Marcus theory of a parallel effect on α for hydride transfer reaction between NAD+ analogues

Article abstract of DOI:10.1021/ja963768l

Rate and equilibrium constants for hydride transfer from a series of 1,3-dimethyl-2-substituted phenylbenzimidazolines to a pyridinium ion, a quinolinium ion, and a phenanthridinium ion have been evaluated. Each oxidizing agent gives a linear Bronsted plot with slope, α. The α values vary systematically with the spontaniety of the reactions. They are in reasonable agreement with the predictions of modified Marcus theory. Their trend is very accurately predicted, showing a parallel (Leffler-Hammond) effect. These results make a multistep mechanism, involving high energy intermediates, very unlikely.

Full text of DOI:10.1021/ja963768l

2722
J. Am. Chem. Soc. 1997, 119, 2722-2728
Marcus Theory of a Parallel Effect on R for Hydride Transfer
Reaction between NAD+ Analogues
In-Sook Han Lee,*,† Eun Hee Jeoung,† and Maurice M. Kreevoy*,‡
Contribution from the Department of Science Education, Kangweon National UniVersity,
Chuncheon 200-701, Korea, and Department of Chemistry, UniVersity of Minnesota,
Minneapolis, Minnesota 55455-0431
ReceiVed October 29, 1996X
Abstract: Rate and equilibrium constants for hydride transfer from a series of 1,3-dimethyl-2-substituted phenyl-
benzimidazolines to a pyridinium ion, a quinolinium ion, and a phenanthridinium ion have been evaluated. Each
oxidizing agent gives a linear Brønsted plot with slope, R. The R values vary systematically with the spontaniety
of the reactions. They are in reasonable agreement with the predictions of modified Marcus theory. Their trend is
very accurately predicted, showing a parallel (Leffler-Hammond) effect. These results make a multistep mechanism,
involving high energy intermediates, very unlikely.
Ai*+ + AiH f Ai*H + Ai+
Aj*+ + AjH f Aj*H + Aj+
(6)
(7)
Introduction
Marcus theory of the relation between rate and equilibrium
constants has been applied successfully and widely to proton
transfer,1 hydride transfer,2 and group transfer3 as well as
electron transfer reactions.4 Application of a modification of
Marcus theory to the hydride transfer reaction shown in eq 1
leads to an interpretation of the Brønsted R, defined as [d(ln
k)/d(ln K)] in terms of a parallel (Leffler-Hammond) effect
and a perpendicular (Thornton) effect.5
As shown in eq 2, ∆G* is taken as the sum of two parts.
The first, Wr, is that part of ∆G* which is independent of ∆G°.5b
The second is a function of ∆G° and estimated as shown. If
∆G° ) 0 the second term in eq 2 reduces to λ/4, which is called
the intrinsic barrier. λ is given by eq 3, in which λi and λj are
the λ values for the symmetrical reactions shown in eqs 6 and
7. Since, if Wr can be estimated, λi and λj can be obtained from
the rate constants for the symmetrical reactions shown in eqs 6
and 7, an estimate of Wr makes it possible to evaluate all the
parameters of the theory. In the present work we have
consistently assumed Wr to be -2 kcal mol-1, as before,2
because of the likelihood that the reactants form a weak charge
transfer complex before the covalency changes are initiated.
In early applications of Marcus theory λ/4 was regarded as a
constant, characteristic of a particular class of reactions, but in
modified Marcus theory it is recognized that λi (and/or λj) may
vary systematically with ∆G°°, the standard free energy of
reaction of Ai+ with a standard hydride donor.5,6 Any hydride
donor could have been chosen as the reference. For historic
reasons, and reasons of convenience, 10-methylacridan has been
used.2 If λi (and/or λj) is assumed to be a linear function of
∆G°° eqs 8-10 follow.5 These equations relate the Brønsted
R to the Marcus parameters and define a new tightness
parameter, τ.
Ai+ + AjH f Aj+ + AiH
(1)
The Marcus formalism can be summarized in eqs 2 and 3. It
can be expected to work best if Ai and Aj are structurally related.
Equations 4 and 5 give the standard thermodynamic expression
for K and quasithermodynamic expression for k, respectively.
∆G* ) Wr + (1 + ∆G°/λ)2.λ/4
λ ) (λi + λj)/2
(2)
(3)
K ) exp(-∆G°/RT)
(4)
(5)
k ) kBT/h exp(-∆G*/RT)
∆G* is the free energy of activation of the reaction, and ∆G°
is the standard free energy of the reaction.
† Kangweon National University.
R ) ø ( 1/2(τ - 1) - 1/2(∆G°/λ)2.(τ - 1)
ø ) (1 + ∆G°/λ)/2
(8)
(9)
‡ University of Minnesota.
X Abstract published in AdVance ACS Abstracts, February 15, 1997.
(1) (a) Hassid, A. I.; Kreevoy, M. M.; Liang, T.-M. Symp. Faraday Soc.
1985, 10, 69-77. (b) Kreevoy, M. M.; Konasewich, D. E. AdV. Chem. Phys.
