J. Phys. Chem. 1995,99, 13103- 13108
13103
Theoretical Studies on the Identity S N ~Reactions1 ' Young Sook Park, Chang Kon Kim, Bon-Su Lee, and Ikchoon Lee* Department of Chemistry, Inha University, Inchon 402-751, Korea Received: February 16, 1995; In Final Form: June I , 1995@
Ab initio M O studies are carried out on the identity gas phase nucleophilic substitution reactions of CH2CHCH2X by X- with X = H, F, and C1 using the 6-31++G** basis sets including electron correlation at the MP2 level. With the weakest nucleofuge, X = H, the reaction proceeds by a stepwise sN2' mechanism in which the breakdown of a stable intermediate is rate-limiting, whereas with the strongest nucleofuge, X = C1, the concerted S Nreaction ~ is the most favored. For X = F all three pathways, Le., anti-S~2', syn-S~2', and S32, are competitive, with a little preference for the anti-S~2'path. In all cases, the syn-S~2'reaction is found to be the least favored. The possibility of 1,3-sigmatropic rearrangement within the allylic system taking place in parallel with nucleophilic displacement can be precluded.
Introduction
Bimolecular nucleophilic displacement of a nucleofuge (LG) by a nucleophilic (Nu) accompanied by an allylic rearrangement, &2', has long been a subject of controversy.2 Three pathways are possible for nucleophilic displacement with an allylic substrate: the nucleophile may attack the n-bond at Cy with either a syn or an anti relationship to the nucleofuge or directly displace the LG from saturated carbon in an sN2 mechanism (eqs la-c).
N" /
I
LG
In the former two processes, l a and lb, in addition to the stereochemistry involved, there is the question of concertedness; the S N ~displacement ' may proceed in a stepwise manner through a stable intermediate, I, or concertedly.
H la
iG
Ih
The experimental results of predominant syn-S~2'stereochemistry in solution reported by Stork3have attracted considerable attention of the theoretical chemists, leading to searches for a justification for this interesting observation. On the basis @Abstractpublished in Advance ACS Abstracts, August 1, 1995.
0022-3654/95/2099- 13103$09.00/0
of ab initio MO calculations, Yates et a1.,2dproposed an anti mode of substitution for anions and a syn mode for neutral nucleophiles as a result of electrostatic interactions and nonbonded attractions in the transition state (TS). Bach et al.2hcarried out ab initio calculations using the 4-31G basis set on the TS structures for syn-S~2',anti-s~z',and sN2 attack by C1- on 3-chloropropene and concluded that the synsN2' process is the least favored of the three possible pathways with the C1- nucleophile. They concluded that "the theoretical rationale resulting in an infatuation with a preferential syn-S~2' reaction was unfounded" and that for the adequate explanation of the observed solution phase stereochemistry an explicit consideration of nonbonded interactions, ion pairing, and solvation effects is essential. In these previous works,2d-' the levels of the basis set used were rather low, and in addition the effect of electron correlation had not been considered. In order to gain further information as to the stereochemistry and concertedness involved in the gas phase sN2' reactions, we have carried out in this work ab initio studies using an extended basis set with diffuse and polarization functions (6-31++G**)4 and incorporating the electron correlation effect (at the MP2 l e ~ e l )on ~ . the ~ identity exchanges of X- with CH2=CHCH2X for X = H, F, and C1. Our discussion is limited to the gas phase processes since solvent effects are not considered in this work. Calculations
The 6-31G extended basis set with diffuse (++) and polarization (**) functions (6-31++G**) was used in the determination of equilibrium and TS structures and energy barriers, the overall activation barrier relative to separated reactants, AI??,and the activation barrier relative to the reactant ion-molecule complex, AP0. To account for the electron correlation, second-order Moller-Plesset perturbation theory (MP2) was adopted. Two types of results are reported: HF (HF/6-3 l++G**/A-IF/6-31++G**) and MP2 (Mw6-3 l++G**/ /MP2/6-3 1++G**).Single-point computations were also carried out at MP3, MP4SDQ, and QCISD levels for sN2' processes. Geometries of reactants, intermediates, and TSs were fully optimized, and all the respective HF and MP2 (except for X = C1) structures were confirmed by vibrational frequency calculations. Zero-point energy corrections were applied to the 0 1995 American Chemical Society
Park et al.
