A classical but new kinetic equation for hydride transfer reactions

Article abstract of DOI:10.1039/c3ob40831k

A classical but new kinetic equation to estimate activation energies of various hydride transfer reactions was developed according to transition state theory using the Morse-type free energy curves of hydride donors to release a hydride anion and hydride acceptors to capture a hydride anion and by which the activation energies of 187 typical hydride self-exchange reactions and more than thirty thousand hydride cross transfer reactions in acetonitrile were safely estimated in this work. Since the development of the kinetic equation is only on the basis of the related chemical bond changes of the hydride transfer reactants, the kinetic equation should be also suitable for proton transfer reactions, hydrogen atom transfer reactions and all the other chemical reactions involved with breaking and formation of chemical bonds. One of the most important contributions of this work is to have achieved the perfect unity of the kinetic equation and thermodynamic equation for hydride transfer reactions. The Royal Society of Chemistry.

Full text of DOI:10.1039/c3ob40831k

Organic &
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A classical but new kinetic equation for hydride
transfer reactions†
Cite this: Org. Biomol. Chem., 2013, 11,
6071
Xiao-Qing Zhu,* Fei-Huang Deng,‡ Jin-Dong Yang,‡ Xiu-Tao Li, Qiang Chen,
Nan-Ping Lei, Fan-Kun Meng, Xiao-Peng Zhao, Su-Hui Han, Er-Jun Hao and
Yuan-Yuan Mu
A classical but new kinetic equation to estimate activation energies of various hydride transfer reactions
was developed according to transition state theory using the Morse-type free energy curves of hydride
donors to release a hydride anion and hydride acceptors to capture a hydride anion and by which the
activation energies of 187 typical hydride self-exchange reactions and more than thirty thousand hydride
cross transfer reactions in acetonitrile were safely estimated in this work. Since the development of the
kinetic equation is only on the basis of the related chemical bond changes of the hydride transfer reac-
tants, the kinetic equation should be also suitable for proton transfer reactions, hydrogen atom transfer
reactions and all the other chemical reactions involved with breaking and formation of chemical bonds.
One of the most important contributions of this work is to have achieved the perfect unity of the kinetic
equation and thermodynamic equation for hydride transfer reactions.
Received 24th April 2013,
Accepted 16th July 2013
DOI: 10.1039/c3ob40831k
www.rsc.org/obc
our lab.32–35 Meanwhile, for many typical organic hydride
acceptors, such as olefin, imine, quinone, carbonyl com-
I. Introduction
Hydride transfer is one of the most fundamental chemical pounds, various organic cations etc., the free energy changes
processes.1–9 The research on organic hydride transfer of them to capture hydride anions in acetonitrile have also
reactions has become a very important field of chemistry, been determined in our lab.36–38 It is true that for many impor-
because of their importance in chemical and biochemical tant organic hydride transfer reactions in acetonitrile, the thermo-
reactions,10–14 wide applications to reducing unsaturated dynamic problems should have received good solutions.32–38
organic compounds15–27 and the potential in hydrogen However, for hydride transfer reactions, the activation energy
storage.28–30 There are two most fundamental scientific pro- cannot be estimated reliably according to some related para-
blems about the hydride transfer reactions (eqn (1)): one is the meters of the reactants to date. The main reason is that the
thermodynamic problem, i.e., how to safely predict the thermo- factors affecting the kinetics of hydride transfer reactions are
dynamic driving forces of hydride transfer reactions (ΔG° = ?); much more complicated and diversified than those affecting
the other is the kinetic problem, i.e., how to reliably predict the thermodynamics. In fact, no suitable theoretical
the activation energy of hydride transfer reactions (ΔG≠ = ?). approaches have been reported to date to accurately estimate
As to the thermodynamic problem, as long as the free energy the activation energy of hydride transfer reactions except that
change of the hydride donor (XH) to release a hydride anion in some research groups tried to apply Marcus theory for some
solution ½ΔG°HꢀDðXHÞꢁ and the free energy change of the hydride transfer reactions in a mixed solvent.39–44 Since
hydride acceptor (Y+) to capture a hydride anion in solution Marcus theory was developed by Rudolph A. Marcus in 1956
½ΔG°HꢀAðYþÞꢁ are available, this problem can be solved accord- for the outer sphere electron transfer reactions in solution45
ing to eqn (2).31 In fact, for many of the most important and has been identified to violate the law of conservation of
organic hydride donors, the free energy changes of them to energy,46 it is necessary to develop a scientific method to esti-
release hydride anions in acetonitrile have been determined in mate the activation energy of hydride transfer reactions. In
this manuscript, a classical but new equation was introduced
which can be used to safely estimate the activation energy of
various hydride transfer reactions in acetonitrile. In fact, the
kinetic equation developed in this work is not only suitable to
State Key Laboratory of Elemento-Organic Chemistry, Department of Chemistry,
Nankai University, Tianjin 300071, China. E-mail: xqzhu@nankai.edu.cn
†Electronic supplementary information (ESI) available. See DOI: 10.1039/
estimate the activation energy of hydride transfer reactions but
also suitable to estimate the activation energy of proton
c3ob40831k
‡These two authors contributed equally.
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Organic & Biomolecular Chemistry
transfer reactions, hydrogen atom transfer reactions and all
the other chemical reactions only involved with breaking and
formation of chemical bonds.
XH þ Yþ ! Xþ þ YH
ΔG° ¼ ΔG°HꢀDðXHÞ þ ΔG°HꢀAðYþÞ
ð1Þ
ð2Þ
Fig. 2 The free energy changes of hydride transfer from XH to Y+ to form X+
and YH can be described by two different Morse-type free energy curves: the
left one refers to the chemical process of XH to release a hydride anion; the
right one refers to the chemical process of Y+ to capture H−.
II. Development of the kinetic equation for
hydride transfer reactions
As is well known, for any hydride transfer reaction from
hydride donors (XH) to hydride acceptors (Y+), the process of
hydride transfer contains two chemical processes: one is the
X–H bond dissociation for XH to release a hydride anion (H−),
and the other is the Y–H bond formation for Y+ to capture the
released hydride anion. According to transition state theory
(TST),47 the process of hydride transfer from XH to Y+ can be
described by Scheme 1.
From Scheme 1, it is clear that the process of the hydride
transfer from XH to Y+ may be regarded as two combined
chemical processes: one is the dissociation of the X–H bond of
XH to form X+ and H− and the other is the formation of the
Y–H bond of Y+ from Y+ and H−. Since the free energy changes
of XH due to the X–H bond dissociation and of Y+ due to the
Y–H bond formation from Y+ and H− can be described using
the Morse-type free energy curves (Fig. 1),48–51 the free energy
change of the reaction system as the hydride transfers can be
described by two different Morse-type free energy curves in the
same reaction coordinate system and the free energy of XH at
the ground state may be defined as zero (Fig. 2).
capture hydride anions. The intersecting point of the two
Morse-type free energy curves is just a symbol that the reaction
of hydride transfer from XH to Y+ has reached the transition
state, because across the intersecting point of the two Morse-
type curves, the sum of the state energy of the reaction system
(XH and Y+) would change from an increase to a decrease as
the hydride continues transfer. However, the free energy of the
G-axis at the intersecting point is not the activation energy of
the reactions, because the left Morse-type curve does not rep-
resent the reactants system. Since the left Morse-type curve in
Fig. 2 is to describe the state free energy change of the hydride
donor (XH), the right one is to describe the state free energy
change of the hydride acceptor (Y+), the activation free energy
of the hydride transfer reaction should equal the sum of the
absorbed free energy of the X–H bond due to the activation in
the transition state, ΔG=HꢀDðXH=YþÞ, and the released free
energy of the Y–H bond due to the formation in the transition
state, ΔG=HꢀAðYþ=XHÞ. In eqn (3), ΔGH=ꢀDðXH=YþÞ is called the
X–H bond activation energy of XH in the transition state, and
ΔG=HꢀAðYþ=XHÞ is called the Y–H bond formation energy of Y+
in the transition state.