1971, 21, 243-252. (c) Kreevoy, M. M.; Oh, S. J. Am. Chem. Soc. 1973,
95, 4805-4810. (d) Kresge, A. J. Chem. Soc. ReV. 1973, 2, 475-503.
(2) Kreevoy, M. M.; Ostovic D.; Lee, I.-S. H.; Binder, D. A.; King, G.
W. J. Am. Chem. Soc. 1988, 110, 524-530.
(3) (a) Albery, W. J. Annu. ReV. Phys. Chem. 1980, 31, 227-263. (b)
Marcus, R. A. J. Phys. Chem. 1968, 72, 891-899. (c) Hine, J. J. Am. Chem.
Soc. 1971, 93, 3701-3708. (d) Albery, W. J.; Kreevoy, M. M. AdV. Phys.
Org. Chem. 1978, 16, 87-153. (e) Lewis, E. S.; Hu, D. D. J. Am. Chem.
Soc. 1984, 106, 3292-3296. (f) Guthrie, J. P. Can. J. Chem. 1996, 74,
1283-1296. (g) Reference 3f provides a large number of additional relevant
references.
τ - 1 ) dλi/d(∆G°°)
(10)
ø, which is defined in eq 9, is a measure of the parallel effect
on the transition state and gives the Leffler-Hammond con-
tribution to R. It becomes progressively smaller than unity as
(5) (a) Kreevoy, M. M.; Lee, I.-S. H. J. Am. Chem. Soc. 1984, 106,
2550-2553. (b) Kim, Y.; Truhlar, D. G.; Kreevoy, M. M. J. Am. Chem.
Soc. 1991, 113, 7837-7846. (c) Lewis, E. S.; Hu, D. D. J. Am. Chem. Soc.
1984, 106, 3292-3296.
(4) (a) Marcus, R. A. J. Chem. Phys. 1957, 26, 867-871. (b) Marcus,
R. A. J. Chem. Phys. 1957, 26, 872-877. (c) Marcus, R. A. Annu. ReV.
Phys. Chem. 1964, 15, 155-196.
(6) In the present work, we assumed Wr to be constant and to have -2
kcal mol-1 according to ref 2.
S0002-7863(96)03768-7 CCC: $14.00 © 1997 American Chemical Society

Rate and Equilibrium Constants for Hydride Transfer
J. Am. Chem. Soc., Vol. 119, No. 11, 1997 2723
agreement with the values given by eq 8.
the reaction becomes more spontaneous because the transition
state structures become more similar to the reactants and less
similar to the products. The perpendicular effect on the
transition state is represented by (τ - 1) and gives the Thornton
contribution to R. τ can be measured experimentally as shown
in eq 10. The upper signs in eq 8 are to be used when the
structural variation is in the hydride acceptor, Ai+, and the lower
signs are used when the variation is in the hydride donor, AjH.7
In each case the other reactant is not varied. The third term on
the right hand side of eq 8 is the cross term. As shown in eq
8, the Brønsted R is mainly determined by the parallel effect
(ø) and the perpendicular effect (τ - 1) since the cross term is
negligible in most cases.
Py+(1) + Z-BIH(4H) f PyH(1H) + Z-BI+(4) (11)
Q+(2) + Z-BIH(4H) f QH(2H) + Z-BI+(4) (12)
Ph+(3) + Z-BIH(4H) f PhH(3H) + Z-BI+(4) (13)
PyH(1H) + Q+(2) f Py+(1) + QH(2H)
(14)
When the structural variation for the hydride transfer reaction
is in the hydride donor as shown in eqs 11-13, the perpendicular
effect on R is the same for all three systems, and the magnitude
of the variation of R depends entirely on the ø. Ratios of R
values are given by equations like 15.
RQ+/RPy+ ) d(ln kQ+)/d(ln kPy
)
(15)
+
These ratios demonstrate the Leffler-Hammond or parallel
effect. They are much less dependent on the accuracy of the K
values than the individual R values. These ratios will be shown
to be in excellent agreement with those given by eq 8.
The rate constants were all measured spectrophotometrically
at 25 °C in a solvent consisting of four parts of 2-propanol to
one part of water by volume. This solvent system was chosen,
because it dissolves all the participants in the reaction, and the
2-propanol in the mixed solvent is known as an efficient trapper
of free radicals.9 1,3-Dimethyl-2-phenylbenzimidazoline has
been reported to undergo the free-radical chain reaction with
R-haloketones,10 but in our solvent system free-radical chain
reactions should be minimized. And also, it is a great advantage
for the present work to utilize the considerable infrastructure
of data already available in this solvent.2
To tie these results more firmly to the main body of reaction
rate correlations, acid dissociation constants, Ka, have been
measured in our solvent system for substituted benzoic acids
with the same substituents as those used in the variants of 4.
The Ka values are shown to be related to the hydride transfer
rate and equilibrium constants in the expected ways, that is,
the effect of the substituent on Ka will appear to be opposite to
that on k and K.
