e d t o be 21.7 and 7.1 k c a l / m o l below the e n e r g y o f the r e a c t a n t s a t the 3-21+G l e v e l . More s u r p r i s i n g l y , f u r t h e r s e a r c h f o r a n o t h e r t e t r a v a l e n t s p e c i e s f o u n d the p l a n a r a d d u c t 11 w i t h C symmetry ( F i g u r e 6) as a s e c o n d t r a n s i t i o n s t a t e , a g a i n v e r i f i e d by the v i b r a t i o n a l a n a l y s e s . I n f a c t , 11 i s 1.6 k c a l / m o l lower i n e n e r g y t h a n 10; the two s t r u c t u r e s s i t on a r i d g e between the r e a c t a n t s and p r o d u c t s and were f o u n d t o be s e p a r a t e d by a b a r r i e r o f o n l y 0.7 k c a l / m o l ( 1 2 ) . The v a l l e y s t o 10 and 11 b o t h emanate from the i o n - d i p o l e complex 9 and are i l l u s t r a t e d by the s t r u c t u r e s i n F i g u r e s 4 and 6, and by the e n e r g y p r o f i l e s i n F i g u r e 5. 2 v

However, the s t r u c t u r e f o r 11 i s u n u s u a l w i t h l o n g C - C i bond l e n g t h s o f 2.62 Â as opposed t o 2.24 À f o r 10. T h i s suggests that the more compact structure 10 might become r e l a t i v e l y more f a v o r a b l e when e l e c t r o n c o r r e l a t i o n i s i n c l u d e d . Consequently, Miller-Plesset perturbation theory t o t h i r d - o r d e r was used to compute the c o r r e l a t i o n e n e r g i e s w i t h the 6-31+G(d) b a s i s s e t on the 3-21+G o p t i m i z e d g e o m e t r i e s f o r the stationary points in r e a c t i o n 4. I n the s t a n d a r d n o t a t i o n (23), t h e s e c a l c u l a t i o n s a r e designated MP3/MP2/6-31+G(d)//3-21+G. The effects on the e n e r g e t i c s f o r the pathway l e a d i n g t o the t e t r a h e d r a l a d d u c t 10 with C symmetry are n o t g r e a t ; 9 and 10 a r e now 16.7 and 1.4 k c a l / m o l below the r e a c t a n t s . However, the C s t r u c t u r e 11 i s d i f f e r e n t i a l l y d e s t a b i l i z e d so t h a t i t i s 11.6 k c a l / m o l above 10 and i s u n d o u b t e d l y no l o n g e r a t r a n s i t i o n s t a t e . Nevertheless, the b a r r i e r t o i n v e r s i o n o f 10 t h r o u g h 11 i s r e m a r k a b l y low. Though i t c o u l d be a r g u e d t h a t a p l a n a r s t r u c t u r e a n a l o g o u s t o 11 f o r a c e t y l c h l o r i d e would be d i s f a v o r e d by s t e r i c c r o w d i n g between the c h l o r i n e s and the m e t h y l group, t h i s was n o t f o u n d t o s

2 v




208

F i g u r e 5. 3-21+G energy p r o f i l e s f o r r e a c t i o n s 4 and 5. The reaction coordinate i s d e f i n e d as t h e d i f f e r e n c e i n t h e two C-Ci d i s t a n c e s .


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be a dominant e f f e c t w i t h t h e 3-21+G c a l c u l a t i o n s . I n s t e a d adduct 13 i n F i g u r e 7 was f o u n d t o be the o n l y t r a n s i t i o n s t a t e ; i t i s 5.2 k c a l / m o l lower i n energy t h a n a s t r u c t u r e a n a l o g o u s t o 10 w i t h a CCO a n g l e o f 140°. The r e a s o n f o r the i n c r e a s e d p r e f e r e n c e f o r the C 2 - l i k e structure c a n be attributed to the substantial p o s i t i v e c h a r g e on the c a r b o n y l c a r b o n t h a t i s a p p a r e n t from population analyses. Thus, t h e R-C-0 fragment i n 11 and 13 has s i g n i f i c a n t a c y l c a t i o n c h a r a c t e r t h a t i s s t a b i l i z e d by the m e t h y l substituent.