In Fig. 2, the left Morse-type curve describes the free energy
changes of the species XH to release hydride anions, and the
right one describes the free energy changes of the species Y+ to
ΔG= ¼ ΔGH=ꢀDðXH=YþÞ þ ΔGH=ꢀAðYþ=XHÞ
ð3Þ
From eqn (3) it is clear that for a hydride transfer reaction
from XH to Y+ in solution, as long as the X–H bond activation
energy of XH, ΔG=HꢀDðXH=YþÞ, and the Y–H bond formation
energy of Y+, ΔGH=ꢀAðYþ=XHÞ, are available, the activation
energy (ΔG≠) can be obtained by the addition of the two physi-
cal parameters, which is just like the derivation of the free
energy change (ΔG°)31 of the reactions from the free energy
change of XH to release a hydride anion ½ΔG°HꢀDðXHÞꢁ and the
Scheme 1 The mechanism of hydride transfer from hydride donors (XH) to
hydride acceptors (Y+).
free energy change of Y+ to capture
a hydride anion
½ΔG°HꢀDðYþÞꢁ (see eqn (2)). However, unlike ΔG°HꢀDðXHÞ,
ΔG=HꢀDðXH=YþÞ is not a characteristic parameter (constant) of
the hydride donors (XH), because the magnitude of
ΔG=HꢀDðXH=YþÞ is not only dependent on the nature of XH,
but also dependent on the nature of Y+. Similarly,
ΔG=HꢀDðYþ=XHÞ is not a characteristic parameter (constant) of
the hydride acceptors (Y+), either, since the magnitude of
ΔG=HꢀDðYþ=XHÞ also depends on the nature of XH. Evidently,
the strategy to derive the activation energy (ΔG≠) of hydride
Fig. 1 The dependence of the free energy change of the hydride donor (XH)
to release a hydride anion on the internuclear separation can be described
using the Morse-type free energy curve.
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reactions and hydride cross transfer reactions) can be derived
from eqn (4).
III. Determination of ΔG=HꢀDðXHÞ and
ΔG=HꢀAðYþÞ and the results in acetonitrile
According to eqn (4), it is clear that if ΔG=HꢀDðXHÞ of various
hydride donors XH in solution and ΔG=HꢀAðYþÞ of various
hydride acceptors Y+ in solution are available, the activation
energy of various hydride transfers from hydride donors (XH)
to hydride acceptors (Y+) in the solution can be estimated, so it
is necessary to determine ΔG=HꢀDðXHÞ and ΔGH=ꢀAðXþÞ of
various hydride donors XH and their corresponding salts (X+)
in solution.
Fig. 3 Relationships of four Morse-type free energy curves corresponding to
the four partial reactions: XH → X+ + H− (bold line on the left), Y+ + H− → YH
(bold line on the right), YH → Y+ + H− (dashed line on the left), and X+ + H−
XH (dashed line on the right).
→
transfer reactions using ΔG=HꢀDðXH=YþÞ and ΔG=HꢀAðYþ=XHÞ
according to eqn (3) does not work.
For the hydride self-exchange reaction: XH + X+ → X+ + XH,
since
In order to develop the direct dependence of the activation
energy (ΔG≠) of hydride transfer reactions on the characteristic
parameters of the two reactants themselves (XH and Y+), the
geometrical relationship among the four intersecting points
formed from the four Morse curves corresponding to the four
related partial reactions (XH → X+ + H− and its inverse reaction
as well as Y+ + H− → YH and its inverse reaction) was exam-
ined in Fig. 3. The result clearly shows that for the general
hydride transfer reactions with the type of XH + Y+ → X+ + YH,
the sum of ΔG=HꢀDðXH=YþÞ and ΔGH=ꢀAðYþ=XHÞ should be
equal to or quite close to the sum of ΔG=HꢀDðXH=XþÞ and
ΔG=HꢀAðYþ=YHÞ. Thus, eqn (3) can be replaced by eqn (4).
ΔG=ðXH=XþÞ ¼ ΔGH=ꢀDðXHÞ þ ΔG=HꢀAðXþÞ
ð5Þ
ð6Þ
ð7Þ
and
so
ΔGH=ꢀAðXþÞ ¼ ΔG=HꢀDðXHÞ þ ΔG°HꢀAðXþÞ
ΔG=HꢀDðXHÞ ¼ 1=2½ΔG= ðXH=XþÞ ꢀ ΔG°HꢀAðXþÞꢁ
From eqn (7), it is conceived that for a hydride self-
exchange reaction, as long as the activation energy of the
hydride self-exchange reaction, ΔG≠(XH/X+), can be deter-
mined, ΔG=HꢀDðXHÞ can be obtained from eqn (7), because the
free energy change of the many important hydride acceptors
(X+) in solution ½ΔGH° ꢀAðXþÞꢁ has been obtained in our lab.33–38
Thus, the remaining work is just to determine the activation
ΔG= ¼ ΔGH=ꢀDðXH=XþÞ þ ΔGH=ꢀAðYþ=YHÞ
ð4Þ
In eqn (4), ΔG=HꢀDðXH=XþÞ [abbreviated as ΔG=HꢀDðXHÞ energies ΔG≠(XH/X+) of various hydride self-exchange reac-
below] is the X–H bond activation energy of XH at the tran- tions in solution.
sition state for the hydride self-exchange reaction of XH with
As is well known, for electron or proton self-exchange reac-
X+ (XH + X+ → XH + X+), i.e., the energy that the hydride donor tions, the activation energy of the reactions can be determined
XH absorbs when the reaction proceeds from the initial state using dynamic EPR and dynamic NMR techniques, since the
to the transition state. ΔG=HꢀAðYþ=YHÞ [abbreviated as rates of electron and proton self-exchange reactions are gener-
ΔG=HꢀAðYþÞ below] is the Y–H bond formation energy of Y+ at ally fast enough to meet the criteria of the dynamic EPR and
the transition state for the hydride self-exchange reaction of Y+ dynamic 1H NMR measurements [k2(self-exchange) within
with YH (Y+ + YH → YH + Y+), i.e., the energy that the hydride 102–106 M−1 s−1].52 But for hydride self-exchange reactions, the
acceptor Y+ releases when the reaction proceeds from the dynamic NMR method cannot be applied to determine the
initial state to the transition state. Since X+ is the conjugate activation energy of the reactions, because the rates of hydride
cation of XH, the nature of X+ should depend on that of self-exchange reactions are quite slow, generally much smaller
the corresponding hydride donors XH, which indicates that than 1 × 102 M−1 s−1. In fact, no effective experimental method
ΔG=HꢀDðXHÞ like ΔGH° ꢀDðXHÞ is also one of characteristic para- has been reported to determine the rates of hydride self-
meters of hydride donors (XH), i.e., the magnitude of exchange reactions in solution.
ΔG=HꢀDðXHÞ only depends on the nature of XH. Similarly,
Although direct experimental determination of the acti-
ΔG=HꢀAðYþÞ like ΔGH° ꢀAðYþÞ is also one of the characteristic vation energies of hydride self-exchange reactions in solution
parameters of the hydride acceptor (Y+), i.e., the magnitude of is impossible, the activation energies of the hydride cross
ΔGH=ꢀAðYþÞ only depends on the nature of Y+. Thus, if the transfer reactions (XH + Y+ → X+ + YH, X ≠ Y) generally can be
characteristic parameters ΔG=HꢀDðXHÞ of various hydride determined using conventional experimental techniques as
donors (XH) and ΔG=HꢀAðYþÞ of various hydride acceptors (Y+) long as the thermodynamic driving forces of the hydride cross
in solution are available, the activation energies of various transfer reactions are appropriate. This fact induces us to
hydride transfer reactions (including hydride self-exchange develop a method to estimate the activation energies of
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Table 1 Free energy change values of hydride acceptors (X+ and Y+) to
capture hydride aions in acetonitrile at 298 K and the activation energies of
hydride transfer from XH to Y+ in acetonitrile
a
a
XH
Y+
ΔG°HꢀAðXþÞ
ΔG°HꢀAðYþÞ
ΔG≠ b
+
A1H
A1H
A2H
A2+
A3+
A3
−66.4
−66.4
−76.2
−76.2
−90.2
−90.2
17.9
12.6
14.5
a Derived from experimental measurements using ITC or HPLC, the
unit is kcal mol−1, and the uncertainty is smaller than 0.5 kcal mol−1
b Derived from experimental measurements using a stopped-flow UV-
vis spectrometer; the uncertainty is smaller than 0.1 kcal mol−1
.
Scheme 2 Structures of three well-chosen organic hydride donors and the
corresponding cations.