In the present paper, we report the rate constants, k, for the
reactions of the type shown in eq 1. The NAD+ analogues,
1-benzyl-3-carbamoylpyridinium ion, 1; 1-benzyl-3-cyanoquino-
linium ion, 2; and 5-benzylphenanthridinium ion, 3a, were used
as the oxidizing agents, Ai+. 1,3-Dimethyl-2-substituted phe-
nylbenzimidazolines (p-CH3, H, p-F, p-Cl, m-F, m-Cl, m,m′-
Cl2) 4H, which are regarded as analogues of NADH, were used
as reducing agents, AjH. (NAD+ is the enzyme cofactor,
Nicotinamide Adenine Dinucleotide, and NADH is its dihy-
droderivative.)
We chose the 2-phenylbenzimidazoline derivatives as reduc-
ing agents, because these substances have been reported to have
high standard reduction potentials (i.e., E°4b ) -1.780 V)8
which should make it possible to measure quite a wide range
of the reaction rates. We found the reduction potential of 4b
to be much less negative than reported, but the variants of 4
served our purpose, and, with one exception, we were able to
measure all of the intended rate constants.
We have also measured the rate constants for reduction of
substituted 2-phenylbenzimidazolium ions, 4, by 1-benzyl-3-
carbamoyl-1,4-dihydropyridine, 1H. This allowed the evalua-
tion of the equilibrium constants and standard free energies for
the reactions shown in eq 11. In this paper, when a parameter
refers specifically to reactions involving one of our three
oxidizing agents, it will be identified by an appropriate subscript.
Thus the equilibrium constants for the reactions shown in eq
11 are designated KPy.
Equation 12 can be generated from eq 11 by adding eq 14 to
it. So the standard free energies of the reactions shown in eq
12, ∆G°Q, can be obtained from the corresponding ∆G°Py by
adding ∆G°14, where the latter is the standard free energy of
the reaction shown in eq 14. The ∆G°Ph can be obtained
analogously. Since ∆G°Q and ∆G°Ph are related to ∆G°Py by
additive, substituent-independent quantities, Brønsted plots could
be made using the rate constants for the reduction of 2 and 3
and the KPy values. The slopes of these plots have their usual
significance. It will be shown that they are in satisfactory
Experimental Section
Materials. Compounds 1, 2, and 3 are well-known substances which
were prepared by benzylation of the corresponding bases and identified
by their physical and spectroscopic properties.5,11 Compounds 4a-g
were prepared by the method of Craig and co-workers with small
modifications.12 The typical procedure was as follows:
4b (X ) I): A mixture of benzoic acid (3.07 g), o-phenylenediamine
(2.71 g), and polyphosphoric acid (10.48 g) was heated with stirring at
175-180 °C for 1.5 h and then cooled to room temperature. About
100 mL of 6% NH4OH was added to neutralize unreacted acid. The
solid was filtered off, thoroughly rinsed with the NH4OH solution, and
then dried to give 2-phenylbenzimidazole. The yield was generally
over 90%, mp 290 °C. The product was identified by 1H-NMR.
Without further purification, 3 g of this product was treated with 8 g
of methyl iodide in 15 mL of methanol containing 0.64 g of NaOH.
The reaction mixture was heated at 110 °C overnight in a pressure
tube. The longer the reaction period, the higher was the yield of the
salt, especially for the substances having the electron-withdrawing
substituents. The crude product was decolorized by the activated carbon
in hot aqueous ethanol (EtOH:H2O, 5:1 v/v). After removal of the
(9) Fieser, L. F.; Williamson, K. L. Organic Experiments, 3rd ed.; D. C.
Heath; Lexington, MA, 1975; pp 242-243.
(10) Tanner, D. D.; Chen, J. J. J. Org. Chem. 1989, 54, 3842-3846.
(11) Ostovic, D.; Roberts, R. M. G.; Kreevoy, M. M. J. Am. Chem. Soc.
1983, 105, 7629-7631.
(7) Kreevoy, M. M.; Lee, I.-S. H. Z. Naturforsch. 1989, 44a, 418-426.
(8) Timofeeva, Z. N.; El’tsov, A. V. Zh. Obshch. Khim. 1967, 37, 2599-
2602.
(12) Craig, J. C.; Ekwuribe, N. N.; Fu, C. C.; Walker, K. A. M. Synthesis
1981, 303-305.

2724 J. Am. Chem. Soc., Vol. 119, No. 11, 1997
Lee et al.
solvent, the product was recrystallized from absolute ethanol. The yield
was over 80%.
4-H), 8.02 (s, 2 H, 2′-H), 8.13 (s, 1 H, 4′-H); UV (2-propanol-H2O,
4:1 v/v) λmax nm (log ꢀ) 282 (4.10).
