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The SN2 transition state. Part 4: α-substituents and the SN2-SN1 borderline problem in the SN2 identity reaction
Journal of Molecular Structure (Theochem), 138 (1986) 163-169 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE SN2 TRANSITION STATE. PART 4: ar-SUBSTITUENTS AND THE SN2-SNl BORDERLINE PROBLEM IN THE SN2 IDENTITY REACTION*
DANIEL KOST** and KALMAN AVIRAM Department (Israel)
of Chemistry,
Ben Gurion University
of the Negev, Beer Sheva, 84105
(Received 27 June 1985)
ABSTRACT The optimized CH,NH; (C,, symmetry) SN2 transition state serves as a model to study SN2SNl borderline phenomena by application of SCF-MO theory. n-Interactions between the nitrogen lone-pair and the n-type orbital associated with the reaction coordinate, which are repulsive in the SN2 transition state but stabilizing in a carbocation, are examined as a function of C-nucleophile and C-leaving group distances. It is shown that the corresponding Mulliken n-overlap population changes gradually from repulsive (tight SN2 transition state) to attractive (loose, SNl-like transition state), whereas no such change is observed in the “off” conformation, in which the lone pair is turned by 90” relative to the reaction coordinate and overlap is minimal. A distinct geometrical preference is associated with the change in mechanism: in a tight SN2 transition state the nitrogen lone pair is turned to avoid repulsive interaction, while it parallels the reaction coordinate in a loose, SNllike transition state.
The effect of cu-substituents on the rates of SN2 reactions is quite intriguing [2] . While an unsubstituted alkyl halide, such as methyl chloride, readily undergoes nucleophilic displacement, substitution of one methyl hydrogen by another halogen atom (e.g., methylene chloride) causes a dramatic rate retardation [3] . However, no such rate retardation is observed when oxygen, rather than a halogen, replaces one of the methyl hydrogens: methoxymethyl chloride (CH30CH&1) is highly reactive towards nucleophiles even under strict SN2 conditions [ 41. In a previous communication, we have shown that this seemingly inconsistent behavior due to electronegative substituents in the c-position can be rationalized in terms of n-interactions between substituent and central carbon orbitals at the SN2 transition state (1) [la]. The frontier orbit& involved in this interaction are the lone-pair p-orbital of the o-halogen substituent and the three-center n-type orbital aligned with the reaction coordinate axis (Fig. la). In the simplest model for the SN2 transi-
*For previous papers of this series see ref. 1. **Author to whom correspondence should be addressed. 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
164
H
H H
H b
a
Fig. 1. SN2 transition states for a-halo (a) and walkoxy (b) substituted molecules.
tion state, the D3h CH; structure, the latter MO corresponds to one below the HOMO (the HOMO being a nonbonding MO centered essentially only on nucleophile and leaving group, and lacking any n-type symmetry). Since both orbitals are doubly occupied, the overall n-interaction is repulsive, and raises the transition-state energy. As aresult, the SN2 reaction for a-halo substituted substrates is slow relative to unsubstituted molecules.
