- Email: [email protected]
A theoretical study of steric effects in SN2 reactions
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
14 August 1992
A theoretical study of steric effects in SN2 reactions F r a n k Jensen Department of Chemistry, Odense University, DK-5230 Odense M., Denmark Received 4 February 1992; in final form 22 May 1992
The gas phase reaction of chloride ion with alkyl chlorides (methyl, ethyl, propyl, i-propyl,/-butyl, t-butyl and neo-pentyl ) has been studied by ab initio methods. Geometries of stationary points along the reaction coordinate have been optimized at the MP2/6-31 G* level of theory and improved energies have been calculated with the 6-311 + G (2d) basis. Although all reactions are "narcissistic", i.e. reactant and product are identical, it is found that some of the transition structures have unequal C-CI bond lengths. The breaking/forming C-CI bond for the t-butyl system is significantly longer than for the other alkyl groups, for which the change with increasing steric bulk is as expected. The calculated relative activation energies are compared with available gas-phase data and relevant solution values.
1. Introduction
The SN2 reaction of alkyl halides is a textbook example of how steric factors can alter reaction rates [ 1 ]. Substantial experimental work has established that in solution the relative rates of RX, with R being different alkyl groups, are relatively constant for a variety of X [ 1,2 ]. Experimental results for gas-phase reactions are scarce but the available data show the same ordering, although steric effects appear to be roughly a factor two larger than in solution [ 3]. A large number of publications, both theoretical and experimental, have reported detailed investigations of the SN2 reaction. It is impractical here to include a full list of references, below is a selection of some of the more relevant articles, the most recent may be consulted for references to prior work. In the gas phase the Sr~2 reaction proceeds via initial formation of an ion-dipole complex of the nucleophile with the reagent, which then in a single kinetic step is transformed to a complex of the product and the leaving group [ 3-11 ]. In solution the ion complexes are destabilized relative to the separated reagents and in water they may be completely absent [121. Correspondence to: F. Jensen, Department of Chemistry, Odense University, DK-5230 Odense M., Denmark.
368
In connection with other work [ 13] we became interested in how the geometry of the transition state (TS) varies as a function of R. The majority of previous calculations has concentrated on reactions of the type X - + CH3Y with X and Y being small species such as H, F and C1 [ 9-11 ]. An investigation of the C 1 - + R B r reaction with R being methyl, ethyl and i-propyl at the H F / M I N I level has also appeared [8 ]. In the present work we investigate the SN2 identity reaction CI- + RCI, with R being methyl, ethyl, propyl, i-propyl,/-butyl, t-butyl and neo-pentyl. The methyl, ethyl, i-propyl and t-butyl species form a series with increasing substitution at the a-carbon while ethyl, propyl, /-butyl and neo-pentyl form a series with increasing 1~substitution. Although the reaction series X - + RX with X = F or H would be easier to treat computationally it was thought that the small size of hydrogen and fluorine would tend to obscure the effect of steric bulk of the R group. It is likely that elimination reactions will compete with substitution for the branched R groups but we have chosen to concentrate on the steric effect in SN2 reactions in this work, regardless of whether other lower energy reactions exist. For studying the present reaction sequence which includes rather large R groups like neo-pentyl, a judicious choice of computational method has to be made. It is clearly desirable to include electron cor-
0009-2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
relation, which necessitates a basis set of at least DZP quality, and the anionic nature of the system suggests that the basis set should include diffuse functions [ 14 ]. Meeting these standards makes the computational problem quite large. The major effect of diffuse functions is usually on (relative) energies and less on geometries. TS geometries, however, may change significantly if the addition of diffuse functions alter the overall reaction energy, e.g. if the reaction becomes more exothermic it is likely that the TS becomes "earlier". In the present case all the reactions are thermoneutral and it is thus likely that TS geometries are insensitive to the presence of diffuse functions. We have therefore selected the M P 2 / 6-31 G* method as a common level for studying the reaction sequence. Test calculations for the methyl system (see below) suggest that the 6-31 G* basis set gives geometries comparable to those from better basis sets. Improved energies of stationary points have been obtained by extending the MP2/6-31G* calculations both with respect to additional electron correlation and basis functions.
2. Computational details All calculations have been performed with the GAUSSIAN 90 program package [ 15 ]. A description of notation and procedures used in this paper can be found in ref. [ 14]. The geometries have in general been optimized without any symmetry constraints which should ensure that only genuine TSs and minima are located (i.e. no higher-order saddle points in TS searches and no TSs in minimum searches). The resulting stationary points on the potential energy surface (PES) however, do, with one exception, have at least one element of symmetry as discussed below.
3. Results and discussion The reaction of C1- with CHIC1 was used for probing the sensitivity of stationary point geometries to the size of the basis set. At the HF/6-31 G* level the C-CI distance at the TS is 2.38 A compared to 2.31 A at when electron correlation is included by the MP2 procedure. Table 1 shows how the geometry
14 August 1992
Table 1 Geometriesof MP2 stationarypoints on the PES for CI- + CH3CI. D is the C-CI distance (,~) and a is the H-C-CI angle (deg) Basis
6-31G* 6-31 +G* 6-311 +G(2d)
TS D 2.307 2.316 2.301
Complex
DI
D2
ot
3.158 3.265 3.169
1.812 1.809 1.829
109.0 108.9 108.3
of the ion complex and TS vary as a function of basis sets at the MP2 level. The TS geometry is insensitive to extending the basis set beyond 6-31G*, while changes up to 0.1 ,~ occur for the non-bonded C-C1 distance in the complex. However, the PES as a function of this distance is very fiat, e.g. the energy is lowered by only 0.1 kcal/mol upon reoptimization of the MP2/6-31G* structure with the 6-31 + G * basis, and consequently the use of geometries obtained with the 6-31 G* basis for higher-level calculations introduce little error. The TS for the methyl system must by virtue of symmetry belong to the D3h point group. For the ethyl system one might a priori have predicted the TS to have two equal C-CI distances with a plane of symmetry, g, including the two carbon atoms and the two hydrogens on the reacting carbon (i.e. approximately perpendicular to the C1-C-C1 "axis"), as the reaction is "narcissistic", i.e. reactant and product are identical [ 16 ]. Indeed this is the case at the H F / 6-31G* level as proven by a frequency calculations which showed one imaginary frequency (367i c m - l , the lowest real frequency is 16 c m - ~). An alternative structure with the methyl group rotated 30 ° such that one of the C - H bonds eclipses one of the C-C1 bonds has also C~ symmetry with the mirror plane being defined by the reacting carbon and the two chlorine atoms, this type of mirror plane will be denoted t~' in the following. This structure is a second-order saddle point at the HF level, hut it is only 0.003 kcal/mol higher in energy and the second imaginary frequency (corresponding to a methyl group rotation) is very low, 10i cm-~. At the MP2 level the situation is reversed, here the a ' symmetric species is the genuine TS. The geometry with a o-type of mirror plane is a second-order saddle point (second imaginary fre369
Volume 196, number 3,4
14 August 1992
CHEMICAL PHYSICS LETTERS
( t'xl
d
r-la.