13104 J. Phys. Chem., Vol. 99, No. 35, I995
Product Complex (PC)
Atom
Charge
Ca CP CY
-0.6 1
H’ H2 H3 H4 H5 H6 H7
-0.46
-0.32 0.1 8 0.1 9 0.1 8 0.19 0.20 0.20 -0.74
interactions7which provide the stability to the syn adduct. The destabilizing electrostatic repulsion between the two elongated hydrides of the syn stereochemistry is in contrast weak (16.1 kcaVmol by point-charge calculation at the MP2 level) since the electronegativity of H is low, resulting in the weak polarization of the C-H bonds. Nevertheless the Hd-***Hdelectrostatic repulsion together with that between the other two eclipsing H atom pairs seems to cause one of the CH3 groups to rotate,8 thereby returning to the planar carbon atom frame, and results in an anti stereochemistry in the TS. The intermediate has a propane-like structure so that the rotational barrier of the terminal CH3 group is relatively low (7.56 kcaYmol at the MP2 level). The relevant energetics (in kcallmol) at the HF and MP2 levels for the two pathways, sN2 and sN2’, involved in the nucleophilic attack of propene by hydride anion are summarized in Table 1. H
H
TS C 1-sym.
8’
A Atom
TS(SYN)
-0.61 -0.78 0.13 0.16 H6
A
Charge
0.17 0.10
l-f1
H
H
INT Cs-sym.
Figure 2. The MP2 TS and intermediate structures for the s N 2 ’ reaction
of propene with hydride anion. Bond lengths are in A bond angles are in deg. (The values in parentheses are those for the reactant.)
1
Ha-
H
calculated energy barriers (except for X = C1 at the MP2 level). All calculations were carried out using the GAUSSIAN92 programs .6 In this work, we have carried out calculations on the sN2’ processes and the 1,3-~igmatropicallylic rearrangements. For the identity allyl transfer sN2 reactions, X- 4- CH2CHCH2X== XCH2CHCH2 with X = H, F, and C1, we have used the results from our previous report. The energy level scheme with various energy differences is presented in Figure 1. Because of the “degenerate” substitutions involved, the intermediate is symmetrical and the two transition states, TS1 and TS2, are identical, and hence the barrier heights from the reactants, A F , and AP2, are the same in all cases. Results and Discussion
In the reaction of propene with hydride anion, the nucleophile and nucleofuge are H-, and both syn- and anti-S~2’attack by H- resulted in only one type of TS, with an anti relationship to the nucleofuge. This indicates that the anti stereochemistry is inherently more favored than the syn mode in the TS of the gas phase identity sN2’ processes. The TS (Figure 2) is of an early type, with the nucleophile still at ca. 2 A away from Cy and the Ca leaving group bond elongated by only -1%. Other structural changes are also minor. In contrast, however, the intermediate is a syn adduct (Figure 2) of C, symmetry; the central carbon (Cp) in this syn intermediate is pyramidalized with an sp3 carbanion. The two elongated (-4%) C-H bonds (Ca-H and Cy-H) are trans with respect to the sp3-hybridized nonbonding orbital (n) on Cp. Thus there are two relatively strong vicinal trans n-o*C-H
TS(ANT1)
