Primary kinetic isotope effects on hydride transfer from 1,3-dimethyl-2-phenylbenzimidazoline to NAD+ analogues

Article abstract of DOI:10.1021/ja004232+

Primary kinetic isotope effects (KIE) have been determined spectrophotometrically for the reaction of NAD⁺ analogues (pyridinium, quinolinium, phenanthridinium, and acridinium ions) with 1,3-dimethyl-2-phenylbenzimidazoline in a 4:1 mixture of

Full text of DOI:10.1021/ja004232+

7492
J. Am. Chem. Soc. 2001, 123, 7492-7496
Primary Kinetic Isotope Effects on Hydride Transfer from
1,3-Dimethyl-2-phenylbenzimidazoline to NAD+ Analogues
In-Sook Han Lee,*,† Eun Hee Jeoung,† and Maurice M. Kreevoy*,‡
Contribution from the Department of Science Education, Kangwon National UniVersity,
Chuncheon 200-701, Korea, and Department of Chemistry, UniVersity of Minnesota,
Minneapolis, Minnesota 55455-0431
ReceiVed December 11, 2000
Abstract: Primary kinetic isotope effects (KIE) have been determined spectrophotometrically for the reaction
of NAD+ analogues (pyridinium, quinolinium, phenanthridinium, and acridinium ions) with 1,3-dimethyl-2-
phenylbenzimidazoline in a 4:1 mixture of 2-propanol and water by volume at 25 °C. The values of KIE
varied systematically from 6.27 to 4.06 as the equilibrium constant changed from around 10 to around 1012.
This is consistent with Marcus theory of atom transfer, assuming that there are no high-energy intermediates.
Within this theory, the perpendicular effect is responsible for most of the change in KIE. The Marcus theory
of atom transfer is consistent with a linear, triatomic model of the reaction. Perpendicular effects arise from
the systematic decrease of bond distances and increase of bond orders in the critical complexes of the two
related degenerate hydride transfer reactions as their C-H bonds become stronger. The parallel effect (Leffler-
Hammond effect) is attenuated by the fairly high intrinsic barrier (λ/4 is around 92 kJ/mol) and makes a
smaller contribution to the change in the KIE.
Introduction
essential requirement for the applicability of Marcus theory is
that the reactants and products should be structurally similar,
so that the potential surface has the same general shape on either
side of the ridge.6 Reactions in which hydride is transferred
from one carbon to another meet this requirement, and Marcus
theory gives a very good approximation of the change in the
Gibbs free energy of activation, ∆G*, with the change in the
overall Gibbs free energy of reaction, ∆G°.7-9
Kinetic isotope effects, especially primary kinetic hydrogen
isotope effects (KIE), are among the simplest and most direct
manifestation of the quantum nature of matter. Within the
Born-Oppenheimer approximation isotopic replacement does
not affect the potential energy surface of the molecule nor does
it perturb the electronic energy levels. Only molecular vibrations,
rotations, and translations change. Mainly it is changes in
vibrations which change reaction rate and which carry mecha-
nistic information.1,2
Marcus theory is summarized in eqs 2 and 3 for a one-step
reaction of the type shown in eq 1
Ai+ + AjX f AiX + Aj+
(1)
An expression for the relation between primary kinetic
hydrogen isotope effect and equilibrium constant, K, comes out
of the Marcus theory of atom transfer.3 The Marcus theory4 is
consistent with a linear, triatomic model of an atom transfer
reaction.5 This model provides an approximate but quantitative
potential energy surface for the reaction, in which the ridge
separating reactants from products changes systematically as
the strength of the donor and acceptor bonds changes.5 The most
∆G* ) Wr + (1 + ∆G°/λ)2‚λ/4
λ ) (λi + λj)/2
(2)
(3)
The subscripts i and j indicate the hydride acceptor and donor,
respectively. In the absence of a subscript the subscript ij can
be inferred. Wr was originally regarded as the free energy
required to form a metastable “encounter complex”3,4 or
“reaction complex”10,11 from the separated reactants. In fact, it
appears to represent only that part of ∆G* which is insensitive
to the value of ∆G°.5 Nonzero values of Wr were required to fit
computed rate constants to Marcus theory, even though the
potential energy surfaces from which they were calculated had
† Kangwon National University.
