Rationalization of strain and steric effects by molecular mechanics calculations

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Rationalization of strain and steric effects by molecular mechanics calculations

MULLER, Paul, MILIN, Didier Jean

Abstract

Nous avons examiné des constantes d'équilibre et de vitesse de réactions dans lesquelles le centre reactionnel subit un changement d'hybridation entre sp³ et sp² en utilisant des calculs de mécanique moléculaire. Des modèles empiriques sont appliqués afin de simuler les propriétés stériques des états transitoires de ces réactions. Les calculs permettent de rationaliser l'hypothèse du "I-strain" de Brown et les vitesses de l'oxydation chromique des alcools secondalres et de la solvolyse des dérivées tertiaires.

MULLER, Paul, MILIN, Didier Jean. Rationalization of strain and steric effects by molecular mechanics calculations.

Journal de Chimie Physique et de Physico-Chimie Biologique

, 1992, vol. 89, p. 1639-1645

Available at:

http://archive-ouverte.unige.ch/unige:152047

Disclaimer: layout of this document may differ from the published version.

1 / 1

Rationalization of strain and steric effects by molecular mechanics calculations

P MOiier*, D Milin

Departement de Chimie Organique, Universite de Geneve, 1211Geneve4, Switzerland

• Correspondence and reprints

RESUME: Nous avons examine des constantes d'equilibre et de vitesse de reactions dans lesquelles le centre reacUonnel subit un changement d'hybridaUon entre sp3 et sp2 en utillsant des calculs de mecanique moleculaire. Des modeles empiriques sont appliques afin de simuler les proprietes steriques des etats trans1toires de ces reactions. Les calculs permettent de rationaliser l'hypothese du "I-strain" de Brown et Jes vitesses de l'oxydation chromique des alcools secondalres et de la solvolyse des derivees tertiaires.

SUMMARY: We have examined rate and equilibrium constants for reactions in which the re- acting centre undergoes hybridization change between sp3 and sp2 by means of molecular me- chanics calculations. Empirical models have been used in order to simulate the steric require- ments of the transition state of these reactions. The calculations provide a rationalization for Brown's "I-strain" hypothesis, for the rate constants of the chromic acid oxidation of secondary al- cohols. and of the solvolysis of tertiary derivatives.

1. Introduction

The interpretation of strain and steric effects in chemical reactions is a classical problem in mechanistic organic chemistry [l). It requires quantitative estimation of strain in the reacting molecule and in the product in the case of equilibria, or of transition states in the case of rate constants. In the past. such knowledge was obtained from thermochemical measurements. by correlation with steric substituent constants or by comparison of series of related reactions.

Molecular mechanics calculations [2] provide a simple empirical method for computation of en- thalpies of formation and for strain energies of organic compounds. The method is particularly re- liable for hydrocarbons. It is also parametrized for molecules containing functional groups. but in this case, the calculations are associated with considerable uncertainties.

In this conununication we discuss application of molecular mechanics calculations (mostly MM2) (3) towards reactions where the reaction centre undergoes a hybridization change from sp3 to sp2 and vice-versa.

2. Equilibrium Constants

Equilibrium constants provide a suitable testing ground for molecular mechanics calcula- tions, because the structures and energies of reactants and products are in principle well known, or accessible by spectroscopic and thermochemical methods respectJvely. In connection with investigations on the "I-strain" [4) hypothesis, the dissociation constants for the cyanohydrines of

-1640-

monocyclic ketones have been determined (5). Owing to the very small ster1c requirements of the cyano group (A-value of 0.15-0.25 (6)) the strain and steric effects operating in this reaction may be approximated by those occurr1ng between alcohols and the corresponding ketones. The latter have been determined exper1mentally by reacting the alcohols with cyclohexanone in the presence of a catalyst such as alumtnum tsopropoxide or Raney nickel (7):

5 I-

ol

~CHOH + C6H₁₀0 =

Kcq

~C=O + C₆H₁₁0H

Kcq

= ^[~C=O)[C₆^H₁₁^0H)/[R₂^CHOH)[C₆^H₁₀⁰⁾ .6.G0x = - Rf In K"cq_

-t.Str•in t.t.G

6- ^·r

9 8

11

~ ¹⁰

11 7 •

s ."f{)~

6 '

OL

All .