The energetics in Table 1 reveal that the sN2 pathway is highly unfavorable, with a substantial activation barrier (49.90 kcal/mol at the MP2 level). On the other hand, the sN2’ process is seen to proceed through the stable intermediate, which is lower by 14.02 kcallmol than the reactant complex (RC) which in turn is lower by 5.23 kcaVmo1 than the reactants level. Thus, the rate-limiting barrier (AF02) of 26.57 kcaVmol at the MP2 level is provided by the breakdown step of the intermediate. The barrier to formation (Mol)of the intermediate (12.56 kcaV mol at the MP2 level) is less than half of this rate-limiting barrier. Inclusion of the electron correlation effect lowers the first energy barrier, AFol, but the second barrier, Ap02, is in contrast raised due to a greater stabilization of the intermediate at the MP2 level; the intermediate is lower than the reactant complex by 0.38 and 14.02 kcaVmol at the HF and MP2 levels, respectively. The single-point calculations at higher levels which incorporate the electron correlation effect, MP3, MP4SDQ, and QCISD, do not change the relative trends of energetics discussed at the MP2 level of the theory. The energetics for the nucleophilic substitution of CH2CHCH2F by F- are more complex since the three pathways, sN2, syn-S~2’,and anti-S~2’,are competitive in this case (Table 2). At the HF level, both the syn- and anti-S~2’processes proceed through a respective intermediate which is, however, not stable enough to give a rate-limiting second step. At the MP2 level, the situation becomes more simplified: now the intermediate in the anti-S~2’pathway has disappeared and the anti-S~2’pathway becomes a single-step process. For the
Theoretical Studies on the Identity S,2’ Reactions
J. Phys. Chem., Vol. 99, No. 35, 1995 13105
TABLE 1: Energetics for Reaction of Propene with Hydride Anion (kcaymol) HF
E of reactants (RH
+ H-)b
- 117.57279
MP2
- 118.01500
MP3“
MP4SDQ“
QCISD.
-118.05198
- 118.05923
-I 18.06273
9.45
9.43
9.98
25.60
25.39
25.52
sN2
A??I APO,
63.62 (61.83) 67.07
49.90 (47.29) 55.13
20.52 (21.3lY 23.98 24.28 (21.03) -0.29
7.33 (8.05) 12.56 26.57 (22.67) - 14.02
sN2’ (anti)
A P I (=AI?>) APoi APn2d APo‘
“ Single-point calculation. In au. Values in parentheses are those corrected for zero-point energies. The intermediate is a syn-S~2’-typewith C, symmetry. e AE?o - A,!?”] - AI?o~. TABLE 2: Energetics for Reaction of 3-Fluoropropene with Fluoride Anion (kcaymol) HF
E of reactants (RF
+ F-)b
-315.35627
MP2 -3 16.15218
MP3“
MP4SDQ
QCISD.
-3 16.16655
-3 16.18652
-316.18708
7.72 (6.97)’ 21.12
-0.28 (-1.12) 14.99
7.16 (7.17) 20.56 1.57 (1.18) 18.99
-2.36 (-2.55) 12.91 0.13 (-0.11) 12.78
0.63
6.78 (6.42) 20.18 0.08 (-0.05) 20.10
-2.68 (-2.42) 12.59
0.45
0.71
-0.65
0.08 -0.73
-0.53 0.16 -0.68
Single-point calculation. In au. Values in parentheses are those corrected for zero-point energies. AI?” = A F O 1- A P o ~
fluoride exchange (X = F), inclusion of the electron correlation effect results in a lowering of all energy barrier^,^ including the second barrier, A,??o~, due to a relatively minor stabilization of the intermediate, which is below the reactants’ level by only 2.49 kcal/mol at the MP2 level. This is in contrast to a large depression of the intermediate level found for the hydride exchange (X = H) when the electron correlation effect is included. Thus the charge delocalization within the anionic tetrahedral intermediate I appears to be substantially more efficient, leading to a considerable decrease in the electronic repulsion when the nucleofuge (and nucleophile) has a low electronegativity (0.74 eV for H-) compared to when the nucleofuge is a highly electronegative anion (3.40 eV for F-).’O All three barrier heights, for sN2, syn-S~2’,and anti-SN2’ (A,??o~ is 14.99, 12.91, and 12.59 kcal/mol, respectively, at the MP2 level), are similar, and the difference between the syn- and antisN2‘ paths is marginal. Nonetheless, the lowest barrier is provided by the anti-S~2’path. For the syn-S~2’process at the MP2 level, the second barrier after