Reference scales for the characterization of cationic electrophiles and neutral nucleophiles

Article abstract of DOI:10.1021/ja010890y

Twenty-three diarylcarbenium ions and 38 π-systems (arenes, alkenes, allyl silanes and stannanes, silyl enol ethers, silyl ketene acetals, and enamines) have been defined as basis sets for establishing general reactivity scales for electrophiles and nucleophiles. The rate constants of 209 combinations of these benzhydrylium ions and π-nucleophiles, 85 of which are first presented in this article, have been subjected to a correlation analysis to determine the electrophilicity parameters E and the nucleophilicity parameters N and s as defined by the equation log k(20°C)=s(N+E) (Mayr, H.; Patz, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 938-957). Though the reactivity scales thus obtained cover more than 16 orders of magnitude, the individual rate constants are reproduced with a standard deviation of a factor of 1.19 (Table 1). It is shown that the reactivity parameters thus derived from the reactions of diarylcarbenium ions with π-nucleophiles (Figure 3) are also suitable for characterizing the nucleophilic reactivities of alkynes, metal-π-complexes, and hydride donors (Table 2) and for characterizing the electrophilic reactivities of heterosubstituted and metal-coordinated carbenium ions (Table 3). The reactivity parameters in Figure 3 are, therefore, recommended for the characterization of any new electrophiles and nucleophiles in the reactivity range covered. The linear correlation between the electrophilicity parameters E of benzhydryl cations and the corresponding substituent constants σ⁺ provides Hammett σ⁺ constants for 10 substituents from -1.19 to -2.11, i.e., in a range with only very few previous entries.

Full text of DOI:10.1021/ja010890y

9500
J. Am. Chem. Soc. 2001, 123, 9500-9512
Reference Scales for the Characterization of Cationic Electrophiles
and Neutral Nucleophiles†,‡
Herbert Mayr,* Thorsten Bug, Matthias F. Gotta,§ Nicole Hering, Bernhard Irrgang,
Brigitte Janker, Bernhard Kempf, Robert Loos, Armin R. Ofial,
Grigoriy Remennikov, and Holger Schimmel
Contribution from the Department Chemie der Ludwig-Maximilians-UniVersita¨t Mu¨nchen, Butenandtstrasse
5-13 (Haus F), D-81377 Mu¨nchen, Germany
ReceiVed April 5, 2001
Abstract: Twenty-three diarylcarbenium ions and 38 π-systems (arenes, alkenes, allyl silanes and stannanes,
silyl enol ethers, silyl ketene acetals, and enamines) have been defined as basis sets for establishing general
reactivity scales for electrophiles and nucleophiles. The rate constants of 209 combinations of these
benzhydrylium ions and π-nucleophiles, 85 of which are first presented in this article, have been subjected to
a correlation analysis to determine the electrophilicity parameters E and the nucleophilicity parameters N and
s as defined by the equation log k(20 °C) ) s(N + E) (Mayr, H.; Patz, M. Angew. Chem., Int. Ed. Engl. 1994,
33, 938-957). Though the reactivity scales thus obtained cover more than 16 orders of magnitude, the individual
rate constants are reproduced with a standard deviation of a factor of 1.19 (Table 1). It is shown that the
reactivity parameters thus derived from the reactions of diarylcarbenium ions with π-nucleophiles (Figure 3)
are also suitable for characterizing the nucleophilic reactivities of alkynes, metal-π-complexes, and hydride
donors (Table 2) and for characterizing the electrophilic reactivities of heterosubstituted and metal-coordinated
carbenium ions (Table 3). The reactivity parameters in Figure 3 are, therefore, recommended for the
characterization of any new electrophiles and nucleophiles in the reactivity range covered. The linear correlation
between the electrophilicity parameters E of benzhydryl cations and the corresponding substituent constants
σ+ provides Hammett σ+ constants for 10 substituents from -1.19 to -2.11, i.e., in a range with only very
few previous entries.
Introduction
nucleophiles.7 Kane-Maguire and Sweigart reported analogous
relationships for reactions of electrophilic metal-π-complexes
with phosphines, amines, and arenes.8,9 These results indicated
that electrophile-nucleophile combinations that do not involve
the cleavage of a C-X bond in the rate-determining step follow
a much simpler reactivity pattern than the SN2 type reactions
that were investigated earlier.
Lapworth was the first to recognize that polar reagents fall
into two categories which he termed “cationoid” and “anionoid”
(1925).1 Shortly after, Ingold suggested the alternative designa-
tions “electrophilic” and “nucleophilic” for these classes of
compounds,2 two terms that are now in general use for
discussing organic reactivity.
In view of the results of Ritchie, Kane-Maguire, and Sweigart
it was not astonishing that many reactions of carbocations with
olefins were also found to follow constant selectivity relation-
ships.10 To satisfactorily describe the reactivities of a larger
variety of nucleophiles, however, the introduction of a second
parameter for nucleophiles11-13 was found to be necessary. In
1994, we subjected the rate constants of 327 reactions of
carbocations, metal-π-complexes, and diazonium ions with π-,
σ-, and n-nucleophiles to a correlation analysis on the basis of
eq 1,
Attempts to quantify these terms started in 1953, when Swain
and Scott characterized nucleophiles by one parameter (n) and
electrophiles by two parameters (s, log kH O).3 Succeeding
2
investigations added more and more parameters,4,5 and finally
Bunnett listed 17 factors that have to be considered in a
quantitative description of nucleophilicity.6 On this background,
Ritchie’s “constant selectivity relationship” attracted much
attention because it calculates the rates of the reactions of
carbocations or diazonium ions with nucleophiles from only a
single parameter for electrophiles and a single parameter for
* To whom correspondence should be addressed. Telefax: int. +89-
2180-7717, E-mail: Herbert.Mayr@cup.uni-muenchen.de.
† Dedicated to Prof. Ju¨rgen Sauer on the occasion of his 70th birthday.