⁶ 0

^{. ,} "cE)...oH

4

0

₄

I 1£H ^{//0-r»i 110~}

o(

-AG ox

I

^{·5 I -OG} OX

0 5 ^{· 5 0 5}

Fig. 1 (left) Plot of MG for dissociation of cyclic cyanohydr1nes vs . .6G₀x (slope 1.02;

r=0.989); right: Plot of -.6stra1n (R₂C=O - R₂CHOH) vs. -.6.G₀x (slope 0.92, r=0.966).

In Fig. 1 (left) the .AG₀x-values are plotted against the dissociation constants of the cyanohy- dr1nes of the same ketones, (expressed in terms of free energies) relative to that of cyclohexanone.

The data correlate well with the MM2-calculated strain differences between ketones and alcohols (Fig. 1, r1ght): however, a discrepancy occurs in the case of the very strained 2-btcyclo(2. l . 1 Jhexa- none and cyclobutanone. This is probably due to an inadequate parametrization. In fact, the en- thalpies of formation of cyclobutanone are not definitely established. The most recent compilation

of Liebman (8) lists only an estimated value of -21 kcal/mol, and MM2 gives -21.0 [9). An experi- mental value of -21.9 has been reported by Rocek and Radkovsky [ 10). but another detennination [11) arrives at -24.5. The reliability of this latter work has however been questioned [9J.

The equilibrium data ^(-~Goxl suggest that cyclobutanone (1.67) should be less strained with respect to cyclobutanol than cyclohexanone (0.0) with respect to cyclohexanol, and more strained than cyclopentanone (2.16) With respect to cyclopentanol. These tendencies are reflected in the rates of alcohol oxidation with chromic acid which decrease in the series cyclopentanol > cy- clobutanol > cyclohexanol, although the rate variations are small [9J. Recently, the enthalpies for reduction of some monocyclic ketones with L1Et₃BH have been determined for cyclobutanone (-

12.7) cyclopentanone (-10.9) and cyclohexanone (-14.1 kcal/mol) [lOJ. The data correlate well with the ^~G0^x-values. This confirms, that the deviation of cyclobutanone in Fig. I (right) must be due to the calculations, and not to an experimental error.

3. Reaction Rates

The requirements for applicability of molecular mechanics calculations to rate constants are that steric effects dominate the reactivity, and that the reaction series obeys an isokineUc rela- tionship [12). The problem then is to have a transition state model available, the strain of which may be calculated. Such models can be designed by intuition or by trial and error on the grounds of detailed knowledge of the reaction mechanism. or by ab iniiio calculations [13J.

3.1. Chromic Acid Oxidation of Secondary Alcohols

The rate-determining step of the alcohol oxidation With chromic acid consists in the break- down of an intermediate chromate ester in the steady state. to yield ketone and a chromium(4) species. Experimental evidence suggests. that the properties of the carbonyl group should be at least partly developed in the transition state and, therefore. the carbonyl group may be used as a transition state model. The rate constants for oxidation may therefore be correlated with the strain changes between ketone and alcohol (Fig. 2, left.) [14]. As expected, the highly strained al- cohols are the most reactive ones. while alcohols leading to strained ketones react more slowly.

The slope of the regression line (0.35) indicates that only ea. 40% of the strain changes between alcohol and ketone are reflected in the rates of oxidation. A perfect TS model would have a slope of unity if the relative reactivities were expressed in terms of free energies of activation.

-1642-

I . ^{log k2}

(r~I~ I'\

^t::..a*

A Ii.