‡ University of Minnesota.
(1) Melander, L.; Saunders, W. H, Reaction Rates of Isotopic Molecules;
Wiley: New York, 1980; pp 152-154.
(2) (a) Westheimer, F. H. Chem. ReV. 1961, 61, 265-273. (b) Bunton,
C. A.; Shiner, V. J. J. Am. Chem. Soc. 1961, 83, 3214-3220. (c) Albery,
W. J. Trans. Faraday Soc. 1967, 63, 200-206. (d) Kreevoy, M. M. In
Isotopes in Organic Chemistry; Buncel, E., Lee, C. C., Eds; Elsevier: New
York, 1976; Vol. 2, pp 1-31. (e) Tucker, S. C.; Truhlar, D. G. In New
Theoretical Concepts for Understanding Organic Reactions; Berfran, J.,
Csizmadia, I. G., Eds.; Kluwer Academic Publishers: New York, 1989;
pp 299-346. (f) Duan, X.; Scheiner, S. J. Am. Chem. Soc. 1992, 114, 5849-
5856. (g) Benedict, H.; Limbach, H.-H.; Wehlan, M.; Fehlhammer, W.-P.;
Golubev, N. S.; Janoschek, R. J. Am. Chem. Soc. 1998, 120, 2939-2950.
(h) Kohen, A.; Klinman, J. P. Chem. Biol. 1999, 6, R191-R198. (i) The
foregoing is only a small sample for a very large literature.
(3) Marcus, R. A. J. Phys. Chem. 1968, 72. 891-899.
(6) Magnoli, D. E.; Murdoch, J. R. J. Am. Chem. Soc. 1981, 103, 7465-
7469.
(7) Kreevoy, M. M.; Ostovic´, D.; Lee, I.-S. H.; Binder, D. A.; King, G.
W. J. Am. Chem. Soc. 1988, 110, 524-530.
(8) Albery, W. J.; Kreevoy, M. M. AdV. Phys. Org. Chem. 1978, 16, 87.
(9) Lee, I.-S. H.; Jeoung, E. H.; Kreevoy, M. M. J. Am. Chem. Soc,
1997, 119, 2722-2728.
(10) Kreevoy, M. M.; Konasewich, D. E. AdV. Chem. Phys. 1971, 21,
243-252.
(11) Hassid, A. I.; Kreevoy, M. M.; Liang, T.-M. Symp. Faraday Soc.
1975, 10, 69-77.
(4) Marcus, R. A. Annu. ReV. Phys. Chem. 1964, 15, 155-196.
(5) Kim, Y.; Truhlar, D. G.; Kreevoy, M. M. J. Am. Chem. Soc. 1991,
113, 7837-7847.
10.1021/ja004232+ CCC: $20.00 © 2001 American Chemical Society
Published on Web 07/13/2001

Primary Kinetic Isotope Effects on Hydride Transfer
J. Am. Chem. Soc., Vol. 123, No. 31, 2001 7493
no metastable intermediates.5,12 Thus Wr is little more than an
adjustable parameter that enables this very simplified theory to
give a faithful account of the results. For reactions of the present
type Wr has been taken as -8 kJ/mol.5 We used this value for
the present work. λ/4 is called the intrinsic barrier. It is (∆G*
- Wr) for the reaction of this type in which ∆G° is zero. For
the nondegenerate reactions λ is the average of λ and λ , the
The reactions for which kii are the rate constants all have
equilibrium constants of unity. However, the kii vary systemati-
cally with the affinity of Ai+ for X- because twice the affinity
of Ai+ for X- in the critical configuration is, in general, different
than the affinity of Ai+ for X- in the reactant or product.
Equation 8 defines τ so that it will be zero if the critical
configuration is completely dissociative. In that case, if the
affinity of Ai+ for X- increases, as indicated by an increase in
i
j
values of 4(∆G* - Wr) for the two related degenerate reactions.