X N
I
C---L
e-w
H
1
H
The a-alkoxy substituent, on the other hand, is able to avoid the four electron repulsive interaction at the SN2 transition state simply by torsion about the C-O bond, such that the p-lone pair orbital on oxygen is perpendicular to the reaction coordinate axis, and n-overlap is minimized (the n-interaction is then said to be “turned off”, Fig. lb). Similar repulsive n-overlap which may operate in this transition state conformation between the in-plane hybrid lone pair on oxygen and the reaction coordinate orbital has been shown to be of little significance, due to the lower energy and the unfavorable orientation of this orbital [la]. These qualitative considerations were extensively supported by ab-initio SCF-MO calculations on model systems with various a-substituents, including planar NH2 and BH2, which serve as typical n-donor and acceptor substituents, respectively, that can be turned on and off at will and enable direct observation of this effect. The same SN2 transition state (l),in thecase of the identity exchange reaction (i.e., N = L), may also be viewed as a planar t&coordinate carbocation, solvated by two distant axial ligands or solvent molecules [ 51. From this point of view, the results discussed above may appear rather strange; it is well known that carbocations are substantially stabilized by adjacent n-donor atoms which effectively conjugate with the vacant p-orbital on the electron deficient carbon. And yet in 1, n-donors are found to have a destabilizing
165
effect. It seems that the very same n-interaction that causes SN2 rate retardation can act to accelerate SNl displacements. The purpose of the present study has been to clarify this point and to investigate the gradual change from one type of mechanism to the other. It is quite obvious that the question whether 1 describes an SN2 transition state or a solvated carbocation depends on the relative distances of the nucleophile and leaving group from the central carbon. An extremely “loose” SN2 transition state may be referred to as an “SNl-like SN2 transition state”, whereas a very tight transition state belongs to a strict SN2 reaction. Clearly, in presence of a poor leaving group, which in the identity reaction corresponds also to a powerful nucleophile, the transition state will be tight. In case of a strong leaving group and a poor nucleophile, the SNl mechanism will be preferred, and a loose transition state is expected. This situation may occur, for instance, when N and L are neutral molecules, such as water or ammonia, which are stable by themselves and do not require the strong association with the substrate molecule. Ideally one would wish to study the gradual transformation between the SN2 and SNl extremes of the mechanistic spectrum by means of a continuous variation in nucleophilicity of the N group. However such variation is not possible in reality. In fact, the choice of groups which differ markedly in nucleophilic power and also meet the practicality requirements for SCF-MO calculations is very limited. We chose, therefore, a model system for the changing power of nucleophile and (identical) leaving group, Realizing that a powerful leaving group will shift the mechanism towards the SNl side and impose a loose transition state, we approach the problem from the other end, i.e., by extending the C-nucleophile and C-leaving group distances artificially we attempt to mimic a gradual shift of mechanism towards the SNl end. This model may be understood as either changing the N and L groups for a weaker nucleophile and stronger leaving group, respectively, or as a gradual change in the reaction medium such that the N and L groups gradually become more stabilized by the solvent. The model transition state (Fig. 2) consist of an e-aminocarbocation, with H- groups at various distances serving as nucleophile and leaving group. The NH2 group was kept planar in both “on” and “off” conformations. The
‘Off’
‘Oil’
Fig. 2. Model SN2 transition states showing “on” and “off” geometries.
166
initial geometry was the fully optimized (4-31G basis set) CZVstructure for each of the model transition states, and the symmetry was maintained throughout the calculations. The results are presented in Table 1, and shown graphically in Fig. 3 [6, 71. Examination of Fig. 3 reveals that the energies of both model transition states rise with the extension of the axial C-H distances. This is due to the departure of both structures from their minimum energy conformations. However, the ascent of the curve for the NH2-off model is significantly steeper than that for the transition state with the n-interaction “turned on” TABLE 1 Relative energy as a function of C-H, CH,NH; transition states
distance for “on” and “off” conformations
Relative energy (kcal mol-I)
C-H, (A)
“on”
“Off”
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
13.8 11.5 10.8 11.3 12.8 15.1 18.0 21.3 25.0 29.1
0.0 1.6 4.7 8.9 14.0 19.7 25.8 32.2 38.7 45.2
-95.43
[
,
1.7
1.8
I I.9
I 2.0
I 2.1
C-Nucleophile
Fig. 3. Effect of extension of C-H,
I 2.2
r 2.3
disfonce,
I 2A
1 2.5
I 2d
d
distance on SN2 transition state energy.