.
various hydride self-exchange reactions in solution according
to the activation energies of the related hydride cross transfer
reactions. In order to determine ΔG=HꢀDðXHÞ of the various
hydride donors (XH) in acetonitrile and establish the data
library, A1H, A2H and A3H in Scheme 2 were carefully chosen
as three typical organic hydride donors to construct three
different hydride cross transfer reactions (eqn (8)–(10)).
latter were determined by the stopped-flow UV-vis method (see
Fig. 4); ΔG°H ðA2þÞ and ΔGH° ðA2þÞ are the free energies of
ꢀA
ꢀA
the hydride acceptors A2+ and A3+ to capture the hydride anion
in acetonitrile at 298 K, respectively, which can be derived
from experimental measurements using ITC or HPLC.53
Table 1 lists the free energy change values of the three
+
+
+
hydride acceptors (A1 , A2 and A3 ) to capture hydride anions
in acetonitrile at 298 K and the activation energies of the three
hydride cross transfer reactions (eqn (8)–(10)) in acetonitrile at
298 K.
þ
A1H þ A2 ! A1þ þ A2H
ð8Þ
ð9Þ
þ
A1H þ A3 ! A1þ þ A3H
By examining eqn (11)–(13), it is found that eqn (11)–(13)
contain three isolated variables: ΔG=H ðA1HÞ, ΔGH= ðA2HÞ
þ
A2H þ A3 ! A2þ þ A3H
ð10Þ
ꢀD
ꢀD
and ΔG=H ðA3HÞ. If the three eqn (11)–(13) are treated together
ꢀD
According to eqn (8)–(10), the three eqn (11)–(13) can be
derived from eqn (4) by introducing eqn (6).
to get a simultaneous solution after substituting the known
data in Table 1 into the equations, the X–H bond activation
energies of the three hydride donors (A1H, A2H and A3H) for
their hydride self-exchange reactions (eqn (14)–(16)) in aceto-
nitrile at 298 K can all be obtained at the same time. The
ΔG=ðA1H=A2þÞ ¼ ΔGH= ðA1HÞ þ ΔGH= ðA2HÞ
ꢀD
ꢀD
þ ΔG°H ðA2þÞ
ð11Þ
ð12Þ
ð13Þ
ꢀA
result is that ΔG=H ðA1HÞ = 46.1 kcal mol−1 for A1H (eqn (14)),
ΔG=ðA1H=A3þÞ ¼ ΔGH= ðA1HÞ þ ΔGH= ðA3HÞ
ꢀD
ꢀD
ꢀD
ΔG=H ðA2HÞ = 48.0 kcal mol−1 for A2H (eqn (15)) and
ꢀD
þ ΔG°H ðA3þÞ
ꢀA
ΔG=H ðA3HÞ = 56.7 kcal mol−1 for A3H (eqn (16)) in aceto-
ꢀD
ΔG=ðA2H=A3þÞ ¼ ΔGH= ðA2HÞ þ ΔGH= ðA3HÞ
nitrile at 298 K.
ꢀD
ꢀD
þ ΔG°H ðA3þÞ
þ
ꢀA
A1H þ A1 ! A1þ þ A1H
ð14Þ
ð15Þ
ð16Þ
In eqn (11)–(13), ΔG≠(A1H/A2 ), ΔG≠(A1H/A3 ) and
+
+
þ
A2H þ A2 ! A2þ þ A2H
+
ΔG≠(A2H/A3 ) are the activation energies of the three hydride
cross transfer reactions (eqn (8)–(10)) in acetonitrile, respect-
ively, which can be directly derived from the corresponding
rate constants at 298 K according to the Eyring equation; the
þ
A3H þ A3 ! A3þ þ A3H
+
Since A2 is a strong hydride acceptor and ΔG=H ðA2HÞ
ꢀD
(48.0 kcal mol−1) and ΔGH° ðA2HÞ (−76.2 kcal mol−1 35b
)
have
ꢀA
been determined, it is not difficult to get ΔG=HꢀDðXHÞ of any
another hydride donor (XH) in solution according to eqn (11)
+
by constructing a hydride cross transfer reaction with A2 (eqn
(17)). In this work, the second order rate constants (k2) at
298 K and the corresponding activation energies of 187 typical
hydride cross transfer reactions in acetonitrile were deter-
mined, and the detailed results are summarized in Table 2. In
order to examine the dependence of ΔG≠ on ΔG° for the
hydride transfer reactions and the effect of the free energy
changes of the hydride transfer reactions (ΔG°) on the
ΔG=HꢀDðXHÞ, as well as the relationship between ΔG=HꢀDðXHÞ
and ΔG°HꢀDðXHÞ, the free energy changes (ΔG°) of the 187
typical hydride cross transfer reactions from XH to Y+ in
+
Fig. 4 Profile of the UV-vis absorbance of A3 at λmax = 495 nm during the
+
+
hydride transfer from A2H to A3 (G = p-CH3O). Conditions: 0.12 mM A3
,
3.15 mM A2H in dry acetonitrile at 298 K.
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Table 2 Second-order rate constants (k2) and molar free energy changes (ΔG°) of the hydride transfer from XH to Y+ or to Y+ from XH in acetonitrile at 298 K
together with the corresponding reaction activation energies (ΔG≠) and the X–H bond activation free energies ½ΔGH=ꢀ DðXH=YþÞꢁ
ΔG≠ b
ΔG° c
½ΔG=HꢀDðXH=YþÞꢁ
a
d
No.
Hydride donors or acceptors
k2
1He
R = Me
1.65
2.04
17.15
17.02
17.36
20.28
16.98
18.65
14.73
14.82
14.88
14.91
15.11
15.52
15.53
15.57
15.74
15.84
15.93
16.09
15.23
15.29
15.41
15.55
15.62
16.09
17.55
17.60
17.75
17.83
18.29
17.68
17.71
17.91
18.10
18.52
18.86
14.09
14.20
14.70
13.99
15.52
−16.7
−16.9
−16.9
−16.9
−16.9
−17.0
−18.0
−17.5
−16.9
−16.8
−16.1
−14.8
−14.9
−14.6
−14.0
−13.9
−13.5
−12.1
−16.2
−15.9
−15.3
−15.2
−14.5
−13.2
−11.4
−11.0
−10.6
−10.6
−8.5
40.67
40.51
40.68
42.13
40.48
41.27
38.81
39.11
39.44
39.50
39.95
40.81
40.76
40.93
41.32
41.42
41.66
42.44
39.96
40.14
40.50
40.62
41.01
41.89
43.52
43.74
44.02
44.06
45.34
43.84
44.05
44.50
44.64
45.36
46.27
37.29
37.75
37.65
37.54
41.41
Et
iPr
1.15
tBut
8.30 × 10−3
2.20
Bn
Ph
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
G = p-MeO
p-Me
p-H
1.30 × 10−1
9.70 × 101
8.36 × 101
7.61 × 101
7.16 × 101
5.16 × 101
2.58 × 101
2.55 × 101
2.38 × 101
1.77 × 101
1.49 × 101
1.28 × 101
9.81
2He
3He
4He
4.18 × 101
3.80 × 101
3.10 × 101
2.45 × 101
2.17 × 101
9.91
5He
6He
8.42 × 10−1
7.71 × 10−1
5.97 × 10−1
5.18 × 10−1
2.38 × 10−1
6.68 × 10−1
6.41 × 10−1
4.55 × 10−1
3.32 × 10−1
1.61 × 10−1
9.20 × 10−2
2.88 × 102
2.38 × 102
1.02 × 102
3.43 × 102
2.58 × 101
p-F
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
−10.9
−10.5
−9.8
−9.7
−8.7
p-CN
R = Me
Et
−7.2
7He
−20.4
−19.6
−20.3
−19.8
−13.6
iPr
nBut
8He
9He
8.34 × 101
4.38 × 101
1.90 × 104
2.61 × 104
9.13 × 101
1.65
14.82
15.21
11.61
11.42
14.77
17.15
−17.3
−15.2
−28.1
−33.1
−19.6
−12.9
39.21
40.45
32.20
29.61
38.03
42.57
10He
11He
12He
13He
14He
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Table 2 (Contd.)
a
d
No.
Hydride donors or acceptors
G = p-MeO
k2
ΔG≠ b
ΔG° c
½ΔG=HꢀDðXH=YþÞꢁ
15He
1.23 × 101
8.35
4.62
15.96
16.19
16.54
17.14
17.18
16.05
16.38
16.68
17.43
17.43
14.41
−14.3
−13.6
−12.3
−10.9
−10.7
−15.7
−15.1
−13.8
−12.1
−12.0
−11.8
41.27
41.74
42.56
43.57
43.68
40.62
41.09
41.89
43.11
43.16
41.75
p-Me
p-H
p-Cl
1.66
p-Br
1.57
16He
G = p-MeO
p-Me
p-H
p-Cl
p-Br
1.06 × 101
6.00
3.63
1.02
1.02
17He
18He
19He
1.68 × 102
2.18
0.52
3.02
16.98
17.83
16.79
−12.0
−5.3
−7.2
42.94
46.71
45.24
20He
21He
G = p-NMe2
p-MeO
p-Me
p-H
p-Cl
p-CF3
p-CN
p-NO2
p-OH
o-OH
o-Me
9.24 × 102
3.05 × 102
2.42 × 102
1.77 × 102
7.54 × 101
4.29 × 101
2.59 × 101
1.80 × 101
1.56 × 102
1.56 × 102
7.21
13.40
14.06
14.19
14.38
14.88
15.22
15.52
15.73
14.45
14.45
16.27
14.45
13.31
−30.5
−28.2
−27.7
−27.0
−25.9
−24.6
−24.4
−24.0
−28.5
−27.3
−29.7
−27.9
−31.6
31.90
33.37
33.69
34.14
34.94
35.76
36.00
36.31
33.42
34.02
33.73
33.72
31.30
o-Cl
1.56 × 102
1.08 × 103
22He
23He
G = p-MeO
p-Me
p-H
p-Br
p-CF3
3.84 × 10−2
2.72 × 10−2
2.17 × 10−2
1.09 × 10−2
0.49 × 10−2
1.16 × 10−1
19.37
19.58
19.71
20.12
20.59
18.72
−23.3
−23.0
−22.5
−21.7
−20.7
−27.4
38.48
38.73
39.05
39.65
40.39
36.10
24He
25He
9.24 × 101
6.20 × 101
3.21
14.76
15.00
16.75
11.20
−23.5
−21.9
−10.5
−16.5
36.08
37.00
43.57
45.50
26He
27Hi
28Hf
3.78 × 104
29Hf
2.77 × 102
14.11
−16.2
47.10
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Table 2 (Contd.)
a
d
No.
