A R T I C L E S
Minegishi et al.
Table 4. Approximate Solvent Nucleophilicity Parameters (N1) for
Solvent Mixtures Calculated by Eq 6
who found a linear correlation between the aminolysis rates of
methyl 4-nitrobenzenesulfonate (SN2 reaction) and the corre-
sponding rates of amine additions to the 1-methyl-4-vinylpy-
ridinium ion with a slope of 2.27 ()1/0.44).28 Bunting’s and
Richard’s reports of linear correlations between Ritchie’s N+-
parameters (nucleophilicities toward carbocations)26 and Swain’s
and Scott’s n-parameters (nucleophilicities toward CH3Br)29 with
slopes of 2 also indicate that variations of nucleophiles affect
b
c
solventa
N
T
N
1
70E30W
30E70W
95A5W
-0.20
-0.93
-0.49
-0.42
-0.52
-0.70
-0.83
-0.96
-1.11
-1.23
-0.46
-0.37
-0.54
-0.66
-0.84
-1.12
-3.30
-2.19
-1.76
-0.94
-0.64
-0.34
0.08
6.5d
5.7d
6.1
6.2
6.0
5.7
5.5
5.3
5.1
4.9
6.1
6.2
6.0
5.8
5.5
5.1
1.8
3.5
4.1
5.4
5.8
6.3
6.9
-1.2
1.0
2.4
3.0
3.1
4.1
70A30W
60A40W
50A50W
40A60W
30A70W
20A80W
10A90W
80D20W
70D30W
60D40W
50D50W
40D60W
20D80W
97T3We
80T20We
80T20E
2
reactivities toward electrophilic Csp centers to a larger extent
than toward electrophilic Csp centers.28,30 In accordance with
3
these findings, l-values (according to eq 2) greater than 1 have
been found for solvolyses of chloroformate when nucleophilic
addition to the carbonyl group was rate-determining.31
Because linear correlations between NT, N′T, NOTs, and N′OTs
have previously been reported,2 it is not surprising that the
nucleophilicity parameters N1 derived from reactions with
benzhydrylium ions in this work also correlate linearly with
N′T, NOTs, and N′OTs (Figures S1-S3, Supporting Information).
Because of the good correlation between N1 and NT shown
in Figure 4, we suggest the employment of eq 6 for estimating
N1 of further solvent mixtures from reported NT values (Table
4). Although the data obtained in this way have to be considered
as approximate, they are most useful for designing syntheses
in these solvents.
60T40E
50T50E
40T60E
20T80E
97H3We
90H10We
70H30We
50H50We
HCO2H
-5.26
-3.84
-2.94
-2.49
-2.44
-1.78
The linear correlation shown in Figure 4 implies that the
solvent nucleophilicities N1 toward carbocations reported in this
work are controlled by the same factors as the solvent nucleo-
philicities NT toward methylsulfonium ions. A major advantage
of the new parameters N1 is that they can be combined with
the electrophilicity parameters E of carbocations, using eq 5,
so as to estimate absolute lifetimes of carbocations which are
produced solvolytically in aqueous or alcoholic solutions.33
CH3CO2H
a Unless otherwise stated, mixtures of solvents are given as (v/v),
solvents: M ) methanol, E ) ethanol, W ) water, T ) trifluoroethanol,
A ) acetone, D ) dioxane, H ) hexafluoro-2-propanol. b From ref 2. c A
slope parameter of s ) 0.9 is recommended for these solvents (compare s
parameters in Table 3). d Not by using eq 6, but by interpolating data for
aqueous ethanol from Table 3. e Mixtures of solvents are given as (w/w).
The flattening of the log k versus E correlations for k > 108
L mol-1 s-1 also prevents the calculation of the exact point,
where the enforced change from SN1 to SN2 mechanisms is
taking place. According to Jencks, this point is related to the
lifetimes of intermediates, which cannot be shorter than the
duration of a bond vibration (ca. 10-13 s).35 Having in mind
the flattening of the correlation lines for s(E + N) > 8,34 one
can only derive a lower limit and conclude that solvolysis with
s(E + N) < 13 will not proceed via enforced SN2 type
mechanisms.