O
II rc
ll
tt') O
o v-
$°
e-
rr
o
..=
8
o')
~o
o~
c~
0")
O~
"6 II Ct"
II IT
.2 ,7,
e~
"F .-2
q p~ O ¢0
o xt
3~
0) U rt"
II tr
¢q ¢O Q
() 370
tt'J ¢O
cd
t'M
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
14 August 1992
Table 2 Geometries of MP2/6-31G* stationary points on the PES for C!- + RCI. D is the C-CI distance (/~) and a is the C1-C-CIangle (deg) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
TS
Complex
D1
D2
a
D,
D2
2.307 2.342 2.356 2.419 2.355 2.604 2.405
2.307 2.369 2.356 2.419 2.391 2.637 2.412
180.0 165.3 165.2 158.5 160.5 178.0 149.7
3.158 3.345 3.385 3.744 3.558 3.844 3.402
1.812 1.819 1.813 1.830 1.808 1.845 1.814
quency is 8 li c m - ~) located 0.11 kcal/mol higher in energy. A drawing of the MP2 TS is shown in fig. 1, selected bond lengths and angles can be found in table 2. Apparently there is no strong preference for a specific orientation of the methyl group and the exact conformation depends on the level of theory. It is likely that similar low energy rotations also exist for the other alkyl groups described below. We note that the correct TS is located by starting the optimization from a trial geometry without any symmetry. Substituting the methyl group with an ethyl moiety, making the propyl system, produces a TS with a atype plane of symmetry as shown in fig. 1. Note that the propyl TS is not simply obtained by substituting a hydrogen by a methyl group in the ethyl TS, it also requires a 30 ° rotation of the carbon group neighbour to the reaction center. The i-propyl system has both types of mirror planes and belongs to the Czv point group, while the/-butyl TS has only a a'-type plane of symmetry. The methyl groups in the t-butyl TS are oriented as in the ethyl system with a a ' type of mirror plane. One of the methyl groups has a C - H bond parallel to one of the C-C1 bonds while the two other methyl groups have a C - H bond approximately parallel to the other C-C1 bond. Finally the orientation in the neo-pentyl TS is analogous to the ethyl TS except for the substitution of a C (CH 3 ) group for C H 3. The consequence of unequal C-C1 bond lengths for the ethyl, /-butyl, t-butyl and neo-pentyl TSs is that there exist two equivalent TSs for the degenerate chloride exchange. If the reaction is made unsymmetrical, e.g. by going to the C1- + RBr reaction, or by isotopic substitution (35C1/37C1), the equiva-
180.0 167.4 143.5 174.4 126.5 180.0 138.2
lence will be lost. This may result in two TSs of slightly different energy or in the transformation of one of the TSs into a higher-order saddle point. Of course it is possible that higher-level calculations may produce TSs with equal C-C1 bond lengths for all the current species. The overall variation of the breaking/forming C-C1 distance in the series is, except for the t-butyl species, fairly small. The trend in both the ct and 13 series is as expected, the addition of methyl groups on the a-carbon increases the C-C1 distance by 0.05, 0.1 1 and 0.31 A (ethyl, i-propyl and t-butyl relative to methyl) while the corresponding effect for the 13carbon is 0.00, 0.02 and 0.05/~ (propyl,/-butyl and neo-pentyl relative to ethyl). An interpretation of bond distances in terms of energy can be obtained by employing a Morse potential, in this case we have chosen a common dissociation energy of 80 kcal/mol and a force constant of 524 kcal/mol/12 [ 17 ]. The energy cost of stretching the C-C1 bond to its TS value, relative to breaking it completely, gives a measure of the amount of bond breaking/forming at the TS. With this approach the t-butyl TS has C-C1 bonds that are 59% broken while the value for the other alkyl groups is in the range 38%-45%. The C1-C-C1 angle is 180 ° for the methyl system and it deviates more and more from linearity as the size of one of the three groups on the reacting carbon grows. The angle for the ethyl TS is 165 ° which hardly changes upon going to the propyl species. Adding another methyl group on the 13 position, forming/-butyl, lowers the angle to 161 ° and further methyl substitution to the neo-pentyl TS decreases the angle to 150 °. 371
?
() 0..
rn II
II
II IT" % % % 0
o~ c~
%
©
c~
d)
?
~) E
8~P II
o
II
iI .o
cd ! I
d~ ()
d)
d)
II U II
%
I c0
cd I
\
d)
rr
II I'T"
©
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
The geometries of the C1-/RC1 complexes for the ethyl, propyl, i-propyl and neo-pentyl complexes all have a a ' type of mirror plane. The methyl and t-butyl systems have the full C3v symmetry, while the ibutyl complex is the only nonsymmetric species found. Drawings of all complexes are shown in fig. 2. The non-bonded C-C1 distance increases systematically through the u series while in the 13 series the neo-pentyl distance is somewhat shorter than for ibutyl. In order to obtain improved relative energies we have performed calculations with the 6-311 + G (2d) basis and included electron correlation up to MP4 (tables 3 and 4). As seen in table 3 the complexation energy is insensitive both to improving the basis and inclusion of electron correlation beyond MP2. For the TS the effect of increasing the basis set is to lower the activation energy by 2-4 kcal/mol at the MP2 level. Extending the perturbation series beyond sec-
Table 3 Complexationenergiesof CI- + RCI relativeto the reagents (kcal/ tool ) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
6-31G* MP2 11.0 12.4 10.6 14.1 14.5 16.2 10.5
HF
8.5 8.9 7.1 9.1 7.8 9.7 6.9
6-31 l+G(2d) MP2
MP3
MP4
10.6 11.8 10.5 13.1 13.0 14.7 10.8
10.3 11.5
10.5 11.7
Table 4 TS energies of C1- +RC1 relative to the reagents (kcal/mol) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
6-31G* MP2 4.6 8.4 7.1 11.6 9.1 22.2 10.4
HF
6.8 10.3 9.9 12.4 12.1 16.9 18.5
6-311 +G(2d) MP2
MP3
MP4
2.3 5.7 3.9 8.6 6.0 18.2 12.2
3.8 7.0
1.3 4.3
14 August 1992
