Solvent effects on methyl transfer reactions. 1. The Menshutkin Reaction

Article abstract of DOI:10.1021/ja983736t

A full quantum mechanical description of the Menshutkin Reaction has been obtained for gas phase and solution by using density functional theory (DFT) and the self-consistent isodensity polarizable continuum model (SCI-PCM). Ammonia and pyridine are compared as nucleophiles, and methyl chloride and bromide are used as methyl transfer reagents. In the gas phase, all of the reactions proceed via an initial dipole complex, followed by a transition state leading to an ion pair. Methyl bromide shifts the position of the transition state to an earlier position than that found with methyl chloride. In the reaction with methyl chloride, replacing ammonia with pyridine stabilizes the transition state by 3 kcal/mol and stabilizes the ion pair by 17 kcal/mol. In the SCIPCM solvent effect calculations, the dipole complex disappears in both cyclohexane and DMSO. The transition state is shifted to an earlier stage of the reaction and is stabilized with respect to the gas phase. The ion pair product is strongly stabilized, and in DMSO it is calculated to dissociate into free ions. The reactions also were studied using Monte Carlo free energy perturbation. The results were in good agreement with the reaction field calculations. The rates of reaction between pyridine and methyl bromide were determined at 25°C in cyclohexane, di-n-butyl ether, and acetonitrile and compared with the computational results. Activation free energies calculated using the SCRF-SCIPCM model agree remarkably well with the experimental values.

Full text of DOI:10.1021/ja983736t

J. Am. Chem. Soc. 1999, 121, 2139-2146
2139
Solvent Effects on Methyl Transfer Reactions. 1. The Menshutkin
Reaction
,†
Henry Castejon* and Kenneth B. Wiberg*
Contribution from the Department of Chemistry, Yale UniVersity, New HaVen, Connecticut 06520-8107
ReceiVed October 26, 1998
Abstract: A full quantum mechanical description of the Menshutkin Reaction has been obtained for gas phase
and solution by using density functional theory (DFT) and the self-consistent isodensity polarizable continuum
model (SCI-PCM). Ammonia and pyridine are compared as nucleophiles, and methyl chloride and bromide
are used as methyl transfer reagents. In the gas phase, all of the reactions proceed via an initial dipole complex,
followed by a transition state leading to an ion pair. Methyl bromide shifts the position of the transition state
to an earlier position than that found with methyl chloride. In the reaction with methyl chloride, replacing
ammonia with pyridine stabilizes the transition state by 3 kcal/mol and stabilizes the ion pair by 17 kcal/mol.
In the SCIPCM solvent effect calculations, the dipole complex disappears in both cyclohexane and DMSO.
The transition state is shifted to an earlier stage of the reaction and is stabilized with respect to the gas phase.
The ion pair product is strongly stabilized, and in DMSO it is calculated to dissociate into free ions. The
reactions also were studied using Monte Carlo free energy perturbation. The results were in good agreement
with the reaction field calculations. The rates of reaction between pyridine and methyl bromide were determined
at 25 °C in cyclohexane, di-n-butyl ether, and acetonitrile and compared with the computational results.
Activation free energies calculated using the SCRF-SCIPCM model agree remarkably well with the experimental
values.
4
1
. Introduction
theoretical study. The studies for solutions have generally been
concerned with the reaction in water, even though this is not
the solvent commonly used for this reaction. The reaction of
methyl chloride with ammonia in water has been studied using
Methyl (or alkyl) transfer reactions are important in organic
1
2
syntheses, and in a wide variety of biochemical processes
including the conversion of homocysteine to methionine, the
methylation of glutamate residues in chemoreceptors, and in
gene regulation. These processes are always carried out in
solution, and it is known that some of them are strongly affected
by solvent polarity. We have been interested in making use of
computational methods to explore the effects of nucleophilicity,
leaving groups, and medium on some representative reactions.
There are two general types of these reactions using neutral
nucleophiles:
4
d
a hybrid QM/MM approach, and the reaction with methyl
bromide in water was studied using both a supermolecule
approach, and via a continuum representation of the solvent.4g
Most of the other studies have used a reaction field model such
as the polarizable continuum model. In view of the strong
hydrogen bonding found in aqueous medium, a reaction field
model does not appear to be appropriate. However, it should
be noted that a model of this type has reproduced the results of
4
h
the QM/MM study.
Despite the extensive investigations of this reaction, there
does not appear to be any study in which the reaction variables
+
-
N: + CH X f CH N + X
(1)
(2)
3
3
(leaving group, nucleophile, and solvent) have been examined
+
+
N: + (CH ) X f CH N + (CH )
X
3
n
3
3 n-1
in a systematic fashion. In the following, ammonia and pyridine
will be compared as nucleophiles, and methyl chloride and
bromide will be used as methyl transfer reagents. The course
An oxonium or sulfonium salt would be a typical methyl
donor in the latter reaction. In the first reaction, the transition
state structure is more polar than the reactants, and polar solvents
will lead to increased rates of reaction. On the other hand, with
the second reaction, the charge is dispersed in the transition
state, and polar solvents would be expected to lead to reduced
rates of reaction.
(3) (a) Menshutkin, N. Z. Phys. Chem. 1890, 5, 589; 1890, 6, 41. (b)
Cox, H. E. J. Chem. Soc. 1921, 119, 142. (c) Grimm, H. G.; Ruf, H.; Wolff,
H. Z. Physik. Chem. 1931, B13, 301. (d) Pickles, N. J. T.; Hinshelwood, C.
N. J. Chem. Soc. 1936, 1353. (e) Raine, H. C.; Hishelwood, C. N. J. Chem.
Soc. 1939, 1378. (f) Tommila, E.; Kauranen, P. Acta Chem. Scand. 1954,
8, 1152. (g) Arnett, E. M.; Reich, R. J. Am. Chem. Soc. 1980, 102, 5892.