v

The 3-21+G r e a c t i o n p a t h t o 13 i s i l l u s t r a t e d i n F i g u r e 7 and i n v o l v e s the i n t e r m e d i a c y o f t h e i o n - d i p o l e complex 12. As shown i n F i g u r e 5, t h e w e l l - d e p t h f o r 12 i s r e d u c e d t o 14.3 k c a l / m o l s i n c e t h e c h l o r i d e i o n i s k e p t by the m e t h y l group about 1.5 Â f a r t h e r from the c a r b o n y l c a r b o n t h a n i n 9. This interaction e n e r g y f o r C i " · · - C ^ C O C i compares f a v o r a b l y w i t h t h e v a l u e o f 11 kcal/mol estimated by Asubiojo and Brauman from their ICR experiments ( 4 ) . Of c o u r s e , t h e l o n g C - C i bonds i n 13 a g a i n s u g g e s t that electron correlation should s i g n i f i c a n t l y a f f e c t the results. Assuming t h e e f f e c t s a r e q u a n t i t a t i v e l y s i m i l a r t o t h o s e f o r r e a c t i o n 4, t h e t e t r a h e d r a l t r a n s i t i o n s t a t e w o u l d end up about 8 k c a l / m o l lower i n energy t h a n 13 and r o u g h l y 4 k c a l / m o l above the energy o f the r e a c t a n t s . A s u b i o j o and Brauman a l s o a d d r e s s e d t h i s point. Though t h e y c o u l d e x p l a i n the o b s e r v e d e f f i c i e n c y f o r r e a c t i o n 5 t h r o u g h RRKM c a l c u l a t i o n s i n w h i c h t h e t r a n s i t i o n s t a t e i s c a . 7 k c a l / m o l below t h e energy o f t h e r e a c t a n t s , a r e s u l t a n t p r o b l e m i s an i m p l i e d , u n r e a s o n a b l y h i g h e l e c t r o n a f f i n i t y f o r C h ^ C C ^ O r a d i c a l ( 4 ) . The h i g h e r energy f o r t h e t r a n s i t i o n s t a t e s u g g e s t e d h e r e would h e l p a l l e v i a t e the l a t t e r dilemma. ( c ) F" + HCOF. The r e a c t i o n o f f l u o r i d e i o n w i t h f o r m y l f l u o r i d e was a l s o s t u d i e d w i t h 3-21+G c a l c u l a t i o n s f o r comparison. Briefly, t h i s system i s f o u n d t o have the t r i p l e - w e l l energy p r o f i l e shown i n F i g u r e 8. Two e q u i v a l e n t i o n - d i p o l e complexes a n a l o g o u s t o 9 now f l a n k the t e t r a h e d r a l i n t e r m e d i a t e , 14, w h i c h i s a l s o an e n e r g y minimum. I n t h i s c a s e , i n v e r s i o n t h r o u g h the F

F

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I C F^|^F Η

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14

15

p l a n a r form 15 i s h i g h l y u n f a v o r a b l e w i t h 15 as a maximum 40 k c a l / m o l above 14. The r e q u i r e d s t r e t c h i n g o f the C-F bonds i s f a r more c o s t l y i n energy t h a n f o r the weaker C - C i bonds i n 11. T a k i n g a l l o f t h e s e r e s u l t s t o g e t h e r , some g e n e r a l p a t t e r n s emerge. Foremost, the t e t r a h e d r a l a d d u c t s 1 a r e f o u n d t o be e n e r g y minima when the s u b s t i t u e n t s X and Y a r e b o t h f i r s t - r o w elements. However, when X and Y a r e b o t h second-row e l e m e n t s , the t e t r a h e d r a l s p e c i e s i s a t r a n s i t i o n s t a t e and the o n l y minima a r e ion-dipole complexes, 2. Clearly, two key factors i n the f o r m a t i o n o f the t e t r a h e d r a l adduct 1 a r e the d i f f e r e n c e i n gasphase b a s i c i t i e s f o r the two a n i o n s (X" and 1) and the d i f f e r e n c e




210

F i g u r e 7. 3-21+G o p t i m i z e d s t r u c t u r e s f o r r e a c t i o n 5.