the intermediate is somewhat high. Here again the results of single-point calculations at higher levels which incorporate the electron correlation effect seem to support the conclusions reached with the MP2 results. One interesting point is that barrier heights rise somewhat using MP3 but MP4SDQ and QCISD bring them down again. Overall, however, the barrier heights AZ?, are slightly higher than those calculated with MP2. For X = F, the O*C+ level is much lower than the B*C-H level (12.6 and 19.4 eV, respectively, in Table 4) so that the vicinal trans n-a* interaction’ becomes relatively stronger; this in turn leads to a relatively low energy barrier to C-F bond cleavage with low TS levels which are 2.36 and 2.68 kcaYmo1 below the reactants level (Table 2) for the syn- and anti-S~2’ processes, respectively. As a result, the barrier to the CH2F group rotation is relatively high (13.35 and 12.24 kcaYmol, respectively) and a planar syn intermediate with no pyramidalization of the CD carbon is preferred. The syn form is, of course,
favored due to the two stabilizing vicinal trans (or anti periplanar) n-o*C-F interactions afforded in the structure. The large part of the stability gained by the two vicinal trans n-o* interactions in the syn intermeidate is, however, lost by the strong F6-*.*F6- electrostatic repulsion. In this respect, a neutral nucleophile should result in a more attractive interaction than an anionic nucleophile, leading to a more stabilized TS. The relevant MP2 TS and intermediate structures are presented in Figure 3. Both syn- and anti-S~2‘TSs are rather tight, with C-F elongation of 6 and 13%, respectively, with little n electron delocalization within the allylic system; the C-C bond length changes by only 3-5% in the TS and the intermediate. Thus, for the nucleophilic substitution of 3-fluoropropene by fluoride anion, the single-step, anti-S~2’process is preferred to the other two, sN2 and syn-S~2‘,processes in the gas phase. Differences in the activation barriers are, however, very small so that all three pathways may become competitive. We note here again that the anti-S~2’mode is favored over the syn-S~2’ path. The energetics for the reaction of 3-chloropropene with chloride anion are summarized in Table 3. Examination of this table reveals that direct S Ndisplacement ~ at the “electrophilic” allylic carbon provides the lowest pathway among the three possible reaction paths.2h The S Npath ~ is energetically more favored over the anti- and syn-S~2’reactions, which are both concerted, by 3.3 and 12.4 kcaYmo1 at the MP2 level, respectively. The lowest reactivity predicted for the syn-S~2’ path is in agreement with the results of Bach et aLZhThe energy barrier difference between the two sN2’ processes is 9.1 kcaY mol in favor of the anti mode at the MP2 level (MP2/631++G**), which is greater by a factor of 2 compared to that obtained at the MP2/3-21G level (4.6 kcaYmol).2h The use of higher level basis sets including the diffuse and polarization functions therefore makes the syn-Sp~2‘mode much more unfavorable relative to the anti-S~2‘path. For X = C1 also, incorporation of the electron correlation effect lowers the energy
13106 J. Phys. Chem., Vol. 99, No. 35, 1995
Park et al. Atom
Charge
cfl
0.06 -0.66 -0.1 1 0.19 0.16 0.16 0.18 0.18
CI’ c y
6
H H H
3
H
TS (SYN) Ci-sym.
0‘ /H 1.086
H H
5
F
7
-0.55 -0.71
Atom
Charge
Cap’)
0.03
c fi
F
-0.70 0.19 0.16 0.17 -0.60
Atom
Charge
H’ H 2
6
H INT (SYN) Cs-sym.
7
c (4I ) c I’ 6
H H2 H3 F
0.03 -0.69 0.19 0.17 0.17 -0.63
TS (ANTI) Cz-sym.