of
167
[8]. At first, at the tight transition state end, the “on” structure is higher in energy due to four-electron repulsion. As the N-C-L distance increases, this repulsion gradually is released, such that the energy increase due to departure from optimum geometry is partly offset. As the structures become looser, the energies of the models approach each other, until they are equal. At that point there is no preference for one of the structures over the other, Further extension of the transition states brings about a crossover of the energy profiles: the n-interaction present at the “on” conformation becomes stabilizing, as a carbocationic center develops. Consequently, the “on” model becomes the preferred transition state structure. Thus, while in terms of energy there is a smooth change from an SN2 mechanism to an SNl-like transition state, TABLE 2 Mulliken x,-overlap populations for CH,NH; “on” C-H,
WI
GINO
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
0.0035 0.0049 0.0062 0.0076 0.0088 0.0100 0.0111 0.0121 0.0131 0.0139
0.0046 0.0094 0.0140 0.0181 0.0219 0.0252 0.0281 0.0306 0.0328 0.0346
transition statea CONI
CoNo
-0.0052 -0.0032 -0.0014 0.0001 0.0015 0.0027 0.0038 0.0049 0.0059 0.0068
-0.0350 -0.0275 -0.0211 -0.0158 -0.0115 -0.0079 -0.0049 -0.0025 -0.0004 0.0014
aOverlap between px inner and outer components on C and N, where x is the reaction coordinate axis. CI and Co express inner and outer px functions on carbon. Nr and No express the corresponding functions on nitrogen. TABLE 3 Mulliken n,-overlap populations for CH,NH; “off” C-H,
CI%
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
0.0001 0.0004 0.0006 0.0008 0.0011 0.0013 0.0015 0.0017 0.0019 0.0021
aSee footnote
to Table 2.
GINO
-0.0032 -0.0025 -0.0018 -0.0011 -0.0006 -0.0001 0.0003 0.0006 0.0008 0.0010
transition statea CONI
-0.0062 -0.0059 -0.0056 -0.0054 -0.0051 -0.0049 -0.0048 -0.0046 -0.0044 -0.0043
CON0
-0.0206 -0.0199 -0.0193 -0.0190 -0.0190 -0.0192 -0.0197 -0.0205 -0.0214 -0.0226
168
we identify here for the first time a sudden change in geometry, which signifies the mechanistic crossover: within the tight SN2 transition state region, the n-interaction is repulsive and hence the “off” transition state is more stable. At the borderline this interaction becomes insignificant, and at looser transition states, i.e., in the SNl-like mechanism region, the transition state geometry changes to the “on” arrangement. It can be shown that the changes in relative energies upon extension of the transition state really result from changes in the amount of n-interaction between nitrogen and carbon p-orbit&. Tables 2 and 3 list the Mulliken npopulations between carbon and nitrogen px orbit& in the “on” and “off” models, respectively. These are also displayed in Figs. 4 and 5. Since a split valence shell basis set was used, there are four different terms describing the n-overlap population between the C and N p-functions in the reaction coordinate direction for each transition state. Without attempting a complete analysis of the meaning of changes in each of the individual n-overlap components, the data in Figs. 4 and 5 strongly support the PM0 analysis discussed. Three out of the four curves in Fig. 5 are almost horizontal lines, situated near the zero line. The fourth line is slightly descending, and is negative. The overall variation in n-overlap of the “off” model as a function of C-H,, distance is extremely small. On the other hand, all four lines describing the “on” conformation (Fig. 4) are ascending, and two of them rather steeply. In other words, all four n-overlap terms in the “on” conformation increase with increasing C-H,, distance. Thus “loosening” of the model transition state is associated with substantial increase in n-bonding between carbon and nitrogen, from overall negative (i.e., antibonding) to positive ‘bonding. It may be of interest to note that the smallest changes in n-overlap are found in the “off” conformation, in which the energy change is most significant, whereas in the “on” model, where the energy change is relatively small, a rather dramatic increase in x,-overlap is observed. 0.04.