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i n bond e n e r g i e s between a C-0 π-bond and a C-X s i n g l e bond. The former is remarkably strong a t about 90 k c a l / m o l (28), w h i l e some C-X s i n g l e bond e n e r g i e s a r e f o r X - Ν (69-75), 0 (85-91), F (116), S ( 6 6 ) , C i (79), Br (66), and I ( 5 2 ) . Furthermore, s i n c e t h i o l a t e , c h l o r i d e , bromide, and i o d i d e i o n s a r e much weaker b a s e s i n the gas phase t h a n a l k o x i d e s (29), t h e s e n u c l e o p h i l e s should a l l f a v o r i o n - d i p o l e complexation over formation o f t e t r a h e d r a l adducts f o r most acyl electrophiles including acid halides, amides, and e s t e r s . Thus, the t e t r a h e d r a l a d d u c t w i l l o f t e n n o t be an e n e r g y minimum i n t h e s e c a s e s . I n c o n t r a s t , C-F bonds a r e unusually s t r o n g and f l u o r i d e i o n i s comparable i n b a s i c i t y t o alkoxides i n the gas phase ( 2 9 ) . Therefore, formation of the tetrahedral adduct should be favored by fluoride as the nucleophile and s i n g l e or t r i p l e - w e l l energy s u r f a c e s can be expected. S i m i l a r analyses propose t h a t l e s s s t a b l e a l k o x i d e s and OH" should yield tetrahedral intermediates with acyl e l e c t r o p h i l e s , w h i l e s t a b i l i z e d a l k o x i d e s may prefer ion-dipole complexation. These notions are fully supported by the t h e o r e t i c a l and e x p e r i m e n t a l r e s u l t s r e v i e w e d h e r e , and p r o v i d e a r i c h v a r i e t y o f energy s u r f a c e s f o r n u c l e o p h i l i c r e a c t i o n s w i t h a c y l e l e c t r o p h i l e s i n the gas phase. The

E f f e c t o f H y d r a t i o n on

the R e a c t i o n o f OH"

