Kinetic, thermodynamic and mechanistic studies on the reduction of carbenium ions by NAD(P)H analogues

Article abstract of DOI:10.1002/(SICI)1099-1395(199707)10:7<577::AID-POC920>3.0.CO;2-T

Hydride transfer mechanisms of the reductions of xanthylium ion by NAD(P)H analogues (i.e. BNAH, HEH and AcrH₂) were investigated. Both the kinetic observations and an analysis of thermodynamic driving forces for each mechanistic step in all the possible mechanisms indicate that the reductions are initiated by a rate-determining electron transfer, followed by a fast hydrogen atom abstraction. The mechanism of the reductions of 9-phenylxanthylium and triphenylmethylium ions by BNAH were also investigated and are similarly discussed.

Full text of DOI:10.1002/(SICI)1099-1395(199707)10:7<577::AID-POC920>3.0.CO;2-T

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)
KINETIC, THERMODYNAMIC AND MECHANISTIC STUDIES ON THE
REDUCTION OF CARBENIUM IONS BY NAD(P)H ANALOGUES
JIN-PEI CHENG* AND YUN LU
Department of Chemistry, Nankai University, Tianjin 300071, China
Hydride transfer mechanisms of the reductions of xanthylium ion by NAD(P)H analogues (i.e. BNAH, HEH and AcrH2 )
were investigated. Both the kinetic observations and an analysis of thermodynamic driving forces for each mechanistic
step in all the possible mechanisms indicate that the reductions are initiated by a rate-determining electron transfer,
followed by a fast hydrogen atom abstraction. The mechanism of the reductions of 9-phenylxanthylium and
triphenylmethylium ions by BNAH were also investigated and are similarly discussed. © 1997 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 10, 577–584 (1997) No. of Figures: 4 No. of Tables: 4 No. of References: 26
Keywords: carbenium ions; reduction; NAD(P)H analogues
Received 23 September 1996; revised 30 January 1997; accepted 6 February 1997
INTRODUCTION
electron–hydrogen atom transfer.
Although most of the existing evidence seems to be in
favor of the multi-step pathways, controversies about the
two types of mechanisms have not been solved. For
The mechanisms of NAD(P)H model-mediated reductions
have long been a subject of extensive investigations owing
to their potential linkage to the in vivo situation for many
biological functions of this coenzyme. Two different types
of mechanisms have been proposed to describe this
reduction, i.e. the one-step hydride transfer and the multi-
step hydride transfer, which is initiated first by an electron
7
example, Yausi and Ohno indicated that distinct electron
transfer occurs only under electro- or photochemical
8
9
conditions. Powell and Bruice and Carlson et al. pointed
out that the exclusive electron transfer is significant only
when the substrate can be readily reduced (i.e. possesses a
high reduction potential). In an effort to combine these two
Ϫ
+
Ϫ
Ϫ
•
1
transfer (i.e. e –H –e or e –H pathways). As early as
2
1
955, Mauzerall and Westheimer provided evidence to
10
mechanisms, Bunting recently suggested that the two
show that the hydride ion was directly transferred from a
simple model, 1-benzyl-1,4-dihydronicotinamide (BNAH),
to the substrates in reductions of malachite green and
thiobenzophenones. Later, however, the generality of this
one-step mechanism was questioned by others since the
hydrogen exchange at the C-4 atom of the model molecule
with hydrogens in solvent was observed in the reductions of
kinds of transfers be merged into a unified mechanism in
terms of an imbalanced development of electronic charge
and C–H bond fission in the transition state. All these
arguments reveal that there is still considerable debate on
the mechanistic details of reductions mediated by NAD(P)H
models.
3
4
Kinetic or thermodynamic parameters, especially a
combination of the two, are believed to be most useful in
evaluating mechanisms for many types of organic reactions.
However, to our knowledge, no thermodynamic details in a
single solvent about the reductions mediated by NAD(P)H
models have been reported, mostly due to the transient
nature of the intermediate species involved in each step of
the reduction. In this paper, we report the first estimates of
the thermodynamic driving forces (Gibbs free energy) for
each individual steps as shown in Scheme 1 for the
arenediazonium and thiobenzophenones. In addition, it is
also reported that primary kinetic isotope effect was found
to be much smaller than the isotope ratio found in product
in the reduction of ␣,␣,␣-triflurophenone with 1-propyl-
1
,4-dihydronicotinamide, suggesting that the reaction may
proceed via a charge-transfer complex transition state (T.S.)