0.04-
0.03-
/---
5 0.02-
-1
x/l
/"I O.OlI_-+--' s+ o.oo_----~~~,r-=-I~~~~~~~~~
2
,/
+~+-~~~~~~~~~~~-t-n a*+-D-4-x
co--P-o
-O.Ol-
-0.02-
,//
J -0.02-
O.Olo,oo_
/de
;-O.Ol-
0.03002-
__+--F---l _
_+_--+--'
-0.03-
x/
/
o-.-+--a--o--o-+-‘--.3_._((
-003-
-0.04{{, 1.6 1.7 1.8 1.9 2.0 2.1 22 C-Hax
distance,
2.3 24 H
2.5 2.6
-o.O4jj, 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 24 C-H,,distance,
2.5 2.6
A
distance on mulliken rr,-overlap populations in “on” Fig. 4. Effect of extension of C-H, transition state. (+) CIN~; (X) GINO; (0) CON,; (0) CoNo. distance on mulliken r,-overlap Fig. 5. Effect of extension of C-H, “off” transition state. (+) C~NI ; (X ) GINO; (0) CONI ; (0) CoNo.
populations
in
169
While examining Fig. 4 it is tempting to speculate on the roles of the different overlap population terms. It appears that most of the repulsive interaction at the tight “on” transition state is due to negative n-overlap of the outer pX functions on N and C, whereas n-bonding at the loose (carbocationic) end is brought about mostly by overlap of the inner p function on carbon with the outer function on nitrogen. ACKNOWLEDGEMENT
Financial support by the Fund for Basic Research, administered by the Israel Academy of Sciences and Humanities, is gratefully acknowledged. REFERENCES 1 For previous papers in the series see: (a) D. Kost and K. Aviram, Tetrahedron Lett., 23 (1982) 4157. (b) D. Kost and K. Aviram, Bull. Sot. Chim. Belg., 91 (1985) 357. (c) A. Pross, K. Aviram, R. C. Klix, D. Kost and R. D. Bach, Nouv. J. Chim., 8 (1984) 711. 2 For other recent theoretical studies of substituent effect on SN2 reaction rate see: (a) S. S. Shaik, J. Am. Chem. Sot., 105 (1983) 4359. (b) S. Wolfe, D. J. Mitchell and H. B. Schlegel, Can. J. Chem., 60 (1982) 1291. 3 (a) P. Petrenko-Kritschenko and V. Opotsky, Chem. Ber., 59B (1926) 2131. (b) P. Petrenko-Kritschenko, A. Rawikowitsch, V. Opotsky, E. Pnjata and M. Kiakowa, Chem. Ber., 61B (1928) 845. (c) W. C. Davies, E. B. Evans and F. L. Hulbert, J. Chem. Sot., (1939) 412. (d) J. Hine, C. H. Thomas and S. J. Ehrenson, J. Am. Chem. Sot., 77 (1955) 3886. (e) J. Hine, S. J. Ehrenson and W. H. Brader, Jr., J. Am. Chem. Sot., 78 (1956) 2282. 4 (a) W. R. Kirner, J. Am. Chem. Sot., 48 (1926) 2745. (b) J. Hine, Physical Organic Chemistry, 2nd edn., McGraw-Hill, New York, 1962, pp. 169-178. (c) P. Bailinger, P. B. D. de la Mare, G. Kohnstam and B. M. Prestt, J. Chem. Sot., (1955) 3641. (d) R. Leimu and P. Salomaa, Acta Chem. Stand., 1 (1947) 353. (e) P. SaIomaa, in S. Patai (Ed.), The Chemistry of the Carbonyl Group, Wiley, New York, 1966. (f) T. C. Jones and E. R. Thornton, J. Am. Chem. Sot., 89 (1967) 4863. 5 W. P. Jencks, Act. Chem. Res., 13 (1980) 161. 6 The GAUSSIAN-76 program system was used with its built-in 4-31G basis set: J. S. Binkley, R. A. Whiteside, P. Hariharan, R. Seeger, J. A. Pople, W. J. Hehre and M. D. Newton, QCPE, 11(1979) 368. 7 Each extension of the C-H, distance was followed by geometry optimization of ail other geometrical parameters. 8 The minimum energy C-H, distance for the “on” transition state is 1.90 A and hence the ascent of the curve starts at this distance.