+ HoC-0

The i m p o r t a n c e o f s o l v a t i o n on r e a c t i o n s u r f a c e s i s e v i d e n t in s t r i k i n g medium dependence o f r e a c t i o n r a t e s , p a r t i c u l a r l y f o r p o l a r r e a c t i o n s , and i n v a r i a t i o n s o f p r o d u c t d i s t r i b u t i o n s as f o r methyl formate discussed above and of relative reactivities (18,26). Thus, i n o r d e r t o o b t a i n a m o l e c u l a r l e v e l u n d e r s t a n d i n g o f the i n f l u e n c e o f s o l v a t i o n on the e n e r g e t i c s and c o u r s e s o f r e a c t i o n s , we have c a r r i e d out s t a t i s t i c a l mechanics s i m u l a t i o n s t h a t have y i e l d e d f r e e e n e r g y o f a c t i v a t i o n p r o f i l e s (30) for s e v e r a l o r g a n i c r e a c t i o n s i n s o l u t i o n (11.18.19.31). The computational procedure t y p i c a l l y involves three main s t e p s . F i r s t , the minimum energy r e a c t i o n p a t h i s d e t e r m i n e d f o r the gas phase u s i n g ab i n i t i o c a l c u l a t i o n s . The e n e r g e t i c and g e o m e t r i c v a r i a t i o n s a l o n g the r e a c t i o n path are then f i t to continuous functions of the reaction coordinate. Then, i n t e r m o l e c u l a r p o t e n t i a l f u n c t i o n s are obtained to d e s c r i b e the i n t e r a c t i o n s between the r e a c t i n g system and a s o l v e n t m o l e c u l e . These usually vary with the reaction coordinate and are r e p r e s e n t e d t h r o u g h Coulomb and Lennard-Jones i n t e r a c t i o n s between s i t e s n o r m a l l y s i t u a t e d on the atoms. F o r aqueous s o l u t i o n s , the solute-water p o t e n t i a l functions are d e r i v e d from numerous ab i n i t i o r e s u l t s f o r complexes o f the r e a c t i n g system and a water m o l e c u l e , w h i l e the w a t e r - w a t e r i n t e r a c t i o n s a r e d e s c r i b e d by the well-proven TIP4P model (32)· Finally, with analytical descriptions of the gas-phase reaction path and of the i n t e r m o l e c u l a r p o t e n t i a l f u n c t i o n s , Monte C a r l o s i m u l a t i o n s are c a r r i e d out t o c a l c u l a t e the f r e e e n e r g y p r o f i l e f o r the r e a c t i o n path i n s o l u t i o n . A c t u a l l y a series of simulations a r e needed w i t h "importance s a m p l i n g " t o c o v e r the f u l l range o f the r e a c t i o n coordinate (18). The q u a n t i t y t h a t i s u l t i m a t e l y computed i s the p r o b a b i l i t y o f o c c u r r e n c e , g ( r ) , o f each v a l u e o f the r e a c t i o n c



212

coordinate, r . I n t u r n , t h i s i s r e l a t e d t o the f r e e energy change a l o n g the r e a c t i o n c o o r d i n a t e o r " p o t e n t i a l o f mean f o r c e " by w ( r ) - -kgT In g ( r ) + const. B e s i d e s the thermodynamic results, the simulations also yield a d e t a i l e d view o f the s t r u c t u r a l and e n e r g e t i c changes i n s o l v a t i o n a l o n g the r e a c t i o n path. I t s h o u l d be emphasized t h a t we have o n l y b e e n computing the e f f e c t s o f s o l v a t i o n on the gas-phase r e a c t i o n p a t h s ; changes i n mechanism i n s o l u t i o n a r e n o t p r o v i d e d f o r so f a r . A f t e r the i n i t i a l work on SJJ2 r e a c t i o n s , the methodology was a p p l i e d t o the a d d i t i o n o f h y d r o x i d e i o n t o f o r m a l d e h y d e . The ab initio c a l c u l a t i o n s f o r the gas-phase MERP and the potential f u n c t i o n s were a l l c a r r i e d out w i t h the 6-31+G(d) b a s i s s e t ( 1 1 ) . As i l l u s t r a t e d i n F i g u r e 9, the a p p r o a c h a t l a r g e s e p a r a t i o n i s coplanar with the hydroxide ion on the dipole axis of formaldehyde. An a p p a r e n t i o n - d i p o l e minimum o c c u r s a t a C-0 separation o f 2.74 À w i t h a b i n d i n g e n e r g y o f 19 k c a l / m o l , as shown by the s o l i d c u r v e i n the l o w e r p a r t o f F i g u r e 10. However, an a c t i v a t i o n e n e r g y o f o n l y 1 k c a l / m o l i s needed to reach the transition s t a t e w i t h r(C-O) - 2.39 Â a t w h i c h p o i n t the h y d r o x y l fragment has lifted out of the plane to assume the more t e t r a h e d r a l , f i n a l approach. The e n e r g y change i s t h e n r a p i d as covalent b o n d i n g s e t s i n between the t r a n s i t i o n s t a t e and the t e t r a h e d r a l p r o d u c t a t r ( C 0 ) - 1.47 Â. The o v e r a l l e n e r g y change for the reaction is calculated t o be -35.2 kcal/mol. The e x i s t e n c e o f the i o n - d i p o l e minimum i s c l e a r l y t e n t a t i v e and may n o t s u r v i v e f u r t h e r i n c r e a s e s i n the l e v e l o f t h e o r y . Thus, the e n e r g y s u r f a c e c o u l d be a s i n g l e - w e l l , though the a p p r o a c h has two s t a g e s dominated r e s p e c t i v e l y by i o n - d i p o l e and c o v a l e n t forces s e p a r a t e d n e a r 2.5 Â. c