5
rather than a simple hydride transfer T.S. These observa-
tions, together with other evidence collected by means of
6
a–c
6d
6e
kinetic,
thermodynamic and product analysis as well
f 6g 6h
6
as by ESR, UV and CIDNP techniques, suggest that the
apparent hydride transfer may be a result of a transfer
sequence including electron–proton–electron transfer or
+
+
reductions of xanthylium ions (Xn and 9-PhXn ) and trityl
cation by NAD(P)H models including BNAH and
1
0-methyl-9,10-dihydroacridine (AcrH ). The second-order
2
*
Correspondence to: J.-P. Cheng.
rate constants, kinetic isotope effects, activation parameters
and radical inhibitor effect for the reductions by BNAH,
Contract grant sponsor: Natural Science Foundation of China.
©
1997 by John Wiley & Sons, Ltd.
CCC 0894–3230/97/070577–08 $17.50

5
78
J.-P. CHENG AND Y. LU
Scheme 1
AcrH and Hantzsch ester (HEH) have also been investi-
9-phenylxanthenol (Aldrich) and triphenylmethanol
(Aldrich), respectively, with 48% HBF4 in
(CH CH CO ) O. All the compounds synthesized in this
2
gated [equation (1)]. Free energy changes (⌬G) of each of
the primary steps in various mechanisms (Scheme 1) were
derived through appropriate thermochemical cycles (see
14
3
2
2 2
work were characterized by verifying their melting points
using a Yanaco micro melting-point apparatus (uncorrected)
Results section) by combining pK values and the relevant
a
1
redox data for the species involved. Based on these
measurements, a reasonable mechanism is suggested for the
and by the H NMR spectra recorded on a JEOL 90Q NMR
spectrometer. Acetonitrile (spectroscopic grade) was
refluxed over KMnO and K CO for several hours and was
+
reduction of Xn by the NAD(P)H models used in this
4
2
3
work. The mechanism for the reductions of 9-phenyl-
doubly redistilled before use. The 30% CH CN–70% H O
3
2
+
+
xanthylium (9-PhXn ) and triphenylmethylium (Ph C )
phosphate buffer was adjusted to pH 6·90 at different
temperatures on a Beckman ␾ 71 pH meter which was
calibrated by a general method prior to use. The o-phthalate
buffer was similarly treated and was adjusted to pH 4·00.
Purification of DMSO solvent and preparation of dimsyl
3
ions with BNAH is also presented according to a similar
analytical strategy.
EXPERIMENTAL
Ϫ
2
+
base (CH SOCH K ) were carried out according to the
+
3
Materials. 1-Benzylnicotinamide bromide (BNA ),
15
standard procedure. Commercial tetrabutylammonium
hexafluorophosphate (Bu NPF , Aldrich) was recrystallized
1
4
-benzyl-1,4-dihydronicotinamide (BNAH) and its
4
6
,4Ј-dideuterated analogue (BNAH-d ) were prepared
2
from CH Cl and vacuum dried at 110 °C overnight before
1
1
2
2
according to the procedure in literature. N-Methylacridin-
ium ion (AcrH ) and 10-methyl-9,10-dihydroacridine
preparation of the supporting electrolyte solution.
+
(
1
AcrH ) were obtained by the method as described in Ref.
Reduction of 9-phenylxanthylium and trityl cations
by BNAH. To a mixture of carbenium ion (0·5 mmol) and
BNAH (0·5 mmol) was added 3 ml of deaerated acetonitrile
2
2. Hantzsch ester (HEH) was synthesized by a general
13
procedure. Xanthydrol was obtained from Aldrich and
recrystallized from aqueous ethanol. 9-Phenylxanthylium
and trityl ions were prepared by dehydroxylation of
containing 0·5 ml of CF COOD in the dark under argon. Ten
3
minutes later, water was added to quench the reaction. The
©
1997 by John Wiley & Sons, Ltd.
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

REDUCTION OF CARBENIUM IONS BY NAD(P)H ANALOGUES
579
product mixture was extracted with benzene and was
isolated by preparative TLC to give 9-phenylxanthene
by adding dimsyl base to a solution containing AcrH2
(enough to produce 1 m anion) under very strict air-tight
M
(
(
(
9-pHXnH) (62%) as the sole product, m.p. 142·0–143·0 °C
conditions. Immediately after preparation of the anion, a CV
was recorded by a similar procedure as described above.