‡ A comprehensive listing of nucleophilicity and electrophilicity param-
eters can be found from October 2001 at http://www.cup.uni-muenchen.de/
oc/mayr/.
(7) (a) Ritchie, C. D. Acc. Chem. Res. 1972, 5, 348-354. (b) Ritchie,
C. D. J. Am. Chem. Soc. 1975, 97, 1170-1179. (c) Ritchie, C. D.; Sawada,
M. J. Am. Chem. Soc. 1977, 99, 3754-3761. (d) Ritchie, C. D.; Van Verth,
J. E.; Virtanen, P. O. I. J. Am. Chem. Soc. 1982, 104, 3491-3497. (e)
Ritchie, C. D. J. Am. Chem. Soc. 1984, 106, 7187-7194. (f) Ritchie, C. D.
Can. J. Chem. 1986, 64, 2239-2250.
§ Current address: Bayer AG, D-51368 Leverkusen, Germany.
(1) Lapworth, A. Nature 1925, 115, 625.
(8) Kane-Maguire, L. A. P.; Honig, E. D.; Sweigart, D. A. Chem. ReV.
1984, 84, 525-543.
(2) (a) Ingold, C. K. Recl. TraV. Chim. Pays-Bas 1929, 42, 797-812.
(b) Ingold, C. K. J. Chem. Soc. 1933, 1120-1127. (c) Ingold, C. K. Chem.
ReV. 1934, 15, 225-274.
(9) Pike, R. D.; Sweigart, D. A. Coord. Chem. ReV. 1999, 187, 183-
222.
(10) Mayr, H.; Schneider, R.; Grabis, U. J. Am. Chem. Soc. 1990, 112,
4460-4467.
(3) Swain, C. G.; Scott, C. B. J. Am. Chem. Soc. 1953, 75, 141-147.
(4) (a) Edwards, J. O. J. Am. Chem. Soc. 1954, 76, 1540-1547. (b)
Edwards, J. O. J. Am. Chem. Soc. 1956, 78, 1819-1820.
(5) Parker, A. J. Chem. ReV. 1969, 69, 1-32.
(11) Mayr, H.; Patz, M. Angew. Chem. 1994, 106, 990-1010; Angew.
Chem., Int. Ed. Engl. 1994, 33, 938-957.
(12) Mayr, H.; Kuhn, O.; Gotta, M. F.; Patz, M. J. Phys. Org. Chem.
1998, 11, 642-654.
(6) Bunnett, J. F. Annu. ReV. Phys. Chem. 1963, 14, 271-290. See also:
Nucleophilicity (AdV. Chem. Ser. 215); Harris, J. M., McManus, S. P., Eds.;
American Chemical Society: Washington, DC, 1987.
(13) Mayr, H.; Patz, M.; Gotta, M. F.; Ofial, A. R. Pure Appl. Chem.
1998, 70, 1993-2000.
10.1021/ja010890y CCC: $20.00 © 2001 American Chemical Society
Published on Web 09/11/2001

Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9501
In both cases the originally published E, N, and s parameters11
were kept unchanged. As a consequence, rate constants that had
entered our data collection at an early stage (before 1994)
received higher weight than data that were introduced later.
An alternative and more consequent way of handling the
kinetic data would be a complete correlation analysis of all
available rate constants after the addition of each new entry.
This procedure is not practicable, however, because it would
continuously alter all reactivity parameters and thus cause
confusion.
The use of all available rate constants for the determination
of E, N, and s by correlation analysis would cause an additional
problem: Imagine the case that a reaction series, investigated
for the elucidation of the reactivity parameters of a structurally
unique reagent, matches eq 1 only moderately. One would then
have to decide whether the benefit of obtaining the new
reactivity parameter compensates for the deterioration of the
quality of the overall correlation, which is associated with the
incorporation of a poorly matching reaction series. An unam-
biguous decision would often be impossible!
We will now provide a solution for these problems by
deriving E, N, and s parameters for a set of well-behaved
reference electrophiles and nucleophiles. Because of the clearly
defined origin of the reactivity parameters presented in this
article, future reparametrizations are not intended, and it will
be shown that the parameters determined in this way can be
used for characterizing any further reagents in the reactivity
range covered.
Electrophile Basis Set: Benzhydryl Cations. Previous work
has shown perfect linear reactivity-reactivity correlations for
reactions of benzhydryl cations with numerous classes of
nucleophiles,11,28 probably because the steric situation at the
reaction centers is kept constant while the reactivities of the
benzhydrylium ions are modified by variation of the para-
substituents. For that reason the choice of benzhydryl cations
as reference electrophiles appeared attractive. However, whereas
we had characterized numerous benzhydrylium ions with 6 >
E > 0, the 4,4′-bis(dimethylamino)benzhydrylium ion was the
only diarylcarbenium ion with a negative E value studied so
far. For the construction of benzhydryl cation based reactivity
scales, the characterization of more benzhydryl cations with E
< 0 was, therefore, necessary.
log k(20 °C) ) s (N + E)
(1)
where E is the electrophilicity parameter, N is the nucleophilicity
parameter, and s is the nucleophile-dependent slope parameter,
and obtained N and s parameters of 56 nucleophiles and E
parameters of 43 electrophiles.11
Despite the large structural variety of substrates and reactions
considered, the rate constants k calculated by the three-parameter
eq 1 were usually found to be accurate within a factor of 10-
100, when reagents of obvious steric bulk (e.g., tritylium ions)
were excluded. This precision is quite remarkable in view of
the fact that each of the scales covered 18 orders of magnitude,
resulting in an overall reactivity range of appoximately 36 orders
of magnitude. Because solvent effects are small in ion molecule
reactions,11,14,15 their influence is already included in the
aforementioned error-limits.