^{I I -4}

M·\

⁰

_{· ~ I I .~} ^~

"o

~

⁰

4 I

c a \ . c 0

t.Est

I

^{I a}

I .\

-·~ _; .A\ ' ' • •

L

^{.lE•t \}

_, £ \: t\ I

^{_a o a}

Fig. 2 (left) Plot of log k for alcohol oxidation us. strain difference (6.E₅

J

between ketone and alcohol (slope -0.35, r=0.940). (light) Plot of .1.G• for acetolysis of sec. tosylates us.

ster1c energy difference 6.E₅₁ (ROH - R+J: (slope 0.67, r=0.958).

3.2. Solvolysis of Secondazy Tosylates

Intuitively one might expect some resemblance between oxidation of secondary alcohols and the solvolysis of the corresponding secondary p-toluene sulfonates. since in both cases hybridiza- tion change from sp3 to sp2 at the reacting centre is involved. Unfortunately, matters are not as simple as that. Solvolysis is in fact an extremely complicated reaction. Compounds which are known to solvolyze with solvent participation, anchimertc assistance, or which suffer leaving group hindrance upon solvolysis may not be treated with molecular mechanics calculations at the present stage of development. However, if one considers only

kc

substrates, it is possible to design a force-field for carberuum ions as transition state model. which results in a satisfactory correla- tion of .1.strain (RzCH+- R₂CHOH) with log k for acetolysis (Fig. 2 (right)) [15).

3.3. Solvolvsis ofTertiarv Substrates

An analogous correlation results. if the rates of solvolysis of tertiary bridgehead derivatives (16) are plotted against the changes in steric energies between R3C+ and R3C-H (Fig. 3 (left)) [17).

Contrary to previous findings [18), front strain plays no major role With these substrates. and all compounds of the sertes can be correlated with only one equation and the same set of parameters.

The correlation may be extended to include tertiary non-bridgehead derivatives: however this ex- tension deteriorates the fit of the correlation (20). The non-bridgehead derivatives exhibit much more scatter in the strain-reactivity plot (Fig. 3 (right)). and appear to be slightly accelerated over the bridgehead derivatives, which solvolyze in a mechanistically more homogeneous manner.

Differences in solvation of the transition state for bridgehead as compared to non-bridgehead derivatives as well as solvent participation (ks-pathways) in solvolysis of the latter, should be the main reasons for the different behaviour of the two series of compounds. Some of the additional scatter may however be ascribed to the use of the OH group as leaving group model in the calcu- lations. This introduces some minor artefacts which disappear with other leaving groups, such asBr.

L•t l t•l•TLIY)

. .?>

·~

p· tB

IOI- log k

0"$

_{G> ' 0}

~ ~0~

~.e"'~~

•• 1$" ^~ 4' ^i:J

⁰

&.

~

f[),

• I

·•

~ ~

~

~~A

.f:1

. ---

-10

••

..

~•

.. ..

^{-10 0 10 20 JO}

Fig. 3 (left) Plot of log k for solvolysis vs. steric energy difference ..:iE₅t (R+ - R-H) for bridgehead derivatives. (slope -0.45, r=0.996). (right) Plot of log k for solvolysis vs ^..:iE₅₁ (R+ - ROH) for bridgehead and non-bridgehead derivatives (slope -0.47, r=0.983).

Although the carbenium ion force-field gives satisfactory correlations with most of the conventional compounds, it fails for carbenium ions which suffer severe strain owing to angle deformation at the cationic centre, such as the cyclobutyl cation. A typical example for this devia- tion is found in the case of 7-methyl-7-norbomyl derivatives (Fig. 2(left)). In addition, the force- field cannot handle cations of the nortricyclyl type, where the cationic centre carries a cyclo- propane ring in p-position. We have now developed two sets of parameters to account also for these situations. The parameters were adjusted in such a way that the best possible agreement with the strain-reactlvity plot for bridgehead derivatives, which served as mechanistic models, was obtained. It turned out. that the parameter set for the cyclobutyl and cubyl cations is at the samer time applicable to tertiary 7-norbomyl cations. Fig. 4 shows a strain-reactivity plot with Br as

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leaving group model for 49 tertiary compounds, including the normal bridgehead dertvatlves, ter- tiary non-bridgehead substrates and nortrtcyclyl and cyclobutyl compounds. Current experiments are directed towards determination of the enthalpies of formation of these ions. This determina- tion should provide a conclusive test for the parametrization, and for the relevance of the gas phase stability of carbentum ions for their rate of formation in solvolytlc reactions.