4b (X ) ClO4): The iodide counterion was exchanged by perchlo-
rate. 4b (1 g) was dissolved in 50 mL of hot water and treated with
10 mL of hot aqueous solution containing excess NaClO4 (3.5 g). The
exchange reaction took place instantaneously, and the perchlorate
precipitated when the solution was cooled. It was recrystallized from
EtOH:H2O (10:1 v/v) to give a 90% yield (0.85 g). The perchlorate
product was identified by a negative silver nitrate test and an IR
spectrum showing the presence of perchlorate. It should be noted that
for the reverse reaction of 4 (X ) I) with 1H the formation of a charge
transfer complex between I- and the product, 1, which also results in
an absorbance band at 360 nm, interferes with the monitoring of the
decay of 1H at 360 nm. Therefore, the counterion was exchanged from
iodide to perchlorate to prevent the formation of the complex.
4bH: To a solution of 3 g of 4b in 80 mL of methanol was slowly
added 1.19 g of NaBH4. The reaction took place instantaneously to
give a cloudy, white suspension. The reaction mixture was stirred
vigorously for 1 h under N2. After removal of the solvent under reduced
pressure, the white solid was recrystallized from EtOH:H2O (2:1 v/v)
to give a colorless crystalline product. The yield was over 90% (1.86
g).
Anal. Calcd for C15H13Cl3N2O4 (391.64): C, 46.00; H, 3.34; N,
7.15; Cl, 27.16. Found: C, 45.83; H, 3.23; N, 6.99; Cl, 27.40.
4aH: 80%, mp 90-1 °C; IR (KBr) 3047 (w), 2949 (w), 2863 (w),
2795 (w), 1604 (m), 1495 (s), 1450 (m), 1368 (s), 1297 (m), 1116
(m), 837 (m), 778 (m), 730 (m) cm-1; 1H-NMR (DMSO-d6) δ 2.40 (s,
3 H, CCH3), 2.51 (s, 6 H, NCH3), 4.85 (s, 1 H, 2-H), 6.44 (dd, 2 H,
5-H), 6.60 (dd, 2 H, 4-H), 7.23 (d, 2 H, 3′-H), 7.41 (d, 2 H, 2′-H); UV
(2-propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 312 (3.82), 260 (3.70)
Anal. Calcd for C16H18N2 (238.33); C, 80.63; H, 7.61; N, 11.76.
Found: C, 80.75; H, 7.40; N, 11.79.
4bH: 80% mp 93-4 °C (lit.12 93-4 °C); IR (KBr) 3038 (w), 2953
(w), 2861 (w), 2801 (w), 1601 (m), 1495 (s), 1456 (m), 1368 (s), 1295
(m), 1234 (m), 1157 (m), 1121 (m), 1061 (m), 777 (m), 741 (m), 700
1
(m) cm-1; H-NMR (DMSO-d6) δ 2.52 (s, 6 H, NCH3), 4.88 (s, 1 H,
2-H), 6.46 (m, 2 H, 5-H), 6.64 (m, 2 H, 4-H), 7.44-7.59 (m, 5 H,
phenyl); UV (2-propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 312 (3.82),
260 (3.70).
Anal. Calcd for C15H16N2 (224.31): C, 80.32; H, 7.19; N, 12.49.
Found: C, 80.12; H, 6.98; N, 12.29.
4cH: 80%; mp 116-8 °C; IR (KBr) 3061 (w), 2959 (w), 2864 (w),
2803 (w), 1602 (m), 1496 (s), 1450 (m), 1367 (s), 1294 (m), 1215
The yields, melting points, spectroscopic properties, and elemental
analyses of the materials used were as follows.
1
(m), 1118 (m), 848 (m), 736 (m) cm-1; H-NMR (DMSO-d6) δ 2.51
4a: 75%; mp 217-218 °C (lit.8 207.5 °C); IR (KBr) 3066 (w), 1613
(s, 6 H, NCH3), 4.87 (s, 1 H, 2-H), 6.46 (m, 2 H, 5-H), 6.64 (m, 2 H,
4-H), 7.28 (dd, 2 H, 3′-H), 7.61 (dd, 2 H, 2′-H); UV (2-propanol-
H2O, 4:1 v/v) λmax nm (log ꢀ) 312 (3.84), 260 (3.74).
Anal. Calcd for C15H15FN2 (242.30): C, 74.35; H, 6.24; F, 7.84;
N, 11.57. Found: C, 74.52; H, 6.34; F, 8.03; N, 11.45.
4dH: 95%; mp 93-4 °C; IR (KBr) 3044 (w), 2952 (w), 2864 (w),
2798 (w), 1598 (m), 1493 (s), 1356 (w), 1296 (m), 1196 (m), 1116
(m), 840 (m), 775 (m), 731 (m) cm-1; 1H-NMR (DMSO-d6) δ 2.50 (s,
6 H, NCH3), 4.90 (s, 1 H, 2-H), 6.47 (m, 2 H, 5-H), 6.63 (m, 2 H,
4-H), 7.52 (d, 2 H, 3′-H), 7.59 (d, 2 H, 2′-H); UV (2-propanol-H2O,
4:1 v/v) λmax nm (log ꢀ) 312 (3.82) 260 (3.72).