c

c

A s e c o n d t r a j e c t o r y was a l s o s t u d i e d as i n d i c a t e d by the dashed c u r v e s i n F i g u r e 10. I n t h i s c a s e , the 0C0 a n g l e was f i x e d a t i t s v a l u e o f 127° a t the t r a n s i t i o n s t a t e f o r a l l s e p a r a t i o n s beyond r ( C 0 ) - 2.39 Â. The more t e t r a h e d r a l a p p r o a c h c o r r e s p o n d s t o t r a d i t i o n a l i d e a s about a p p r o a c h v e c t o r s i n a d d i t i o n r e a c t i o n s (33). The ion-dipole minimum no longer occurs for this t r a j e c t o r y , though the e n e r g y s u r f a c e has a r e l a t i v e l y f l a t r e g i o n between r ( C 0 ) - 1.9 and 2.4 Â. The Monte C a r l o c a l c u l a t i o n s were s u b s e q u e n t l y e x e c u t e d f o r the r e a c t i n g system s u r r o u n d e d by 269 TIP4P w a t e r m o l e c u l e s i n a r e c t a n g u l a r box w i t h p e r i o d i c boundary c o n d i t i o n s a t 25°C and 1 atm. The d e t a i l s are r e p o r t e d e l s e w h e r e (11), though the key r e s u l t s a r e i n the top p a r t o f F i g u r e 10. The f r e e e n e r g y c u r v e s f o r the two t r a j e c t o r i e s i n w a t e r r i s e o n l y g r a d u a l l y f r o m the reactants to r(C0) ca. 3 Â. Loss in hydroxide-water i n t e r a c t i o n s i s l a r g e l y o f f s e t by i n c r e a s e i n the i o n - f o r m a l d e h y d e a t t r a c t i o n i n t h i s region. Then, the c h a r g e d e l o c a l i z a t i o n s e t s i n , w h i l e the gas-phase e n e r g y i s r e l a t i v e l y c o n s t a n t between 2 and 3 Â. C o n s e q u e n t l y , the weakening s o l v a t i o n i s no longer b a l a n c e d and the f r e e e n e r g y o f a c t i v a t i o n c u r v e s r i s e r a p i d l y t o the t r a n s i t i o n s t a t e w h i c h i s p r e d i c t e d t o o c c u r a t r ( C 0 ) 2.05 Â. From t h e r e , the gas-phase e n e r g y descends q u i c k l y , t o the t e t r a h e d r a l a d d u c t and the p o t e n t i a l o f mean f o r c e f o l l o w s s u i t . I t i s a l s o n o t a b l e t h a t no e v i d e n c e i s f o u n d f o r any i n t e r m e d i a t e s o t h e r t h a n the p r o d u c t i n water, and t h a t the a c t i v a t i o n b a r r i e r


12.

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0

-

ι

7

1 1 1 1 1 1 -

5

3 1 1 3 REACTION COORDINATE (ft)

5

1 7

F i g u r e 8. 3-21+G energy p r o f i l e f o r t h e r e a c t i o n o f F" + HCOF. The r e a c t i o n c o o r d i n a t e i s t h e d i f f e r e n c e i n t h e two CF distances.

F i g u r e 9. 6-31+G(d) o p t i m i z e d s t r u c t u r e s p a t h f o r t h e r e a c t i o n o f OH" + H C-0.