Since 1994, numerous other types of reactions have been
found to follow eq 1. N and s parameters of further classes of
nucleophiles, e.g., amine boranes,15 metal-π-complexes,16,17
heteroarenes,18 silyl enol ethers,19 and silyl ketene acetals,19 have
been determined by plotting the rate constants (log k) of their
reactions with previously characterized electrophiles versus the
published E parameters11 of the electrophilic reaction partners.
Electrophilicity parameters E of dithiocarbenium ions,20
iminium ions,21,22 propargyl cations with cobalt carbonyl
stabilization23 or (arene)Cr(CO)3 substituents,24,25 cationic allyl
palladium complexes,26 and Fe(CO)3-coordinated tropylium
ions27 have been derived from the rate constants of the reactions
of these electrophiles with nucleophiles that were characterized
by the reactivity parameters N and s in the 1994 paper.11 Ideally,
the electrophilicity parameter Ei of a certain electrophile i should
not depend on the choice of nucleophile j used for its
determination. In practice, the electrophilicity parameters ob-
tained from reactions of the electrophile i with various nucleo-
philes differed slightly, and Ei was taken as the arithmetic mean
of the values calculated with different reaction partners (eq 2)
n
n
log kij
1
1
Ei )
E )
- Nj
(2)
∑
∑
ij
(
)
n j ) 1
n j ) 1 sj
where n is the number of nucleophiles used for the characteriza-
tion of the new electrophile; Eij is the E parameter of electrophile
i derived from the reaction with the nucleophile j; sj and Nj are
the slope and nucleophilicity parameters published in 1994 (ref
11).
(14) Mayr, H.; Schneider, R.; Schade, C.; Bartl, J.; Bederke, R. J. Am.
Chem. Soc. 1990, 112, 4446-4454.
(15) Funke, M. A.; Mayr, H. Chem. Eur. J. 1997, 3, 1214-1222.
(16) Mayr, H.; Mu¨ller, K.-H. Collect. Czech. Chem. Commun. 1999, 64,
1770-1779.
(17) Mayr, H.; Kuhn, O.; Schlierf, C.; Ofial, A. R. Tetrahedron 2000,
56, 4219-4229.
(18) Gotta, M. F.; Mayr, H. J. Org. Chem. 1998, 63, 9769-9775.
(19) Burfeindt, J.; Patz, M.; Mu¨ller, M.; Mayr, H. J. Am. Chem. Soc.
1998, 120, 3629-3634.
Since previous work showed a correlation between pKR+
values and the electrophilicity parameters E of carbocations,13,23
we searched for benzhydrylium ions with pKR+ > -5.71.
(20) Mayr, H.; Henninger, J.; Siegmund, T. Res. Chem. Intermed. 1996,
22, 821-838.
(21) Bo¨ttger, G. M.; Fro¨hlich, R.; Wu¨rthwein, E.-U. Eur. J. Org. Chem.
2000, 1589-1593.
(22) Mayr, H.; Ofial, A. R. Tetrahedron Lett. 1997, 38, 3503-3606.
(23) Kuhn, O.; Rau, D.; Mayr, H. J. Am. Chem. Soc. 1998, 120, 900-
907.
However, while dozens of benzhydrylium ions with pKR+
<
-5.71 have been reported in the literature,29,30 the 4,4′-bis-
(28) Mayr, H. Angew. Chem. 1990, 102, 1415-1428; Angew. Chem.,
Int. Ed. Engl. 1990, 29, 1371-1384.
(24) Mu¨ller, T. J. J.; Ansorge, M.; Polborn, K. Organometallics 1999,
18, 3690-3701.
(29) (a) Deno, N. C.; Jaruzelski, J. J.; Schriesheim, A. J. Am Chem. Soc.
1955, 77, 3044-3051. (b) Deno, N. C.; Schriesheim, A. J. Am Chem. Soc.
1955, 77, 3051-3054.
(25) Netz, A.; Mu¨ller, T. J. J. Tetrahedron 2000, 56, 4149-4155.
(26) Kuhn, O.; Mayr, H. Angew. Chem. 1999, 111, 356-358; Angew.
Chem., Int. Ed. 1999, 38, 343-346.
(30) (a) Mindl, J.; Vecˇerˇa, M. Collect. Czech. Chem. Commun. 1971,
36, 3621-3632. (b) Mindl, J.; Vecˇeˇra, M. Collect. Czech. Chem. Commun.
1972, 37, 1143-1149.
(27) Mayr, H.; Mu¨ller, K.-H.; Ofial, A. R.; Bu¨hl, M. J. Am. Chem. Soc.
1999, 121, 2418-2424.

9502 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
(dimethylamino)-substituted cation was the only one with a
higher pKR+ value so far characterized. The surprising lack of
compounds in this range mirrors the shortage of substituents
Scheme 1
+
with Hammett σp parameters more negative than -0.78.31,32
We have not been successful in synthesizing benzhydrylium
ions with a p-dimethylamino group on one phenyl ring and
p-alkoxy on the other ring,33 and problems were encountered
when preparing bis(3-Me,4-NMe2)-substituted benzhydrylium
ions.34 Probably because of electrophilic attack at nitrogen, the
generation of such carbenium ions was not well reproducible,
and for that reason we have not selected such species as
reference electrophiles.
was achieved in the presence of potassium tert-butoxide.
Reduction of 4 with sodium borohydride39 gave the 4,4′-
diaminobenzhydrols 5, which were treated with tetrafluoroboric
acid to generate the corresponding tetrafluoroborates of
(mpa)2CH+, (dpa)2CH+, and (pyr)2CH+.
We have been able, however, to isolate and characterize ten
Ar2CH+ analogues of Michler’s Hydrol Blue, the syntheses of
which are summarized in Schemes 1-3.
Since pure 4,4′-bis(morpholino)benzhydrylium tetrafluorobo-
rate was not obtained by this procedure, the benzhydrol 5-(mor)2
was ionized with tritylium tetrafluoroborate according to eq 3.