Hydride donors or acceptors
G = p-MeO
k2
ΔG≠ b
ΔG° c
½ΔG=HꢀDðXH=YþÞꢁ
30Hf
5.01 × 103
3.85 × 103
2.55 × 103
1.19 × 103
1.28 × 103
0.93 × 103
3.56 × 103
3.23 × 103
1.50 × 103
1.37 × 103
0.99 × 103
3.88 × 103
2.97 × 103
1.24 × 103
1.27 × 103
0.92 × 103
4.76 × 101
12.40
12.55
12.80
13.25
13.21
13.40
12.60
12.66
13.11
13.17
13.36
12.55
12.71
13.23
13.21
13.40
15.16
−23.3
−22.7
−21.7
−20.3
−20.8
−20.0
−23.8
−22.6
−19.7
−20.4
−18.7
−22.2
−22.0
−21.1
−21.2
−20.8
−19.0
42.70
43.07
43.70
44.62
44.35
44.85
42.55
43.18
44.85
44.53
45.48
43.32
43.50
44.21
44.15
44.45
46.22
p-Me
p-H
p-Br
p-Cl
m-Cl
G = p-MeO
p-Me
p-Br
p-Cl
m-Cl
G = p-MeO
p-Me
p-Br
p-Cl
m-Cl
31Hf
32Hf
33Hf
34Hf
35Hf
9.50 × 10−1
17.47
−21.7
46.03
G = p-MeO
p-Me
p-H
4.17 × 10−1
3.73 × 10−1
3.51 × 10−1
3.10 × 10−1
2.23 × 10−1
2.59 × 103
1.81 × 103
1.53 × 103
6.22 × 102
2.79 × 102
4.38 × 103
3.35 × 103
2.20 × 103
9.36 × 102
3.60 × 102
3.98 × 103
2.04 × 103
1.47 × 103
5.87 × 102
2.45 × 102
2.34 × 103
3.51 × 103
4.75 × 103
17.96
18.03
18.06
18.14
18.33
12.79
13.00
13.10
13.63
14.11
12.48
12.64
12.89
13.39
13.96
12.54
12.93
13.12
13.67
14.19
12.85
12.61
12.43
−17.8
−17.5
−18.8
−17.0
−16.3
−37.4
−37.0
−36.4
−35.2
−33.9
−38.6
−38.1
−37.5
−36.0
−34.7
−40.4
−39.9
−39.0
−37.1
−35.4
−35.7
−37.5
−38.4
48.23
48.41
47.78
48.71
49.16
40.39
40.70
41.05
41.91
42.80
39.64
39.97
40.39
41.39
42.33
38.76
39.21
39.76
40.98
42.09
41.27
40.25
39.71
p-Cl
p-NO2
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
R = H
Me
36Hg
37Hg
38Hg
39Hg
40Hg
Et
G = p-MeO
p-Me
p-H
3.78 × 105
3.31 × 105
2.99 × 105
1.73 × 105
1.09 × 105
4.06 × 105
3.50 × 105
3.12 × 105
1.81 × 105
1.15 × 105
3.22 × 105
2.81 × 105
2.29 × 105
1.56 × 105
9.81 × 104
1.44 × 105
1.45 × 106
9.85 × 105
9.84
9.92
9.98
10.30
10.57
9.80
−40.0
−39.7
−39.3
−38.7
−37.8
−40.4
−40.2
−39.8
−39.0
−38.1
−40.9
−40.7
−40.4
−39.6
−38.6
−37.3
−42.6
−41.5
37.62
37.81
38.04
38.50
39.09
37.40
37.54
37.77
38.34
38.92
37.22
37.36
37.57
38.08
38.72
39.25
35.92
36.58
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
41Hg
42Hg
9.88
9.95
p-Cl
10.27
10.54
9.93
10.01
10.14
10.36
10.64
10.41
9.04
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
R = H
Me
43Hg
44Hh
Et
9.27
G = p-MeO
p-Me
p-H
4.21 × 102
3.53 × 102
2.95 × 102
2.66 × 102
13.87
13.97
14.08
14.14
−23.4
−22.5
−21.7
−21.2
40.68
41.18
41.63
41.92
p-F
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Table 2 (Contd.)
a
d
No.
Hydride donors or acceptors
G = p-MeO
k2
ΔG≠ b
ΔG° c
½ΔG=HꢀDðXH=YþÞꢁ
45Hi
25.57 × 102
23.09 × 102
17.26 × 102
9.11 × 102
2.86 × 102
4.68 × 104
12.80
12.86
13.03
13.41
14.09
11.08
−29.2
−28.1
−27.5
−26.4
−24.7
−13.0
42.05
42.63
43.02
43.76
44.95
49.19
p-Me
p-H
p-Cl
p-CF3
46Hi
47Hi
48+ j
1.81 × 101
15.73
−26.0
45.01
G = p-MeO
p-Me
p-H
6.81 × 10−1
8.92 × 10−1
1.77
17.67
17.51
17.11
16.73
16.00
17.67
17.50
17.47
17.17
17.02
15.76
15.19
14.96
14.65
14.35
11.08
−13.6
−14.2
−16.2
−18.9
−22.5
−12.4
−13.5
−14.8
−16.5
−19.1
−16.7
−17.6
−18.1
−19.0
−20.5
−19.4
p-Cl
3.35
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
1.15 × 101
6.87 × 10−1
9.13 × 10−1
9.60 × 10−1
1.58
49+ j
2.04
50+k
1.73 × 101
4.53 × 101
6.63 × 101
1.11 × 102
1.87 × 102
4.68 × 104
p-CF3
51+k
52+k
G = p-MeO
p-Me
p-H
2.21 × 102
3.24 × 102
3.61 × 102
5.08 × 102
6.93 × 102
1.67 × 104
2.14 × 104
3.78 × 104
6.62 × 104
6.15 × 104
1.14 × 105
4.94 × 104
3.06 × 104
9.78 × 104
1.97 × 102
14.25
14.02
13.96
13.75
13.57
11.69
11.54
11.20
10.87
10.91
10.55
11.04
11.33
10.64
14.31
−17.3
−18.1
−19.8
−21.4
−24.1
−20.5
−20.9
−21.9
−22.8
−23.8
−22.1
−21.6
−23.4
−25.9
−22.3
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
53+l
p-Br
p-CF3
m-MeO
m-Me
m-CF3
54+m
55+n
9.13 × 10−1
2.69 × 104
17.50
11.40
−11.0
−26.6
56+o
a k2 is the second-order rate constant of the hydride transfer in acetonitrile at 298 K. The data of k2 (M−1 s−1) were obtained from experimental
measurements by the UV-vis method. The uncertainty is smaller than 5%. b Derived from the Eyring equation (T = 298 K); the unit is kcal mol−1
.
c Derived from the corresponding reaction heats, because for the hydride transfer reactions with the type of XH + Y+ → X+ + YH, the free energy
change of the reactions in acetonitrile (ΔG°) has been verified to be equal to or quite close to the corresponding reaction heat (see ESI).31 The
d
latter were directly derived from experimental measurements by ITC. The reproducibility is 0.5 kcal mol−1. ΔGH=ꢀDðXH=YþÞ were derived from
the corresponding ΔG≠ and ΔGH° ꢀDðXHÞ according to eqn (7). The unit is kcal mol−1
.
e To react with 10-methylacridinium (46+) in acetonitrile at
298 K. f To react with 9-phenylxanthylium [53+ (G = p-H)] in acetonitrile at 298 K. g To react with 4-acetamido-2,2,6,6-tetramethyl-1-
oxopiperidinium (56+) in acetonitrile at 298 K. h To react with 5-methylphenazinium (54+) in acetonitrile at 298 K. i To react with thioxanthylium
(51+) in acetonitrile at 298 K. j To react with 1-benzyl-1,4-dihydronicotinamide [2H (G = p-H)] in acetonitrile at 298 K. k To react with 10-methyl-
9,10-dihydroacridine (46H) in acetonitrile at 298 K. l To react with β-D-glucopyranosyl-1,4-dihydronicotinamide acetate (28H) in acetonitrile at
298 K. m To react with 1-phenyl-1,4-dihydronicotinamide [15H (G = H)] in acetonitrile at 298 K. n To react with 1-benzyl-1,4-dihydropyridine-3-
carbonitrile [6H (G = H)]) in acetonitrile at 298 K. o To react with 9-phenyl-10-methyl-9,10-dihydroacridine [49H (G = H)] in acetonitrile at 298 K.