ond-order gives results that are slightly oscillating, but relative activation energies change little by going to the MP4 level. The most recent value for the complexation energy of CI- and CH3CI is 12.2+2 kcal/mol [5], which is slightly higher than a previous value of 8.6 + 0.2 kcal/mol [ 6 ]. The calculated energy of 10.5 kcal/mol compares favourably with these results. Other computational work including electron correlation has yielded values from 9 to 11 kcal/mol [ 9 ]. The experimental t-butyl complexation energy is 14.3 kcal/mol [5] which also agrees with the calculated 14.7 kcal/mol. We have been unable to find experimental data for the other alkyl chloride complexes studied here. Experimental TS energies are difficult to measure for isodesmic gas-phase reactions of the type studied here [ 3,4 ]. For the methyl system Barlow, Doren and Bierbaum have recently obtained a value of 1 + 1 kcal/mol by fitting experimental data to an R R K M model [7]. Calculations at CEPA, CISD and MP2 levels of theory with D Z P type basis sets give values somewhat higher than this, 3-10 kcal/mol [ 9,10 ]. Our value of 1.3 kcal/mol obtained at our best theoretical level is in complete agreement with the experimental data, although this may well be fortuitous. It is generally observed that the steric effect of alkyl groups in solution is rather constant for a range of nucleophiles and leaving groups [ 2 ]. As there are no experimental results for the C1- + RC1 system, except for R = methyl, we have chosen to compare the theoretical values with experimental data for the closely related C I - + R B r and B r - + R B r reactions. The former reaction is close to thermoneutrality and thus the TS should be fairly "symmetric" with respect to bondbreaking/formation. Experimental gas-phase results have been reported for the C1- + RBr reaction [ 3 ], and corresponding solution phase data in D M F [ 18 ] and acetone are also available [ 19 ]. These data, together with those for the B r - + R B r reaction in acetone [20], are given in table 5. The H F / M I N I activation energies for ethyl and i-propyl relative to methyl for the C1- + RBr reaction are 6.1 and 16.5 kcal/mol [8], which are considerably higher than the current MP2/6311 + G ( 2 d ) values of 3.4 and 6.3 kcal/mol. We also note that M N D O calculations give relative activation energies which are roughly a factor two larger 373
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
14 August 1992
Table 5 Relative TS energies for X- +RY (kcal/mol) a) R
/~kgtco X=CI Y=C1
/~kggas X=CI Y=Br
~kEDMF X=CI Y=Br
~Ace I X=CI Y=Br
AEAce2 X=Br Y=Br
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
0.0 3.4 1.6 6.3 3.7 15.9 9.9
0.0 3.3 2.0 b) 7.6 8.2
0.0 1.3 1.9 3.0 1.8 3.3 8.4
0.0 1.9 1.8 3.1 2.4 5.3 (7.6) c) 6.0
0.0 1.7 1.7 3.9 3.1 6.0 6.2
) AEteoare MP2/6-311 + G ( 2d ) values from table 4, z ~ s are gas-phase data for the CI- + RBr reaction [ 3 ], AEDMFare corresponding values in DMF [ 18], ~SA~etare values obtained in acetone [ 19] and AEA~2are values for the Br- +RBr reaction in acetone [20]. b) Value for n-butyl. c~ Value redetermined in ref. [ 18]. than the current results [21 ]. Comparing the two last columns in table 5, it is seen that the steric effect in solution is fairly independent on whether the nucleophile is C1 or Br, or whether acetone or D M F is used as the solvent. The gas-phase effects for ethyl, propyl and i-propyl are roughly a factor of two larger than the corresponding solution data, while the value for/-butyl is significantly higher. The theoretical values for the three smaller systems compare favourably with the gas phase data, but again the experimental value for ibutyl appears too high. The calculated steric effect for t-butyl is much larger than expected from the solution phase data, with the possible exception of the redetermined value in acetone by Cook and Parker [ 18 ]. Solution phase rate constants for t-butyl, however, are inherently difficult to obtain experimentally. The major reaction o f t-butyl halides is elimination [ 18 ] and only a small percentage o f the total reaction is due to displacement, thus the activation energies in table 5 may well have substantial uncertainties. The calculations clearly indicate that neopentyl should react faster than t-butyl in an SN2 reaction. Accepting the theoretical values as representative o f gas-phase effect, it is also apparent from the data in table 5 that steric effects are reduced by roughly a factor two in solution compared to the gas phase. The correlation between the calculated energies and those for the C I - + R B r reaction in acetone (using the redetermined value by Cook and Parker) gives a correlation 374
coefficient of 0.98 with a slope of 0.47. A reasonable explanation of the reduced steric effect in solution may be that solvation of the anionic nucleophile/ leaving group results in a TS with longer breaking/ forming bonds than in the gas phase.
4. Summary Steric effects in the SN2 reaction of C I - with RCI ( R = m e t h y l , ethyl, propyl, i-propyl, /-butyl, t-butyl and neo-pentyl) have been studied by ab initio calculations. For the ethyl,/-butyl, t-butyl and neo-pentyl systems the MP2/6-31G* optimized TS geometry has unequal C-C1 bond lengths, indicating that two equivalent TSs exist for these reactions. The breaking/forming C-C1 bond length at the TS is 2.31-2.42 ~ with the t-butyl value being significantly larger, 2.62 A. The TS geometries and calculated activation energies show the expected trend as a function of increased substitution at either the a- or [3-carbon. Comparison to experimental data suggests that solution phase activation energies for tbutyl are too low and the gas phase value for/-butyl may be too high. The calculations clearly indicate that neo-pentyl should be more reactive than t-butyl. In general it appears that steric effects in solution are about half the gas-phase values.
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
Acknowledgement This work was supported in part by a grant from t h e D a n i s h N a t u r a l Science R e s e a r c h C o u n c i l ( G r a n t No. 11-9276).