The ferrocenium/ferrocene (Fc /Fc) redox couple was
1
CRC, 145·0–146·0 °C); H NMR (␦ CDCl ), 7·01–7·52
3
+
m, 13H), 5·32–5·41 (s, 1H). For the latter case, triphenyl-
methane (Ph CH) (50%) was isolated, m.p. 91·0–93·0 °C
taken as an internal standard in all cases.
3
1
(
Aldrich, 93–94 °C); H NMR (␦, CDCl ), 7·09–7·53
3
(m, 15H), 5·58–5·65 (s, 1H).
RESULTS
Kinetics. The kinetic data were obtained in 30%
CH CN–70% H O (v/v) at pH 6·90 (phosphate buffer) and
an ionic strength of 1·0 (KCl) for the reductions of Xn with
17
3
2
+
Kinetics
BNAH and HEH or at pH 4·00 (o-phthalate buffer) with
In aqueous solution, xanthylium cation is in equilibrium
with its hydroxide adduct (xanthydrol, XnOH):
AcrH at a certain temperature. The reactions were followed
2
+
KR
by monitoring the changes in absorbance at 358 nm for
+
*
+
Xn +H
O) XnOH+H
2
BNAH, 365 nm for HEH and 450 nm for N-methylacri-
+
↓
k2[BNAH]
(4)
dinium ion (AcrH ) under pseudo-first-order conditions
XnH
(20–100-fold excesses of xanthydrol). The concentrations
of BNAH, HEH and AcrH were 0·04, 0·04 and 0·02 m
M
,
2
Therefore, the pseudo-first-order rate constant (k ) for
reduction of xanthylium cation (Xn ) by an NAD(P)H
model can be evaluated by varying the concentration of
XnOH at a certain temperature. In all cases, kobs is found to
respectively. In a typical run, xanthydrol (XnOH) solution
of a certain concentration was first placed in a thermostatic
bath for 15 min at 25 °C. Then 2·5 ml of solution were
delivered into a UV cell (10 mm path). The cell was sealed
with a silicon-rubber stopper and placed in a cell compart-
ment maintained at 25 °C for another 15 min. Then 10 ␮l of
obs
+
be proportional to the substrate concentration ([XnOH])
app
(
r>0·997). The apparent second-order rate constant (k2 ) is
then obtained from the slope of kobs vs [XnOH]. The linear
0
·01
M
BNAH solution in acetonitrile were injected into the
+
plots of kobs vs [XnOH] for reductions of Xn with BNAH
cell.
and HEH at different temperatures are shown in Figure 1.
The pH-dependent pseudo-second-order rate constant
Immediately after thorough mixing of the reactants, the
changes in absorption at 358 nm vs time were recorded on
a Beckman DU-8B UV–VIS spectrophotometer. Pseudo-
first-order rate constants (kobs ) were calculated according to
Guggenheim’s method as described in the equations
(
k2 ) is defined by
d[BNAH]
+
Ϫ
=k [Xn ][BNAH]
2
dt
Ϫln(A ϪA )=kobst+C
(2)
(3)
t
t+⌬
Ϫln(At+⌬ ϪA )=kobst+C
+
t
[
H ][XnOH]
=
k2
[BNAH]
where A and A represent absorbances at time t and t+⌬
t
t+⌬
KR [H O]
+
2
(⌬ was generally 1—3 half-times), respectively. The data
app
were treated by linesar regression and the correlation
coefficients were always better than 0·999. The observed
rate constant (kobs) is the average of at least two independent
runs. In the case where the reaction rate was taken in the
presence of m-dinitrobenzene (DNB), a radical inhibitor,
=
k2 [XnOH][BNAH]
(5)
(6)
(7)
+
[H ]
app
k2 =k2
KR
+
[H O]
2
1
5 ␮L of DNB in acetonitrile solution (0·5 M), was injected
before BNAH was added.