Figure 3. The MP2 TS and intermediate structures for the S N ~reaction ’ of 3-fluoropropene with fluoride anion. Bond lengths are in A and bond angles are in deg. (The values in parentheses are those for the reactant .)
barriers, except the two values of Ap01 for the sN2 and synsN2’ processes. The single-point higher level calculations do not change the conclusion reached by the results of the MP2 calculations, although the barrier for syn-S~2’is depressed and that of anti-S~2’is elevated somewhat. Similar trends are reported for the identity methyl transfer reaction^.^ Thus in agreement with experimental observations in solution,’ the major pathway for the nucleophilic substitution of 3-chloropropene by C1- is found to be the classical sN2 nucleophilic displacement in solution as well as in the gas phase. For this reaction also, the anti mode is favored over the synsN2’ path (by 2.3 kcal/mol at the MP2 level). The MP2 TS structures are presented in Figure 4. Analyses of the energetics for the gas phase reactions of XCH2CHCHzX can be summarized as follows: the reaction with X = H proceeds by a stepwise sN2’ reaction with the ratelimiting breakdown of the stable intermediate, whereas a direct sN2 substitution is preferred for the reaction with X = C1. For the reaction with X = F, the situation is more complex, and both sN2 and sN2’ pathways may compete albeit the latter is marginally favored. In all cases however the anti mode is preferred to the syn stereochemistry in the sN2’ processes. The mechanistic changeover from a stepwise (for X = H) to a concerted (for X = Cl) pathway is reminiscent of a similar change involved in the aminolyses of carbonyl compounds. Such reactions usually exhibit nonlinear Bronsted-type plots, showing a break (at pK0 = pKa(amine) = pKa(leaving group)) from a large Vnuc= 0.8-1.0) to a small Vnuc= 0.1-0.3) rate dependence on basicity of the attacking amine (Nu) as the basicity of the nucleophile increases.12 The break of this type has been attributed to a change in the rate-determining step from breakdown of the leaving group (LG) to formation of a
+
tetrahedral intermediate, 11, in the reaction path. Since this mechanistic change takes place at a PKa value of the Nu which is approximately the same as that of the LG, the rate-limiting breakdown of the intermediate takes places over a wider range of the nucleophile PKa and hence is more likely to occur the higher the PKa value of the LG, i.e., the weaker the nucleofugicity (or the lower the leaving ability) of the LG. 0
I I
NU- C-
W
11
The electronegativity of the radical and anionic forms of X has been shown to increase in the order H- -= F- < C1- (0.74, and 3.40, and 3.62 eV for H-, F-, and C1-, re~pectively),’~ hence the nucleofugicity is expected to increase in the same order. With the worst LG, X = H, therefore, the intermediate can be relatively stable, leading to its rate-limiting breakdown, but for the much better LG, C1-, the intermediate becomes least stable and a direct concerted displacement mechanism prevails.’o In between the two rather extreme cases, there is an intermediate case of X = F. Similar trends are found in the thermoneutral carbonyl addition-elimination reactions. Tetrahedrally coordinated methoxide was obtained by the reaction of H- with formaldehyde using a helium buffer gas to collisionally deactivate the adduct.14 On the other hand, the complex binding energies for F- and C1- with a series of neutral molecules, including aldehydes, esters, and ketones, were measured. The C1 affinity was low and most consistent with an electrostatic complex, not a stable adduct.15 Ab initio studies on the reaction of F- with acrolein showed that an ion-dipole complex was comparable in stability to the tetrahedral adduct.16 The frontier MOs (FMOs) for the reaction systems studied in the present work in Table 4 support such an interpretation. We note that the HOMO of the nucleophile (nx-) is the highest for X = H, while the antibonding a*LUMO for the C-X bond (a*cx) is the lowest for X = C1. As a result, for X = H the interfrontier level gap, ACFMO,is the narrowest (7.50 eV) between nH- and n*c< and the widest between nH- and