References [ 1 ] C.K. Ingold, Structure and mechanism in organic chemistry, 2nd Ed. (CorneU Univ. Press, Ithaca, 1969); P.B.D. de la Mare, L. Fowlen, E.D. Hughes, C.K. Ingold and J.D.H. Mackie, J. Chem. Soc. (1955) 3200. [2] A. Streitweiser Jr., Chem. Rev. 56 (1956) 571; D.F. DeTar, D.F. McMullen and N.P. Luthra, J. Am. Chem. Soc. 100 (1978) 2484; J.M. Riveros, S.M. Jose and K. Takashima, Advan. Phys. Org. Chem. 21 (1985) 197. [3] G. Caldwell, T.F. Magnera and P. Kebarle, J. Am. Chem. Soc. 106 (1984) 959. [4] D.K. Bohme and L.B. Young, J. Am. Chem. Soc. 92 (1970) 7354; L.B. Young, E. Lee-Ruff and D.K. Bohme, J. Chem. Soc. Chem. Commun. (1973) 85; D.K. Bohme, G.I. Mackay and J.D. Payzant, J. Am. Chem. Soc. 96 (1974) 4027; C.A. Lieder and J.l. Brauman, J. Am. Chem. Soc. 96 (1974) 4029; J.1. Brauman, W.N . Olmstead and C.A. Lieder, J. Am. Chem. Soc. 96 (1974) 4030; J.D. Payzant, K. Tanaka, L.D. Betowski and D.K. Bohme, J. Am. Chem. Soc. 98 (1976) 894; W.N. Olmstead and J.l. Brauman, J. Am. Chem. Soc. 99 (1977) 4219; O.I. Asubiojo and J.I. Brauman, J. Am. Chem. Soc. 101 (1979) 3715; M.J. Pellerite and J.I. Brauman, J. Am. Chem. Soc. 102 (1980) 5993; R. Damrauer, C.H. DePuy and V.M. Bierbaum, Organometallics 1 (1982) 1553; M.J. Pellerite and J.I. Brauman, J. Am. Chem. Soc. 105 (1983) 2672; R.N. McDonald and A.K. Chowdhury, J. Am. Chem. Soc. 107 (1985) 4123; D.K. Bohme and A.B. Raksit, Can. J. Chem. 63 (1985) 3007; C.-C. Han, J.A. Dodd and J.l. Brauman, J. Phys. Chem. 90 (1986) 471; J.A. Dodd and J.I. Brauman, J. Phys. Chem. 90 (1986) 3559; C.H. DePuy, S. Gromet, A. Mullin and V.M. Bierbaum, J. Am. Chem. Soc. 112 (1990) 8650; S. Gronert, C.H. DePuy and V.M. Bierbaum, J. Am. Chem. Soc. 113 ( 1991 ) 4009;
14 August 1992
A.A. Viggiano, J.S. Paschkewitz, R.A. Morris, J.F. Paulson, A. Gonzalez-Lafont and D.G. Truhlar, J. Am. Chem. Soc. 113 (1991) 9404; S.T. Graul and M.T. Bowers, J. Am. Chem. Soc. 113 ( 1991 ) 9696; D.M. Cyr, L.A. Posey, G.A. Bishea, C.-C. Han and M.A. Johnson, J. Am. Chem. Soc. 113 ( 1991 ) 9697; J.L. Wilbur and J.I. Brauman, J. Am. Chem. Soc. 113 ( 1991 ) 9699. [5]J.W. Larson and J.B. McMahon, J. Am. Chem. Soc. 106 (1984) 517. [6] R.C. Dougherty, J. Dalton and J.D. Roberts, Org. Mass. Spectrom. 83 (1974) 77. R.C. Dougherty and J.D. Roberts, Org. Mass. Spectrom. 8 (1974) 81. [7] S.E. Barlow, J.M.V. Doren and V.M. Bierbaum, J. Am. Chem. Soc. l l 0 (1988) 7240. [8] K. Hirao and P. Kebarle, Can. J. Chem. 67 (1989) 1261. [9] S.C. Tucker and D.G. Truhlar, J. Phys. Chem. 93 (1989) 8138; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 112 (1990) 6789; R. Vetter and L. Zulicke, J. Am. Chem. Soc. 112 (1990) 5136. [ 10 ] F. Kiel and R. Ahlrichs, J. Am. Chem. Soc. 98 ( 1976 ) 4787. B.T. Luke, G.H. Loew and A.D. McLean, Intern. J. Quantum Chem. 29 (1986) 883. [ l I ] S. Wolfe, D.J. Mitchell and H.B. Schlegel, J. Am. Chem. Soc. 103 (1981) 7692, 7694; S.S. Shaik and A. Pross, J. Am. Chem. Soc. 104 (1982) 2708. S.S. Shaik, J. Am. Chem. Soc. 105 (1983) 4359; M. Urban, I. ~ernu~k and V. Kello, Chem. Phys. Letters 105 (1984) 625; T. Minato and S. Yamabe, J. Am. Chem. Soc. 107 (1985) 4621; D.J. Mitchell, H.B. Schlegel, S.S. Shaik and S. Wolfe, Can. J. Chem. 63 (1985) 1642; I. ~ernu~ik, G.H.F. Diercksen and M. Urban, Chem. Phys. Letters 128 (1986) 538; J.D. Evanseck, J.F. Blake and W.L. Jorgensen, J. Am. Chem. Soc. 109 (1987) 2349; I. ~ernug~ik and M. Urban, Collection Czech. Chem. Commun. 53 (1988) 2239; R. Vetter and L. Zulicke, J. Mol. Struct. THEOCHEM 170 (1988) 85; T. Minato and S. Yamabe, J. Am. Chem. Soc. 110 (1988) 4586; Z. Havlas, A. Merkel, J. Kalcher, R. Janoschek and R. Zahradnik, Chem. Phys. 127 (1988) 53; A. Merkel, Z. Havlas and R. Zahradnik, J. Am. Chem. Soc. 110 (1988) 8355; M. Urban, G.H.F. Diercksen, I. ~ernug~ik and Z. Haulas, Chem. Phys. Letters 159 (1989) 155; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 111 ( 1989 ) 1575; S.C. Tucker and D.G. Truhlar, J. Am. Chem. Soc. 112 (1990) 3338;
375
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
S.R.V. Linde and W.L. Hase, J. Phys. Chem. 94 (1990) 6148; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 113 ( 1991 ) 1072, 2434; Z. Shi and R.J. Boyd, J. Phys. Chem. 95 ( 1991 ) 4698; O.K. Kabbaj, M.B. Lepetit, J.P. Malrieu, G. Sini and P.C. Hiberty, J. Am. Chem. Soc. 113 ( 1991 ) 5619; S. Gronert, J. Am. Chem. Soc. 113 ( 1991 ) 6041. [12] D.K. Bohme and G.I. Mackay, J. Am. Chem. Soc. 103 (1981) 978. S.S. Shaik, 7. Am. Chem. Soc. 106 (1984) 1227; J. Chandrasekhar, S.F. Smith and W.L. Jorgensen, J. Am. Chem. Soc. 106 (1984) 3049; 107 (1985) 154; W.L. Jorgensen and J.K. Buckner, J. Phys. Chem. 90 (1986) 4651; B.J. Gertner, K.R. Wilson and J.T. Hynes, J. Chem. Phys. 90 (1989) 3537. [ 13 ] F. Jensen, J. Am. Chem. Soc. 114 (1992) 1596. [ 14] W.J. Hehre, L. Radom, P. yon R. Schleyer andJ. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986 ).
376
14 August 1992
[ 15 ] M.J. Frisch, M. Head-Gordon, G.W. Tucks, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M.A. Robb, J.S. Binkley, C. Gonzales, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90 (Gaussian, Inc., Pittsburgh PA, 1990). [ 16] L. Salem, J. Durup, G. Bergeron, D. Gazes, X. Chapuisat and H. Kagan, J. Am. Chem. Soc. 92 (1970) 4472; J.W. Mclver, Accounts Chem. Res. 7 (1974) 72. [ 17] A.J. Gordon and R.A. Ford, The chemist's companion (Wiley-Interscience, New York, 1972). [18] D. Cook and A.J. Parker, J. Chem. Soc. B (1968) 142. [ 19 ] E.D. Hughes, C.K. Ingold and J.D.H. Mackie, J. Chem. Soc. (1955) 3173. [20] P.B.D. de la Mare, J. Chem. Soc. (1955) 3180. [ 21 ] F. Carrion and M.J.S. Dewar, J. Am. Chem. Soc. 106 (1984) 3531.