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acetonitrile at 298 K were determined. The detailed results are ΔG°HꢀAðXþÞ ½ΔG°HꢀAðXþÞ ¼ ꢀΔG°HꢀDðXHÞꢁ are compared with
also summarized in Table 2.
each other, the former is even smaller than half of the latter.
This result indicates that for any organic hydride donor (XH),
z
ΔG ðXH=A2þÞ
the numerical value of ΔGH= ðXþÞ is always smaller than that
þ
XH þ A2 ꢀꢀꢀꢀꢀꢀ! Xþ þ A2 H
ð17Þ
ꢀ
ðAXHÞ. Actually, the X–H bond acti-
CH3CN
of the corresponding ΔGH=
ꢀ
vation energy of XH, ΔG=HꢀDDðXHÞ, is the resistant force of the
hydride transfer and the X–H formation energy of X+,
ΔG=HꢀAðXþÞ, is the driving force. According to the character of
the Morse-type curve, it is evident that when the hydride trans-
fer takes place from the initial state to the transition state, the
instantaneous driving force ½@G=HꢀAðYþÞ=@rꢁ is always smaller
than the instantaneous resistant force ½@G=HꢀDðXHÞ=@rꢁ and the
difference gradually becomes small until zero. When the
hydride transfer takes place from the transition state to the
final state, the instantaneous driving force ½@G=HꢀAðYþÞ=@rꢁ is
always larger than the instantaneous resistant force
½@G=HꢀDðXHÞ=@rꢁ and the difference gradually increases.
From the related data in Table 2, the values of ΔG=HꢀDðXHÞ
of the 187 hydride donors (XH) for their hydride self-exchange
reactions in acetonitrile at 298 K can be derived according to
eqn (11) or similar equations. The results are summarized in
Table 3. The values of ΔG=HꢀAðXþÞ for the corresponding
187 hydride acceptors (X+) in acetonitrile at 298 K can be
derived from the corresponding ΔG=HꢀDðXHÞ using eqn (6), and
the results are also listed in Table 3. In order to conveniently
compare ΔG=HꢀDðXHÞ with ΔGH° ðXHÞ and ΔG=HꢀAðXþÞ with
ꢀD
ΔG°HꢀAðXþÞ, the ΔGH° ꢀDðXHÞ values of the 187 hydride donors
(XH) and the ΔG°HꢀAðXþÞ values of the 187 hydride acceptors
(X+) in acetonitrile at 298 K are also listed in Table 3.
V. The factors affecting ΔG=HꢀDðXHÞ and
ΔG=HꢀAðYþÞ
IV. Scales of ΔG=HꢀDðXHÞ and ΔGH=ꢀAðXþÞ of
various XH and X+ in acetonitrile
By examining the dependence of ΔG=HꢀDðXHÞ on ΔGH° ꢀDðXHÞ
(Fig. 7), it is found that ΔG=HꢀDðXHÞ increases with an increase
of ΔG°HꢀDðXHÞ, which implies that the thermodynamic pro-
perties ΔG°HꢀDðXHÞ should be one main factor to determine
the ΔG=HꢀDðXHÞ. However, the relationship between
ΔG=HꢀDðXHÞ and ΔGH° ꢀDðXHÞ is not of a good linearity and
many scattered points appear in the diagram, which indicates
From column 2 in Table 3, it is clear that the X–H bond acti-
vation energies ΔG=HꢀDðXHÞ of the 187 organic hydride donors
(XH) for hydride self-exchange reactions in acetonitrile range
from 39.6 kcal mol−1 for 12H to 65.8 kcal mol−1 for 52H (G =
p-CF3). Among the 187 hydride donors, 12H as the hydride
donor is the easiest to be activated, whereas 52H (G = p-CF3) as
the hydride donor is the most difficult to be activated. Such a
large scale of the X–H bond activation energies (39.6–65.8 kcal
mol−1) indicates that the X–H bond activation energies of
hydride donors are strongly dependent on the nature and
structure of the hydride donors. For a convenient search of
ΔG=HꢀDðXHÞ for various types of hydride sources, a simple over-
view figure is provided (Fig. 5). From column 3 in Table 3, it is
clear that the scale of ΔG=HꢀAðXþÞ for the 187 diverse hydride
acceptors (X+) ranges from −1.9 kcal mol−1 for 24+ to
−37.1 kcal mol−1 for 56+. Among the 187 X+, 24+ is the kineti-
cally weakest hydride acceptor, whereas 56+ is the kinetically
strongest one. Such a large scale of the X–H bond formation
energies of X+ in the transition states (−1.9 to −37.1 kcal
mol−1) indicates that the X–H bond formation energies of X+
(i.e., the free energy change of X+ from the initial state to the
transition state) is also strongly dependent on the nature and
the structure of the hydride acceptors (X+). For a convenient
search of ΔG=HꢀAðXþÞ for various types of hydride acceptors, a
simple overview figure is provided (Fig. 6). If the ΔG=HꢀDðXHÞ
values of the 187 XH and the ΔG=HꢀAðXþÞ values of the corres-
ponding 187 X+ are compared, it is found that the easiest acti-
vation of the X–H bond does not indicate the easiest formation
that ΔG°H ðXHÞ is not the only factor to affect ΔG=HꢀDðXHÞ.
ꢀD
From the kinetic theoretic model proposed in this work,
ΔG=HꢀDðXHÞ is dependent not only on ΔGH° ꢀDðXHÞ, but also on
the distance between the donor and the acceptor (Δr) [Δr = 2 ×
reffi(XH), reffi(XH) is the efficient radius of XH molecule]. For
hydride cross transfer reactions (XH + Y+ → X+ + YH, X ≠ Y),
the reaction free energy change ΔG° is also an important
factor to affect ΔG=HꢀDðXH=YþÞ. If these effects were examined
qualitatively the results were as follows. In general, for hydride
self-exchange reactions, when the distance between the
hydride donor and the hydride acceptor (Δr) is kept constant,
ΔG=HꢀDðXHÞ is proportional to ΔGH° ꢀDðXHÞ (Fig. 8). For
instance, some hydride donors in Table 3, such as 2H–6H,
15H–16H, 21H, 23H, 30H–32H, 37H, 38H, 48H–50H, 52H,
53H, etc. gave excellent experimental evidence. Similarly, for
hydride self-exchange reactions, when the ΔG°HꢀDðXHÞ is kept
constant, the increase of Δr (i.e., the efficient size of XH) can
result in a larger ΔG=HꢀDðXHÞ (Fig. 9). In addition, for a hydride
cross transfer reaction, when the Δr is kept constant, the more
negative the ΔG° is, the smaller the ΔG=HꢀDðXH=YþÞ is (Fig. 10).