CH2Cl2
5-(mor)2 + Ph3C+ BF4
8 (mor)2CH+ BF4
(3)
-
-
Ar2CH+ a
R1
R2
R3
R4
-Ph3COH
(lil)2CH+
-(CH2CH2)-
-(CH2CH2CH2)-
-(CH2CH2)-
-(CH2CH2CH2)-
-(CH2CH2CH2)-
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(mpa)2CH+
(mor)2CH+
(dpa)2CH+
(mfa)2CH+
(pfa)2CH+
Oxidation of the trifluoroethylamino-substituted40 diphenyl-
methanes 6-(mfa)2 and 6-(pfa)2 with DDQ in methanol and
reduction of the resulting benzophenones with sodium borohy-
dride gave the bis(diarylmethyl) ether 7 (R ) Me) and the
benzhydrol 5-(pfa)2 (R ) Ph), respectively (Scheme 3). Treat-
ment of these compounds with tetrafluoroboric acid yielded the
CH3
CH3
H
H
-(CH2CH2CH2)-
H
H
H
H
H
H
H
-(CH2CH2CH2CH2)-
CH3
C6H5
-(CH2CH2OCH2CH2)-
C6H5
CH2CF3
CH2CF3
H
H
H
H
H
H
H
b
CH3
CH3
C6H5
CH3
corresponding benzhydrylium salts (mfa)2CH+ BF4- and (pfa)2-
-
CH+ BF4
.
C6H5
Since the synthetic procedures illustrated in Schemes 1-3
still require optimization, we will describe details of these
syntheses later.
a For abbreviations, see ref. 35. b Michler’s Hydrol Blue.
The tetrafluoroborate salts of (lil)2CH+, (jul)2CH+,36 (ind)2-
CH+, and (thq)2CH+ were generated by phosphorus oxychloride-
promoted coupling of the arenes 1 with the corresponding
carbaldehydes 237 and successsive treatment with an aqueous
solution of sodium tetrafluoroborate analogous to a procedure
described by Jutz38 (Scheme 1).
The 4,4′-diaminobenzophenones 4-(pyr)2 and 4-(mor)2 were
obtained by heating sulfolane or dimethyl sulfoxide solutions
of 4,4′-difluorobenzophenone 3 and excess pyrrolidine or
morpholine, respectively, as described by Hepworth et al39
(Scheme 2). The analogous formation of 4-(mpa)2 and 4-(dpa)2
In contrast to the yellow or red alkyl- and alkoxy-substituted
benzhydryl cations, which have absorption maxima between 435
and 510 nm,41,42 the p-amino-substituted benzhydrylium ions
are blue due to their absorption maxima between 590 and 680
nm.36,39,43 Details of the UV-vis spectra are given in Table
S19 of the Supporting Information.
Nucleophile Basis Set: πCC-Systems. Previous work has
shown that the reactions of benzhydrylium ions with many types
of nucleophiles, including aliphatic and aromatic π-systems,
metal π-complexes, hydride donors, and n-nucleophiles, follow
linear reactivity-reactivity correlations of comparable quality.11
For that reason, representatives of all of these classes of
compounds may be considered as potential reference nucleo-
philes. Since carbon-carbon double-bonded systems, including
substituted benzenes, heteroarenes, alkenes, allylsilanes, silyl
enol ethers, and enamines, represent the largest group of
structurally related nucleophilessall these compounds share an
sp2-hybridized carbon atom as the center of nucleophilicitys
representatives of these classes of compounds were selected as
(31) Exner, O. Correlation Analysis of Chemical Data; Plenum Press:
New York, 1988.
(32) Shorter, J. In Supplement F2, The chemistry of amino, nitroso, nitro
and related groups; Patai, S., Ed.; Wiley: Chichester, 1996; Chapter 11,
pp 479-531.
(33) Saadatjou, N. J. Sci. I. R. Iran 1989, 1, 39-43.
(34) Castelino, R. W.; Hallas, G. J. Chem. Soc. B 1971, 1471-1473.
(35) The following abbreviations are used (in alphabetical order): ani:
p-anisyl () 4-methoxyphenyl); dpa: 4-(diphenylamino)phenyl; fc: ferro-
cenyl; fur: 2,3-dihydrobenzofuran-5-yl; ind: N-methyl-2,3-dihydro-1H-
indol-5-yl; jul: julolidin-9-yl () 2,3,6,7-tetrahydro-1H,5H-pyrido[3,2,1-
ij]quinolin-9-yl); lil: lilolidin-8-yl () 1,2,5,6-tetrahydro-4H-pyrrolo[3,2,1-
ij]quinolin-8-yl); mfa: 4-(methyl(trifluoroethyl)amino)phenyl; mor: 4-(N-
morpholino)phenyl; mpa: 4-(methylphenylamino)phenyl; pcp: p-chlorophenyl;
pfp: p-fluorophenyl; pfa: 4-(phenyl(trifluoroethyl)amino)phenyl; pop:
p-phenoxyphenyl; pyr: 4-(N-pyrrolidino)phenyl; thq: N-methyl-1,2,3,4-
tetrahydroquinolin-6-yl; tol: p-tolyl () 4-methylphenyl).
(36) For a synthesis of bis(julolidin-9-yl)methylium perchlorate, see:
Mikhailenko, F. A.; Balina, L. V. Khim. Geterotsikl. Soedin. 1982, 450-
452.
(39) Beach, S. F.; Hepworth, J. D.; Jones, P.; Mason, D.; Sawyer, J.;
Hallas, G.; Mitchell, M. M. J. Chem. Soc., Perkin Trans. 2 1989, 1087-
1090.
(40) Armstrong, L.; Jones, A. M. Dyes Pigm. 1999, 42, 65-70.
(41) Bartl, J.; Steenken, S.; Mayr, H.; McClelland, R. A. J. Am. Chem.
Soc. 1990, 112, 6918-6928.