CHEMICAL PHYSICS LETTERS
14 August 1992
A theoretical study of steric effects in SN2 reactions F r a n k Jensen Department of Chemistry, Odense University, DK-5230 Odense M., Denmark Received 4 February 1992; in final form 22 May 1992
The gas phase reaction of chloride ion with alkyl chlorides (methyl, ethyl, propyl, i-propyl,/-butyl, t-butyl and neo-pentyl ) has been studied by ab initio methods. Geometries of stationary points along the reaction coordinate have been optimized at the MP2/6-31 G* level of theory and improved energies have been calculated with the 6-311 + G (2d) basis. Although all reactions are "narcissistic", i.e. reactant and product are identical, it is found that some of the transition structures have unequal C-CI bond lengths. The breaking/forming C-CI bond for the t-butyl system is significantly longer than for the other alkyl groups, for which the change with increasing steric bulk is as expected. The calculated relative activation energies are compared with available gas-phase data and relevant solution values.
1. Introduction
The SN2 reaction of alkyl halides is a textbook example of how steric factors can alter reaction rates [ 1 ]. Substantial experimental work has established that in solution the relative rates of RX, with R being different alkyl groups, are relatively constant for a variety of X [ 1,2 ]. Experimental results for gas-phase reactions are scarce but the available data show the same ordering, although steric effects appear to be roughly a factor two larger than in solution [ 3]. A large number of publications, both theoretical and experimental, have reported detailed investigations of the SN2 reaction. It is impractical here to include a full list of references, below is a selection of some of the more relevant articles, the most recent may be consulted for references to prior work. In the gas phase the Sr~2 reaction proceeds via initial formation of an ion-dipole complex of the nucleophile with the reagent, which then in a single kinetic step is transformed to a complex of the product and the leaving group [ 3-11 ]. In solution the ion complexes are destabilized relative to the separated reagents and in water they may be completely absent [121. Correspondence to: F. Jensen, Department of Chemistry, Odense University, DK-5230 Odense M., Denmark.
368
In connection with other work [ 13] we became interested in how the geometry of the transition state (TS) varies as a function of R. The majority of previous calculations has concentrated on reactions of the type X - + CH3Y with X and Y being small species such as H, F and C1 [ 9-11 ]. An investigation of the C 1 - + R B r reaction with R being methyl, ethyl and i-propyl at the H F / M I N I level has also appeared [8 ]. In the present work we investigate the SN2 identity reaction CI- + RCI, with R being methyl, ethyl, propyl, i-propyl,/-butyl, t-butyl and neo-pentyl. The methyl, ethyl, i-propyl and t-butyl species form a series with increasing substitution at the a-carbon while ethyl, propyl, /-butyl and neo-pentyl form a series with increasing 1~substitution. Although the reaction series X - + RX with X = F or H would be easier to treat computationally it was thought that the small size of hydrogen and fluorine would tend to obscure the effect of steric bulk of the R group. It is likely that elimination reactions will compete with substitution for the branched R groups but we have chosen to concentrate on the steric effect in SN2 reactions in this work, regardless of whether other lower energy reactions exist. For studying the present reaction sequence which includes rather large R groups like neo-pentyl, a judicious choice of computational method has to be made. It is clearly desirable to include electron cor-
0009-2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
relation, which necessitates a basis set of at least DZP quality, and the anionic nature of the system suggests that the basis set should include diffuse functions [ 14 ]. Meeting these standards makes the computational problem quite large. The major effect of diffuse functions is usually on (relative) energies and less on geometries. TS geometries, however, may change significantly if the addition of diffuse functions alter the overall reaction energy, e.g. if the reaction becomes more exothermic it is likely that the TS becomes "earlier". In the present case all the reactions are thermoneutral and it is thus likely that TS geometries are insensitive to the presence of diffuse functions. We have therefore selected the M P 2 / 6-31 G* method as a common level for studying the reaction sequence. Test calculations for the methyl system (see below) suggest that the 6-31 G* basis set gives geometries comparable to those from better basis sets. Improved energies of stationary points have been obtained by extending the MP2/6-31G* calculations both with respect to additional electron correlation and basis functions.
2. Computational details All calculations have been performed with the GAUSSIAN 90 program package [ 15 ]. A description of notation and procedures used in this paper can be found in ref. [ 14]. The geometries have in general been optimized without any symmetry constraints which should ensure that only genuine TSs and minima are located (i.e. no higher-order saddle points in TS searches and no TSs in minimum searches). The resulting stationary points on the potential energy surface (PES) however, do, with one exception, have at least one element of symmetry as discussed below.
3. Results and discussion The reaction of C1- with CHIC1 was used for probing the sensitivity of stationary point geometries to the size of the basis set. At the HF/6-31 G* level the C-CI distance at the TS is 2.38 A compared to 2.31 A at when electron correlation is included by the MP2 procedure. Table 1 shows how the geometry
14 August 1992
Table 1 Geometriesof MP2 stationarypoints on the PES for CI- + CH3CI. D is the C-CI distance (,~) and a is the H-C-CI angle (deg) Basis
6-31G* 6-31 +G* 6-311 +G(2d)
TS D 2.307 2.316 2.301
Complex
DI
D2
ot
3.158 3.265 3.169
1.812 1.809 1.829
109.0 108.9 108.3
of the ion complex and TS vary as a function of basis sets at the MP2 level. The TS geometry is insensitive to extending the basis set beyond 6-31G*, while changes up to 0.1 ,~ occur for the non-bonded C-C1 distance in the complex. However, the PES as a function of this distance is very fiat, e.g. the energy is lowered by only 0.1 kcal/mol upon reoptimization of the MP2/6-31G* structure with the 6-31 + G * basis, and consequently the use of geometries obtained with the 6-31 G* basis for higher-level calculations introduce little error. The TS for the methyl system must by virtue of symmetry belong to the D3h point group. For the ethyl system one might a priori have predicted the TS to have two equal C-CI distances with a plane of symmetry, g, including the two carbon atoms and the two hydrogens on the reacting carbon (i.e. approximately perpendicular to the C1-C-C1 "axis"), as the reaction is "narcissistic", i.e. reactant and product are identical [ 16 ]. Indeed this is the case at the H F / 6-31G* level as proven by a frequency calculations which showed one imaginary frequency (367i c m - l , the lowest real frequency is 16 c m - ~). An alternative structure with the methyl group rotated 30 ° such that one of the C - H bonds eclipses one of the C-C1 bonds has also C~ symmetry with the mirror plane being defined by the reacting carbon and the two chlorine atoms, this type of mirror plane will be denoted t~' in the following. This structure is a second-order saddle point at the HF level, hut it is only 0.003 kcal/mol higher in energy and the second imaginary frequency (corresponding to a methyl group rotation) is very low, 10i cm-~. At the MP2 level the situation is reversed, here the a ' symmetric species is the genuine TS. The geometry with a o-type of mirror plane is a second-order saddle point (second imaginary fre369
Volume 196, number 3,4
14 August 1992
CHEMICAL PHYSICS LETTERS
( t'xl
d
r-la.