1
(m), 1520 (s), 1472 (m), 1090 (vs, νCldO), 837 (m), 768 (s) cm-1; H-
NMR (DMSO-d6) δ 2.49 (s, 3 H, CH3), 3.88 (s, 6 H, NCH3), 7.59 (d,
2 H, 3′-H), 7.74 (d, 2 H, 2′-H), 7.76 (dd, 2 H, 5-H), 8.11 (dd, 2 H,
4-H); UV (2-propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 282 (4.22), 244
(4.20).
Anal. Calcd for C16H17ClN2O4 (336.77); C, 57.06; H, 5.09; N, 8.32;
Cl, 10.53. Found: C, 56.82; H, 4.96; N, 8.22; Cl, 10.48.
4b: 90%; mp 222-3 °C (lit.8 212-4 °C); IR (KBr) 3006 (w), 1608
(m), 1477 (m), 1090 (vs, νCldO), 767 (m), 717 (m), 716 (m), 629 (m)
1
cm-1; H-NMR (DMSO-d6) δ 3.92 (s, 6 H, NCH3), 7.88-7.94 (m, 5
H, phenyl), 7.76 (m, 2 H, 5-H), 8.13 (m, 2 H, 4-H); UV (2-propanol-
H2O, 4:1 v/v) λmax nm (log ꢀ) 282 (4.15).
Anal. Calcd for C15H15ClN2 (258.75): C, 69.63; H, 5.84; Cl, 13.70;
N, 10.83. Found: C, 69.79; H, 5.60; Cl, 13.58; N, 10.83.
Anal. Calcd for C15H15ClN2O4 (322.73): C, 55.82; H, 4.68; N, 8.68;
Cl 10.99. Found: C, 55.80; H, 4.77; N, 8.63; Cl, 11.12.
4c: 90%; mp 232-3 °C; IR (KBr) 3077 (w), 1607 (m), 1472 (s),
237 (m), 1092 (vs, νCldO), 858 (m), 761 (m) cm-1; 1H-NMR (DMSO-
d6) δ 3.89 (s, 6 H, NCH3), 7.66 (m, 2 H, 3′-H), 7.76 (dd, 2 H, 5-H),
7.99 (m, 2 H, 2′-H), 8.14 (dd, 2 H, 4-H); UV (2-propanol-H2O, 4:1
v/v) λmax nm (log ꢀ) 282 (4.26), 238 (4.27).
4eH: 60%; mp 92-3 °C; IR (KBr) 3039 (w), 2950 (w), 2868 (w),
2803 (w), 1599 (m), 1493 (s), 1357 (m), 1297 (m), 1248 (m), 1118
(m), 901 (m), 789 (m), 732 (m) cm-1; 1H-NMR (DMSO-d6) δ 2.51 (s,
6 H, NCH3), 4.93 (s, 1 H, 2-H), 6.47 (m, 2 H, 5-H), 6.64 (m, 2 H,
4-H), 7.28 -7.53 (m, 4 H, aromatic H); UV (2-propanol-H2O, 4:1
v/v) λmax nm (log ꢀ) 312 (3.84), 260 (3.79).
Anal. Calcd for C15H15FN2 (242.30): C, 74.35; H, 6.24; F, 7.84;
Anal. Calcd for C15H14ClFN2O4 (340.74): C, 52.87; H, 4.14; N,
8.22; Cl, 10.41; F, 5.58. Found: C, 52.66; H, 4.30; N, 8.21; C, 10.61;
F, 5.66.
4d: 95%; mp 289-90 °C (lit.8 276 °C); IR (KBr) 3081 (w), 2960
(vw), 1605 (m), 1522 (m), 1476 (m), 1103 (vs, νCldO), 843 (m), 762
(m), 621 (m) cm-1; 1H-NMR (DMSO-d6) δ 3.90 (s, 6 H, NCH3), 7.78
(dd, 4 H, 2′,3′-H), 8.16 (m, 2 H, 4-H); UV (2-propanol-H2O, 4:1 v/v)
λmax nm (log ꢀ) 282 (4.23), 244 (4.23).
N, 11.57. Found: C, 74.25; H, 6.36; F, 7.76; N, 11.43.
4fH: 85%; mp 99 °C; IR (KBr) 3065 (w), 2960 (w), 2869 (w),
2805 (w), 1577 (m), 1491 (s), 1442 (m), 1357 (m), 1284 (m), 1192
(m), 1116 (m), 895 (m), 781 (m), 734 (m) cm-1; 1H-NMR (DMSO-d6)
δ 2.52 (s, 6 H, NCH3), 4.93 (s, 1 H, 2-H), 6.47 (dd, 2 H, 5-H), 6.64
(dd, 2 H, 4-H), 7.51 (m, 3 H, 4′,5′,6′-H), 7.60 (s, 1 H, 2′-H); UV (2-
propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 312 (3.80) 260 (3.70)
Anal. Calcd for C15H15ClN2 (258.75): C, 69.63; H, 5.84; Cl, 13.70;
N, 10.83. Found: C, 69.79; H, 5.74; Cl, 13.91; N, 10.63.