(4) (a) Viers, J. W.; Schug, J. C.; Tovall, M. D.; Seeman, J. I. J. Comput.
Chem. 1984, 5, 598. (b) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L.
J. Am. Chem. Soc. 1985, 107, 154. (c) Sola, M.; Lledos, A.; Duran, M.;
Bertran, J.; Abboud, J.-L. J. Am. Chem. Soc. 1991, 113, 2873. (d) Gao, J.;
Xia, X. J. Am. Chem. Soc. 1993, 115, 9667. (e) Maran, U.; Pakkanen, T.
A.; Karelson, M. J. Chem. Soc., Perkin Trans. 2 1994, 2445. (f) Shaik, S.;
Ioffe, A.; Reddy, A. C.; Pross, A. J. Am. Chem. Soc. 1994, 116, 262. (g)
Fradera, X.; Torrent, A. M.; Mestres, J.; Constans, P.; Besalu, E.; Marti,
J.; Simon, S.; Lobato, M.; Oliva, J. M.; Luis, J. M.; Sola, A. M.; Carbo,
R.; Duran, M. J. Mol. Struct. 1996, 371, 171. (h) Truong, T. N.; Truong,
T. T.; Stefanovich, E. V. J. Chem. Phys. 1997, 107, 1881. (i) Amovilli, C.;
Mennucci, B.; Floris, F. M. J. Phys. Chem. B 1998, 102, 3023.
The present study is concerned with the Menshutkin reaction
in which N: is an amine base. This type of reaction is known
to give large solvent effects3 and has received extensive
†
Present address: Science Computing, University of Notre Dame, Notre
Dame, IN 46556.
(
1) For a review of the Menshutkin reaction, see Abboud, J.-L. M.;
Notario, R.; Betran, J.; Sola, M. Prog. Phys. Org. Chem. 1993, 19, 1.
2) Cf. Stryer, L. Biochemistry, 4th ed.; Freeman: New York, 1995; pp
28, 722, and 998.
(
3
1
0.1021/ja983736t CCC: $18.00 © 1999 American Chemical Society
Published on Web 02/19/1999

2140 J. Am. Chem. Soc., Vol. 121, No. 10, 1999
Castejon and Wiberg
of the reactions will first be examined by ab initio calculations
for the reaction in the gas phase. The effect of cyclohexane,
di-n-butyl ether, and dimethyl sulfoxide as solvents will be
Table 1. Total Energies and Zero Point Energies in kcal/mol at
B3LYP/6-31+G*
compound
zpe
gas phase
cyclohexane
DMSO
5
studied making use of a reaction field model, and the effect of
MeCl
MeBr
NH3
pyridine
CH3NH3
23.40 -500.11152 -500.11285 -500.11460
23.05 -2611.63242 -2611.63371 -2611.63541
dimethyl sulfoxide, acetonitrile, and water as the solvent will
be examined using the Monte Carlo free energy perturbation
21.23
-56.55699
-56.55930
-56.56250
6
54.09 -248.29579 -248.29770 -248.30049
49.10 -96.21602 -96.27622 -96.33053
80.35 -287.97883 -288.02402 -288.06387
-460.27472 -460.32119 -460.36285
-2571.80219 -2571.84551 -2571.88399
method. Experimental data on the solvent effect for the reaction
+
of pyridine with methyl bromide also will be presented.
+
Pyr-CH3
-
Cl
2. Gas-Phase Calculations
Br-
NH3CH3Cl(dp)a 45.21 -556.67103
The reactions that have been studied are:
NH3CH3Cl(ts)
NH3CH3Cl(ip)
47.32 -556.62008 -556.63851 -556.65509
48.32 -556.62105 -556.65319
NH3CH3Br(dp) 45.26 -2668.19517
NH3CH3Br(ts)
NH3CH3Br(ip)
Pyr-CH3Cl(dp) 78.31 -748.40944
Pyr-CH3Cl(ts)
Pyr-CH3Cl(ip)
Pyr-CH3Br(dp) 78.26 -2859.93655
Pyr-CH3Br(ts)
Pyr-CH3Br(ip)
47.30 -2668.14652 -2668.16467 -2668.18028
48.20 -2668.14750 -2668.17869
78.88 -748.36147 -748.37524 -748.388642
79.74 -748.36988 -748.39649
78.83 -2859.89143 -2859.90452 -2859.91741
79.89 -2859.89971 -2859.92474
a
dp refers to the dipole complex, ts to the transition state, and ip to
the ion pair.
To obtain satisfactory calculations of the solvent effects, it
is first necessary to be able to model the reaction in the gas
phase with reasonable accuracy. Previous calculations have used
Table 2. Reaction Free Energies and Entropies
∆
G
r
(kcal/mol)
4h
a variety of theoretical models including MP2/6-31G**, MP3/
q
reaction
Cl + NH f CH
Br + NH f CH
Cl + Pyr f CH
Br + Pyr f CH
∆S
r
∆S
calcd expt
6
-31G*,4 CAS(4,4)/6-311G**, and DFT/6-31G**. Here we
e
4i
4h
+
+
-
-
7
CH
CH
CH
CH
3
3
3
3
3
3
NH
NH
3
+ Cl
-7.2 -30.1 118 111 ( 5
-7.6 -30.9 114 105 ( 5
-8.8 -31.2 102
-9.2 -31.9 99
have chosen to use the B3LYP/6-31+G* theoretical level. This
density functional model has been shown to give very satisfac-
tory results for a variety of reactions. The basis set is fairly
3
3
3
+
+ Br
-
3
Pyr + Cl
Pyr + Br
98 ( 5
93 ( 5
8
+
-
3
flexible, and includes diffuse functions that are thought to be
9
important for the proper description of lone pairs and anions.
affinity13 and the known proton affinity of pyridine, leading to
Geometry optimizations were carried out for all of the
compounds in the above reactions giving the data summarized
in Table 1. The zero-point energies were calculated at the
B3LYP/6-31+G* theoretical level and were scaled by a factor
of 0.98. The calculated energies were corrected using the zero-
point energies to give heats of formation. The reactions lead to
significant entropy changes, and they were estimated using the
1
4
∆
Hf ) 173 kcal/mol. Using this value, the calculated energy
changes for the reactions of pyridine were obtained and are in
good agreement with the experimental values (Table 2).