of (X–H)≠. That is because the ΔGH° ꢀDðXHÞ values of the VI. Estimation of the activation energies of
187 XH in acetonitrile are different from each other.
various hydride transfer reactions in acetonitrile
If ΔG=HꢀDðXHÞ of various hydride donors (XH) are
compared with the corresponding ΔG°H ðXHÞ, such a relation The data in Table 3 are very useful. From ΔGH° ꢀDðXHÞ and
ꢀ
1=2ΔG°H ðXHÞ , ΔG=HꢀDðXHÞ , ΔG° ꢀDðDXHÞ
could
be ΔG°H ðXþÞ, the thermodynamic driving forces (ΔG°) of the A2187
ꢀD
H
ꢀA
observed. Similarly, if the numerical values of ΔGH=ꢀAðXþÞ and (34 782) hydride cross-transfer reactions (XH + Y+ → X+ + YH,
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Table 3 The X–H bond activation free energies of the 187 hydride donors (XH) ½ΔG=Hꢀ DðXHÞꢁ and the X–H bond formation free energies of X+ ½ΔG=H
ꢀ
ðXþÞꢁ in the
transition state for the hydride self-exchange reactions in acetonitrile as well as the free energy changes of XH releasing a hydride anion ½ΔG°HꢀDðXHÞꢁAand the free
energy changes of X+ capturing a hydride anion ½ΔG°HꢀAðXþÞꢁ together with the activation energies of the hydride self-exchange reactions [ΔG≠(XH)] in acetonitrile
a
b
c
d
Hydride donors (XH)
ΔG=HꢀDðXHÞ
½ΔG=HꢀAðXþÞꢁ
ΔG°HꢀDðXHÞ
½ΔG°HꢀDðXþÞꢁ
ΔG≠(XH)e
1H
2H
3H
4H
R = Me
Et
45.31
45.18
45.52
48.44
45.14
46.81
42.89
42.98
43.04
43.07
43.27
43.68
43.69
43.73
43.92
44.00
44.09
44.25
43.39
43.45
43.57
43.71
43.78
44.25
45.71
45.76
45.91
45.99
46.45
45.84
45.87
46.07
46.36
46.68
47.02
42.25
42.36
42.86
42.15
43.68
42.98
43.37
39.77
39.58
42.93
45.31
44.12
44.35
44.70
45.30
45.34
44.21
44.54
44.84
45.59
45.59
42.57
45.14
45.99
44.95
−14.19
−14.12
−13.78
−10.86
−14.16
−12.39
−15.31
−15.72
−16.26
−16.33
−16.83
−17.72
−17.61
−17.87
−18.28
−18.3
59.5
59.3
59.3
59.3
59.3
59.2
58.2
58.7
59.3
59.4
60.1
61.4
61.3
61.6
62.2
62.3
62.7
64.1
60.0
60.3
60.9
61.0
61.7
63.0
64.8
65.2
65.6
65.6
67.7
65.3
65.7
66.4
66.5
67.5
69.0
55.8
56.6
55.9
56.4
62.6
58.9
61.0
48.1
43.1
56.6
63.3
61.9
62.6
63.9
65.3
65.5
60.5
61.1
62.4
64.1
64.2
64.4
64.2
70.9
69.0
−59.5
−59.3
−59.3
−59.3
−59.3
−59.2
−58.2
−58.7
−59.3
−59.4
−60.1
−61.4
−61.3
−61.6
−62.2
−62.3
−62.7
−64.1
−60.0
−60.3
−60.9
−61.0
−61.7
−63.0
−64.8
−65.2
−65.6
−65.6
−67.7
−65.3
−65.7
−66.4
−66.5
−67.5
−69.0
−55.8
−56.6
−55.9
−56.4
−62.6
−58.9
−61.0
−48.1
−43.1
−56.6
−63.3
−61.9
−62.6
−63.9
−65.3
−65.5
−60.5
−61.1
−62.4
−64.1
−64.2
−64.4
−64.2
−70.9
−69.0
31.1
31.1
31.7
37.5
30.9
34.4
27.6
27.3
26.7
26.8
26.5
26.0
26.1
25.8
25.6
25.7
25.5
24.4
26.8
26.6
26.3
26.4
25.9
25.5
26.6
26.4
26.2
26.4
25.2
26.3
26.1
25.8
26.3
25.9
25.0
28.7
28.2
29.9
28.0
24.8
27.1
25.8
31.5
36.1
29.2
27.3
26.3
26.1
25.5
25.3
25.1
27.9
27.9
27.2
27.1
27.0
20.8
26.0
21.1
20.9
iPr
tBut
Bn
Ph
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
−18.61
−19.85
−16.61
−16.85
−17.33
−17.29
−17.92
−18.75
−19.09
−19.44
−19.69
−19.61
−21.25
−19.46
−19.83
−20.33
−20.14
−20.82
−21.98
−13.55
−14.24
−13.04
−14.25
−18.92
−15.92
−17.63
−8.33
p-CN
G = p-MeO
p-Me
p-H
5H
6H
p-F
p-CN
G = p-MeO
p-Me
p-H
p-F
p-Cl
p-CN
R = Me
Et
7H
iPr
nBut
8H
9H
10H
11H
12H
13H
14H
15H
−3.52
−13.67
−17.99
−17.78
−18.25
−19.20
−20.00
−20.16
−16.29
−16.56
−17.56
−18.51
−18.61
−21.83
−19.06
−24.91
−24.05
G = p-MeO
p-Me
p-H
p-Cl
p-Br
G = p-MeO
p-Me
p-H
p-Cl
p-Br
16H
17H
18H
19H
20H
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Table 3 (Contd.)
a
b
c
d
Hydride donors (XH)
ΔG=HꢀDðXHÞ
½ΔG=HꢀAðXþÞꢁ
ΔG°HꢀDðXHÞ
½ΔG°HꢀDðXþÞꢁ
ΔG≠(XH)e
21H
G = p-NMe2
41.56
42.22
42.35
42.54
43.04
43.38
43.68
43.89
42.61
42.61
44.43
42.61
41.47
47.53
47.74
47.87
48.28
48.75
46.88
42.92
43.16
53.71
45.21
48.12
46.41
46.56
46.81
47.26
47.22
47.41
46.61
46.67
47.12
47.18
47.37
46.56
46.72
47.24
47.22
47.41
49.17
51.48
51.97
52.04
52.07
52.15
52.34
49.92
50.13
50.23
50.76
51.24
49.61
49.77
50.02
50.52
51.09
49.67
50.06
50.25
50.80
51.32
49.98
49.74
49.56
−4.14
−5.78
45.7
48.0
48.5
49.2
50.3
51.6
51.8
52.2
47.7
48.9
46.5
48.3
44.6
52.9
53.2
53.7
54.5
55.5
48.8
52.7
54.3
65.7
69.7
75.7
68.3
68.9
69.9
71.3
70.8
71.6
67.8
69.0
71.9
71.2
72.9
69.4
69.6
70.5
70.4
70.8
72.6
69.9
73.8
74.1
72.8
74.6
75.3
63.3
63.7
64.3
65.5
66.8
62.1
62.6
63.2
64.7
66.0
60.3
60.8
61.7
63.6
65.3
65.0
63.2
62.3
−45.7
−48.0
−48.5
−49.2
−50.3
−51.6
−51.8
−52.2
−47.7
−48.9
−46.5
−48.3
−44.6
−52.9
−53.2
−53.7
−54.5
−55.5
−48.8
−52.7
−54.3
−65.7
−69.7
−75.7
−68.3
−68.9
−69.9
−71.3
−70.8
−71.6
−67.8
−69.0
−71.9
−71.2
−72.9
−69.4
−69.6
−70.5
−70.4
−70.8
−72.6
−69.9
−73.8
−74.1
−72.8
−74.6
−75.3
−63.3
−63.7
−64.3
−65.5
−66.8
−62.1
−62.6
−63.2
−64.7
−66.0
−60.3
−60.8
−61.7
−63.6
−65.3
−65.0
−63.2
−62.3
37.5
36.4
36.2
35.8
35.7
35.2
35.6
35.6
37.5
36.3
42.3
36.9
38.4
42.1
42.2
42.1
42.1
42.0
45.0
33.1
32.1
41.7
20.7
20.5
24.5
24.3
23.7
23.3
23.6
23.2
25.4
24.4
22.3
23.2
21.9
23.8
23.8
23.9
24.0
24.0
25.8
33.1
30.2
29.9
31.4
29.7
29.3
36.5
36.5
36.1
36.1
35.6
37.1
37.0
36.8
36.3
36.2
39.1
39.4
38.8
38.0
37.3
35.0
36.2
36.9
p-MeO
p-Me
p-H
−6.15
−6.66
p-Cl
−7.26
p-CF3
p-CN
p-NO2
p-OH
o-OH
o-Me
o-Cl
−8.22
−8.12
−8.31
−5.09
−6.29
−2.07
−5.69
22H
23H
−3.13
G = p-MeO
p-Me
p-H
p-Br
p-CF3
−5.37
−5.46
−5.83
−6.22
−6.75
24H
25H
26H
27H
28H
29H
30H
−1.92
−9.78
−11.14
−11.99
−24.49
−27.58
−21.89
−22.34
−23.09
−24.04
−23.58
−24.19
−21.19
−22.33
−24.78
−24.02
−25.53
−22.84
−22.88
−23.26
−23.18
−23.39
−23.43
−18.42
−21.83
−22.06
−20.73
−22.45
−22.96
−13.38
−13.57
−14.07
−14.74
−15.56
−12.49
−12.83
−13.18
−14.18
−14.91
−10.63
−10.74
−11.45
−12.8
G = p-MeO
p-Me
p-H
p-Br
p-Cl
m-Cl
G = p-MeO
p-Me
p-Br
p-Cl
m-Cl
G = p-MeO
p-Me
p-Br
p-Cl
31H
32H
m-Cl
33H
34H
35H
G = p-MeO
p-Me
p-H
p-Cl
p-NO2
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
R = H
Me
36H
37H
38H
39H
−13.98
−15.02
−13.46
−12.74
Et
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Table 3 (Contd.)