4gH: 80%; mp 105-6 °C; IR (KBr) 3049 (w), 2956 (w), 2872 (w),
2799 (w), 1571 (m), 1497 (s), 1440 (m), 1347 (s), 1291 (m), 1116
(m), 801 (m), 772 (m), 732 (m) cm-1; 1H-NMR (DMSO-d6) δ 2.50 (s,
6 H, NCH3), 4.96 (s, 1 H, 2-H), 6.47 (dd, 2 H, 5-H), 6.62 (dd, 2 H,
4-H), 7.58 (s, 2 H, 2′-H), 7.68 (s, 1 H, 4′-H); UV (2-propanol-H2O,
4:1 v/v) λmax nm (log ꢀ) 312 (3.86), 260 (3.76).
Anal. Calcd for C15H14Cl2N2O4 (357.20): C, 50.44; H, 3.95; N,
7.84; Cl, 19.85. Found: C, 50.23; H, 4.14; N, 7.75; Cl, 19.76.
4e: 80%; mp 274 °C; IR (KBr) 3076 (w), 2964 (vw), 1592 (m),
1528 (s), 1474 (s), 1271 (m), 1077 (vs, νCldO), 895 (s), 806 (m), 756
(s), 623 (s) cm-1; 1H-NMR (DMSO-d6) δ 3.94 (s, 6 H, NCH3), 7.72-
7.58 (m, 4 H, aromatic H), 7.76 (m, 2 H, 5-H), 8.15 (dd, 2 H, 4-H);
UV (2-propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 282 (4.18), 234 (4.15).
Anal. Calcd for C15H14ClFN2O4 (340.74): C, 52.87; H, 4.14; N,
8.22; Cl, 10.41; F, 5.58. Found: C, 52.76; H, 4.39; N, 8.43; Cl, 10.36;
F, 5.66.
4f: 80%; mp 235-6 °C (lit.8 229 °C); IR (KBr) 3071 (w), 2961
(vw), 1522 (m), 1464 (m), 1408 (w), 1077 (vs, νCldO), 760 (s), 623
(w) cm-1; 1H-NMR (DMSO-d6) δ 3.89 (s, 6 H, NCH3), 7.77 (m, 2 H,
5-H), 7.81-8.00 (m, 3 H, 4′,5′,6′-H), 8.05 (s, 1 H, 2′-H), 8.12 (m, 2
H, 4-H); UV (2-propanol-H2O, 4:1 v/v) λmax nm (log ꢀ) 282 (4.17).
Anal. Calcd for C15H14Cl2N2O4 (357.20): C, 50.44; H, 3.95; N,
7.84; Cl, 19.85. Found: C, 50.52; H, 4.12; N, 7.78; Cl, 20.01.
4g: 70%; mp 296-8 °C; IR (KBr) 3071 (w), 1562 (m), 1525 (s),
1479 (m), 1089 (vs, νCldO), 872 (m), 765 (m), 623 (m) cm-1; 1H-NMR
(DMSO-d6) δ 3.89 (s, 6 H, NCH3), 7.71 (dd, 2 H, 5-H), 8.15 (dd, 2 H,
Anal. Calcd for C15H15Cl2N2 (293.20): C, 61.44; H, 4.81; Cl, 24.19;
N, 9.56. Found: C, 61.28; H, 5.00; Cl, 24.12; N, 9.62.
Measurements. All kinetic measurements were conducted in a
solvent containing four parts of 2-propanol to one part of water by
volume at 25 ( 0.1 °C to facilitate comparison with a large body of
analogous results which have been reported.2 2-Propanol and water
were distilled before use. In previous work solvents have been distilled
from a small amount of H2SO4 in order to remove any basic impurity.
This resulted in slightly acidic solutions (pH around 5). However 4H
is subject to acid catalyzed hydrolysis and oxidation. For the slower
reactions it is not adequately stable at a pH of 5. Therefore, solvents
were distilled without using H2SO4. Rates of reactions of 1 and 3 with
4Hb and of 1H with 4b were the same in unbuffered solutions and in

Rate and Equilibrium Constants for Hydride Transfer
J. Am. Chem. Soc., Vol. 119, No. 11, 1997 2725
solutions buffered to a pH of 7.5 with a boric acid-borate buffer.
Table 1. Rate Constants and Equilibrium Constants for Hydride
Transfer Reactions
Therefore, unbuffered solutions which had measured pH around 6 were
+
used, except the reactions of 2, which has a pKR of 5.11 in the present
oxidant, k (M-1 s-1
)
reductant
solvent system.13 The solution of 2 was made acidic by using 4.58 ×
10-4 M of HClO4 in the solvent to give the reaction mixture a pH of
3.4. For this reaction 4Hb was adequately stable at this pH, as the
reactions required only a few minutes.