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30

i 1

1 1 1 1 1 1 2

1

3

4 5 6 7 8 REACTION COORDINATE (A) F i g u r e 10. C a l c u l a t e d p o t e n t i a l e n e r g i e s i n t h e gas phase (bottom) and p o t e n t i a l s o f mean f o r c e i n aqueous solution (top) f o r the A d r e a c t i o n o f OH" + h^C-O. Solid lines r e p r e s e n t t h e c o l l i n e a r MERP w i t h C symmetry i n t h e gas phase, w h i l e t h e dashed l i n e s a r e f o r a more p e r p e n d i c u l a r initial approach. The r e a c t i o n coordinate i s the C-0 distance. N

s

H


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for the addition reaction is entirely solvent-induced. The s o l v e n t e f f e c t s a r e c l e a r l y p r o f o u n d ; the o r i g i n o f the b a r r i e r was c a r e f u l l y s t u d i e d and i s a t t r i b u t a b l e t o the weakening o f h y d r o g e n bonds to the substrates t h a t accompanies the charge d e l o c a l i z a t i o n i n s i d e r(CO) - 3 À . The average number o f s t r o n g h y d r o g e n bonds i s c o n s t a n t a t 6-7 a l o n g the e n t i r e r e a c t i o n p a t h ; however, the average w a t e r - i o n i n t e r a c t i o n weakens from c a . 20 k c a l / m o l f o r the h y d r o x i d e i o n to 13 k c a l / m o l f o r the p r o d u c t


(11). The energetic results a r e s i m i l a r to e x p e r i m e n t a l d a t a o f G u t h r i e (34) and the t h e o r e t i c a l p r e d i c t i o n s o f Weiner e t a l . (13) for a l k a l i n e hydrolyses of amides. For t h e i r systems, the a c t i v a t i o n energy f o r the a d d i t i o n s t e p i s about 22 k c a l / m o l and the t e t r a h e d r a l i n t e r m e d i a t e i s 9-18 k c a l / m o l above the r e a c t a n t s . Ester hydrolyses are typically more facile with activation energies of 15-20 kcal/mol (34)· The combined quantum and m o l e c u l a r mechanics a p p r o a c h o f Weiner e t al. a l s o l e d to a p r e d i c t e d CO d i s t a n c e o f about 2.0 Â i n the aqueous transition s t a t e f o r the a d d i t i o n o f OH" to formamide. T h u s , the t r a n s i t i o n states for these endoergic processes are geometrically very product-like. For formaldehyde, the computed endoergicity o v e r e s t i m a t e s the a v a i l a b l e e x p e r i m e n t a l d a t a by c a . 15 k c a l / m o l (34) Î the computed r e s u l t i s more i n l i n e w i t h d a t a f o r k e t o n e s , where f o r m a t i o n o f h y d r a t e s i s l e s s f a v o r a b l e . The d i s c R r e p a n c y l i k e l y comes from o v e r l y e x o t h e r m i c h y d r a t i o n o f the h y d r o x i d e i o n w h i c h lowers the r e a c t a n t end o f the f r e e energy c u r v e s . This results from use o f two-body p o t e n t i a l functions t h a t do n o t adequately t r e a t p o l a r i z a t i o n . Nevertheless, the f e a s i b i l i t y o f p e r f o r m i n g such c a l c u l a t i o n s i n s o l u t i o n has been e s t a b l i s h e d and the i n s i g h t s on the v a r i a t i o n i n s o l v a t i o n a l o n g the r e a c t i o n p a t h a r e most l i k e l y v a l i d , though somewhat a m p l i f i e d . O v e r a l l , an e x c i t i n g p e r i o d has c l e a r l y been e n t e r e d i n w h i c h theoretical c a l c u l a t i o n s c a n p r o v i d e extreme d e t a i l s on the c o u r s e o f o r g a n i c r e a c t i o n s b o t h i n the gas phase and i n s o l u t i o n . Acknowledgments Gratitude National programs.

is e x p r e s s e d t o the N a t i o n a l S c i e n c e F o u n d a t i o n and Institutes of Health for support of our research

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