∆G° and ∆G* can be related to the equilibrium constant, K,
and the rate constant, k, through the standard thermodynamic
and quasithermodynamic expressions, shown in eqs 4 and 5.
o
Kij , then kii will decrease by the same factor, making d(ln kii)/
o
d(ln Kij ), in eq 8a, equal to -1, and giving τ the indicated
value, zero. If bond making and bond breaking are perfectly
coordinated, so that twice the affinity of Ai+ for X- in the critical
configuration is just equal to the affinity of Ai+or X- in the
reactant, then the derivative would have the value zero, and τ
would have the value +1. If X is divalent in the critical
K ) exp(-∆G°/RT)
(4)
(5)
k ) [kBT/h] exp(-∆G*/RT)
o
configuration (not possible if X is H), an increase in Kij will
From eqs 2-5 the Brønsted R can be derived in terms of the
Marcus parameters12,13 with the result shown in eqs 6-8.
lead to an equal increase in kii. In that case the derivative is
1.0, and τ has the value +2.
In nondegenerate reactions, the effect of changing K by
changing the affinity of the donor for X- is opposite, in some
respects, to the effect of an equal change in K, achieved by
changing the affinity of the acceptor. In a partially dissociative
reaction, if K is decreased by making the affinity of Aj+ for X-
stronger the reaction goes slower not only because ∆G° is more
positive but also because λ becomes larger. The Brønsted R is
increased by the increase in λ. However, if K is decreased by
reducing the affinity of Ai+ for X-, λ becomes smaller (eq 3),
making the decrease in rate smaller, and thus decreasing R. But
the change in τ is the same, because an increase in the affinity
of Aj+ for X- has the same effect on τ as a decrease in the
affinity of Ai+ for X- (eqs 8 and eqs 8 and 9 of ref 5). Hence
the choice of signs in eq 6 depends on the location of the
structural variation. The upper signs are used if structure is
varied in the acceptor, the lower signs are used if structure is
varied in the donor.
At least qualitatively, the critical configuration donor-
acceptor distance and the charge on the in-flight atom or group,
X, should be correlated with the value of τ. A large critical
configuration donor-acceptor distance leads to weak A+-X-
affinity in the critical configuration, a large partial negative
charge for X in the critical configuration, and a value of τ less
than unity. A value of τ near 1.0 implies that the in-flight X is
near-neutral.13,14 The distance in the critical configuration is only
a little more than twice the normal A-X. One of the virtues of
this treatment is that eqs 8 permit a quantitative, experimental
determination of τ, and thereby give insight into the charge
distribution and reactive bond distances in the critical config-
uration.
R ) ø ( 0.5(τ - 1) - 0.5(RT ln K/λ)2(τ - 1)
ø ) 0.5[1 - (RT ln K/λ)]
(6)
(7)
o
τ - 1 ) d(ln kii)/d(ln Kij )
(8a)
(8b)
o
-(τ - 1) ) d(ln kjj)/d(ln Kij )
The equilibrium constant for some member of the set is K and
the rate constant for a degenerate reaction Ai with AiX is kii.
Equations 7 and 8 define ø and τ, quantities which carry
information about the structure of the critical configuration13,14
and considerably simplify the form of eq 6.
The Leffler-Hammond parameter is ø. It is 0.5 when K is
unity. Since the general shape of the reactant valley and the
product valley in the potential surface is the same, a K value of
unity implies that the critical configuration equally resembles
the reactants and the products. As the reaction becomes more
spontaneous, and K becomes larger, the critical configuration
occurs closer to the reactant.15 This is indicated by a smaller
value of ø. The value of λ determines the sensitivity of ø to
changes in K. It has often been assumed that R has the physical
significance of ø.16 The two are only the same for the special
case that τ ) 1.0.