O*CX (20.61 eV). Since the charge transfer stabilization in the initial stage of the reaction is inversely related to AcFM0,l7the Hnucleophile attacks Cy (double bond), leading to formation of a relatively stable intermediate (SN2’). In contrast the AEFMO between ncl- and O*C-CIis the narrowest among the three Xs, and the direct sN2 mechanism is the most favorable with X = C1. Of course, the concerted anti-S~2’path can compete (Tables 3 and 4), but the sN2 process is favored over the anti-S~2’path because of the preference of n-a* (direct charge transfer to a*cx) to n-n* (indirect charge transfer to a*cx) interaction in nucleophilic substitution reactions.’ * Once again, for the case of X = F, the situation is more complex since there is no dominant interaction available; it is intermediate between the two extreme cases. What about the anti preference obtained in all three cases for the sN2’ paths? It seems that the rationalization provided by Bach et a1.2h is reasonable: Within the anti-S~2’TS, the partial negative charges of the anionic species (X) are opposed to one another, and this dipole effect partially lowers the TS energy. This is supported by a greater charge separation achieved in the anti- than in the syn-S~2’TS. The natural bond order (NBO) analysesi9have shown that the anti forms have greater negative charges for X developed in the TS relative to the syn-S~2’TS; anti/syn = -0.627F0.604 for X = F and
Theoretical Studies on the Identity S,2' Reactions
J. Phys. Chem., Vol. 99, No. 35, 1995 13107
TABLE 3: Energetics for Reaction of 3-Chloropropene with Chloride Anion (kcaymol) MP2
MP3"
MP4SDQ"
QCISD"
- 1036.20403
- 1036.25383
- 1036.26034
- 1036.20403
HF
E of reactants (RCl sN2 API APOl SN2'byn) APo I APO I SN2'(anti) AP, APoi
+ C1-)
-1035.52435 9.04 (8.3l)c 16.82
8.11 18.80
22.51 (21.87) 30.30
20.54 3 1.23
17.91
17.28
16.95
15.37 (14.64) 23.16
11.46 22.14
15.08
14.34
13.77
" Single-point calculation. In au. Values in parentheses are those corrected for zero-point energies. TABLE 5: Energetics for the Reaction of l,3-Sigmatropic Allylic Rearrangements (kcaymol)
X=CI 1
Atom
Charge
ca(Y)
-0.20
cp
-0.52 0.21 0.21
H
0.22 -0.58
F
H1 H2
H CI
X
c1
HF
MP2
103.39 (99.60>" 75.13 (72.91) 53.01 (51.20)
86.77 (83.23) 64.26 (62.69) 59.21 (57.77)
TS (SYN) Cs-sym a
Values in parentheses are those corrected for zero-point energies.
8
6
Atom
Charge
CU'*
-0.1 5
Cb
-0.51
'
0.21
H2 H3
0.22 0.22
CI
-0.65
H 7
1084
100 60
TS Cz-sym. LCaCPCrH= 0.6
TS (ANTI) Cz-sym
Figure 4. The MP2 TS and intermediate structures for the sN2' reaction of 3-chloropropene with chloride anion, Bond lengths are in 8, and bond angles are in deg. (The values in parentheses are those for the reactant.)
TABLE 4: The FMO and AEFMO Calculated at the HF Level for the Nucleophilic Substitution Reactions of Allylic Systems in eV TS Cs-sym.
H -1.18 F -4.85 C1 -4.09
19.42 12.61 9.02
-9.90 -10.59 -10.76
LCaCPCYF= 33.3'
6.32 6.10 6.22
20.61 17.45 13.11
7.50 10.95 10.3 1
-0.649k0.578 for X = C1. The greater charge separation can be afforded in the anti-S~2'TSs but not in the syn forms due to the unfavorable Coulombic repulsions. Thus in the gas phase, Coulombic interactions play an important role in determining the preferred geometry in the TS. In solution, however, the enhanced repulsive interaction between the two Xs in the synS N ~TS ' will be partially compensated by the ion-dipole (or dipole-dipole) attraction due to an increase in the dipole moment. Finally there is a possibility of 1,3-sigmatropic rearrangement within the allylic compound taking place in parallel with nucleophilic displacement. The results of our studies are presented in Table 5. Reference to this table reveals that the activation barriers are prohibitively large for all three cases of X = H, F, and C1, and hence such sigmatropic shift cannot compete with the displacement reactions. As in the substitution reactions, the inclusion of the electron correlation effect (MP2) leads to a lowering of the energy barrier for X = H and F; in contrast, the energy barrier is elevated for X = C1. Zero-point
TS Cs-sym LCUCPCYCl = 45.;
Figure 5. The MP2 TS structures for the 1,3-sigmatropic rearrangements.