O
II rc
ll
tt') O
o v-
$°
e-
rr
o
..=
8
o')
~o
o~
c~
0")
O~
"6 II Ct"
II IT
.2 ,7,
e~
"F .-2
q p~ O ¢0
o xt
3~
0) U rt"
II tr
¢q ¢O Q
() 370
tt'J ¢O
cd
t'M
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
14 August 1992
Table 2 Geometries of MP2/6-31G* stationary points on the PES for C!- + RCI. D is the C-CI distance (/~) and a is the C1-C-CIangle (deg) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
TS
Complex
D1
D2
a
D,
D2
2.307 2.342 2.356 2.419 2.355 2.604 2.405
2.307 2.369 2.356 2.419 2.391 2.637 2.412
180.0 165.3 165.2 158.5 160.5 178.0 149.7
3.158 3.345 3.385 3.744 3.558 3.844 3.402
1.812 1.819 1.813 1.830 1.808 1.845 1.814
quency is 8 li c m - ~) located 0.11 kcal/mol higher in energy. A drawing of the MP2 TS is shown in fig. 1, selected bond lengths and angles can be found in table 2. Apparently there is no strong preference for a specific orientation of the methyl group and the exact conformation depends on the level of theory. It is likely that similar low energy rotations also exist for the other alkyl groups described below. We note that the correct TS is located by starting the optimization from a trial geometry without any symmetry. Substituting the methyl group with an ethyl moiety, making the propyl system, produces a TS with a atype plane of symmetry as shown in fig. 1. Note that the propyl TS is not simply obtained by substituting a hydrogen by a methyl group in the ethyl TS, it also requires a 30 ° rotation of the carbon group neighbour to the reaction center. The i-propyl system has both types of mirror planes and belongs to the Czv point group, while the/-butyl TS has only a a'-type plane of symmetry. The methyl groups in the t-butyl TS are oriented as in the ethyl system with a a ' type of mirror plane. One of the methyl groups has a C - H bond parallel to one of the C-C1 bonds while the two other methyl groups have a C - H bond approximately parallel to the other C-C1 bond. Finally the orientation in the neo-pentyl TS is analogous to the ethyl TS except for the substitution of a C (CH 3 ) group for C H 3. The consequence of unequal C-C1 bond lengths for the ethyl, /-butyl, t-butyl and neo-pentyl TSs is that there exist two equivalent TSs for the degenerate chloride exchange. If the reaction is made unsymmetrical, e.g. by going to the C1- + RBr reaction, or by isotopic substitution (35C1/37C1), the equiva-
180.0 167.4 143.5 174.4 126.5 180.0 138.2
lence will be lost. This may result in two TSs of slightly different energy or in the transformation of one of the TSs into a higher-order saddle point. Of course it is possible that higher-level calculations may produce TSs with equal C-C1 bond lengths for all the current species. The overall variation of the breaking/forming C-C1 distance in the series is, except for the t-butyl species, fairly small. The trend in both the ct and 13 series is as expected, the addition of methyl groups on the a-carbon increases the C-C1 distance by 0.05, 0.1 1 and 0.31 A (ethyl, i-propyl and t-butyl relative to methyl) while the corresponding effect for the 13carbon is 0.00, 0.02 and 0.05/~ (propyl,/-butyl and neo-pentyl relative to ethyl). An interpretation of bond distances in terms of energy can be obtained by employing a Morse potential, in this case we have chosen a common dissociation energy of 80 kcal/mol and a force constant of 524 kcal/mol/12 [ 17 ]. The energy cost of stretching the C-C1 bond to its TS value, relative to breaking it completely, gives a measure of the amount of bond breaking/forming at the TS. With this approach the t-butyl TS has C-C1 bonds that are 59% broken while the value for the other alkyl groups is in the range 38%-45%. The C1-C-C1 angle is 180 ° for the methyl system and it deviates more and more from linearity as the size of one of the three groups on the reacting carbon grows. The angle for the ethyl TS is 165 ° which hardly changes upon going to the propyl species. Adding another methyl group on the 13 position, forming/-butyl, lowers the angle to 161 ° and further methyl substitution to the neo-pentyl TS decreases the angle to 150 °. 371
?
() 0..
rn II
II
II IT" % % % 0
o~ c~
%
©
c~
d)
?
~) E
8~P II
o
II
iI .o
cd ! I
d~ ()
d)
d)
II U II
%
I c0
cd I
\
d)
rr
II I'T"
©
Volume 196, number 3,4
CHEMICALPHYSICSLETTERS
The geometries of the C1-/RC1 complexes for the ethyl, propyl, i-propyl and neo-pentyl complexes all have a a ' type of mirror plane. The methyl and t-butyl systems have the full C3v symmetry, while the ibutyl complex is the only nonsymmetric species found. Drawings of all complexes are shown in fig. 2. The non-bonded C-C1 distance increases systematically through the u series while in the 13 series the neo-pentyl distance is somewhat shorter than for ibutyl. In order to obtain improved relative energies we have performed calculations with the 6-311 + G (2d) basis and included electron correlation up to MP4 (tables 3 and 4). As seen in table 3 the complexation energy is insensitive both to improving the basis and inclusion of electron correlation beyond MP2. For the TS the effect of increasing the basis set is to lower the activation energy by 2-4 kcal/mol at the MP2 level. Extending the perturbation series beyond sec-
Table 3 Complexationenergiesof CI- + RCI relativeto the reagents (kcal/ tool ) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
6-31G* MP2 11.0 12.4 10.6 14.1 14.5 16.2 10.5
HF
8.5 8.9 7.1 9.1 7.8 9.7 6.9
6-31 l+G(2d) MP2
MP3
MP4
10.6 11.8 10.5 13.1 13.0 14.7 10.8
10.3 11.5
10.5 11.7
Table 4 TS energies of C1- +RC1 relative to the reagents (kcal/mol) R
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
6-31G* MP2 4.6 8.4 7.1 11.6 9.1 22.2 10.4
HF
6.8 10.3 9.9 12.4 12.1 16.9 18.5
6-311 +G(2d) MP2
MP3
MP4
2.3 5.7 3.9 8.6 6.0 18.2 12.2
3.8 7.0
1.3 4.3
14 August 1992