In a series of degenerate reactions of the type shown in eq 1
the rate constants, kii, will usually change systematically with
the affinity of A+ for X- even though all the equilibrium
constants are all unity.13,14 In Marcus theory this can be
accommodated by a systematic variation in λ with the affinity
of A+ for X-. The tightness parameter, τ, is designed to achieve
this. It is defined in eqs 8.13,14 The slope of a logarithmic plot
In the present case Aj-X is an NADH-like hydride donor,
and Ai+ is an NAD+-like hydride acceptor. The sum of the
hydride affinities of the donor and acceptor in the critical
configuration is less than the reactant hydride affinity, so τ is
o
of kii or kjj as a function of Kij determines τ. This is not a
Brønsted plot. The Kijo are equilibrium constants for the transfer
of X- from a standard donor to the various Ai+ or from the
various AjX to a standard acceptor. Ln Kijo is a measure of the
affinity of the various Ai+ for X-. The sign changes because
X- is transferred to the Ai+ from the standard donor, but from
the AjX to the standard acceptor.
o
less than unity. Kij is the equilibrium constant for hydride
o
transfer from a standard donor, Aj-H, to acceptors, Ai+. Kij
measures the strength of the Ai-H bond. For reasons of practical
convenience, 9,10-dihydro-10-methylacridine has been used as
the standard donor.7 A value somewhat less than unity was
found for τ.
(12) Kreevoy, M. M.; Ostovic´, D.; Truhler, D. G. J. Phys. Chem. 1986,
90, 3766-3774.
(13) Kreevoy, M. M.; Lee, I.-S. H. J. Am. Chem. Soc. 1984, 106, 2550-
Perpendicular effects on reactivity (τ * 1.0) are examples of
Bernasconi’s principle of nonperfect synchronicity, which
provides an evaluation of the transition state imbalance.17 The
formation of the new bonds is not perfectly coupled with the
2583.
(14) Lewis, E. S.; Hu, D. D. J. Am. Chem. Soc. 1984, 106, 3292-3296.
(15) (a) Leffler, J. E. Science 1953, 117, 340-341. (b) Hammond, G. S.
J. Am. Chem. Soc. 1955, 77, 334-338.
(16) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic
Chemistry, 3rd ed.; Harper and Row: New York, 1987; p 148.
(17) (a) Bernasconi, C. F. Acc. Chem. Res. 1992, 25, 9-16. (b)
Bernasconi, C. F. AdV. Phys. Org. Chem. 1992, 27, 119-238.

7494 J. Am. Chem. Soc., Vol. 123, No. 31, 2001
Han Lee et al.
breaking of the old bonds. Bernasconi’s treatment, however,
can be qualitatively related to ideas such as resonance and
solvation, which are widely used to systematize organic
chemistry. Williams has explored parallel and perpendicular
effects very effectively in a wide range of reactions by
measuring Brønsted parameters for the same reaction at a
number of sites.18 Both Williams and Bernasconi have reached
conclusions similar to ours.
garded as an NADH analogue.22 5H(D) was chosen as the
reducing agent for exploring the primary kinetic isotope effects
because it is powerful and regioselective and has only one
equivalent hydrogen for efficient reduction.19 (It should be noted,
however, that the reduction potential of 5H has been greatly
overestimated in a previous paper.24)
Since the lowest allowed vibrational energy of a deuterium
compound is less than the lowest allowed vibrational energy of
the corresponding hydrogen compound, and these vibrational
energies are proportionately reduced when the critical config-
uration is formed,1 it is clear that λH, for hydride transfer, should
generally be smaller than λD, for deuteride transfer. Less
obviously, τH and τD are also probably different. In the minimum
energy path for hydride transfer the Ai-Aj distance is com-
pressed. Then the hydride (or deuteride) transfer occurs by
tunneling. The most probable Ai-Aj distance for tunneling is
larger than that in the classical transition state, saving compres-
sion energy.19 Because of the greater mass of deuterium,
deuteride tunneling occurs at an Ai-Aj distance smaller than
the hydride transfer distance.12,19 Since τ is inversely correlated
with the donor-acceptor distance, τH is less than τD. That is,
hydride transfer is more dissociative than deutride transfer.
Since the Brønsted R is a function of λ and τ, and both of
these are expected to change on isotopic substitution of the in-
flight hydrogen, separate Brønsted relations are expected for
hydride and deuteride transfer. These are shown in eqs 9 and
10. When ln kD is subtracted from ln kH and appropriate
substitution is made for τ, eq 11 is obtained. The KIE is kH/kD.