THE SN2 TRANSITION STATE. PART 4: ar-SUBSTITUENTS AND THE SN2-SNl BORDERLINE PROBLEM IN THE SN2 IDENTITY REACTION*
DANIEL KOST** and KALMAN AVIRAM Department (Israel)
of Chemistry,
Ben Gurion University
of the Negev, Beer Sheva, 84105
(Received 27 June 1985)
ABSTRACT The optimized CH,NH; (C,, symmetry) SN2 transition state serves as a model to study SN2SNl borderline phenomena by application of SCF-MO theory. n-Interactions between the nitrogen lone-pair and the n-type orbital associated with the reaction coordinate, which are repulsive in the SN2 transition state but stabilizing in a carbocation, are examined as a function of C-nucleophile and C-leaving group distances. It is shown that the corresponding Mulliken n-overlap population changes gradually from repulsive (tight SN2 transition state) to attractive (loose, SNl-like transition state), whereas no such change is observed in the “off” conformation, in which the lone pair is turned by 90” relative to the reaction coordinate and overlap is minimal. A distinct geometrical preference is associated with the change in mechanism: in a tight SN2 transition state the nitrogen lone pair is turned to avoid repulsive interaction, while it parallels the reaction coordinate in a loose, SNllike transition state.
The effect of cu-substituents on the rates of SN2 reactions is quite intriguing [2] . While an unsubstituted alkyl halide, such as methyl chloride, readily undergoes nucleophilic displacement, substitution of one methyl hydrogen by another halogen atom (e.g., methylene chloride) causes a dramatic rate retardation [3] . However, no such rate retardation is observed when oxygen, rather than a halogen, replaces one of the methyl hydrogens: methoxymethyl chloride (CH30CH&1) is highly reactive towards nucleophiles even under strict SN2 conditions [ 41. In a previous communication, we have shown that this seemingly inconsistent behavior due to electronegative substituents in the c-position can be rationalized in terms of n-interactions between substituent and central carbon orbitals at the SN2 transition state (1) [la]. The frontier orbit& involved in this interaction are the lone-pair p-orbital of the o-halogen substituent and the three-center n-type orbital aligned with the reaction coordinate axis (Fig. la). In the simplest model for the SN2 transi-
*For previous papers of this series see ref. 1. **Author to whom correspondence should be addressed. 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
164
H
H H
H b
a
Fig. 1. SN2 transition states for a-halo (a) and walkoxy (b) substituted molecules.
tion state, the D3h CH; structure, the latter MO corresponds to one below the HOMO (the HOMO being a nonbonding MO centered essentially only on nucleophile and leaving group, and lacking any n-type symmetry). Since both orbitals are doubly occupied, the overall n-interaction is repulsive, and raises the transition-state energy. As aresult, the SN2 reaction for a-halo substituted substrates is slow relative to unsubstituted molecules.