ond-order gives results that are slightly oscillating, but relative activation energies change little by going to the MP4 level. The most recent value for the complexation energy of CI- and CH3CI is 12.2+2 kcal/mol [5], which is slightly higher than a previous value of 8.6 + 0.2 kcal/mol [ 6 ]. The calculated energy of 10.5 kcal/mol compares favourably with these results. Other computational work including electron correlation has yielded values from 9 to 11 kcal/mol [ 9 ]. The experimental t-butyl complexation energy is 14.3 kcal/mol [5] which also agrees with the calculated 14.7 kcal/mol. We have been unable to find experimental data for the other alkyl chloride complexes studied here. Experimental TS energies are difficult to measure for isodesmic gas-phase reactions of the type studied here [ 3,4 ]. For the methyl system Barlow, Doren and Bierbaum have recently obtained a value of 1 + 1 kcal/mol by fitting experimental data to an R R K M model [7]. Calculations at CEPA, CISD and MP2 levels of theory with D Z P type basis sets give values somewhat higher than this, 3-10 kcal/mol [ 9,10 ]. Our value of 1.3 kcal/mol obtained at our best theoretical level is in complete agreement with the experimental data, although this may well be fortuitous. It is generally observed that the steric effect of alkyl groups in solution is rather constant for a range of nucleophiles and leaving groups [ 2 ]. As there are no experimental results for the C1- + RC1 system, except for R = methyl, we have chosen to compare the theoretical values with experimental data for the closely related C I - + R B r and B r - + R B r reactions. The former reaction is close to thermoneutrality and thus the TS should be fairly "symmetric" with respect to bondbreaking/formation. Experimental gas-phase results have been reported for the C1- + RBr reaction [ 3 ], and corresponding solution phase data in D M F [ 18 ] and acetone are also available [ 19 ]. These data, together with those for the B r - + R B r reaction in acetone [20], are given in table 5. The H F / M I N I activation energies for ethyl and i-propyl relative to methyl for the C1- + RBr reaction are 6.1 and 16.5 kcal/mol [8], which are considerably higher than the current MP2/6311 + G ( 2 d ) values of 3.4 and 6.3 kcal/mol. We also note that M N D O calculations give relative activation energies which are roughly a factor two larger 373
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
14 August 1992
Table 5 Relative TS energies for X- +RY (kcal/mol) a) R
/~kgtco X=CI Y=C1
/~kggas X=CI Y=Br
~kEDMF X=CI Y=Br
~Ace I X=CI Y=Br
AEAce2 X=Br Y=Br
Me Et Pr i-Pr i-Bu t-Bu neo-Pen
0.0 3.4 1.6 6.3 3.7 15.9 9.9
0.0 3.3 2.0 b) 7.6 8.2
0.0 1.3 1.9 3.0 1.8 3.3 8.4
0.0 1.9 1.8 3.1 2.4 5.3 (7.6) c) 6.0
0.0 1.7 1.7 3.9 3.1 6.0 6.2
) AEteoare MP2/6-311 + G ( 2d ) values from table 4, z ~ s are gas-phase data for the CI- + RBr reaction [ 3 ], AEDMFare corresponding values in DMF [ 18], ~SA~etare values obtained in acetone [ 19] and AEA~2are values for the Br- +RBr reaction in acetone [20]. b) Value for n-butyl. c~ Value redetermined in ref. [ 18]. than the current results [21 ]. Comparing the two last columns in table 5, it is seen that the steric effect in solution is fairly independent on whether the nucleophile is C1 or Br, or whether acetone or D M F is used as the solvent. The gas-phase effects for ethyl, propyl and i-propyl are roughly a factor of two larger than the corresponding solution data, while the value for/-butyl is significantly higher. The theoretical values for the three smaller systems compare favourably with the gas phase data, but again the experimental value for ibutyl appears too high. The calculated steric effect for t-butyl is much larger than expected from the solution phase data, with the possible exception of the redetermined value in acetone by Cook and Parker [ 18 ]. Solution phase rate constants for t-butyl, however, are inherently difficult to obtain experimentally. The major reaction o f t-butyl halides is elimination [ 18 ] and only a small percentage o f the total reaction is due to displacement, thus the activation energies in table 5 may well have substantial uncertainties. The calculations clearly indicate that neopentyl should react faster than t-butyl in an SN2 reaction. Accepting the theoretical values as representative o f gas-phase effect, it is also apparent from the data in table 5 that steric effects are reduced by roughly a factor two in solution compared to the gas phase. The correlation between the calculated energies and those for the C I - + R B r reaction in acetone (using the redetermined value by Cook and Parker) gives a correlation 374
coefficient of 0.98 with a slope of 0.47. A reasonable explanation of the reduced steric effect in solution may be that solvation of the anionic nucleophile/ leaving group results in a TS with longer breaking/ forming bonds than in the gas phase.
4. Summary Steric effects in the SN2 reaction of C I - with RCI ( R = m e t h y l , ethyl, propyl, i-propyl, /-butyl, t-butyl and neo-pentyl) have been studied by ab initio calculations. For the ethyl,/-butyl, t-butyl and neo-pentyl systems the MP2/6-31G* optimized TS geometry has unequal C-C1 bond lengths, indicating that two equivalent TSs exist for these reactions. The breaking/forming C-C1 bond length at the TS is 2.31-2.42 ~ with the t-butyl value being significantly larger, 2.62 A. The TS geometries and calculated activation energies show the expected trend as a function of increased substitution at either the a- or [3-carbon. Comparison to experimental data suggests that solution phase activation energies for tbutyl are too low and the gas phase value for/-butyl may be too high. The calculations clearly indicate that neo-pentyl should be more reactive than t-butyl. In general it appears that steric effects in solution are about half the gas-phase values.
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
Acknowledgement This work was supported in part by a grant from t h e D a n i s h N a t u r a l Science R e s e a r c h C o u n c i l ( G r a n t No. 11-9276).