Since the overall reactions are well described at this theoreti-
cal level, the stationary points on the potential energy surface
were located. In each case, the first was an dipole-dipole
complex, which is easily found since it is a minimum on the
surface. The transition state was located by first carrying out a
series of calculations in which the N-C distance was given a
fixed value, and the remaining structural parameters were
optimized. Having an approximate location for the transition
state, its geometry could be fully optimized using the usual
gradient technique. The energies are given in Table 1, and the
most relevant geometrical parameters and relative energies are
summarized in Table 3. Here, %BS is the percent of C-X bond
stretching. A typical asymmetric double-well energy profile with
a late transition state was obtained for all the reactions (Figure
10
usual statistical mechanics method. The values are summarized
in Table 2.
With the first two reactions, experimental data are available,11
and the agreement between experiment and calculations is quite
satisfactory (Table 2). The heat of formation of methylpyri-
dinium ion is not known. It was estimated from a correlation
between the proton affinity of an amine12 and the methyl
(5) (a) Onsager, L. J. Am. Chem. Soc. 1936, 58, 1486. (b) Miertus, S.;
Scocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (c) Cossi, M.; Barone,
V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996, 255, 327. (d) Cances,
M. T.; Mennucci, V.; Tomasi, J. J. Chem. Phys. 1997, 107, 3032. (e)
Foresman, J. B.; Keith, T. A.; Wiberg, K. B.; Snoonian, J.; Frisch, M. J. J.
Phys. Chem. 1996, 100, 16098.
1). The reaction coordinate was taken as the difference between
the C-X and C-N distances.
(
6) Jorgensen, W. L. Acc. Chem. Res. 1989, 22, 84.
(7) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. Lee, C.; Yang, W.;
The first minimum corresponds to the dipole complex formed
as the molecular dipoles align with each other. This is a common
feature of gas-phase reactions involving dipolar reactants. The
second minimum corresponding to the ion pair is quite close to
the transition state in the reaction path and only slightly more
stable, which makes it a transition state-like species. The value
of the HCX angle in the transition state indicates that the methyl
group has almost completely undergone the inversion umbrella
motion.
2a. Effect of the Halogen. Methyl bromide and methyl
chloride were compared as methyl transfer reagents. Bromine
slightly shifts the position of the transition state to an earlier
stage of the reaction and stabilizes it by 3 and 4 kcal/mol in the
Parr, R. G. Phys. ReV. B 1988, 37, 785.
8) Cf. Wiberg, K. B.; Ochterski, J. W. J. Comput. Chem. 1977, 18,
08.
9) Clark, T.; Chandrasekhar, J.; Spitznagel,. W.; Schleyer, P. v. R. J.
Comput. Chem. 1983, 4, 294.
10) Janz, G. J. Estimation of Thermodynamic Properties of Organic
Compounds; Academic Press: New York, 1958.
11) Pedley, J. B. Thermochemical Data and Structures of Organic
(
1
(
(
(
Compounds; Thermodynamics Research Center: College Station, TX, 1994;
Vol. 1.
(
12) Lias. S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data
984, 13, 695.
13) Deakyne, C. A.; Meot-Ner, M. J. Phys. Chem. 1990, 94, 232.
1
(
McMahon, T. B.; Heinis, T.; Nicol, G.; Hovey, J. K.; Kebarle, P. J. Am.
Chem. Soc. 1988, 110, 7591.
(14) Full data are available in the Supporting Information.

SolVent Effects on Methyl Transfer Reactions
J. Am. Chem. Soc., Vol. 121, No. 10, 1999 2141
Table 3. Critical Points in the PES in Gas Phase at
B3LYP/6-31+G*
methyl chloride. This arises from the greater initial electron
population at the methyl group of methyl bromide. The changes
found for the gas phase will be compared to those for reactions
in solution below.
E
rel
entity
r(C-N) r(C-X) ∠ HCX (kcal/mol) %BS
MeCl-NH
1.805
1.813
2.564
2.761
-
3
We were interested in examining the changes in electron
populations that occur when pyridine is converted to pyridinium
ion. Pyridine will react with methyl halides using its in-plane
lone pair. Will the positive charge that develops affect the
electron distribution in the π system? This question is explored
in Table 4 for the reaction of pyridine with methyl cation. The
changes in electron population are separated into σ and π
contributions.