X N
I
C---L
e-w
H
1
H
The a-alkoxy substituent, on the other hand, is able to avoid the four electron repulsive interaction at the SN2 transition state simply by torsion about the C-O bond, such that the p-lone pair orbital on oxygen is perpendicular to the reaction coordinate axis, and n-overlap is minimized (the n-interaction is then said to be “turned off”, Fig. lb). Similar repulsive n-overlap which may operate in this transition state conformation between the in-plane hybrid lone pair on oxygen and the reaction coordinate orbital has been shown to be of little significance, due to the lower energy and the unfavorable orientation of this orbital [la]. These qualitative considerations were extensively supported by ab-initio SCF-MO calculations on model systems with various a-substituents, including planar NH2 and BH2, which serve as typical n-donor and acceptor substituents, respectively, that can be turned on and off at will and enable direct observation of this effect. The same SN2 transition state (l),in thecase of the identity exchange reaction (i.e., N = L), may also be viewed as a planar t&coordinate carbocation, solvated by two distant axial ligands or solvent molecules [ 51. From this point of view, the results discussed above may appear rather strange; it is well known that carbocations are substantially stabilized by adjacent n-donor atoms which effectively conjugate with the vacant p-orbital on the electron deficient carbon. And yet in 1, n-donors are found to have a destabilizing
165
effect. It seems that the very same n-interaction that causes SN2 rate retardation can act to accelerate SNl displacements. The purpose of the present study has been to clarify this point and to investigate the gradual change from one type of mechanism to the other. It is quite obvious that the question whether 1 describes an SN2 transition state or a solvated carbocation depends on the relative distances of the nucleophile and leaving group from the central carbon. An extremely “loose” SN2 transition state may be referred to as an “SNl-like SN2 transition state”, whereas a very tight transition state belongs to a strict SN2 reaction. Clearly, in presence of a poor leaving group, which in the identity reaction corresponds also to a powerful nucleophile, the transition state will be tight. In case of a strong leaving group and a poor nucleophile, the SNl mechanism will be preferred, and a loose transition state is expected. This situation may occur, for instance, when N and L are neutral molecules, such as water or ammonia, which are stable by themselves and do not require the strong association with the substrate molecule. Ideally one would wish to study the gradual transformation between the SN2 and SNl extremes of the mechanistic spectrum by means of a continuous variation in nucleophilicity of the N group. However such variation is not possible in reality. In fact, the choice of groups which differ markedly in nucleophilic power and also meet the practicality requirements for SCF-MO calculations is very limited. We chose, therefore, a model system for the changing power of nucleophile and (identical) leaving group, Realizing that a powerful leaving group will shift the mechanism towards the SNl side and impose a loose transition state, we approach the problem from the other end, i.e., by extending the C-nucleophile and C-leaving group distances artificially we attempt to mimic a gradual shift of mechanism towards the SNl end. This model may be understood as either changing the N and L groups for a weaker nucleophile and stronger leaving group, respectively, or as a gradual change in the reaction medium such that the N and L groups gradually become more stabilized by the solvent. The model transition state (Fig. 2) consist of an e-aminocarbocation, with H- groups at various distances serving as nucleophile and leaving group. The NH2 group was kept planar in both “on” and “off” conformations. The
‘Off’
‘Oil’
Fig. 2. Model SN2 transition states showing “on” and “off” geometries.
166
initial geometry was the fully optimized (4-31G basis set) CZVstructure for each of the model transition states, and the symmetry was maintained throughout the calculations. The results are presented in Table 1, and shown graphically in Fig. 3 [6, 71. Examination of Fig. 3 reveals that the energies of both model transition states rise with the extension of the axial C-H distances. This is due to the departure of both structures from their minimum energy conformations. However, the ascent of the curve for the NH2-off model is significantly steeper than that for the transition state with the n-interaction “turned on” TABLE 1 Relative energy as a function of C-H, CH,NH; transition states
distance for “on” and “off” conformations
Relative energy (kcal mol-I)
C-H, (A)
“on”
“Off”
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
13.8 11.5 10.8 11.3 12.8 15.1 18.0 21.3 25.0 29.1
0.0 1.6 4.7 8.9 14.0 19.7 25.8 32.2 38.7 45.2
-95.43
[
,
1.7
1.8
I I.9
I 2.0
I 2.1
C-Nucleophile
Fig. 3. Effect of extension of C-H,
I 2.2
r 2.3
disfonce,
I 2A
1 2.5
I 2d
d
distance on SN2 transition state energy.