(42) Olah, G. A.; Pittman, C. U.; Symons, M. C. R. In Carbonium Ions;
Olah, G. A., Schleyer, P. v. R., Eds.; Interscience Publishers: New York,
1968; Vol. I, Chapter 5, pp 153-222.
(37) Carbaldehydes 2 were obtained from the corresponding arenes 1
by Vilsmeier-Haack formylations. See also: Gawinecki, R.; Andrzejak,
S.; Puchala, A. Org. Prep. Proced. Int. 1998, 30, 455-460.
(38) Jutz, C. Chem. Ber. 1958, 91, 850-861.
(43) (a) Barker, C. C.; Hallas, G. J. Chem. Soc. B 1969, 1068-1071.
(b) Castelino, R. W.; Hallas, G.; Taylor, D. C. J. Soc. Dyers Colour. 1972,
88, 25-27.

Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9503
Scheme 2
Scheme 3
reference nucleophiles. Electrophilic attack at the π-bond yields
constants kexp (M-1 s-1
kobs ) kexp[Nuc]0.
For slow reactions (τ1/2 > 10 s) the decrease of the absorptions
of the benzhydrylium ions at or close to λmax was followed
photometrically as a function of time by using fiber optics and
the working-station described in ref 14.
) were then calculated from
cationic adducts, which usually undergo fast consecutive reac-
tions (Scheme 4), as proven by the independence of the reaction
rates of the nature and concentration of the counterion.14,19,44
The reaction products are generally analogous to those
identified in previous investigations18,19,44,45 (see Supporting
Information). In some cases, diarylmethanes were isolated as
side products which were presumably formed by hydride transfer
from the reaction products to the benzhydrylium ions.
Details of the kinetic experiments can be found in Tables
S1-S18 of the Supporting Information.
Correlation Analysis for the Basis Set Compounds. Table
1 lists 209 rate constants for the reactions of 23 benzhydrylium
ions with 38 π-nucleophiles,46-56 87 of which have not been
published previously. It is a complete collection of all presently
available rate constants for reaction series consisting of a
benzhydrylium ion with three or more π-nucleophiles. To avoid
ambiguity, this listing does not include rate constants which
cannot definitely be assigned to the relevant carbon-carbon
bond-forming step. For that reason, the gross rate constants for
the reactions of benzhydrylium ions with 2,3-dimethyl-2-
butene10 are omitted, though they match eq 1 very well.
Kinetic Investigations. UV-visible kinetic measurements
of rapid reactions (τ1/2 < 10 s) were performed on a Hi-Tech
SF-61DX2 stopped-flow spectrophotometer system and con-
trolled by using Hi-Tech KinetAsyst 2 software running on an
IBM-compatible PC. The kinetic runs were initiated by mixing
equal volumes of the nucleophile solution and the benzhydryl-
ium salt solution. The temperature of the reactant solutions was
controlled within (0.1 °C using the circulating water bath F25-
HD by Julabo and monitored via the Pt resistance thermometer
of the SF-61DX2 mixing unit. Nucleophile concentrations
[Nuc]0 at least 10 times higher than the benzhydryl cation
concentrations were usually employed, resulting in pseudo-first-
order kinetics with an exponential decay of the benzhydryl cation
concentration. Observed first-order rate constants kobs (s-1) for
the reactions of benzhydrylium ions with nucleophiles were
obtained from at least five runs at each nucleophile concentration
by least-squares fitting of the absorbance data to the single
exponential A ) A0 exp(-kobst) + C. The second-order rate
Following our previous treatment,11 the electrophilicity
parameter of the dianisylcarbenium ion and the slope parameter
of 2-methyl-1-pentene were selected as standard, i.e., E[(ani)2CH+]
) 0 and s(2-methyl-1-pentene) ) 1.00. All other reactivity
(46) Patz, M. Dissertation, Technische Hochschule Darmstadt, 1994.
(47) Patz, M.; Mayr, H. Tetrahedron Lett. 1993, 34, 3393-3396.
(48) Patz, M., unpublished results.
(49) Mayr, H.; Rau, D. Chem. Ber. 1994, 127, 2493-2498.
(50) Funke, M. A. Diplomarbeit, Technische Hochschule Darmstadt,
1993.
(44) Hagen, G.; Mayr, H. J. Am. Chem. Soc. 1991, 113, 4954-4961.
(45) (a) Mayr, H.; Pock, R. Chem. Ber. 1986, 119, 2473-2496. (b) Pock,
R.; Mayr, H. Chem. Ber. 1986, 119, 2497-2509.
(51) Roth, M. Dissertation, Technische Hochschule Darmstadt, 1996.

9504 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
Scheme 4
parameters E, N, and s, as defined by eq 1, were then calculated
by minimizing ∆2 specified by eq 4 using the program
"What’sBest! 4.0 Commercial" by Lindo Systems Inc.57
acetonitrile55 was the deviation between calculated and experi-
mental rate constants greater than a factor of 1.7.
Comparison of the N and E parameters given in Table 1 with
those published in 199411 shows that the parameters remained
almost identical for systems with E g 0 or N e 2, because the
data basis in these regions has only slightly been altered. More
remarkably, however, though (dma)2CH+ is the only electrophile
with E < -3 which has been used in this and in the 1994
correlation, its E parameter and the N parameters of the
nucleophiles linked to it (3 < N < 13) also have not changed
by more than 0.5 units. 2-(Trimethylsiloxy)-4,5-dihydrofuran
is the only compound for which N has to be corrected by as
much as 0.9 units, because the original calculation19 was based
on an erroneously estimated value of s. Since the previous
correlation11 rested predominantly on reactions of electrophilic
metal-π-complexes and heteroaromatic cations in this range,
this agreement implies that the reactivity parameters presented
in this work are transferable to other types of compounds as
demonstrated in detail below.