reactants
-
108.49
108.63
79.16
73.50
-
0.0
-1.0
33.1
33.5
116.1
0.0
0.4
42.0
53.0
dipole complex
transition state
ion pair
3.397
1.769
1.604
1.516
products
MeBr-NH
1.964
1.968
2.707
2.909
-
3
reactants
-
107.97
108.05
78.45
73.2
0.0
-2.6
30.0
30.3
112.3
0.0
0.2
37.8
48.1
dipole complex
transition state
ion pair
3.238
1.771
1.601
1.516
If the methyl group were neutral, it would have 6 σ electrons
along with 2 π electrons (aligned with the π electrons of the
ring) that contribute to the formation of the C-H bonds. The
methyl group in methylpyridinium ion has gained σ electrons
and lost π electrons, making a total gain of 0.4 e. There is little
net effect at the nitrogen atom, with a 0.26 gain in π electrons
and a 0.21 loss of σ electrons for a net gain of 0.05 e.16 It is the
ring CH groups that suffer the net loss of electron population,
and much of this loss is found at the hydrogens. This has also
products
-
MeCl-Pyridine
reactants
-
1.805
1.812
2.461
2.911
108.49
0.0
-0.5
30.2
25.8
99.4
0.0
0.4
36.3
61.3
dipole complex
transition state
ion pair
3.416
1.848
1.504
1.486
108.54
82.85
70.24
-
products
-
MeBr-Pyridine
1
7
reactants
-
1.964
1.965
2.586
3.015
107.97
0.0
-4.1
26.5
20.7
95.7
0.0
0.1
31.7
53.5
been found in other systems
dipole complex
transition state
ion pair
3.158
1.836
1.501
1.486
108.03
82.13
70.26
-
4. Solvent Effects Calculated via Reaction Field Theory
products
-
We have found that the reaction field model is successful in
reproducing experimental solvent effects for a variety of
processes when aprotic solvents having normal polarizabilities
reaction with ammonia and pyridine, respectively. The stabiliza-
tion also occurs at the other critical points of the reaction path,
although it is smaller in the dipole complex. The amount of
negative charge transferred to the halogen increases along the
reaction (Figure 2).14 The positive charge, on the other hand, is
spread over the methyl group and the nucleophile. The increas-
ing polarization is responsible for the destabilization of reaction
complex in gas phase and its strongly stabilizing interaction
with polar solvents. An overall comparison for MeCl and MeBr
reacting with ammonia shows that the reaction energy profile
for the latter is stabilized by about 3 kcal/mol which is about
18
are used. Examples of such solvents include cyclohexane, di-
n-butyl ether, acetonitrile, acetone, and dimethyl sulfoxide. The
model predicts that about 40% of the effect of going from the
gas phase to a highly polar solvent will be found on going from
the gas phase to cyclohexane, and this has been verified
18
experimentally.
In the reaction field model, the solute is placed in a cavity in
the solvent. The surface charges of the solute are calculated,
and their interactions with the solvent are obtained. This leads
to the free energy of solvation. The use of the solvent’s bulk
dielectric constant in these calculations is justified if the solvent
is free to adopt random orientations with respect to the solvent.
This is not the case with hydrogen bonding solvents such as
water and methanol. In addition, if the solvent has high
-
-
the difference in proton affinity between Cl and Br .
2
b. Effect of the Nucleophile. Replacing ammonia by
pyridine in the reaction with methyl chloride stabilizes the
transition state by about 3 kcal/mol. However, as the reaction
proceeds and the charge separation becomes more important,
this stabilization increases to 17 kcal/mol for the final products.
Similar changes are found for the reaction with methyl bromide.
The larger stabilization in the final products appears to be a
19
polarizability or a large quadrupole moment, the solvent effect
will be larger than expected based on the dielectric constant.
Solvents of this type include benzene derivatives and many
chlorides and bromides.
We have calculated the effect of cyclohexane, di-n-butyl ether,
and dimethyl sulfoxide on the energetics of the Menshutkin
1
5
consequence of the greater basicity of pyridine in gas phase.
The effect of pyridine as a nucleophile is stronger beyond the
transition state when the charge separation is close to comple-
tion. Thus, pyridine provides a stronger stabilization of the ion
pair with a larger charge separation.
20
reaction using the SCIPCM model. Here, the cavity is defined
(16) Amine nitrogens generally have an increase in electron population
on going to the corresponding ammonium ion: Wiberg, K. B.; Schleyer,
P. v. R.; Streitiwieser, A. Can J. Chem. 1996, 74, 892.
(
17) Wiberg, K. B.; Ochterski, J.; Streitwieser, A. J. Am. Chem. Soc.
1996, 100, 16162.
18) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. J. Am. Chem. Soc. 1991,
3
. Charge Shifts during the Reaction
(
The electron populations for all of the species in the above
113, 4776. Wong, M. W.; Wiberg, K. B.; Frisch, M. J. J. Am. Chem. Soc.
1992, 114, 523. Wong, M. W.; Wiberg, K. B.; Frisch, M. J. J. Am. Chem.
Soc. 1992, 114, 1645. Cieplak, A. S.; Wiberg, K. B. J. Am. Chem. Soc.
reactions were obtained using the AIM method.14 Little charge
transfer occurs in the dipole complex, but over half of the net
change occurs on going to the transition states. The change for
the amino group at the transition state is larger than for the
methyl group, but both contribute to the increase in charge at
the halogen. On going to the product, the increase in charge
for the methyl group is greater for methyl bromide than for
1
993, 115, 1078. Foresman, J. B.; Wong, M. W.; Wiberg, K. B.; Frisch,
M. J. J. Am. Chem. Soc. 1993, 115, 2220. Wiberg, K. B.; Marquez, M. J.
Am. Chem. Soc. 1994, 116, 2197. Wiberg, K. B.; Keith, T. A.; Frisch, M.
J.; Murcko, M. J. J. Phys. Chem. 1995, 99, 9072. Wiberg, K. B.; Rablen,
P. R.; Rush, D. J.; Keith, T. A. J. Am. Chem. Soc. 1995, 117, 4261. Wiberg.
K. B.; Castejon, H.; Keith, T. A. J. Comput. Chem. 1996, 17, 185. Gonzalez,
C.; Restrepo-Cossio, A.; Marquez, M.; Wiberg, K. B. J. Am. Chem. Soc.
1
996, 118, 8291.
(
15) The proton affinity of ammonia is 204 kcal/mol whereas that for
(19) Perng, B.-C.; Newton, M. D.; Raineri, F. O.; Friedman, H. L. J.
Chem. Phys. 1996, 104, 7153 and 7177. Friedman, H. L.; Raineri, F. O.;
Perng, B.-C.; Newton, M. D. J. Mol. Liq. 1995, 65/66, 7.
pyridine is 221 kcal/mol (ref 12). The greater basicity of pyridine is
presumably associated with its larger size and greater polarizability.