Electrochemical measurements. A 5 ml volume of a
app
log k =log k2 ϪpKR +pH
+
2
16
Since pKR
exact second-order rate constant k2 cannot be directly
calculated, and therefore the k /K ratios for reduction of
+
in 30% CH CN–70% H O is unknown, the
3
2
+
2
m solution of a substrate (i.e. BNAH, AcrH , BNA or
2
+
M
AcrH ) in 0·1
M
Bu NPF –DMSO was placed in an
4 6
R+
2
+
electrochemical cell under argon. The solution was bubbled
with a small stream of argon both before and throughout the
whole process. The cyclic voltagram (CV) was recorded at
Xn by BNAH and by its 4,4Ј-dideuterated analogue
(BNAH-d ) together with the apparent rate constant k2 are
app
2
presented in Table 1. The relative rate measured in the
presence of a radical inhibitor (m-dinitrobenzene, DNB) is
also given.
Ϫ1
a sweep rate of 0·1 V s on a BAS-100B electrochemical
analyzer (Bioanalytical Systems, West Lafayette, IN, USA)
equipped with a three-electrode assembly. The working
electrode was a platinum disk (diameter 1 mm) and the
app
The apparent rate constants (k2 ) and the relative rate
constants (k /KR+ ) of reductions of xanthylium ion by
2
reference electrode was 0·1
M
AgNO /Ag prepared in 0·1
M
BNAH, HEH and AcrH measured at different temperatures
3
2
Bu NPF –DMSO solution. The counter electrode was a
and the activation parameters calculated from the Erying
slope and intercept [equation (8)] (r>0·995) jointly with
4
6
Ϫ
platinum wire. The AcrH anion was generated in DMSO
1997 by John Wiley & Sons, Ltd.
©
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

5
80
J.-P. CHENG AND Y. LU
+
Figure 1. Linear correlations of kobs vs [XnOH] in the reductions of Xn by BNAH (0·04 m
M) (left) and HEH (0·04 m
M) (right) at 25, 33, 40
and 48 °C
equation (7) are summarized in Table 2.
Thermodynamics
All the thermodynamic data were obtained at 25 °C in
DMSO. Free energy changes for each individual primary
steps for the e –H –e mechanism in Scheme 1 were
estimated using the equations
-
-
k2
T
⌬H 1 ⌬S
k
B
Ϫ
+
Ϫ
ln
=Ϫ
+
+ln
(8)
ͩ
ͪ ͩ ͪ
R T
R
h
Ϫ
+
•
+•
Table 1. Relative second-order rate constants for the reduction of
⌬G(e )=ϪF⌬E[(A /A )Ϫ(NAD(P)H /NAD(P)H)] (9)
T
+
a
Xn by BNAH
+
T
+•
+•
⌬
G(H )=2·303RT[pK(NAD(P)H )ϪpK(AH )] (10)
app
Ϫ1 Ϫ1
Ϫ1 Ϫ1
H
D
2
Model
BNAH
k2
(
M
s
)
k2/KR
+
(
M
s
)
k /k
2
Ϫ
T
+•
+
•
⌬
G(e )Ј=ϪF⌬E[(AH /AH)Ϫ(NAD(P) /NAD(P) )](11)
6
1·12
0·795
1·19
8·9ϫ106
6·3ϫ10
BNAH-d2
1·4
+•
+•
6
where
E(BNAH /BNAH),
•
E(AcrH /AcrH )
and
BNAH+DNB
9·4 ϫ10
2
2
5
+
E(XnH /XnH) are the oxidation potentials of BNAH,
AcrH2 and XnH, respectively and E(BNA /BNA ),
a
+
•
In 30% CH
3
CN–70% H
2
O, pH=6·90 and an ionic strength of 1·0 at 25 °C.
Ϫ1 Ϫ1
Ϫ1 Ϫ1
Table 2. Apparent second-order rate constants (
M
s
) and relative rate constants (
M
s
)
+
at different temperatures and activation parameters of the reductions of Xn by NAD(P)H
models
a
a
b
BNAH
HEH
AcrH2
app
app
app
Temperature (K)
k2
k2/KR
+
k2
k2/KR
+
k2
k2 /KR
+
6
7
7
7
7
3
3
4
4
2
3
3
3
98·15
06·15
13·15
21·15
1·12
1·58
2·02
3·09
8·9ϫ107
1·3ϫ107
1·6ϫ107
2·5ϫ10
1·39
2·08
3·37
4·54
1·1ϫ10
1·7ϫ10
2·7ϫ10
3·6ϫ10
0·507
0·878
1·32
5·1ϫ10
8·8ϫ10
1·3ϫ10
2·4ϫ10
2·39
-
Ϫ1
⌬
⌬
H
S
(kcal mol
(cal mol
)
Ϫ1
7·6
9·4
5·2–4·6pKR
12·0
Ϫ1·3–4·6pKR
-
Ϫ1
K
)
Ϫ1·3–4·6pKR
+
+
+
a
In 30% CH
In 30% CH
3
CN–70% H O at pH=6·90 and an ionic strength of 1·0.