A graphical representation of this correlation analysis is given
in Figures 1 and 2. Figure 1, which plots log k versus the E
parameters of the electrophiles shows correlation lines with
slightly different slopes for different nucleophiles. Deviations
from the linear correlations occur as the diffusion limit (5 ×
109 M-1 s-1) is approached,12,59 and for that reason rate
constants kexp > 108 M-1 s-1 have not been considered for the
correlations. For the sake of clarity, only 20 out of 38 correlation
lines are shown in Figure 1, and we have omitted nucleophiles
in regions with a high density of data points.
∆2 ) Σ(log kexp - log kcalc)2 ) Σ(log kexp - s(E + N))2 (4)
Since charge is neither developed nor neutralized during the
combination of the carbocations with the neutral nucleophiles,
solvent effects are usually small (e.g., kCH NO /kCH Cl ) 4),11,14
3
2
2
2
and the few rate constants measured in solvents other than
dichloromethane (footnotes in Table S20) have been used in
the correlation analysis without correction. Comparison of
calculated (eq 1) and experimentally obtained rate constants in
Table 1 shows a standard deviation58 of a factor of 1.19. Only
for 4% of the reactions, predominantly those with rate constants
> 107 M-1 s-1 or those for which k(20 °C) was extrapolated
from measurements at lower temperature, the deviation is higher
than a factor of 1.50. It should be noted, however, that in none
of the eight entries with 5 × 106 < kexp < 1 × 108 M-1 s-1
which have been determined by laser flash spectroscopy in
(52) Schneider, R. Dissertation, Friedrich-Alexander-Universita¨t Erlan-
gen-Nu¨rnberg, 1987.
(53) Mayr, H.; Bartl, J.; Hagen, G. Angew. Chem. 1992, 104, 1689-
1691; Angew. Chem., Int. Ed. Engl. 1992, 31, 1613-1615.
(54) Mayr, H.; Schneider, R.; Irrgang, B.; Schade, C. J. Am. Chem. Soc.
1990, 112, 4454-4459.
(55) (a) Bartl, J.; Steenken, S.; Mayr, H. J. Am. Chem. Soc. 1991, 113,
7710-7716. (b) Bartl, J. Inaugural Dissertation, Medizinische Universita¨t
zu Lu¨beck, 1990.
(56) Wang, Y.; Dorfman, L. M. Macromolecules 1980, 13, 63-65.
(57) The What’sBest!'s nonlinear solver employs both successive linear
programming and generalized reduced gradient algorithms. The minimiza-
tion procedure for ∆2 was performed by solving the model several times
with different initial values of E, N, and s.
An important message can be taken from Figure 1. The
similarities of the slopes and the narrow range accessible by
second-order kinetics (-6 < log k < 9) implies that crossing
can only occur for correlation lines of nucleophiles with closely
(58) The standard deviation σ is defined as log σ ) (∆2/n)0.5 with ∆2
from eq 4. This definition has been criticized by one referee. We did,
however, not find a more straightforward way to characterize the reliability
of the calculated rate constants which result from 23 correlation lines in
Table 1 and from 15 correlation lines in Table 2.
(59) Roth, M.; Mayr, H. Angew. Chem. 1995, 107, 2428-2430; Angew.
Chem., Int. Ed. Engl. 1995, 34, 2250-2252.

Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9505
Table 1. Second-Order Rate Constants k (M-1 s-1, 20 °C, CH2Cl2), Activation Parameters ∆Hq (kJ mol-1), and ∆Sq (J mol-1 K-1), and
Reactivity Parameters (E, N, and s) Determined for the Reactions of Basis Set Benzhydrylium Ions with Basis Set π-Nucleophiles.a The
Complete Content of Table 1 Is Found as Table S20 in the Supporting Information
a The values of kcalc were actually calculated by eq 1 with more decimals of E, N, and s than indicated in the table. The use of the E, N, and s
parameters given in this table leads to slightly deviating results. b This work. c In the presence of 2,6-di-tert-butylpyridine.
similar N parameters. In other words, nucleophiles with suf-
ficiently different N values will not invert relative reactivities
in the experimentally relevant range. Since crossing above log
k > 9 (diffusion control) or below log k < -6 (no reaction at
room temperature) does not have any practical consequences,
the definition of N as the intercepts of the correlation lines with
the abscissa (log k ) 0) provides a useful measure for
nucleophilic reactivities.
It should be noted that eq 1 is mathematically equivalent to
the conventional linear free energy relationship (eq 5), as eq 5

9506 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
Figure 1. Plot of log k(20 °C) vs E for the reactions of benzhydryl cations with π-nucleophiles (for abbreviations, see ref 35).
Figure 2. Plot of (log k)/s versus N for the reactions of benzhydryl cations with π-nucleophiles.
The only difference between eqs 1 and 5 is that the latter
defines nucleophilicities Nu by the intercepts of the correlation
lines with the ordinate (Nu ) log k for E ) 0) whereas the
can be converted to eq 1 by replacement of Nu by sN.
log k ) Nu + sE
(5)

Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9507
Figure 3. Compilation of all compounds used for the determination of E, N, and s. Reactivity parameters of the recommended reference compounds
a
are explicitly listed (s in parentheses). Reference compound, not used for the correlation analysis: see ref 60.
former defines nucleophilicities N by the intersections of
correlation lines with the abscissa (N ) -E for log k ) 0).11-13
Thus N, in contrast to Nu, is generally defined within the
experimentally accessible range, and its use avoids long-range
extrapolations as needed for the determination of Nu values for
very strong (Nu > 8) as well as for very weak nucleophiles
(Nu < -5) according to eq 5.
All 209 reactions of Table 1 are included in Figure 2, in which
each correlation line corresponds to a benzhydryl cation. One
can see that the benzhydryl cations characterized so far,
continuously cover the range -10 < E < 6 and thus allow the
straightforward quantification of nucleophiles with -8 < N <
16. Vice versa, the nucleophiles listed in Table 1 may be used
to characterize electrophiles with -15 < E < 7.