Rate constants and KIE for the special case that K is unity are
superscripted with zero. In deriving eq 11, the isotopic sensitivity
of ø, arising from the isotopic sensitivity of λ, has been neglected
because it has a negligible effect on the ln KIE values which
this paper will report. The novel aspect of eq 11 is the second
term on the right-hand side, which represents the perpendicular
effect on ln KIE, and is linear in ln K. As a result, the common
belief that ln KIE should be a bell shaped function of ln K,
with a maximum at K ) 1.0, is challenged.20,21
Experimental Section
Compounds 1-3 are well-known substances which were prepared
by benzylation using benzyl bromide of the corresponding bases. The
compounds were identified by their physical and spectroscopic proper-
ties.25 Compounds 4a-c were also prepared by methods that have been
previously described.26 Their melting points and spectroscopic properties
agreed with previously reported values.25 The perchlorate of 4a was
prepared by ion-exchange reaction of the corresponding iodide, using
an excess of NaClO4. Acridine was methylated with methyl iodide to
get the iodide of 4a. Compound 5H was prepared by the method of
Craig et al.27 with a slight, previously described modification.9
Compound 5D was prepared by the same method as 5H except using
NaBD4 instead of NaBH4 for reduction. The yield was 90%. This
preparation had 2-6% of contamination with the corresponding hydride
compound, 5H, as determined by its 1H NMR spectrum. It was purified
by sacrificial oxidation with p-chloranil. p-Chloranil (0.1 g, 0.4 mmol)
was partially dissolved in ether (30 mL) and added to the solution of
0.5 g (2.2 mmol) of 5D in ether (30 mL) slowly, with stirring. Reaction
began immediately, to give a dirty yellow precipitate. The stirring was
continued for 30 min. The solvent of the filterate was allowed to
evaporate from the unreacted 5D. The residual was recrystallized twice
from EtOH-H2O (6:1, v/v) to give ivory-colored crystals in 50% yield.
ln kH ) ln kH° + RH ln K
ln kD ) ln kD° + RD ln K
(9)
(10)
ln KIE ) ln KIE° (
0.5 ln[K(τ H - τ D)] - 0.5RT(ln K)2(1/λ H -1/λ D) (11)
1
There was no detectable signal for 5H in the H NMR (500 MHz)
The rate constant is k° when K ) 1, and (ln kHo - ln kDo) is
ln KIE°. In eq 11 (τ H - τ D) should be negative because τ H is
smaller than τ D, which means that the donor-acceptor distance
is larger for H than for D in their critical configurations. In the
Marcus formalism, shown in eq 11, the second term on the right-
hand side corresponds to the perpendicular effect while the last
term corresponds to the parallel effect.
In the present paper we report the primary kinetic hydrogen
isotope effect for the reactions of NAD+ (nicotinamide adenine
dinucleotide) analogues such as pyridinium (1), quinolinium (2),
phenanthridinium (3), and acridinium ions (4a-c), with 1,3-
dimethyl-2-phenylbenzimidazoline (5H(D)), which is also re-
spectrum of 5D. We estimated from this that the isotopic purity of 5D
was >99%. Its melting point was identical with that of 5H (mp 93-4
°C).9 The deuterium content of 5D was confirmed by comparison of a
mass spectrum of 5D with that of 5H, employing the electron impact
ionization technique and introduction via a direct insertion probe inlet
system.
5H m/z (%): 224 (M+, 56), 223 (M+ - H, 58), 147 (M+ - C6H5,
100), 132 (M+ - C6H5 and CH3, 14%).
(22) Tanner, D. D.; Chen, J. J. J. Org. Chem. 1989, 54, 3842-3846.
(23) Chikashita, H.; Ide, H.; Itoh, K. J. Org. Chem. 1986, 51, 5400-
5405.
(24) Timofeeva, Z. N.; El’tsov, A. V. Zh. Obshch. Khim. 1967, 37, 2599-
2602.
(18) Williams, A. AdV. Phys. Org. Chem. 1992, 27, 1-55.