4H
1
2
3a
K
pKa
a
b
c
d
e
f
2.96 × 10-3 2.82 × 102 1.60
6.58 × 10 7.37
1.85 × 10-3 2.08 × 102 1.13
3.60 × 10 7.22
1.03 × 10-3 1.13 × 102 5.41 × 10-1 1.72 × 10 7.10
Values of pH were determined electrometrically with a POPE pH
meter (Model 501) and combined electrode. In order to determine the
correction to the observed pH for our solvent system the apparent pH
values of four standard solutions of HClO4 (10-2-10-4 M) were
measured. An average correction of -0.17, substracted from the
apparent pH values, was required to match the negative logs of the
concentrations.
7.00 × 10-4 9.75 × 10 3.85 × 10-1 4.46
4.72 × 10-4 7.16× 10 3.00 × 10-1 2.52
3.49 × 10-4 3.74× 10 2.13 × 10-1 1.65
6.97
6.88
6.76
g
5.02 × 10-5 a 7.73
3.15 × 10-2 1.12 × 10-1 6.18
a The rate constant for this reaction was too small for accurate
measurement. Values of ln k for reactions of 4H with 1 were a linear
function of ln k values for reactions of ln k values for reactions of 4H
with 2, as would be expected, since both are linear functions of ln K.
The linear relation between the two sets of ln k values was extrapolated
to give the ln k value for reaction of 4Hg with 1. A second value was
obtained from the similar relation between the rate constants for reaction
of 4H with 1 and the reaction of 4H with 3a. The two, very similar,
inferred values of the rate constant for reaction of 4Hg with 1 were
averaged to get the tabulated value.
Reactions of 4H with 5 × 10-4 M 2 had half-lives around 10 s.
The reaction rate constants were determined with a stopped-flow
apparatus (Hi-Tech Scientific, SFA-12) attached to the spectropho-
tometer (Milton Roy 3000) by monitoring the growth of the absorption
due to the product, 4, at 280 nm. Reaction of 1 with 4H was slower,
and the stopped-flow apparatus was not needed. These reactions went
to completion in the presence of excess of 1 (5 × 10-3 M). The rate
constants were measured by monitoring the growth of the absorption
of 1H at 360 nm, where other substances do not interfere.
to about 1% for 4g). The k-1 values were corrected by subtracting 2.4
× 10-7 from them before they were used to calculate k-2 values.
The pKa’s of the corresponding benzoic acids were measured by
pH titration with a glass electrode and a pH meter (Metrohom 686)
with NaOH solution (10-3 M) in the same mixed solvent. And the
activity coefficient, γ(, for the present solvent system was obtained
from the Debye-Huckel formula, eq 17.
The reaction of 3a with 4H was monitored by observing the decay
of the absorption of the reactant, 3a, in the presense of excess of 4H,
at 380 nm. All kinetic experiments were carried out with at least a
20-fold excess of the spectroscopically inactive constituent. Therefore,
k
obs was obtained from the first-order rate law in the usual way.14 The
second-order rate constants, k, were given by kobs/C, where C is the
concentration of substance in excess.
-1.87(I)1/2
1 + 4.05(I)1/2
All kinetic experiments were performed at least four times, in
separate experiments. More than 20 experiments were performed for
the reactions of 2, because the stopped-flow apparatus required small
volumes, which gave rise to greater-than-usual uncertainties in the
concentrations. The average deviations from mean values of kobs were
around 3% for compounds 1 and 3a and 5% for compound 2.
To get the equilibrium constants for the reactions of 1 with the
variants of 4H rate constants for the reverse reactions were needed.
These reactions reached equilibrium with substantial amounts of both
reactants still present, so the rate constants were evaluated using eq
16.15,16
log γ( )
(17)
The mixed solvent correction was redetermined for this equipment
by the method described above. The correction required the substrac-
tion of 0.22 from the observed pH.
Results and Discussion
The rate constants for hydride transfer reactions and the pKa’s
of the benzoic acids are listed in Table 1. The order of reactivity
for the oxidant is 2 > 3a > 1. This corresponds to the order of
their reduction potentials, E°red (i.e., 1: -361 mV; 3a: -222
mV; and 2: -39 mV).16 The measured equilibrium constants
for the reactions of 1 with 4H are also given in Table 1.
With 36 as the value of K for the reaction of 4Hb with 1, we
can calculate the equilibrium constant for the reaction of 4Hb
with 10-methylacridinium ion in the same solvent system by
using a ladder procedure, to give 1.23 × 1011. The equilibrium
constant for the reaction of 1H with 10-methylacridinium ion
is 3.41 × 109.2 This gives a reduction potential of -361 mV
for 1.16 With the value of K, a reduction potential, E°red, of
-407 mV can be obtained for 4b by means of eq 18, where F
is the Faraday constant and n is the number of electrons
transferred; i.e., two in this case.
k-1 ) [xe/(2a - xe)]t-1 ln{[axe + xt(a - xe)]/a(xe - xt)} (16)
The initial concentration of the limiting reactant is a, xe is the equal
concentration of the two products at equilibrium, and xt is the
concentration of the products at time t. These were determined from
the stoichiometry of the reaction mixture and its absorbance at 360
nm, which was entirely due to the dihydropyridine, 1H. The second-
order rate constant for the reverse reaction, k-2, is k-1/C, where C is
the concentration of the reactant in excess. A value of K () k/k-2) is
also required, to calculate xe, since these reactions are too slow to follow
to completion. A trial value of K gave a first estimate of xe. With this
value of xe, k-2 was evaluated. Then K was reevaluated, and a new
value of xe was obtained. The cycle was repeated until consistency
was achieved. Usually no more than two iterations were neccessary.