Because s ≈ 0.9 for all solvents investigated (Table 3), eq 5
predicts that carbocations have a half-life τ1/2 > 10-10 s-1 if E
+ N1 < 11. As 10-10 s-1 is the time needed for solvent
reorganization, one can conclude that in 80% aqueous ethanol
(N1 ) 6.68), carbocations with E < 4.5 will be thermally
equilibrated, while in trifluoroethanol (N1 ) 1.23), thermal
equilibration will already be reached for carbocations of E <
10. Typical E values for carbocations are ca. 8.5 (for (CH3)3C+),34
5.9 (for Ph2CH+),15 and 0.5 (for Ph3C+).20 It should be noted,
however, that eq 5 has been reported to be limited to second-
order rate constants <108 L mol-1 s-1. For faster reactions, the
magnitude of the rate constants will be overestimated because
of the flattening of the correlation curves.34 As a consequence,
thermal equilibration of the intermediate carbocations may also
occur if the sum (E + N1) is slightly higher than 11.
A further advantage of the N1 parameters listed in Table 3 is
their direct comparability to the previously published N param-
eters of π-systems15,16,36-39 and hydride donors.15,40-43 Thus, it
becomes possible to predict nucleophiles which can intercept
(35) (a) Jencks, W. P. Acc. Chem. Res. 1980, 13, 161-169. (b) Jencks, W. P.
Chem. Soc. ReV. 1981, 10, 345-375 (c) Jencks, W. P. Chem. ReV. 1985,
85, 511-527.
(28) Bunting, J. W.; Mason, J. M.; Heo, C. K. M. J. Chem. Soc., Perkin Trans.
2 1994, 2291-2230.
(29) Swain, C. G.; Scott, C. B. J. Am. Chem. Soc. 1953, 75, 141-147.
(30) Richard, J. P.; Toteva, M. M.; Crugeiras, J. J. Am. Chem. Soc. 2000, 122,
1664-1674.
(36) Mayr, H.; Patz, M. Angew. Chem. 1994, 106, 990-1010; Angew. Chem.,
Int. Ed. Engl. 1994, 33, 938-957.
(37) Mayr, H.; Kuhn, O.; Gotta, M. F.; Patz, M. J. Phys. Org. Chem. 1998, 11,
642-654.
(31) (a) Kevill, D. N.; D’Souza, M. J. J. Chem. Soc., Perkin Trans. 2 1997,
1721-1724. (b) Kevill, D. N.; D’Souza, M. J. Can. J. Chem. 1999, 77,
1118-1122.
(38) Mayr, H.; Patz, M.; Gotta, M. F.; Ofial, A. R. Pure Appl. Chem. 1998, 70,
1993-2000.
(32) Nucleophilicities NT of solvent mixtures (v/v) from ref 2: 0.37 (E), 0.17
(M), 0.16 (90E10W), 0 (80E20W), -0.35 (90A10W), -0.37 (80A20W),
-0.39 (60E40W), -0.58 (50E50W), -0.74 (40E60W), -1.16 (20E80W),
-1.31 (10E90W), -1.38 (W), -1.71 (42T58W ) 50T50W, w/w), -1.85
(52T48W ) 60T40W, w/w), -1.98 (63T37W ) 70T30W, w/w), -2.25
(87T13W ) 90T10W, w/w), -3.93 (T).
(39) (a) Kempf, B.; Hampel, N.; Ofial, A. R.; Mayr, H. Chem.-Eur. J. 2003, 9,
2209-2218. (b) Bug, T.; Hartnagel, M.; Schlierf, C.; Mayr, H. Chem.-
Eur. J. 2003, 9, 4068-4076.
(40) Mayr, H.; Basso, N.; Hagen, G. J. Am. Chem. Soc. 1992, 114, 3060-
3066.
(41) Mayr, H.; Basso, N. Angew. Chem. 1992, 104, 1103-1105; Angew. Chem.,
(33) Denegri, B.; Minegishi, S.; Kronja, O.; Mayr, H. Angew. Chem. 2004, 116,
im Druck; Angew. Chem., Int. Ed. 2004, 43, in print.
Int. Ed. Engl. 1992, 31, 1046-1048.
(42) Funke, M.-A.; Mayr, H. Chem.-Eur. J. 1997, 3, 1214-1222.
(43) Mayr, H.; Lang, G.; Ofial, A. R. J. Am. Chem. Soc. 2002, 124, 4076-
4083.
(34) Roth, M.; Mayr, H. Angew. Chem. 1995, 107, 2428-2430; Angew. Chem.,
Int. Ed. Engl. 1995, 34, 2250-2252.
9
5180 J. AM. CHEM. SOC. VOL. 126, NO. 16, 2004