References [ 1 ] C.K. Ingold, Structure and mechanism in organic chemistry, 2nd Ed. (CorneU Univ. Press, Ithaca, 1969); P.B.D. de la Mare, L. Fowlen, E.D. Hughes, C.K. Ingold and J.D.H. Mackie, J. Chem. Soc. (1955) 3200. [2] A. Streitweiser Jr., Chem. Rev. 56 (1956) 571; D.F. DeTar, D.F. McMullen and N.P. Luthra, J. Am. Chem. Soc. 100 (1978) 2484; J.M. Riveros, S.M. Jose and K. Takashima, Advan. Phys. Org. Chem. 21 (1985) 197. [3] G. Caldwell, T.F. Magnera and P. Kebarle, J. Am. Chem. Soc. 106 (1984) 959. [4] D.K. Bohme and L.B. Young, J. Am. Chem. Soc. 92 (1970) 7354; L.B. Young, E. Lee-Ruff and D.K. Bohme, J. Chem. Soc. Chem. Commun. (1973) 85; D.K. Bohme, G.I. Mackay and J.D. Payzant, J. Am. Chem. Soc. 96 (1974) 4027; C.A. Lieder and J.l. Brauman, J. Am. Chem. Soc. 96 (1974) 4029; J.1. Brauman, W.N . Olmstead and C.A. Lieder, J. Am. Chem. Soc. 96 (1974) 4030; J.D. Payzant, K. Tanaka, L.D. Betowski and D.K. Bohme, J. Am. Chem. Soc. 98 (1976) 894; W.N. Olmstead and J.l. Brauman, J. Am. Chem. Soc. 99 (1977) 4219; O.I. Asubiojo and J.I. Brauman, J. Am. Chem. Soc. 101 (1979) 3715; M.J. Pellerite and J.I. Brauman, J. Am. Chem. Soc. 102 (1980) 5993; R. Damrauer, C.H. DePuy and V.M. Bierbaum, Organometallics 1 (1982) 1553; M.J. Pellerite and J.I. Brauman, J. Am. Chem. Soc. 105 (1983) 2672; R.N. McDonald and A.K. Chowdhury, J. Am. Chem. Soc. 107 (1985) 4123; D.K. Bohme and A.B. Raksit, Can. J. Chem. 63 (1985) 3007; C.-C. Han, J.A. Dodd and J.l. Brauman, J. Phys. Chem. 90 (1986) 471; J.A. Dodd and J.I. Brauman, J. Phys. Chem. 90 (1986) 3559; C.H. DePuy, S. Gromet, A. Mullin and V.M. Bierbaum, J. Am. Chem. Soc. 112 (1990) 8650; S. Gronert, C.H. DePuy and V.M. Bierbaum, J. Am. Chem. Soc. 113 ( 1991 ) 4009;
14 August 1992
A.A. Viggiano, J.S. Paschkewitz, R.A. Morris, J.F. Paulson, A. Gonzalez-Lafont and D.G. Truhlar, J. Am. Chem. Soc. 113 (1991) 9404; S.T. Graul and M.T. Bowers, J. Am. Chem. Soc. 113 ( 1991 ) 9696; D.M. Cyr, L.A. Posey, G.A. Bishea, C.-C. Han and M.A. Johnson, J. Am. Chem. Soc. 113 ( 1991 ) 9697; J.L. Wilbur and J.I. Brauman, J. Am. Chem. Soc. 113 ( 1991 ) 9699. [5]J.W. Larson and J.B. McMahon, J. Am. Chem. Soc. 106 (1984) 517. [6] R.C. Dougherty, J. Dalton and J.D. Roberts, Org. Mass. Spectrom. 83 (1974) 77. R.C. Dougherty and J.D. Roberts, Org. Mass. Spectrom. 8 (1974) 81. [7] S.E. Barlow, J.M.V. Doren and V.M. Bierbaum, J. Am. Chem. Soc. l l 0 (1988) 7240. [8] K. Hirao and P. Kebarle, Can. J. Chem. 67 (1989) 1261. [9] S.C. Tucker and D.G. Truhlar, J. Phys. Chem. 93 (1989) 8138; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 112 (1990) 6789; R. Vetter and L. Zulicke, J. Am. Chem. Soc. 112 (1990) 5136. [ 10 ] F. Kiel and R. Ahlrichs, J. Am. Chem. Soc. 98 ( 1976 ) 4787. B.T. Luke, G.H. Loew and A.D. McLean, Intern. J. Quantum Chem. 29 (1986) 883. [ l I ] S. Wolfe, D.J. Mitchell and H.B. Schlegel, J. Am. Chem. Soc. 103 (1981) 7692, 7694; S.S. Shaik and A. Pross, J. Am. Chem. Soc. 104 (1982) 2708. S.S. Shaik, J. Am. Chem. Soc. 105 (1983) 4359; M. Urban, I. ~ernu~k and V. Kello, Chem. Phys. Letters 105 (1984) 625; T. Minato and S. Yamabe, J. Am. Chem. Soc. 107 (1985) 4621; D.J. Mitchell, H.B. Schlegel, S.S. Shaik and S. Wolfe, Can. J. Chem. 63 (1985) 1642; I. ~ernu~ik, G.H.F. Diercksen and M. Urban, Chem. Phys. Letters 128 (1986) 538; J.D. Evanseck, J.F. Blake and W.L. Jorgensen, J. Am. Chem. Soc. 109 (1987) 2349; I. ~ernug~ik and M. Urban, Collection Czech. Chem. Commun. 53 (1988) 2239; R. Vetter and L. Zulicke, J. Mol. Struct. THEOCHEM 170 (1988) 85; T. Minato and S. Yamabe, J. Am. Chem. Soc. 110 (1988) 4586; Z. Havlas, A. Merkel, J. Kalcher, R. Janoschek and R. Zahradnik, Chem. Phys. 127 (1988) 53; A. Merkel, Z. Havlas and R. Zahradnik, J. Am. Chem. Soc. 110 (1988) 8355; M. Urban, G.H.F. Diercksen, I. ~ernug~ik and Z. Haulas, Chem. Phys. Letters 159 (1989) 155; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 111 ( 1989 ) 1575; S.C. Tucker and D.G. Truhlar, J. Am. Chem. Soc. 112 (1990) 3338;
375
Volume 196, number 3,4
CHEMICAL PHYSICS LETTERS
S.R.V. Linde and W.L. Hase, J. Phys. Chem. 94 (1990) 6148; Z. Shi and R.J. Boyd, J. Am. Chem. Soc. 113 ( 1991 ) 1072, 2434; Z. Shi and R.J. Boyd, J. Phys. Chem. 95 ( 1991 ) 4698; O.K. Kabbaj, M.B. Lepetit, J.P. Malrieu, G. Sini and P.C. Hiberty, J. Am. Chem. Soc. 113 ( 1991 ) 5619; S. Gronert, J. Am. Chem. Soc. 113 ( 1991 ) 6041. [12] D.K. Bohme and G.I. Mackay, J. Am. Chem. Soc. 103 (1981) 978. S.S. Shaik, 7. Am. Chem. Soc. 106 (1984) 1227; J. Chandrasekhar, S.F. Smith and W.L. Jorgensen, J. Am. Chem. Soc. 106 (1984) 3049; 107 (1985) 154; W.L. Jorgensen and J.K. Buckner, J. Phys. Chem. 90 (1986) 4651; B.J. Gertner, K.R. Wilson and J.T. Hynes, J. Chem. Phys. 90 (1989) 3537. [ 13 ] F. Jensen, J. Am. Chem. Soc. 114 (1992) 1596. [ 14] W.J. Hehre, L. Radom, P. yon R. Schleyer andJ. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986 ).
376
14 August 1992
[ 15 ] M.J. Frisch, M. Head-Gordon, G.W. Tucks, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M.A. Robb, J.S. Binkley, C. Gonzales, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90 (Gaussian, Inc., Pittsburgh PA, 1990). [ 16] L. Salem, J. Durup, G. Bergeron, D. Gazes, X. Chapuisat and H. Kagan, J. Am. Chem. Soc. 92 (1970) 4472; J.W. Mclver, Accounts Chem. Res. 7 (1974) 72. [ 17] A.J. Gordon and R.A. Ford, The chemist's companion (Wiley-Interscience, New York, 1972). [18] D. Cook and A.J. Parker, J. Chem. Soc. B (1968) 142. [ 19 ] E.D. Hughes, C.K. Ingold and J.D.H. Mackie, J. Chem. Soc. (1955) 3173. [20] P.B.D. de la Mare, J. Chem. Soc. (1955) 3180. [ 21 ] F. Carrion and M.J.S. Dewar, J. Am. Chem. Soc. 106 (1984) 3531.