(19) Kim, Y.; Kreevoy, M. M. J. Am. Chem. Soc. 1992, 114, 7116-
7123.
(25) Robert, R. M. G.; Ostovic´, D.; Kreevoy, M. M. Faraday Discuss.
Chem. Soc. 1982, 74, 257-265.
(26) Kreevoy, M. M.; Lee, I.-S. H. Z. Naturforsch. 1989, 44a, 418-
426.
(20) Reference 1, p 134.
(21) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: New
York, 1980; pp 98-105.
(27) Craig, J. C.; Ekwuribe, N. N.; Fu, C. C.; Walker, K. A. M. Synthesis
1981, 303-305.

Primary Kinetic Isotope Effects on Hydride Transfer
J. Am. Chem. Soc., Vol. 123, No. 31, 2001 7495
Table 1. Rate, Equilibrium Constants, KIE, Perpendicular Effect (A), Parallel Effect (B), and λH for Hydride Transfer Reactions
oxidant
kH(M-1 s-1
)
Kb
KIE(exptl)
Ac
Bc
λH (kJ/mol)
1
2
3
4a
4b
4c
(1.85 ( 0.05) × 10-3
(2.08 ( 0.09) × 102
1.13 ( 0.06
36a
6.27 ( 0.31
4.18 ( 0.33
5.05 ( 0.35
3.95 ( 0.32
4.44 ( 0.26
4.05 ( 0.32
0.04
0.36
0.18
0.32
0.31
0.37
0.00
0.11
0.03
0.09
0.08
0.11
406
402
392
385
458
473
2.73 × 1012a
1.78 × 106a
1.23 × 1011a
7.81 × 1010
6.35 × 1012
(2.94 ( 0.12) × 102
(1.92 ( 0.07) × 10-1
(7.43 ( 0.59) × 10-1
a Values are obtained from ref 9. b Determined by the ladder procedure. (The estimated uncertainty is 10-25%.)30 c Absolute values are obtained
from eq 11 (A is the second term and B is the third term on the right-hand side in the equation). The estimated error for A is less than 3% and that
for B is less than 10% due to the estimated uncertainty of K.
5D m/z (%): 225 (M+, 70), 223 (M+ - D, 41), 148 (M+ - C6H5,
100), 133 (M+ - C6H5 and CH3, 24%). Mass 224 was less than 1%
after correction for the 13C satellite from 223.
1 with 5H and for 4b and 4c with 2H.26 Values of K for reaction
of 1 with 2H are known.9
In the Marcus formalism λH and λD can be obtained from eq
2 with the value of -8 kJ/mol for Wr and rate constants and
equilibrium constants leading to ∆G*and ∆G° using eqs 4 and
5, respectively. The values of λH are given in Table 1. λH and
λD for 4c should be similar to those for 4b, and they are.
Measurement. Rate constants, k, were all measured spectrophoto-
metrically in a solvent containing 4 parts of 2-propanol to one part of
water by volume at 25 ( 0.2 °C. For slow (1) and moderate (3, 4b,c)
reactions a conventional spectrophotometer was used and isotope effects
were determined by simultaneous measurement of kH and kD, to
minimize errors due to temperature fluctuation. For fast reactions (2,
4a) which have a half-life less than 10 s, kobs values were measured
with a stopped-flow apparatus (Hi-Tech scientific SFA-20) which was
attached to the spectrophotometer (Beckman DU-7500). When the
stopped-flow apparatus was used, scatter due to temperature fluctuation
was not avoidable, since simultaneous measurement was not possible.
This makes individual rate constants less reliable. To compensate, kH
and kD were each measured more than 20 times and average values
were used to get KIE values. All kinetic experiments were carried out
with a 25-100-fold excess of the spectroscopically inactive constituent.
In all cases reactions proceeded very close to completion. Therefore,
the rate law for a pseudo-first-order reaction was used, as shown in eq
12.28 In the case of very slow reactions (1 with 5D) At was estimated
from measured At values by using a standard computer program.26
Marcus theory predicts that the effect of a change in K and
the KIE depends on which reactant is altered to change K. Since
(τH - τD) is expected to be negative,5,12 an increase in K
produced by altering the acceptor is expected to reduce the KIE
more than a similar change in K produced by altering the donor.