of
167
[8]. At first, at the tight transition state end, the “on” structure is higher in energy due to four-electron repulsion. As the N-C-L distance increases, this repulsion gradually is released, such that the energy increase due to departure from optimum geometry is partly offset. As the structures become looser, the energies of the models approach each other, until they are equal. At that point there is no preference for one of the structures over the other, Further extension of the transition states brings about a crossover of the energy profiles: the n-interaction present at the “on” conformation becomes stabilizing, as a carbocationic center develops. Consequently, the “on” model becomes the preferred transition state structure. Thus, while in terms of energy there is a smooth change from an SN2 mechanism to an SNl-like transition state, TABLE 2 Mulliken x,-overlap populations for CH,NH; “on” C-H,
WI
GINO
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
0.0035 0.0049 0.0062 0.0076 0.0088 0.0100 0.0111 0.0121 0.0131 0.0139
0.0046 0.0094 0.0140 0.0181 0.0219 0.0252 0.0281 0.0306 0.0328 0.0346
transition statea CONI
CoNo
-0.0052 -0.0032 -0.0014 0.0001 0.0015 0.0027 0.0038 0.0049 0.0059 0.0068
-0.0350 -0.0275 -0.0211 -0.0158 -0.0115 -0.0079 -0.0049 -0.0025 -0.0004 0.0014
aOverlap between px inner and outer components on C and N, where x is the reaction coordinate axis. CI and Co express inner and outer px functions on carbon. Nr and No express the corresponding functions on nitrogen. TABLE 3 Mulliken n,-overlap populations for CH,NH; “off” C-H,
CI%
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
0.0001 0.0004 0.0006 0.0008 0.0011 0.0013 0.0015 0.0017 0.0019 0.0021
aSee footnote
to Table 2.
GINO
-0.0032 -0.0025 -0.0018 -0.0011 -0.0006 -0.0001 0.0003 0.0006 0.0008 0.0010
transition statea CONI
-0.0062 -0.0059 -0.0056 -0.0054 -0.0051 -0.0049 -0.0048 -0.0046 -0.0044 -0.0043
CON0
-0.0206 -0.0199 -0.0193 -0.0190 -0.0190 -0.0192 -0.0197 -0.0205 -0.0214 -0.0226
168
we identify here for the first time a sudden change in geometry, which signifies the mechanistic crossover: within the tight SN2 transition state region, the n-interaction is repulsive and hence the “off” transition state is more stable. At the borderline this interaction becomes insignificant, and at looser transition states, i.e., in the SNl-like mechanism region, the transition state geometry changes to the “on” arrangement. It can be shown that the changes in relative energies upon extension of the transition state really result from changes in the amount of n-interaction between nitrogen and carbon p-orbit&. Tables 2 and 3 list the Mulliken npopulations between carbon and nitrogen px orbit& in the “on” and “off” models, respectively. These are also displayed in Figs. 4 and 5. Since a split valence shell basis set was used, there are four different terms describing the n-overlap population between the C and N p-functions in the reaction coordinate direction for each transition state. Without attempting a complete analysis of the meaning of changes in each of the individual n-overlap components, the data in Figs. 4 and 5 strongly support the PM0 analysis discussed. Three out of the four curves in Fig. 5 are almost horizontal lines, situated near the zero line. The fourth line is slightly descending, and is negative. The overall variation in n-overlap of the “off” model as a function of C-H,, distance is extremely small. On the other hand, all four lines describing the “on” conformation (Fig. 4) are ascending, and two of them rather steeply. In other words, all four n-overlap terms in the “on” conformation increase with increasing C-H,, distance. Thus “loosening” of the model transition state is associated with substantial increase in n-bonding between carbon and nitrogen, from overall negative (i.e., antibonding) to positive ‘bonding. It may be of interest to note that the smallest changes in n-overlap are found in the “off” conformation, in which the energy change is most significant, whereas in the “on” model, where the energy change is relatively small, a rather dramatic increase in x,-overlap is observed. 0.04.