2142 J. Am. Chem. Soc., Vol. 121, No. 10, 1999
Castejon and Wiberg
Figure 1. Potential energy curves for the reaction of methyl chloride and bromide with ammonia and pyridine in the gas phase, in cyclohexane,
and in dimethyl sulfoxide.
Table 4. Charge Separation into σ and π Components
atom
σ
π
total
Pyridine
N1
6.907
5.544
5.545
5.992
5.992
6.021
36.000
1.324
0.855
0.855
1.004
1.004
0.958
6.000
8.231
6.399
6.399
6.996
6.996
6.979
42.000
C
2
C
3
C
4
C
5
C
6
H
H
H
H
H
7
8
9
10
11
total
Methyl-Pyridinium
CH
3
6.501
1.938
1.581
0.860
0.860
0.945
0.945
0.871
8.000
8.439
8.277
6.375
6.375
6.842
6.842
6.851
50.000
N
1
6.696
5.515
5.515
5.897
5.897
5.979
42.000
C
C
C
C
C
2
H
H
H
H
H
7
3
4
5
6
8
9
10
11
total
Difference
CH
N
1
3
6.501
-0.211
-0.029
-0.029
-0.095
-0.095
-0.042
6.000
1.938
0.257
0.005
0.005
8.439
0.046
Figure 2. Changes in group charges on going from the reactants to
the transition state in the reaction between methyl chloride and
ammonia. The changes for the other reactions are similar. Full data
are available as Supporting Information.
C
C
C
C
C
2
H
H
H
H
H
7
-0.024
-0.024
-0.154
-0.154
-0.129
8.000
3
4
5
6
8
9
-0.059
-0.059
-0.087
2.000
10
11
by an isodensity surface of the solute. A value of 0.0004 e/au3
leads to molar volumes that are in good agreement with the
experimental values. Geometry optimizations in the presence
of the solvent were carried out for all of the species in the
reactions. Figure 1 shows the effect of the solvents on the energy
profiles for all of the reactions in this study.
total
The separated reactants are stabilized enough to make the dipole
complex disappear. The transition state has been shifted to an
earlier stage of the reaction and energetically stabilized with
(20) Foresman, J. B.; Keith, T. A.; Wiberg, K. B.; Snoonian, J.; Frisch,
Although cyclohexane has a very low dielectric constant,
significant changes can be observed along the reaction path.
M. J. J. Phys. Chem. 1996, 100, 16098. Clifford, S.; Keith, T. A.; Frisch,
M. J. To be published.

SolVent Effects on Methyl Transfer Reactions
J. Am. Chem. Soc., Vol. 121, No. 10, 1999 2143
Table 5. Critical Points in the PES in Cyclohexane at
B3LYP/6-31+G*
Table 6. Critical Points in the PES in Dimethyl Sulfoxide at
B3LYP/6-31+G*
E
rel
E
rel
entity
r(C-N) r(C-X) ∠ HCX (kcal/mol) %BS
entity
r(C-N) r(C-X) ∠ HCX (kcal/mol) %BS
MeCl-NH
1.808
2.408
3.018
-
3
MeCl-NH
1.815
2.265
-
3
reactants
transition state
ion pair
-
108.39
0.0
23.8
15.7
51.5
0.0
33.2
66.9
reactants
transition state
products
-
108.10
0.0
16.7
-5.6
0.0
24.8
1.960
86.01
71.49
-
2.125
1.500
92.03
-
1.534
1.509
products
MeBr-NH
1.973
2.392
-
3
MeBr-NH
1.968
2.444
3.161
-
3
reactants
transition state
products
-
2.120
1.500
107.55
90.92
-
0.0
14.1
-5.5
0.0
21.2
reactants
transition state
ion pair
-
107.79
77.56
71.50
-
0.0
20.9
10.0
49.7
0.0
24.1
60.6
2.000
1.535
1.509
MeCl-Pyridine
products
reactants
transition state
products
-
2.075
1.484
1.815
2.302
-
108.10
0.0
18.1
-4.4
0.0
26.8
MeCl-Pyridine
90.57
-
reactants
transition state
ion pair
-
1.808
2.385
3.065
108.39
0.0
23.6
11.1
46.1
0.0
31.9
69.5
1.960
1.498
1.486
86.59
70.48
-
MeBr-Pyridine
reactants
transition state
products
-
2.050
1.484
1.973
2.434
-
107.55
0.0
13.3
-4.2
0.0
23.4
products
-
89.64
-
MeBr-Pyridine
reactants
transition state
ion pair
-
1.968
2.510
3.199
107.79
0.0
18.6
8.8
0.0
27.5
62.6
1.942
1.491
1.486
85.98
sulfoxide as the solvent. The ion pairs now completely dissoci-
ate, and the products have slightly more charge transfer in
dimethyl sulfoxide than the ion pairs in cyclohexane.
products
-
-
42.1
In the above, we have only been concerned with how the
potential energy surfaces are affected by the solvation free
energies. The energy changes may also be affected by the change
in cavity size on going from the reactants to the transition states,
and from the change in the repulsion and dispersion energies
between the solute and the solvent during the reaction. It has
been found that these energy terms are approximately equal and
opposite, and therefore will approximately cancel.23 We will
make use of this approximation.