a
b
c
d
Hydride donors (XH)
ΔG=HꢀDðXHÞ
½ΔG=HꢀAðXþÞꢁ
ΔG°HꢀDðXHÞ
½ΔG°HꢀDðXþÞꢁ
ΔG≠(XH)e
40H
41H
42H
G = p-MeO
p-Me
p-H
46.97
47.05
47.11
47.43
47.70
46.93
47.01
47.08
47.40
47.67
47.06
47.14
47.27
47.49
47.77
47.54
46.17
46.40
44.26
44.36
44.47
44.53
49.76
49.82
49.99
50.37
51.05
48.04
52.69
47.53
47.97
49.56
51.88
54.75
46.33
47.26
48.53
49.93
52.38
60.62
60.95
61.22
61.81
63.01
58.64
59.71
60.28
61.92
63.31
65.83
56.68
56.93
57.59
58.16
59.20
57.14
57.13
59.22
61.03
55.81
48.83
63.57
−13.73
−13.95
−14.29
−14.57
−15.20
−13.37
−13.49
−13.82
−14.30
−14.93
−12.74
−12.86
−13.03
−13.61
−14.33
−15.86
−11.93
−12.80
−18.54
−19.34
−20.03
−20.47
−16.64
−17.68
−18.11
−18.83
−19.85
−28.16
−10.51
−25.37
−25.53
−25.94
−26.32
−27.05
−25.37
−25.54
−25.57
−25.87
−26.02
−32.28
−32.85
−33.08
−33.39
−33.69
−36.96
−33.79
−34.02
−34.08
−34.29
−34.47
−33.52
−33.67
−34.01
−34.34
−34.3
60.7
61.0
61.4
62.0
62.9
60.3
60.5
60.9
61.7
62.6
59.8
60.0
60.3
61.1
62.1
63.4
58.1
59.2
62.8
63.7
64.5
65.0
66.4
67.5
68.1
69.2
70.9
76.2
63.2
72.9
73.5
75.5
78.2
81.8
71.7
72.8
74.1
75.8
78.4
92.9
93.8
94.3
95.2
96.7
95.6
93.5
94.3
96.0
97.6
100.3
90.2
90.6
91.6
92.5
93.5
91.8
91.3
93.1
95.6
86.2
77.4
100.7
−60.7
−61.0
−61.4
−62.0
−62.9
−60.3
−60.5
−60.9
−61.7
−62.6
−59.8
−60.0
−60.3
−61.1
−62.1
−63.4
−58.1
−59.2
−62.8
−63.7
−64.5
−65.0
−66.4
−67.5
−68.1
−69.2
−70.9
−76.2
−63.2
−72.9
−73.5
−75.5
−78.2
−81.8
−71.7
−72.8
−74.1
−75.8
−78.4
−92.9
−93.8
−94.3
−95.2
−96.7
−95.6
−93.5
−94.3
−96.0
−97.6
−100.3
−90.2
−90.6
−91.6
−92.5
−93.5
−91.8
−91.3
−93.1
−95.6
−86.2
−77.4
−100.7
33.3
33.1
32.8
32.8
32.5
33.5
33.5
33.3
33.1
32.8
34.4
34.2
34.3
33.9
33.5
31.6
34.3
33.6
25.8
25.1
24.5
24.0
33.2
32.1
31.9
31.6
31.2
19.8
42.2
22.1
22.5
23.7
25.6
27.7
20.9
21.8
22.9
24.0
26.4
28.3
28.1
28.1
28.4
29.3
21.6
25.9
26.3
27.8
29.0
31.3
23.2
23.2
23.6
23.9
24.9
22.4
22.9
25.3
26.4
25.4
20.2
26.5
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
R = H
Me
43H
44H
Et
G = p-MeO
p-Me
p-H
p-F
45H
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
46H
47H
48H
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
49H
50H
p-CF3
51H
52H
G = p-MeO
p-Me
p-H
p-Cl
p-CF3
G = p-MeO
p-Me
p-H
p-Cl
53H
p-Br
p-CF3
m-MeO
m-Me
m-CF3
−34.66
−34.17
−33.88
−34.57
−30.39
−28.57
−37.13
54H
55H
56H
a The values of ΔGH=ꢀDðXHÞ were derived from eqn (11) or the corresponding similar equations. The unit is kcal mol−1. The related parameters were
all derived from Table 2. b Derived from eqn (6), the unit is kcal mol−1 c Derived from molar free energy changes of the hydride transfer reactions
.
listed in Table 2 and the corresponding free energy changes of the hydride acceptors to capture hydride anions in acetonitrile at 298 K. The unit
is kcal mol−1. dΔGH° ꢀAðXþÞ ¼ ꢀ½ΔG°HꢀDðXHÞꢁ. eΔG=ðXH=XþÞ ¼ ΔG=HꢀDðXHÞ þ ΔG=HꢀAðXþÞ. The unit is kcal mol−1
.
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Fig. 5 An overview figure of ΔG=HꢀDðXHÞ for various types of hydride donors in acetonitrile at 298 K; the unit is kcal mol−1
.
X ≠ Y) can be derived from eqn (2). In a similar way, from difficult to understand why the hydride self-exchange reactions
ΔG=HꢀDðXHÞ and ΔG=HꢀAðXþÞ, the activation energies of cannot be directly determined. In fact, for many hydride
187 hydride self-exchange reactions (XH + X+ → X+ + XH) and donors, such as 23H, 24H, 47H, etc., the hydride self-exchange
the A2187 (34 782) hydride cross-transfer reactions (XH + Y+
→
reactions are too slow to take place. For more than thirty thou-
X+ + YH) can be readily derived from eqn (4), respectively. The sand (A1287) hydride cross transfer reactions (XH + Y+ → X+
+
results of the 187 hydride self-exchange reactions (XH + X+ → YH, X ≠ Y), the detailed results of the estimated activation
X+ + XH) are listed in Table 3, which ranges from 19.8 kcal energies were not listed to save space, but a range of data was
mol−1 for 46H to 45.0 kcal mol−1 for 24H. Since the activation given here. The result is from 63.9 kcal mol−1 for the hydride
energies of the hydride self-exchange reactions in acetonitrile transfer from 52H to 24+ to 2.5 kcal mol−1 for the hydride
are all much greater than the highest limit of 14.7 kcal mol−1 transfer from 12H to 56+ in acetonitrile. Evidently, the acti-
[equivalent to kself(XH/X+) = 1 × 102 M−1 s−1] that can be vation energy of the fastest hydride transfer reaction has sur-
1
directly determined by the dynamic H NMR method, it is not passed the activation energy limit of the diffusion limited
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Fig. 6 An overview figure of ΔG=HꢀAðXþÞ for various types of hydride acceptors in acetonitrile at 298 K; the unit is kcal mol−1
.
Fig. 8 Dependence of the bond activation free energies of organic hydride
donors (XH) for the hydride self-exchange reactions, ΔG=HꢀDðXHÞ, on ΔGH° ꢀ DðXHÞ
when Δr is kept constant.
Fig. 7 Relationship between the X–H bond activation free energies of the 187
organic hydrides (XH) for their hydride self-exchange reactions and the corres-
ponding free energy changes of XH to release a hydride anion in acetonitrile at
298 K.
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more than thirty thousand hydride cross-transfer reactions
and 187 hydride self-exchange reactions, the activation energies
of hydride transfer from 1H to 53+ in acetonitrile (eqn (18))
and the activation energies of hydride self-exchange reaction
of AcrH2 with the corresponding cation (AcrH+) in acetonitrile
(eqn (19)) were determined by independent experimental
methods.
The activation energies of hydride transfer reaction from
1H to 53+ in acetonitrile can be measured by the stopped-flow
UV-vis method. The determined results and the corresponding
results predicted according to eqn (4) are listed together in
Table 4. The perfect agreement between the two results55
does indicate not only that the values of ΔG=HꢀDðXHÞ and
ΔG=HꢀAðXþÞ derived from this work are reliable, but also that
eqn (4) is valid to predict the activation energies of the hydride
cross-transfer reactions.35b,56
Fig. 9 Dependence of the bond activation free energies of organic hydride
donors (XH) for the hydride self-exchange reactions on the distance between
the hydride donor and the hydride acceptor (Δr).
ð18Þ
Fig. 10 Dependence of the bond activation free energies of organic hydride
donors (XH) at the transition state for the hydride cross transfer reactions on the
free energy changes of the reactions (ΔG°) when Δr is kept constant.