All compounds used for the determination of E, N, and s in
Table 1 are depicted in Figure 3 (basis set). However, not all
of the basis set nucleophiles are recommended as reference
compounds. Some of them are difficult to handle because of
their volatility, others tend to undergo side reactions, and there
are highly substituted π-systems which can be expected to highly
differentiate reaction partners on the basis of steric strain. To
facilitate the usage of these scales, numerical values for E, N,
and s are only given for those compounds of the basis set in
Figure 3, which are recommended as reference compounds for
the characterization of further electrophiles and nucleophiles.
Reactivity Parameters for Electrophiles and Nucleophiles
Outside the Basis Set. The definition of basis sets and fixation
of the corresponding E, N, and s parameters as described above
is only useful if these parameters can be employed for the
characterization of other types of compounds. We demonstrate
this by analyzing reaction series in which reference compounds
are combined with electrophiles or nucleophiles that do not
belong to the basis set.
Table 2 examines the applicability of the electrophilicity
parameters of benzhydrylium ions listed in Figure 3 for reactions
with alkynes, transition metal π-complexes, hydride donors, and
CC-double-bonded systems not belonging to the basis set. The
standard deviation58 between experimentally obtained and
calculated rate constants listed in Table 2 is a factor of 1.26,
only slightly higher than for the compounds of the basis set,
indicating the general applicability of the E parameters given
in Figure 3. Correlations of comparable quality have also been
obtained for the reactions of benzhydrylium ions with water
and alcohols.65,66 To limit the length of this article, reactions
with n-nucleophiles have not been included in Table 2. In a
forthcoming paper we will show that all n-nucleophiles,

9508 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
Table 2. Second-Order Rate Constants k (M-1 s-1, 20 °C, CH2Cl2)
for the Reactions of Nucleophiles Not Belonging to the Basis Set
with Electrophiles of the Basis Seta
including anions (Ritchie-type nucleophiles7), are characterized
by similar s values and thus give rise to a set of constant
selectivity relationships as a subset of our correlations.
It should be noted that a comparison of calculated with
experimental rate constants is not possible in reaction series
only comprising two electrophiles (kcalc and kexp must then be
identical!) and these entries have been omitted when calculating
the standard deviation. In these cases the similarities of the
slopes s with the slopes of structurally related nucleophiles
indicate the applicability of eq 1.
Table 3 proves that the N parameters of π-nucleophiles listed
in Figure 3 are also suitable for the characterization of other
types of electrophiles. One can see that kexp and kcalc show a
standard deviation58 of a factor of 2.05. This may be considered
being high, but in view of the wide structural variety covered
by the electrophiles in Table 3, the reliability of the predictions
is remarkable, particularly when one considers that a large
percentage of the standard deviation comes from the poorly
matching reactions of the π-allyl palladium complex.26
Comparison of kexp and kcalc for the reactions of the hexa-
carbonyldicobalt coordinated propargylium ions with nucleo-
philes (Table 3) illustrates the advantage of using reference
compounds with fixed E, N, and s parameters. The deviations
between calculated and experimentally obtained rate constants
are rather large for some reactions of these cations, that one
would not want to allow these data to affect the nucleophilicity
parameters of allylsilanes and silyl enol ethers which have been
derived from well-behaved linear free energy relationships. This
would be the case, if all rate constants would uniformly be
employed for the correlation analysis. On the other hand, these
rate constants are presently the best source providing quantitative
information on the electrophilicities of these cobalt complexes,
and we have shown23 that they allow the semiquantitative
analysis of the reactions of these cationic complexes. The
approach presented in this article, which uses fixed E, N, and s
parameters derived from the basis set compounds serves both
requirements.
A final test of the reliability of the approach to employ fixed
reactivity parameters from basis set compounds is given in Table
4, which compares experimentally measured and calculated rate
constants for electrophiles not belonging to the basis set (Table
3) with nucleophiles not belonging to the basis set (Table 2).
The standard deviation58 now is a factor of 6.26 which reflects
the predictive power of this method in practice. It should be
mentioned, however, that the maximum deviation for reactions
with C-nucleophiles is a factor of 3.4, indicating that the
reliability is higher for CC-bond-forming reactions.
(60) By the criteria used for the selection of basis set compounds (Table
1), allyltriphenylsilane should be treated as basis set nucleophile. However,
the rate constants for this compound had not been available at the time the
correlation analysis for the data in Table 1 was performed. For that reason,
the kinetic data for allyltriphenylsilane have only been used for determining
its N and s values, and not for the parametrization of E of its electrophilic
reaction partners.
(61) Mayr, H.; Gonzalez, J. L.; Lu¨dtke, K. Chem. Ber. 1994, 127, 525-
531.
(62) Mayr, H.; Basso, N.; Hagen, G. J. Am. Chem. Soc. 1992, 114, 3060-
3066.
(63) Funke, M. A. Dissertation, Technische Hochschule Darmstadt, 1997.
(64) Mayr, H.; Basso, N. Angew. Chem. 1992, 104, 1103-1105; Angew.
Chem., Int. Ed. Engl. 1992, 31, 1046-1048.
a For abbreviations, see ref 35. The values of kcalc were actually
calculated by eq 1 with more decimals of E, N, and s than indicated in
the table. The use of the E, N, and s parameters given in this table
leads to somewhat deviating results. b See ref 60. c This work. d In
acetonitrile. e -lFrom rate constants determined at different temperatures,
assuming the same activation entropy as for the reactions of this
nucleophile with other benzhydrylium ions: ∆Sq ) e -120; f -104; g
(65) (a) McClelland, R. A.; Kanagasabapathy, V. M.; Steenken, S. J.
Am. Chem. Soc. 1988, 110, 6913-6914. (b) McClelland, R. A.; Kanaga-
sabapathy, V. M.; Banait, N. S.; Steenken, S. J. Am. Chem. Soc. 1989,
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(66) (a) Kirmse, W.; Krzossa, B.; Steenken, S. J. Am. Chem. Soc. 1996,
118, 7473-7477. (b) Kirmse, W.; Guth, M.; Steenken, S. J. Am. Chem.