The quantity of interest is the free energy since it is the
quantity that controls the rate of reaction. The gas phase
enthalpies of reaction are readily converted to free energies since
the entropy terms may be calculated using statistical mechanics
(Table 2). This becomes more of a problem in solution since
translation becomes diffusion, and the overall rotation of the
molecules may be hindered. No completely satisfactory treat-
ment of the problem has appeared. However, it may be noted
that for reactions of nonpolar molecules giving nonpolar
transition states, such as in the dimerization of cyclopentadiene,24
the rates of reaction are often nearly independent of medium,
having essentially the same rate constant in the gas phase as in
any one of several solvents. The entropy change also is found
to be essentially constant. Thus, the use of the gas-phase
entropies should be satisfactory in estimating the change in
entropy resulting from the reactions. A comparison of the
calculated and experimental free energies of activation will be
given below.
respect to the gas phase (Table 5). The ion pair has become a
more product-like species, and it is farther from the transition
state, both energetically as well as along the reaction path. In
general, all the species along the reaction path have been
stabilized by about 30% of their respective relative energies in
gas phase and the overall reaction is less endothermic.
Here, the influence of pyridine on the transition state in the
reaction with methyl chloride is decreased with respect to
ammonia, and it is inverted in the reaction with methyl bromide.
In the former case, it only shifts the transition state to an earlier
stage with virtually no stabilization, while in the latter it delays
its formation.
Figure 2 shows that the amount of charge transfer to the
halogens in the transition states is reduced on going from the
gas phase to cyclohexane, whereas the charge transfer in the
ion pairs is increased. This is accord with the transition states
being earlier in cyclohexane. The ion pairs can be more fully
relaxed in cyclohexane, leading to their greater polarity.
Figure 1 also shows the effect of dimethyl sulfoxide as the
solvent. It is in this solvent where the most dramatic changes
are observed. The dielectric constant of the solvent is large
2
1
enough to separate both the dipole complex and the ion pair,
which are no longer observed as energy minima in the reaction
path. The transition state is shifted far to an earlier stage of the
reaction (Table 6), it is strongly stabilized with respect to that
in both gas phase and cyclohexane, and the reaction becomes
exothermic. The effect of the halogen remains the same, namely
replacing Cl by Br lowers the energy of the transition state and
makes it earlier, whereas using pyridine instead of ammonia
delays the formation of the transition state. This is in accord
with the observation that whereas pyridine is a stronger base
than ammonia in the gas phase, it is a weaker base in most
solvents.22
Monte Carlo Simulations of Solvent Effects. As noted
above, the reaction field model is not appropriate for hydrogen
bonding solvents, although some success has been obtained by
using artificially small molar volumes, which serve to accentuate
2
5
the solvent effect. Monte Carlo free energy perturbation
methods have proven to be quite successful in reproducing
2
6
Figure 2 shows that the charge transfer in the transition states
continues to decrease on going from cyclohexane to dimethyl
solvation effects in polar and protic solvents. Gao and Xia
(23) Cf. Table 2 of ref 4i. It should be noted that the calculation of each
(
21) Ion-pairs involving singly charged ions have been found to exist
of these terms involves considerable uncertainty.
(24) Wasserman, A. Monatsh. 1952, 83, 543.
(25) Cf. Stefanovich, E. V.; Truong, T. N. Chem. Phys. Lett. 1995, 244,
65.
(26) (a) Blake, J. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1991, 113,
7430. (b) Severance D. L.; Jorgensen, W. L. J. Am. Chem. Soc. 1992, 114,
10966.
only in solvent having a dielectric constant less than about 40 (Fuoss, R.
M.; Krauss, C. A. J. Am. Chem. Soc. 1933, 55, 1019).
(
22) In water, the pKa’s of ammonia and pyridinium ion are 9.24 and
.17, respectively (Dean, J. A. Lange’s Handbook of Chemistry, 13th ed.;
McGraw-Hill: New York, 1985). The gas-phase values are given in ref
5.
5
1

2
144 J. Am. Chem. Soc., Vol. 121, No. 10, 1999
Castejon and Wiberg
Table 7. Transition State Structures from BOSS Simulation
have successfully modeled the reaction of ammonia and methyl
chloride by using a combined quantum mechanical and statistical
mechanical method.4d The free energy of activation reported in
that work is in good agreement with the value calculated in
this work using the SCRF method.
q
solvent
r(C-N) r(C-Cl) ∠ HCCl ∆G (kcal/mol)
(
a) MeCl-NH
3
gas phase
1.769
2.069
2.069
2.119
2.564
2.044
2.044
1.995
79.2
96.9
96.9
41.9
22.3
22.9
21.7
acetonitrile
dimethyl sulfoxide
water
The reactions of MeCl with pyridine and ammonia were
studied in acetonitrile, dimethyl sulfoxide, and water using the
100.7
2
7
BOSS program. The calculations were done in two stages.
First, a full characterization of the energy profile in gas phase
was done using the B3LYP/6-31+G* level of theory. The
reaction path was traced from the transition state to the reactants
at intervals of 0.05 Å in the C-N bond distance. This procedure
produced essentially a movie of the reaction between the two
critical points on the energy profile. CHELPG charges and
structural parameters were obtained at every interval of the
reaction path. Calculations for the solvated systems were carried
out in the NPT ensemble at 1.0 atm and 25 °C. The solvated
system in each case consisted of a periodic cube containing the
transition state complex surrounded by 512 water molecules,
(b) MeCl-Pyridine
gas phase
1.848
2.461
2.060
2.060
2.005
82.9
94.6
94.6
97.6
39.5
25.8
24.7
23.4
acetonitrile
dimethyl sulfoxide
water
2.048
2.048
2.098
Table 8. Rates of Reaction of Pyridine with Methyl Bromide, 25
2
8
°
C
1
q
solvent
k, L mol- s-1
∆G (kcal/mol)
cyclohexane
di-n-butyl ether
acetonitrile
3.8(-8)
1.13(-6)
2.04(-4)
27.6
25.6
22.5
400 dimethyl sulfoxide molecules, or 400 acetonitrile molecules.
Preferential sampling was used in the Metropolis algorithm, and
the perturbations along the reaction path were carried out using
double-wide sampling in 24 windows for each solvent. Equili-
bration over 3 million configurations was carried out for each
window, followed by averaging over 5 million configurations.