2
CN–70% H O at pH=4·00 and an ionic strength of 1·0.
2
b
3
©
1997 by John Wiley & Sons, Ltd.
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

REDUCTION OF CARBENIUM IONS BY NAD(P)H ANALOGUES
581
+
•
+
•
•
+
Ϫ
T
E(AcrH /AcrH ) and E(Xn /Xn ) are the reduction poten-
⌬G(H )=⌬G(H )+⌬G(e )Ј
(14)
(15)
T
T
+
+
+
tials of BNA , AcrH , and Xn , respectively. The acid
dissociation constants of radical cations, i.e. pK(XnH ) and
pK(AcrH ), were obtained from a combination of pK(AH)
and oxidation potentials of the neutral molecule [E (AH)]
Ϫ
Ϫ
+
Ϫ
+
•
⌬G(H )⌬G(e )+⌬G(H )+⌬G(e )Ј
T T T T
+
2
•
The basic data necessary for calculating the thermodynamic
quantities of each primary mechanistic step and the free
energy terms thus derived are listed in Tables 3 and 4,
respectively.
ox
Ϫ
and its conjugated base [E (A )] using the equation
ox
+
•
Ϫ
pK(AH )=pK(AH)+F[E (A )ϪE (AH)]/2·303RT (12)
ox
ox
16, 18–20
where AH represents substrate AcrH or XnH.
The
2
DISCUSSION
acidity of radical cation derived from BNAH, i.e.
pK(BNAH ), was estimated from the equation
+
•
+
Mechanism of the reduction of Xn by BNAH
+
•
+•
pK(BNAH )=[⌬G -FE(BNAH /BNAH)
BDE
+
•
+
FE(H /H )]/2.303RT
(13)
Examination of the data in Table 1 shows that there is
essentially no primary kinetic isotope effect (k /k =1·4) in
H
D
2
2
+
using a thermodynamic cycle as shown in Scheme 2. In
the reduction of Xn by BNAH. This implies that electron
+
equation (13), ⌬GBDE is the free energy change of C–H bond
transfer from BNAH to Xn must be the rate-determining
+
•
fission at the 4-position of BNAH and E(H /H ) and
step.- The small activation enthalpy of reduction
+
•
•
Ϫ1
E(BNAH /BNAH) are the oxidation potentials of H and
BNAH, respectively.
(⌬H =7·6 kcal mol in Table 2) also indicates that the C–
H bond fission at the 4-position of BNAH should not be
much involved in the transition state. This mechanistic
analysis can be further examined by comparing the free
energy changes (driving forces) of each individual step for
every possible mechanism (Scheme 1) of this reduction.
From Table 4, it is conceivable that there are two feasible
Free energy changes of hydrogen atom transfer for the
Ϫ
•
e –H mechanism and the direct one-step mechanism can
be evaluated from equations (14) and (15), respectively,
based on the thermodynamic cycles shown in Scheme 1.