As to the hydride self-exchange reaction of AcrH2 with the
corresponding cation (AcrH+) (eqn (19)), the activation energy
of the reaction in acetonitrile cannot be directly determined by
the conventional experimental method, since no spectral
signal can be detected to describe the reaction progress.
However, the activation energy of hydride transfer from
(N–CH3)AcrH2 to (N–CD3)AcrH+ in CD3CN (eqn (20)) can be deter-
mined by the conventional 1H NMR technique, since the
chemical shifts of the CH3-group in AcrH2 (3.36 ppm) and in
AcrH+ (4.76 ppm) are different (Fig. 11) and the kinetic isotope
effect of deuterium in the CD3 group on the hydride transfer
reaction should be quite small (due to the secondary kinetic
isotope effect). The perfect agreement between the experi-
mental result (19.7 kcal mol−1) and the theoretical figure
(19.8 kcal mol−1) does indicate that eqn (4) is also valid to
chemical reactions (in general, ΔG≠ < 3.8 kcal mol−1 (equi-
valent to k > 1010
M
−1 s−1) for the diffusion limited reactions;54
but it is impossible for the slowest one to take place in the
solution at 298 K). As we know, there are many important
organic hydride transfer reactions in vivo or in vitro whose
rates cannot be directly measured by using experimental
methods up to now. The reason is that some reactions are too
fast, some are too slow and some have no detectable signals,
etc. Evidently, a reliable method is urgently required to esti-
mate the activation energies.
VII. Validity of eqn (4)
In order to verify the validity of the kinetic equation (eqn (4)), predict the activation energies of the hydride self-exchange
which has been used to estimate the activation energies of reactions.
Table 4 Experimental and theoretical rate constants of hydride cross transfer reactions from 1H to 53+ in acetonitrile at 298 K
Hydride donors (1H)
Hydride acceptors
ΔG=HꢀD(1H)a
ΔG=HꢀA(53+)b
ΔG≠(calc.)c
ΔG≠(exp.)d
R = H
Me
Et
53+
53+
53+
53+
53+
53+
53+
43.04
45.31
45.18
45.52
48.44
45.14
46.81
−33.52
−33.52
−33.52
−33.52
−33.52
−33.52
−33.52
9.5
11.8
11.7
12.0
14.9
11.6
13.3
9.4
12.0
11.5
11.9
15.1
11.5
13.1
iPr
nBut
Bn
Ph
a From column 2 in Table 3, the unit is kcal mol−1. The uncertainty is smaller than 0.5 kcal mol−1 b From column 3 in Table 3, the unit is
.
kcal mol−1
.
c Derived from eqn (4), the unit is kcal mol−1
.
d Obtained from the experimental measurements by using the UV-vis method; the unit
.
is kcal mol−1. The uncertainty is smaller than 0.1 kcal mol−1
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The magnitude of ΔGH=ꢀAðYþÞ of hydride acceptors (Y+) is
dependent not only on the hydride affinity of Y+ ½ΔGH° ꢀAðYþÞꢁ,
but also on the effective radius of Y+. In general, the larger the
ΔG°HꢀAðYþÞ is and/or the smaller the effective radius of Y+ is,
the larger the ΔG=HꢀAðYþÞ is.
(5) An efficient method was developed to determine
ΔG=HꢀDðXHÞ of hydride donors and ΔGH=ꢀAðYþÞ of hydride
acceptors and the values of ΔG=HꢀDðXHÞ for 187 typical hydride
donors in acetonitrile and the values of ΔG=HꢀAðXþÞ for 187
typical hydride acceptors (X+) in acetonitrile were determined.
(6) The activation energies of 187 typical hydride self-
exchange reactions and more than thirty thousand (A1287
hydride cross transfer reactions in acetonitrile at 298 K were
estimated.
)
Fig. 11 1H NMR spectra changes of the mixture of (N–CH3)AcrH2 (0.0253 mol L−1
and (N–CD3)AcrH+ (0.0126 mol L−1) in CD3CN at 298 K. From top to bottom,
the reaction times are 23 min, 70 min, 118 min, 260 min and 354 min,
respectively.
)
(7) Since the development of the kinetic equation is only on
the basis of the changes of chemical bond of reactants, the
kinetic equation should be also suitable for proton transfer
reactions, hydrogen atom transfer reactions and all the other
chemical reactions involved with breaking and formation of
chemical bonds.
Due to the same formats of eqn (2) and (4), one of the most
significant contributions of this work is to have achieved the
perfect unity between the kinetic equation and thermo-
dynamic equation for hydride transfer reactions.
ð19Þ
IX. Experimental section
Materials
ð20Þ
All reagents were of commercial quality from freshly opened
containers or were purified before use. The reagent grade
acetonitrile was refluxed over KMnO4 and K2CO3 for several
hours and was doubly distilled over P2O5 under argon before
use. The 187 organic hydride compounds (XH) and their
corresponding salts perchlorate (X+ClO4−) were synthesized
according to conventional synthetic strategies,57 or directly
according to a literature method.58 All the target products were
identified by 1H NMR and MS.
VIII. Summary and conclusions
(1) In this work, a classical but new kinetic equation
ΔG= ¼ ΔG=HꢀDðXHÞ þ ΔGH=ꢀAðYþÞ was developed using the
Morse-type free energy curves of hydride donors (XH) to
release a hydride ion and hydride acceptors (Y+) to capture a
hydride ion according to transition state theory, which can be
used to estimate the activation energies of various hydride
transfer reactions.
Isothermal titration calorimetry (ITC)
The titration experiments were performed on a CSC4200 iso-
(2) The bond activation free energy of hydride donors (XH) thermal titration calorimeter in acetonitrile at 298 K as
for the hydride self-exchange reaction ½ΔG=HꢀDðXHÞꢁ as a new described previously.35–39 The performance of the calorimeter
physical concept was defined in this work, which can be used was checked by measuring the standard heat of neutralization
to scale the resistant force of the hydride donors (XH) to of an aqueous solution of sodium hydroxide with a standard
release a hydride ion in kinetics.
aqueous HCl solution. Data points were collected every
(3) The bond formation free energy of hydride acceptors 2 s. The heat of reaction was determined by following 10 auto-
(Y+) in the transition state for the hydride self-exchange reac- matic injections from a 250 μL injection syringe containing a
tion ½ΔG=HꢀAðYþÞꢁ as a new physical concept was defined in this standard solution (2 mM) into the reaction cell (1.30 mL) con-
work, which can be used to scale the driving force of the taining 1 mL of the other concentrated reactant (∼10 mM).
hydride acceptors (Y+) to capture a hydride ion in kinetics.
Injection volumes (10 μL) were delivered in 0.5 s time intervals
(4) The magnitude of ΔG=HꢀDðXHÞ of hydride donors (XH) is with 300–450 s between every two injections. The reaction heat
dependent not only on the strength of the X–H chemical bond was obtained by integration of each peak except the first. Note:
½ΔG°HꢀDðXHÞꢁ, but also on the effective radius of XH. In typically the first injection shows less heat than expected. This
general, the larger the ΔG°HꢀDðXHÞ is and/or the larger the is often due to diffusion across the tip of the needle or to
effective radius of XH is, the larger the ΔG=HꢀDðXHÞ is. difficulties in positioning the burette drive.
6086 | Org. Biomol. Chem., 2013, 11, 6071–6089
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Kinetic measurements
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The kinetics of the hydride transfer reactions were con-
veniently monitored using an Applied Photophysics
SX.18MV-R stopped-flow which was thermostated at 298 to
318 K under strictly anaerobic conditions in dry acetonitrile.59
The method of kinetic measurement was a pseudo-first-order
method. The concentration of the hydride donor was main-
tained at more than 20-fold excess of the hydride acceptor to
attain pseudo-first-order conditions. The kinetic traces were
recorded using an Acorn computer and analysed by Pro-K
Global analysis/simulation software or translated to PC for
further analysis. The data fitting used the equation Abs =
P1 × EXP(−P2 × x) + P3, which was integrated using the Pro-K
Global analysis/simulation software or Origin Software, and P2
was the pseudo-first-order rate constant k1. Thus the second-
order observed rate constant (kobs) was derived from plots of
the pseudo-first-order rate constants versus the concentrations
of the excess reactants. In each case, it was confirmed that the
rate constants derived from three to five independent measure-
ments agreed within an experimental error of 5%.
Acknowledgements
Financial support from the National Natural Science Foun-
dation of China (grant no. 21072104, 20921120403, 20832004
and 21102074), the Ministry of Science and Technology of
China (grant no. 2004CB719905) and the 111 Project (B06005)
is gratefully acknowledged.
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