To increase K by altering the acceptor, its bond to the hydride
must be made stronger, in the critical configuration as well as
in the product. This tends to partially offset the loss of binding
to the donor, in forming the critical configuration. Therefore,
the KIE is reduced. The converse is true if K is increased by
altering the donor.5,12,16 This is a major source of the scatter
observed when the KIE is plotted against ∆pK, without regard
for the location of the structure change.20
kobs ) t-1 ln[(Ao - A∞)/(At - A∞)]
(12)
We can obtain (τH - τD) by plotting ln KIE + [0.5RT/(ln
K)2](1/λH - 1/λD) against ln K, using KIE values obtained by
altering only one of the reactants. Such a plot should be linear,
with a slope of (0.5(τH - τD): the positive sign for structure
variation in Ai, and the negative sign for structure variation in
AjX. The plot is shown in Figure 1. It is acceptably linear, and
negative, as expected. The slope is -0.013 ( 0.002 (r ) 0.952).
τH - τD is -0.025. The kinetic isotope effect for the reaction
of a series of quinolinium compounds (2) with dihydrophenan-
thridine (3H), has been previously reported.12 Those KIE data
are also shown in Figure 1. The structure is altered in the
acceptor, and the slope of the plot is -0.011 with a probable
error of 0.001. Within experimental error the two slopes are
the same, as expected. The intercepts would be expected to be
different, but accidently, they are essentially the same.
The second-order rate constant, k2, was obtained from kobs divided by
the concentration of the excess substrate.
For the reactions of 1 with 5H, the compound 1 was used in excess.
The growth of 1H was monitored at 360 nm. 2 was also used in excess
for reactions with 5H, but the growth of 5 was monitored at 280 nm.
The solution of 2 was made acidic using 4.5 × 10-3 M HClO4 solution
to give the reaction mixture a pH of 3.4, to prevent hydroxylation of
2. 5H was stable enough at this pH for the period of the measurement,
which was no more than several minutes. For the reactions of 3 and
4a-c with 5H, compound 5H was used in excess. The decay of 3 was
monitored at 380 nm while 4a-c was monitored at 420 nm.
The primary kinetic isotope effect is very sensitive to the isotopic
purity of the substrates. However, the results cited above establish that
the isotopic purity of 5H is >99%, which is sufficient to make this an
insignificant source of error.
The difference of τ values between H and D is almost the
same as the difference computed by the VTST (variational
transition state theory)-plus-LCG3 (large curvature ground-state
tunneling) method, in which the potential energy surface of a
three-body model shown in eq 1 can be used to calculate the
rate constant k and primary kinetic isotopic effect.5 In a three-
body model the standard donor C-H bond energy is 305 kJ/
mol.5 The full range of reactions, used in the computation, have
bond dissociation energy, De(CH), of 242-347 kJ/mol.
Results and Discussion
Rate and equilibrium constants and primary kinetic isotope
effects (KIE) for hydride transfer reactions with 5H(D) are given
in Table 1. All values of KIE were replicated more than 4 times.
For the fast reactions using the stopped-flow apparatus the values
of KIE were obtained from dividing kH, the average value out
of more than 20 values, by kD obtained in the same way as in
kH. The average deviations from the mean values were 3-8%
and probable errors of the mean values were 2-4%. Most of
the scatter is probably due to variation in temperature and
solvent composition.
The quasiclassical kinetic isotope effect, KIEqc, is determined
principally by changes in zero-point energy and rotational
partition functions. The transition coefficient, κ, is the ratio of
the thermally averaged quantal transmission probability to the
thermally averaged classical transmission probability, obtained
by the large curvature ground state (LCG3) tunneling ap-
The equilibrium constants, K, for reaction of 4b and 4c with
5H were calculated with the aid of K values for the reaction of
(28) Frost, A. A.; Pearson, R. G. Kinetics and Mechanism, 2nd ed.;
Wiley: New York, 1961; p 29.