Pairwise additive intermolecular potential functions were used
for the solute-solvent and solvent-solvent interactions. No
intramolecular terms were included. TIP4P water, acetonitrile,
and dimethyl sulfoxide were used as defined by the OPLS
potential functions and supplied directly by the BOSS database.
CHELPG charges calculated at every step of the reaction path
were used for the coulomb term of the potential while the
Lennard-Jones parameters were taken from the BOSS database
of all-atom parameters. The energy barriers for the reactions
were obtained by converting the transition state complex into
the reactants in a stepwise fashion along the reaction energy
profile calculated in the gas phase.
stretched from 1.815 to 2.044 Å (13%) in the reaction with
ammonia and to 2.060 Å (14%) in the reaction with pyridine.
These changes represent only 50% of those obtained in the
SCRF calculations. The shift of the transition states to earlier
positions is also accompanied by a reduction of their relative
energy of 2.7 kcal/mol in both reactions. Such an additional
stabilization may be the result of the conformational orientation
of the solvent molecules around the reaction complex. This
reorganization of the solvent may add some configurational
contribution to the polarization of the solvent medium, which
is represented only by the electronic component in the SCRF.
When water is used as the solvent, the effect on the transition
state is more pronounced. The C-Cl bond is only stretched to
1
.995 Å in the reaction of methyl chloride with ammonia, and
to 2.005 Å in the reaction with pyridine. These changes represent
an advance of the reactions of 8 and 11%, respectively. Such
dramatic effect on the structure of the transition state agrees
The Monte Carlo simulation makes use of the gas phase
reaction coordinate. Petersson has shown that because the
reaction coordinate is a relatively “soft” mode in contrast to
the other vibrational modes, reaction coordinates calculated at
a lower theoretical level can be used as the basis for calculations
4d
with that reported by Gao and Xia, who found that “the
transition state is shifted significantly toward the reactants in
water”. Further reduction of the activation free energy in water,
as compared to that in dimethyl sulfoxide and acetonitrile, is
not very significant, despite the considerable changes in the
transition state geometry. A plausible explanation is that
ammonia is strongly solvated by water through the lone pairs
in the nitrogen atom. Thus, the energy required for desolvation
increases the activation energy of the overall reaction. An
examination of snapshots of the reaction complex taken from
the BOSS simulation before the formation of the transition state
showed the solvation of the ammonia molecule. The solvation
29
with higher theoretical levels. The location of the transition
state will move, but to a good approximation it will remain on
the reaction coordinate. The same should hold true for the Monte
Carlo calculations along the gas-phase reaction coordinate.
Starting at the gas-phase transition state geometry and moving
toward reactants, the free energy first increases, and after the
new transition state location is reached, it will begin to decrease.
Table 7 shows the structural parameters of the transition states
obtained from BOSS calculations for the reactions of methyl
chloride with ammonia, and with pyridine in acetonitrile (ꢀ )
30
free energies of ammonia and pyridine in water are -4.3 and
31
-
4.7 kcal/mol, respectively. This will produce the values of
about 17.4 and 18.4 kcal/mol for the activation free energies of
the reaction of methyl chloride with free ammonia and pyridine,
respectively, in aqueous solution.
3
5), dimethyl sulfoxide (ꢀ ) 42), and water (ꢀ ) 78). The first
two solvents lead to the same transition state structures. Despite
the explicit representation of the solvents, the performance of
the Monte Carlo method in this case is similar to that of the
SCRF method, which cannot distinguish between these two
solvents due to their similar dielectric constants. However, the
transition states in the two reactions are shifted to an earlier
position in the reaction path compared to those obtained by the
SCRF method. Thus, the C-Cl bond in methyl chloride is
5
. Experimental Results
To compare the performance of both the statistical mechanics
Monte Carlo method and the quantum SCRF method on the
estimation of the activation free energy of the Menshutkin
reaction, the rate of the reaction of methyl bromide with pyridine
(
(
(
27) BOSS, version 3.6. William L. Jorgensen. Yale University.
28) Breneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361.
29) Malik, D. K.; Petersson, G. A.; Montgomery, J. A., Jr. J. Chem.
(30) Kubo, M. M.; Gallicchio, E.; Levy, R. M. J. Phys. Chem. B 1997,
101, 10527.
(31) Cramer, C. J.; Truhlar, D. G. J. Comput.-Aided Mol. Des. 1992, 6,
629.
Phys. 1998, 108, 5704.

SolVent Effects on Methyl Transfer Reactions
J. Am. Chem. Soc., Vol. 121, No. 10, 1999 2145
Table 9. Activation Free Energies for the Reactions in Solution
SCRF
BOSS
expt
Bu
reaction
GP
C
6
H
12
Bu
2
O
DMSO
MeCN
DMSO
water
C
6
H
12
2
O
MeCN
22.5
MeCl-NH
MeCl-Pyr
MeBr-Pyr
3
41.9
39.5
36.0
32.6
32.9
28.1
27.5
29.5
24.5
25.5
27.4
22.8
22.3
25.8
22.9
24.7
21.7
23.4
27.6
25.6
The use of methyl bromide as methyl transfer reagent instead
of methyl chloride causes a lowering of the energy of all the
species along the reaction path and shifts them to earlier position
in the reaction path, also by almost a constant amount. Switching
from ammonia to pyridine as the base, on the other hand, seems
to have a greater effect on the charged species that appear after
the formation of the transition state, namely, the ion pair and
the ionic products. The gas phase stabilization of these charged
species by pyridine appears to the consequence of the redistribu-
tion of charge in the ring, which affects predominantly to the
CH groups.
The results of the solvent effect calculations show the
transition states become more reactant-like and the reaction
activation free energies decrease with the increasing polariz-
ability of the solvent. The relative nucleophilicity of pyridine
vs ammonia is reversed on going from the gas phase to dimethyl
sulfoxide solutions.