Ϫ
•
Ϫ
candidates (i.e. the e –H and H pathways) among the
three reaction mechanisms listed for the reaction to proceed
if based solely on the thermodynamic driving forces. The
•
•
BNAH → BNA +H
⌬GBDE
•
+
Ϫ
Ϫ
+
•
H → H +e
FE(H /H )
ϪFE(BNAH /BNAH)
Ϫ
T
+
T
two consecutive endothermic reactions (i.e. e and H ) in
+
•
+•
BNAH +e → BNAH
Ϫ
+
Ϫ
the e –H –e multi-step hydride transfer mechanism
make this route the least possible one for the reaction to
choose. Further, since both the kinetic isotope experiment
and the activation enthalpy value obtained in this work
+
•
•
+
+•
BNAH → BNA +H
2·303RTpK(BNAH )
Scheme 2
Table 3. Acid dissociation constants of neutral substrates [pK(AH)] and
+
•
the corresponding radical cations [pK(AH )] and redox potentials of the
relevant species in DMSO at 25 °C
Compound
Ϫ
a
a
+
a
+•
(AH)
pK(AH)
E (A )
E (AH)
ox
E (A )
pK(AH )
ox
rd
b
c
BNAHb
AcrH2
XnH
0·182
0·497
1·135
1·215
1·415
Ϫ1·528
Ϫ0·876
Ϫ0·293
Ϫ0·366
Ϫ0·257
Ϫ8
d
e
f
31·5
Ϫ1·961
Ϫ1·685
Ϫ1·531
Ϫ1·486
Ϫ10
g
30·0
27·9
30·6
Ϫ18
Ϫ18
Ϫ18
g
9
-PhXnH
g
Ph CH
3
a
b
c
p
+
E
values in volts referenced to the ferrocenium/ferrocene (Fc /Fc) couple.
This work.
+•
+
•
Calculated from equation (13), where ⌬GBDE , E(BNAH /BNAH) and E(H /H )
Ϫ1
were taken as 263 kJ mol (estimated from known values of structurally similar
molecules;
Table 3 adjusted to vs NHE by adding 0·537 V) and Ϫ2·48 V (vs NHE),
16, 18–20
Ϫ1
the error is probably within ±10 kJ mol ), 0·72 V (value from
21
respectively.
d
Estimated value based on the pK
Appeared as a shoulder.
Calculated from equation (12).
a
s of similar structures.
e
f
g
+
From Refs 19 and 22; values were adjusted to vs Fc /Fc (from a value vs NHE by
subtracting 0·537 V when necessary).
©
1997 by John Wiley & Sons, Ltd. JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

5
82
J.-P. CHENG AND Y. LU
Ϫ1
Table 4. Free energy changes (kcal mol ) of each mechanistic steps for various hydride
a
transfer mechanisms shown in Scheme 1
Mechanism
Ϫ
+
Ϫ
Ϫ
•
Ϫ
e –H –e
e –H
H
Ϫ
+
T
Ϫ
Ϫ
•
Ϫ
Model/substance
⌬G(eT
)
⌬G(H ) ⌬G(eT )Ј
⌬G(eT
)
⌬G(H ) ⌬G(HT )
T
+
BNAH/Xn
11·0
18·2
12·6
10·1
13·7
11·0
13·7
13·7
Ϫ61·4
Ϫ46·4
Ϫ63·3
Ϫ67·9
11·0
18·2
12·6
10·1
Ϫ47·7
Ϫ35·4
Ϫ49·6
Ϫ54·2
Ϫ36·7
Ϫ17·2
Ϫ37·0
Ϫ44·1
+
AcrH /Xn
2
+
BNAH/9-PhXn
+
BNAH/Ph C
3
a
All values are derived in DMSO at 25 °C using equations (9)–(11), (14) and (15).
Ϫ
T
appeared to disfavor the one-step hydride transfer (i.e. H )
similarly derived can only be considered as the rate
maxima. This is because the proton, a product in the
equilibrium depicted in equation (4), is better solvated by
Ϫ
•
mechanism, the e –H two-step hydride transfer can thus
+
be assigned as the mechanism for the reduction of Xn
cation by BNAH.
H O than by MeCN, and this will shift the equilibrium to the
2
The observation that the rate of reduction remains
virtually unchanged in the presence of a radical inhibitor
left in the case where a mixed solvent is used and thus lead
to a substantial deduction of the apparent KR
+
. Hence the KR
+
(
see entry 3 in Table 1) seems at first glance to conflict with
value in neat water is at its maximum and so is k in water.
2
-
the radical mechanism mentioned above. However, it is
generally understood that if the radical formed is too
unstable to escape from the solvent cage or, in other words,
the follow-up reaction within the cage is too fast to allow
the incipient radical to move out of the solvent cage, the
absence of the ESR signal or radical inhibitor effect could
not then be taken as a criterion to exclude the radical
mechanism. In fact, the follow-up hydrogen atom transfer
On the other hand, ⌬S of this reaction should not exceed
2·3 e.u. (derived assuming pKR =Ϫ0·83) for the same
+
reason.