0.04-
0.03-
/---
5 0.02-
-1
x/l
/"I O.OlI_-+--' s+ o.oo_----~~~,r-=-I~~~~~~~~~
2
,/
+~+-~~~~~~~~~~~-t-n a*+-D-4-x
co--P-o
-O.Ol-
-0.02-
,//
J -0.02-
O.Olo,oo_
/de
;-O.Ol-
0.03002-
__+--F---l _
_+_--+--'
-0.03-
x/
/
o-.-+--a--o--o-+-‘--.3_._((
-003-
-0.04{{, 1.6 1.7 1.8 1.9 2.0 2.1 22 C-Hax
distance,
2.3 24 H
2.5 2.6
-o.O4jj, 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 24 C-H,,distance,
2.5 2.6
A
distance on mulliken rr,-overlap populations in “on” Fig. 4. Effect of extension of C-H, transition state. (+) CIN~; (X) GINO; (0) CON,; (0) CoNo. distance on mulliken r,-overlap Fig. 5. Effect of extension of C-H, “off” transition state. (+) C~NI ; (X ) GINO; (0) CONI ; (0) CoNo.
populations
in
169
While examining Fig. 4 it is tempting to speculate on the roles of the different overlap population terms. It appears that most of the repulsive interaction at the tight “on” transition state is due to negative n-overlap of the outer pX functions on N and C, whereas n-bonding at the loose (carbocationic) end is brought about mostly by overlap of the inner p function on carbon with the outer function on nitrogen. ACKNOWLEDGEMENT
Financial support by the Fund for Basic Research, administered by the Israel Academy of Sciences and Humanities, is gratefully acknowledged. REFERENCES 1 For previous papers in the series see: (a) D. Kost and K. Aviram, Tetrahedron Lett., 23 (1982) 4157. (b) D. Kost and K. Aviram, Bull. Sot. Chim. Belg., 91 (1985) 357. (c) A. Pross, K. Aviram, R. C. Klix, D. Kost and R. D. Bach, Nouv. J. Chim., 8 (1984) 711. 2 For other recent theoretical studies of substituent effect on SN2 reaction rate see: (a) S. S. Shaik, J. Am. Chem. Sot., 105 (1983) 4359. (b) S. Wolfe, D. J. Mitchell and H. B. Schlegel, Can. J. Chem., 60 (1982) 1291. 3 (a) P. Petrenko-Kritschenko and V. Opotsky, Chem. Ber., 59B (1926) 2131. (b) P. Petrenko-Kritschenko, A. Rawikowitsch, V. Opotsky, E. Pnjata and M. Kiakowa, Chem. Ber., 61B (1928) 845. (c) W. C. Davies, E. B. Evans and F. L. Hulbert, J. Chem. Sot., (1939) 412. (d) J. Hine, C. H. Thomas and S. J. Ehrenson, J. Am. Chem. Sot., 77 (1955) 3886. (e) J. Hine, S. J. Ehrenson and W. H. Brader, Jr., J. Am. Chem. Sot., 78 (1956) 2282. 4 (a) W. R. Kirner, J. Am. Chem. Sot., 48 (1926) 2745. (b) J. Hine, Physical Organic Chemistry, 2nd edn., McGraw-Hill, New York, 1962, pp. 169-178. (c) P. Bailinger, P. B. D. de la Mare, G. Kohnstam and B. M. Prestt, J. Chem. Sot., (1955) 3641. (d) R. Leimu and P. Salomaa, Acta Chem. Stand., 1 (1947) 353. (e) P. SaIomaa, in S. Patai (Ed.), The Chemistry of the Carbonyl Group, Wiley, New York, 1966. (f) T. C. Jones and E. R. Thornton, J. Am. Chem. Sot., 89 (1967) 4863. 5 W. P. Jencks, Act. Chem. Res., 13 (1980) 161. 6 The GAUSSIAN-76 program system was used with its built-in 4-31G basis set: J. S. Binkley, R. A. Whiteside, P. Hariharan, R. Seeger, J. A. Pople, W. J. Hehre and M. D. Newton, QCPE, 11(1979) 368. 7 Each extension of the C-H, distance was followed by geometry optimization of ail other geometrical parameters. 8 The minimum energy C-H, distance for the “on” transition state is 1.90 A and hence the ascent of the curve starts at this distance.