Soc. 1996, 118, 10838-10849.
h
i
j
k
l
-110; -105; -115; -97; -130; -86 J mol-1 K-1
.

Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9509
Table 3. Second-Order Rate Constants k (M-1 s-1, 20 °C, CH2Cl2) for the Reactions of Electrophiles Not Belonging to the Basis Set with
Nucleophiles of the Basis Seta
a The values of kcalc were actually calculated by eq 1 with more decimals of E, N, and s than indicated in the table. The use of the E, N, and s
parameters given in this table leads to somewhat deviating results. b In acetone. c In nitromethane, the original rate constant (at 45 °C) was converted
to k(20 °C) assuming ∆Sq ) -100 J mol-1 K-1, see also ref 18. d This rate constant was not used for the determination of E. e In acetonitrile.
f,g From rate constants determined at different temperature assuming the same activation entropy as for the reactions of this nucleophile with
f
benzhydrylium ions: ∆Sq ) -110;g -120 J mol-1 K-1
.
h -mFrom rate constants determined at -70 °C, assuming the same activation entropy as
for the reactions of this nucleophile with benzhydrylium ions: ∆Sq ) h -118; i -123; j -120; k -122; l -121; m -153 J mol-1 K-1 n This work.
.

9510 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
Table 4. Second-Order Rate Constants k (M-1 s-1, 20 ˚C, CH2Cl2)
for the Reactions of Nucleophiles Not Belonging to the Basis Set
(from Table 2) with Electrophiles Not Belonging to the Basis Set
(from Table 3)a
Figure 4. Correlation of Hammett’s σ+ constants31 with the electro-
philicity parameters E of the corresponding symmetrically substituted
benzhydrylium ions (for abbreviations, see ref 35).
is contrasted by a remarkable shortage of substituent constants
for groups that are better electron donors than alkoxy.75
In agreement with earlier studies,76 there is only a moderate
correlation (r ) 0.9955) between the electrophilicity parameters
E of benzhydrylium ions with Σσ+, because in case of unsym-
metrically substituted systems, the twisting angle of the two
aryl rings is different.73 If only symmetrically substituted benz-
hydryl cations are considered, the linear correlation (Figure 4)
is of higher quality, however, and can be used to determine the
σ
+ parameters of a series of new donor substituents (Table 5).
Conclusion
The linear free enthalpy relationships presented in Figures 1
and 2 represent the most extended reactivity-reactivity cor-
relations presently known. Since the E parameters of the
benzhydrylium cations and the N and s parameters of the
π-nucleophiles derived therefrom were found to be a proper
a The values of kcalc were actually calculated by eq 1 with more
decimals of E, N, and s than indicated in the table. The use of the E,
N, and s parameters given in this table leads to somewhat deviating
results. b In acetone. c A second-order rate constant of 3.46 × 10-2 M-1
s-1 (25 °C, CH2Cl2) has been reported in ref 71. d -fFrom rate constants
determined at different temperature assuming the same activation
entropy as for the reactions of this nucleophile with benzhydrylium
(75) For σR° constants of amino substituents, see: Gawinecki, R.;
Kolehmainen, E.; Kauppinen, R. J. Chem. Soc., Perkin Trans. 2 1998, 25-
29.
d
e
f
ions: ∆Sq) -100; -110; -150 J mol-1 K-1
.
(76) Schade, C.; Mayr, H. Tetrahedron 1988, 44, 5761-5770.
(77) For classifications of carbon electrophiles, see: (a) Osella, D.;
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New Hammett Parameters. The Hammett equation is one
of the oldest and the most developed empirical relationship
which has been employed for correlating kinetic and thermo-
dynamic as well as spectroscopic properties.31,72-74 Most
quantitative information about substituent effects have been
derived from Hammett’s σ constants and modifications thereof.
However, as indicated above, the wealth of substituent constants
for electron-withdrawing and weakly electron-donating groups
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Characterization of Cationic Electrophiles and Neutral Nucleophiles
J. Am. Chem. Soc., Vol. 123, No. 39, 2001 9511
Table 5. Hammett σ+ Constants of Donor Substituents
mechanisms83 and for theoretical treatments of organic reactiv-
ity.84 Though a moderate correlation between the electrophilicity
parameters E and the corresponding reduction potentials has
been reported,12 outer sphere SET processes for the reactions
of carbocations with π-nucleophiles have been excluded.83b
Though the reactivity scales presented in this work cover
already 16 orders of magnitude, extensions of the scales in both
directions are desirable. Laser flash experiments have already
been employed to characterize more electrophilic carboca-
tions,41,66,85 and quinone methides have been reported to behave
like highly stabilized carbocations which can be used for the
investigation of stronger nucleophiles.86,87 The integration of
these data is in progress.
Acknowledgment. Financial support by the Deutsche For-
schungsgemeinschaft and the Fonds der Chemischen Industrie
is gratefully acknowledged. We thank H. Huber (Mu¨nchen) for
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organic transformations81 and of carbocationic polymerizations.82
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9512 J. Am. Chem. Soc., Vol. 123, No. 39, 2001
Mayr et al.
measuring the UV-vis spectra as well as Dr. M.-A. Funke and
tions with product characterization, UV-vis spectral data of
Michler’s Hydrol Blue and its analogues, and the complete
version of Table 1 with second-order rate constants, activation
and reactivity parameters for the reactions of basis set benzhy-
drylium ions with basis set π-nucleophiles (PDF). This material
is available free of charge via the Internet at http://pubs.acs.org.
Dr. M. Patz for experimental contributions.
Supporting Information Available: Details and tables with
concentrations and rate constants of the kinetic experiments,
synthetic procedures of the carbocation-nucleophile combina-
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