Based on the considerations discussed above, the mecha-
nism of the reduction of xanthylium ion by BNAH can be
proposed as the following sequence, i.e. (i) a fast pre-
+
equilibrium between BNAH and Xn , (ii)
a
rate-determining electron transfer within an encounter
•
T
Ϫ
•
+•
•
(
H ) in the e –H mechanism is indeed evaluated as
complex leading to BNAH and Xn and (iii) a fast
+• •
•
T
Ϫ1
extremely exothermic [⌬G(H )=Ϫ47·7 kcal mol ], and
therefore it is conceivable that there should be no chance for
the DNB molecule to trap either the Xn radical or the
hydrogen atom transfer from BNAH to Xn to form the
+
final products BNA and XnH. The mechanism is illus-
•
trated in Scheme 3.
+
•
BNAH radical cation before a hydrogen atom is trans-
ferred within the encounter complex. In other words, the
multi-step mechanism does not necessarily mean that the
hydrogen transfer in the e –H mechanism is completely
separated from the initial electron transfer, i.e. the barrier
for the electron transfer is possibly overlapped with the
follow-up hydrogen transfer in the reaction coordinate.
Hence the DNB molecule could not serve as a radical
trapper in such circumstances.
+
Reduction of Xn by HEH and AcrH2
Ϫ
•
+
Similarly to the situation for the reduction of Xn by
BNAH, the largely exothermic hydrogen atom transfer
•
T
Ϫ1
[⌬G(H )=Ϫ35·4 kcal mol in Table 4] can also initiate an
endothermic electron transfer to occur in the reduction of
+
Ϫ
•
Xn by AcrH . Hence the two-step e –H mechanism is
2
also applied, although in this case the relative second-order
3
Ϫ1 Ϫ1
As mentioned previously (Results section), since that the
rate constant (k /KR+ =5·1ϫ10
M
s
at 25 °C) derived
2
pKR
7
+
value in the present working solvent (30% CH CN–
from equation (6) is over 1000 times smaller than that of
3
6
Ϫ1 Ϫ1
0% H O) is unknown, the second-order rate constant of the
BNAH (k /KR+ =8·9ϫ10
M
s ), due primarily to the
2
2
reduction can only be derived in a relative form as k /KR
+
difference of their oxidation potentials (E =0·182 and
2
ox
(
Table 1). However, if we assume that the pK here is the
R+
0·497 V, respectively; Table 3). The difference in the
22a
7
Ϫ1 Ϫ1
same as that in water (Ϫ0·83 ), then k =6·0ϫ10
can be immediately evaluated from equation (7) for
reduction of Xn by BNAH, which agrees well with that
M
s
electron-donating abilities of AcrH and BNAH can also be
2
2
Ϫ1
reflected kinetically by the 4·4 kcal mol difference in their
+
-
Ϫ1
activation enthalpies (⌬H =12·0 vs 7·6 kcal mol in Table
2), since the activation entropies of these two reactions are
almost identical. On the other hand, it is interesting that the
Hantzsch ester (HEH), a reductant of similar electron-
17
previously
reported
s
by
Bunting
and
Conn
7
Ϫ1 Ϫ1
(5·9ϫ10
M
). It should be pointed out that there is an
unknown amount of uncertainty associated with this k2
value due to the change of the solvent (we are grateful to a
referee for bringing this to our attention), and therefore the
23
donating ability to AcrH2 (E =0·446 V and 0·497 V,
ox
respectively), actually reacts much faster than the latter (see
Table 2). The reduction rates by HEH are even faster than
7
Ϫ1 Ϫ1
k2 of 6·0ϫ10
M
s
and also all other literature rate data
©
1997 by John Wiley & Sons, Ltd.
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

REDUCTION OF CARBENIUM IONS BY NAD(P)H ANALOGUES
583
Scheme 3
25
those by BNAH for all the temperatures examined (Table
). This may seem surprising if only the thermodynamic
energy (␭)Ј in the Marcus equation, although the latter
term certainly covers a much wider range of applications
and deserves much more detailed theoretical considera-
tions.