Figure 3. Correlation of the observed activation free energies for the
reaction of methyl bromide with pyridine with the Onsager function,
The self-consistent reaction field and Monte Carlo methods
give similar results in polar aprotic solvents, but the latter
method predicts somewhat earlier transition states. The SCRF
calculations agree remarkably well with the experimental results
for the reaction of methyl bromide with pyridine. Although no
BOSS simulation was possible for this reaction, the similarity
of behavior of both methods in aprotic solvents allows us to
expect similar results from a BOSS simulation for that reaction.
It should be possible to further improve the Monte Carlo
simulations by making use of an SCRF reaction coordinate
calculated for a polar medium. This is a significantly more
computationally intensive approach, but this and other aspects
of comparisons between SCRF and Monte Carlo methods are
under investigation.
(ꢀ - 1)/(2ꢀ + 1).
was determined at room temperature in three different sol-
vents: cyclohexane, di-n-butyl ether, and acetonitrile. The
experimental rate constants and activation free energies are
shown in Table 8. The reaction rate follows the expected trend,
namely, the more polar the solvent, the faster the reaction. The
reactions in acetonitrile and di-n-butyl ether proceeded rapidly
enough to allow the determination of reliable values for the rate
constants in those solvents. In cyclohexane, on the other hand,
the reaction is so slow that the method used to monitor it only
produces values in the precision limit of the technique. However,
because the values of the dielectric constant of the solvents used
span the range of the Onsager function evenly, it is possible to
check whether the rate constant in cyclohexane is reasonable
by plotting the observed activation free energy against the
Onsager function. Figure 3 shows that the experimental value
of the rate constant in cyclohexane correlates well with those
more accurate values obtained in acetonitrile and di-butyl ether,
and extrapolation to the gas phase (i.e. 0.0 in the x axis) gives
Calculations. The ab initio calculations were carried out using
32
Gaussian-95. In the SCI-PCM model, a single origin and 1800
surface points were used for the methyl halide ammonia
reactions, and 2880 for the methyl halide pyridine reactions.
This is achieved by including the following line after the
z-matrix: D 0.0004 60 30 2 where D is the desired dielectric
constant, 0.0004 is the value of F for the isodensity surface, 60
and 30 are the number of θ and φ planes used to define the
surface points, and 2 indicates that a single origin should be
used. With the pyridine reactions, 72 and 40 θ and φ planes
were used. The Monte Carlo calculations were carried out using
BOSS. The nonbonded solvent-solvent (RCUT) and solute-
solvent (SCUT) cutoffs were set to 12 Å, and a value of 200
was used for the WKC parameter in the preferential sampling.
3
3 kcal/mol which is close to the calculated value, 36 kcal/
mol.
Table 9 shows the comparison between the experimental and
the calculated values using both the SCRF and the BOSS
simulation. The calculated values of the activation free energy
for the reaction of methyl bromide and pyridine, obtained using
self-consistent reaction field, agrees very well with the experi-
mental values. No BOSS simulation could be performed for
this reaction due to the lack of BOSS parameters for bromine.
However, a BOSS simulation should be expected to yield similar
values, given the similar performance in aprotic solvent found
for both methods.
7
. Experimental Section
Materials. All chemicals were analytical grade and were used
without further purification. Standard solutions of HCl and NaOH were
obtained from Baker and Mallinckrodt, respectively.
(
32) Frisch, M. J.; Trucks; G. W.; Schlegel, H. B.; Gill, P. M. W.;
6
. Conclusions
Johnson, B. G.; Robb; M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortis, J. V.; Foresman, J. B.; Cioslowski, J.; Sefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 95, Development Version
(Rev. D) Gaussian, Inc., Pittsburgh, PA, 1995.
Density functional theory provides a good description of the
overall path of the Menshutkin Reaction in gas phase. The
calculated values of the activation free energies for all of the
studied reactions fall within the accuracy of the experimental
values.

2146 J. Am. Chem. Soc., Vol. 121, No. 10, 1999
Castejon and Wiberg
Procedure. Pyridine solutions were prepared by mixing measured
amounts of pyridine with the solvent to give the desired concentration
0.0621 M). Methyl bromide solutions were prepared as follows: a
in NaOH volume between the two inflection points. The pseudo-first-
order rate constants were obtained in the usual fashion. The second-
order rate constants were obtained by dividing the observed k by the
average methyl bromide concentration during the reaction and are given
in Table 8.
(
known amount of methyl bromide (determined by pressure and volume)
was placed in a flask and frozen using liquid nitrogen. While cooled,
a known amount of solvent was added to the flask. The mixture was
allowed to warm to room temperature and to equilibrate for 24 h. The
concentration of methyl bromide was 0.312 M. The reaction was
initiated by mixing equal volumes (50 mL) of the two solutions. The
reactions were carried out at 25 °C under pseudo-first-order conditions
with pyridine as the limiting reagent. Rate constants were determined
by monitoring the disappearance of pyridine. At known times, 20 mL
aliquots were taken from the reaction container and quenched with 10
mL of 0.1 N HCl. A potentiometric titration with NaOH was carried
out, and a plot of the pH against the volume of NaOH was prepared.
The first inflection corresponded to titration of excess HCl, and the
second corresponded to the complete conversion of pyridinium ion to
pyridine. The concentration of pyridine was obtained from the difference
Acknowledgment. This investigation was supported by a
grant from the National Institutes of Health. We thank Prof.
W. Jorgensen for supplying a copy of his BOSS program, and
we thank Corky Jensen for his assistance in the use of the
program.
Supporting Information Available: Tables of changes in
charge during the reactions and the correlation between proton
affinities and methyl affinities. This material is available free
of charge via the Internet at http://pubs.acs.org.
JA983736T