20-r~~---r---

log k

15 10 5

0 -

@l~

O L ~

a_.._,__

^L

~

-5

-10

4b

-15 ^l

- +

-20

-30 -10 10

30

6Est(R-RBr)5o

Fig. 4. Plot of log k for solvolysis of 49 tertiary derivatives including tricyclyl and cyclobutyl compounds vs . .6.E₅t(R+ - R-Br); (Slope -0.407, r=0.977).

4. References

(1) C.J.M. Stirling, Tetrahedron. 1985, 41, 1613.

[2] U. Burkert, N.L. Allinger, "Molecular Mechanics", American Chemical Society (1982).

(3) N.L. Allinger, D.Y. Chung, J. Am. Chem. Soc. 1976, 96, 6798; N.L. Allinger, ibid, 1977, 99, 8127; N.L. allinger, Y. Yuh, Quantum Chemistry Program Exchange (QCPE), 1979, 395.

(4) H.C. Brown, K. Ichikawa. Tetrahedron. 1957, 1, 221.

(5) V. Prelog, M. Kobelt, Helv. Chim. Acta, 1949, 32. 1187; O.H. Wheeler, E.C. Rodriguez, J.

Org. Chem. 1964, 29, 718.

(6) F.R Jensen, C.H. Bushweller, Adv. Alicyclic Chem. 1970, 3, 140.

(7) P. Muller, J. Blanc, Helv. Chim. Acta 1980, 63, 1759; Tetrahedron Lett 1981, 22, 715.

[8) S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, RD. Levin, W.G. Mallard, "Gas Phase Ion and Neutral Thennochemist:ry", J. Physi.cal and Chemical Reference Data. 1988, 17, Suppl. No. 1. American Institute of Physics, New York, 1988.

(9) K.B. Wiberg, L.S. Crocker, K.M. Morgan, J. Am. Chem. Soc. 1991, 113, 3447.

[10) J. Rocek, A. Radkovsky, J. Am. Chem. Soc. 1973, 95, 7123.

(11) G. Wolf, Helu. Chim. Acta. 1972, 55, 1446.

(12) B. Giese, Acc. Chem. Res. 1984, 17, 438.

(13) AE. Dongo, K.N. Houk, J. Am. Chem. soc. 1987, 109, 3698; Y.D. Wu, K.N. Houk, J. Am.

Chem Soc. 1987, l 09, 906; K.N. Houk, J. Org. Chem. 1982, 52, 959.

(14) P. Muller, J. Blanc, D. Lenoir, Helv. Chim. Acta.1982, 65, 1212; P. Muller, J.C. Perlberger, J.

Am. Chem. Soc. 1975, 97, 6862; 1976, 98, 8407.

[15) P. Muller, J. Mareda, Helu. Chim Acta. 1985, 68, 119; Tetrahedron Lett 1984, 25, 1703.

(16) T.W. Bentley, K. Roberts, J. Org. Chem. 1985, 50, 5852.

(17) P. Muller, J. Blanc. J. Mareda, Helv. Chim. Acta. 1986, 69. 635; 1987, 70, 1017: Chimia 1984, 38, 389.

(18) RC. Bingham. P.v.R Schleyer, J. Am. Chem. Soc. 1971 93, 3189; W. Parker, RL. Trauter, C.I.F. Watt, L.W.K. Chang, P.v.R Schleyer, J. Am Chem Soc. 1974, 96, 7121.

(19) P. Muller, J. Mareda, in "Cage Hydrocarbons" G.A, Olah, ed. Wiley Intersctences, New York, 1990, chap. 6.; P. Muller, J. Mareda, J. Comput Chem 1989, 10, 863.