2
driving force (i.e. E ) is considered to affect the reaction,
ox
because HEH is actually a poorer electron donor than
BNAH (E =0·446 and 0·182 V, respectively). From the
ox
activation parameters in Table 2, one can immediately see
that the entropy of activation of HEH is 6·5 e.u. less
+
Reductions of 9-phenylxanthylium (9-PhXn ) and trityl
+
-
cations (Ph C ) by BNAH
negative (⌬S =5·2–4·6 pK ) than those of the other two
R+
3
-
models (⌬S =Ϫ1·3–4·6 pKR+ ). Hence the smaller entropy
Examination of entries 3 and 4 in Table 4 reveals that the
free energy changes of each individual steps in every
loss for the former reaction must be a cause of its higher
rate. On the other hand, another point worth mentioning is
that the difference in the activation enthalpies between HEH
+
+
possible mechanism for reductions of 9-PhXn and Ph C
3
-
Ϫ1
by BNAH have a similar pattern to those observed in the
reduction of Xn by BNAH. This implies that the apparent
hydride transfer in these two reductions is again initiated by
a rate-determining electron transfer followed by a fast
hydrogen atom abstraction. The failure to obtain a deut-
erated product (i.e. 9-PhXnD or Ph CD) upon addition of
deuterated trifluoroacetic acid (CF COOD) to the reaction
system indicates that the hydrogen transfer may not be fully
separated from the initial electron transfer, a situation
similar to that described earlier for the reduction of Xn by
and BNAH (⌬⌬H =1·8 kcal mol ) is notably smaller than
the difference in their oxidation potentials
⌬E =0·264 V=6·1 kcal mol ). In other words, the
+
Ϫ1
(
ox
energy gap between these two model compounds on going
+
•
from the neutral molecule to its oxidized form (i.e. HEH
+
•
3
and BNAH ) is attenuated in the T.S. compared with its
initial state. The cause of the gap attenuation is most likely
3
+
the enhanced electrostatic association of HEH with Xn
(presumably through the carbonyl group) within the
+
encounter complex compared with that with BNAH, since
HEH bears two linker groups (i.e. carbonyl) whereas BNAH
has only one. This type of electrostatic interaction has
already been proposed previously by others based on
the same model compound. This also explains why the
kinetics of the reduction of Ph C with BNAH do not
+
3
26
change in the presence of oxygen.
24
quantum mechanical calculations and should contribute in
part, together with the above-mentioned favorable entropy
of activation for HEH, to the reversion of the order of their
thermodynamic driving forces (BNAH>HEH) to the
CONCLUSION
Kinetic quantities such as rate constants, activation parame-
ters and isotope effects for the NAD(P)H model-mediated
reductions of some carbenium ions were investigated. The
thermodynamic driving forces (i.e. Gibbs free energy
changes) of every mechanistically possible primary step for
the overall hydride transfer reactions were derived. The
results suggest that all the apparent hydride transfer
reactions studied here are possibly initiated by a rate-
limiting electron transfer followed by a very fast hydrogen
atom transfer. The molecular binding forces within the
observed order of reactivity (HEH>BNAH). In the cases
+
when no linker group exists (e.g. AcrH /Xn ), the ␲–␲
2
interaction may contribute most to stabilization of the T.S.,
11
which is similar to the situation reported in the literature.
According to these analyses, the encounter complex formed
prior to the rate-determining electron transfer must be
11
productive rather than non-productive.
From the above discussions, it now becomes clear that
the thermodynamic driving force is not often the only factor
influencing the kinetics and, as in the case of the present
study, the entropy effect and the electrostatic interaction in
the T.S. may play an important role in relating the
thermodynamic quantities with kinetic behavior. We think
that it is very likely for the NAD(P)H-type reductions that
the above-mentioned two types of effects may in some
sense be related to the well known term ‘reorganization
+
encounter complex of HEH/Xn , which presumably origi-
nated from the electrostatic association between the two
reactants through a carbonyl linkage, together with its
favorable activation entropy, may be responsible for
reverting the order of the thermodynamic driving forces
(BNAH>HEH) to the observed order of reactivity
(HEH>BNAH).
©
1997 by John Wiley & Sons, Ltd.
JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, VOL. 10, 577–584 (1997)

5
84
J.-P. CHENG AND Y. LU
4211–4219 (1981).
ACKNOWLEDGMENT
1
2. R. M. G. Roberts, D. Ostovic and M. M. Kreevoy, J. Org.
Chem. 48, 2053–2056 (1983).
This research was made possible by a grant from the Natural
Science Foundation of China (NSFC), to whom the authors
express their sincere gratitude.
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