7496 J. Am. Chem. Soc., Vol. 123, No. 31, 2001
Han Lee et al.
Figure 2. The perpendicular effect (circles) and the parallel effect
(squares) on ln KIE as a function of ln K. (The perpendicular effect is
first order in ln K which is the second term on the right-hand side of
eq 11, using the present value of (τH - τD), while the parallel effect is
second order, which is the third term on the right-hand side of eq 11,
using the individually determined values of λH and λD.) This figure
shows that the perpendicular effect on the KIE is much larger than the
parallel effect at all accessible values of K.
Figure 1. ln KIE + C [C ) {0.5RT/(ln K)2}(1/λH - 1/λD)] as a function
of ln K for hydride transfer reactions. The circle points are for the
reactions of various oxidants with 5H(D). The square points are for
the reactions of variants of 2 with 3H(D).12 The vertical bars show the
effect of errors of 3% in KIE. The line is obtained from eq 11, using
the presently determined best value of (τH - τD) and the λ values
obtained from the individual rate constants. The very slight scatter due
to using individual values of λ is not observable on the plot. This plot
shows how well eq 11 represents the variation in KIE with K.
is second order. Thus, the plot of the perpendicular effect should
be linear while the plot of the parallel should be a parabola.
This expectation is shown in Figure 2. The perpendicular effect
is much larger than the parallel effect on the Brønsted R. The
slope of the perpendicular effect against ln K is the same as the
slope of ln KIE against ln K shown in Figure 1, as it should be.
The perpendicular effect depends on the typical transition state
structure for the reaction in question and does not require a
significant change in the structure. The parallel effect, on the
other hand, depends on the change in structure within the series
of reactions studied. For the present system the perpendicular
effect, not the parallel effect, is the main reason for the change
in the KIE.
It is noteworthy that the IR stretching and bending frequencies
for 5H and 5D are quite normal. We would expect a nearly
constant KIE value of around 2.0 if we only consider the
quasiclassical kinetic isotope effect in the present range of the
equilibrium constant.19 This is not the case. Therefore, the
corner-cutting tunneling contribution to the KIE plays a very
important role for the present system.
proximation.29 The tunneling contribution to the kinetic isotope
effect is κH(LCG3)/κD(LCG3). When the quasiclassical contri-
bution to the KIE and the tunneling contribution to the KIE for
hydride transfer reactions are taken into account, the total KIE
increases significantly as the C-H bond energy decreases5 and
as the donor-acceptor distance increases.19
The value of τ gives a semiquantitative measure of the
effective charge on the in-flight atom. In the present case there
is a fractional negative change on the in-flight hydrogen, as
anticipated by theory.13 Williams used a somewhat different
approach for many examples bearing effective charges on the
transferring groups when the group transfer reactions take
place.18 He demonstrated the dependence of the slope of a plot
of the degenerate reaction rate constant on the pKa of phenol
for the reaction of the substituted phenolate ions with the
substituted phenyl diphenylphosphates. The plot showed a
nonlinearity indicating that the transition state structure changes
as the nucleophile changes.18
In conclusion, the Marcus theory expresses the variation of
rate with structure for hydride transfer quite accurately and also
describes the variation of the KIE with structure very well. The
present results also support the involvement of corner-cutting
tunneling in most hydrogen transfer reactions.
In the Marcus formalism shown in eq 11 the perpendicular
effect and the parallel effect on the KIE can be calculated. Those
effects are listed in Table 1. The perpendicular effect which is
the second term in the right-hand side in eq 11 is first order in
ln K whereas the parallel effect which is the last term in eq 11
Acknowledgment. This work was supported by grant No.
1999-2-123-003-5 from the Interdisciplinary Research Program
of the KOSEF.
(29) Truhlar, D. G.; Isaacson, A. D.; Garret, B. C. In Theory of Chemical
Reaction Dynamics; Baer, M., Ed.; CRC Press: Boca Raton, FL, 1985;
Vol. 4, p 65.
(30) Ostovic´, C.; Lee, I.-S. H.; Roberts, R. H. G.; Kreevoy, M. M. J.
Org. Chem. 1985, 50, 4206-4211.
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