energy correction, however, invariably leads to a significant depression of the energy barriers. The TS structure in Figure 5 indicates that the migrating group, H-, is coplanar with carbon atoms, and hydride shift takes place antarafacially20 with a barrier height that is comparable to that of CH bond dissociation,20awhereas fluoride and chloride group shifts are out of plane (-33 and 46") and the shifts proceed suprafacially.21.22 This is in agreement with the results of the previous semiempirical MO analyses.23 It has been shown that the reactivity of
13108 J . Phys. Chem., Vol. 99, No. 35, I995 the group migration is largely controlled by the steric effect in the 4-membered ring TS, an antarafacial process*’ having a greater energy barrier due to a greater steric repulsion. For the migrating groups with lone pairs, the participation of the lone pair orbital eases the steric effect by enabling the FMO interaction with highly polarizable, high-lying, lone pair electrons at a relatively distant range; the involvement of lone pairs in the TS causes an alteration of the symmetry selection rule to that of a 6-electron system with an allowed 1,3-suprafacial migration in contrast to an allowed 1,3-antarafacial shift for a 4-electron system. We therefore conclude that the gas phase degenerate nucleophilic reactions of an allylic system with nucleophiles (and nucleofuge) X = H, F, and C1 proceed by different mechanisms depending on X. For X with a relatively low electronegativity, X = H, the intermediate of the syn form can be stable due to the two stabilizing vicinal trans n-a* interactions of a carbanionic center (n) at Cp with the a*c-x orbitals, which are both trans to n. As a result, the stepwise pathway with the ratelimiting breakdown of the intermediate is favored. An anti form of the Sx2’ path is preferred in the TS, however, with a relatively low CH3 rotational barrier between the TS and the intermediate. For the highly electronegative X, X = C1, the direct-displacement S Nmechanism ~ is the most favored. For X = F, however, the intermediate of the syn form is relatively less stable and all three forms, S N ~syn-S~2’, , and anti-S~2’,can compete. In this case, the rotational barrier of the CH2F group prevents the antiS N ~path ‘ from going through the syn-S~2‘intermediate (as found for X = H), and the anti-S~2’reaction provides the lowest energy path which proceeds concertedly. The 1,3-sigmatropic rearrangement cannot compete with the displacement processes due to high energy barriers. Acknowledgment. We thank the ministry of Education and the Inha University for support of this work. Supporting Information Available: Detailed geometries of all structures and energies studied (7 pages). Ordering information is given on any current masthead page. References and Notes (1) Determination of Reactivity by MO Theory. Part 90. For part 89. see: Lee, I.; Kim, C. K.; Lee, B . 4 . J . Comput. Chem. In press. (2) (a) Bordwell, F. G. Arc. Chem. Res. 1970, 3, 281. (b) Sneen, R. A. Acc. Chem. Res. 1973, 6, 46. (c) Shorter, J. Org. React. Mech. 1981, 349. (d) Yates, R. L.; Epiotis, N. D.; Bemardi, F. J . Am. Chem. SOC. 1975, 97, 6615. (e) Houk, K. N.; Paddon-Row, M. N.; Rondan, N. G. THEOCHEM 1983,103, 197. (f)Carrion, F.; Dewar, M. J. S. J . Am. Chem. SOC.1985, 107, 1352. (g) Dewar, M. J. S. J . Am. Chem. SOC. 1984, 106, 3531. (h) Bach, R. D.; Wolber, G. J. J . Am. Chem. SOC.1985, 107, 1352. (i) Fukui, K.; Fujimoto, H. Bull. Chem. SOC.Jpn. 1966, 39, 2116; 1967, 40, 2018. (j) Fukui, K. Theory of Orientation and Stereoselection;
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