It has been estimated that K values determined in this way are uncertain
by about 10%16 and that estimate is probably applicable to the present
values, as well.
RT ln K ) nF∆E°
(18)
This value is much less negative than the reported value, -1.78
V.8
Under our reaction conditions 1H was found to undergo a pseudo-
first-order oxidation to 1, with a rate constant of around 2.4 × 10-7
s-1
. This very slow reaction (half-life around one month) was not
For all three systems Brønsted plots were made by plotting
the values of ln k against the values of ln K for reaction of 1
with the variants of 4H. This procedure is justified above. All
three plots are quite reasonably linear, as shown in Figure 1.
Their slopes, the Brønsted R values, are given in Table 2, along
with the probable errors of the slopes. Most of the uncertainties
in these R values are due to the uncertainties in the K values
(about 10%, as noted above). Since the same K values were
used for all three Brønsted plots, errors in R values due to errors
in K values are completely compensated when ratios of R values
further investigated, and the oxidizing agent is not known. It is fast
enough to make a significant contribution to the apparent rate constants
for the oxidation of 1H by the variants of 4 (about 10% for 4a, declining
(13) Lee, I.-S. H.; Kim, S. H.; Kreevoy, M. M.; Lee, C. K.; Lee, C. H.
J. Phys. Org. Chem. 1992, 5, 269-274.
(14) Frost, A. A.; Pearson, R. G. Kinetics and Mechanism, 2nd ed.;
Wiley: New York, 1961; p 29.
(15) Reference 14, pp 186-187.
(16) Ostovic, D.; Lee, I.-S. H.; Roberts, R. M. G.; Kreevoy, M. M. J.
Org. Chem. 1985, 50, 4206-4211.

2726 J. Am. Chem. Soc., Vol. 119, No. 11, 1997
Lee et al.
Figure 1. Values of ln k as a function of ln K (Brønsted plots). Points
for reactions of 1 with the variants of 4H are represented by circles.
Points for reaction of 2 are represented by triangles. Points for reaction
of 3a are represented by squares. The slopes of these plots are the
Brønsted R’s. They are shown in Table 2, along with the values given
by modified Marcus theory.
Figure 2. A demonstration of the parallel effect. The slopes are 0.87,
0.92, and 0.96 for I, II, and III, respectively. They are in good agreement
with the ratios of calculated R values, as shown in Table 3. These ratios
vary from unity because of the gradual shift in transition state structures,
which is anticipated by the theory.
Table 3. Demonstrations of the Parallel Effect
Table 2. Equilibrium Constants, Brønsted R’s, and Hammett F’s
for Reduction of Cations by Variants of 4H
oxidant
slopea,b
ratio of F’s
calcd ratio of R’s
Q+-Py+
Q+-Ph+
Ph+-Py+
0.87 ( 0.05
0.92 ( 0.02
0.96 ( 0.03
0.89
0.92
0.96
0.88
0.93
0.95
oxidant
parameter
K a
1
2
3a
36b
2.7 × 1012 c
0.54 ( 0.05d
0.41
98.9
0.51
1.8 × 106 c
0.59 ( 0.04d
0.45
99.0
0.55
a The slopes of plots of ln k in one series against ln k for the same
imidazoline reacting with a different oxidizing agent. b The cited
uncertainties are the probable errors of the slopes.
R(exptl)
0.61 ( 0.03d
ø
0.49
98.9
0.58
λ(kcal mol-1
R(calcd)
F(k)
)
e
obtained is 88.8 kcal mol-1. The three values of λ4b then
obtained are 98.9, 98.9, and 99.0 kcal mol-1 as shown in Table
2. The three values are identical within the limits of their
reliability. In fact, the agreement seems fortuitously good, since
the λ values used in the calculation are probably uncertain by
-1.92 ( 0.12d -1.70 ( 0.18d -1.85 ( 0.15d
-3.15 ( 0.13d
F(K)
a Equilibrium constant for reaction of each oxidant with 4Hb.
b Determined by measuring rate constants for the forward and reverse
reactions. c Determined by the ladder procedure. d The uncertainty is
a probable error. e Determined from eq 2, for the reaction of each
oxidant with 4Hb.
about one kcal mol-1
.
The perfect agreement among the three λ4b values establishes
that the variants of 4/4H are members of the series of hydride
acceptors/donors previously defined and confirms that Marcus
theory applies to their hydride transfer reactions. It justifies
the use of the λ values to calculate the R values, for comparison
with the experimental values.
are taken. Since the R values are not too different, differences
in R values are also almost completely unaffected by errors in
the K values. As a result, such ratios and differences are much
more reliable than would be suggested by the probable errors
of the R values themselves.
The calculated and experimental R values are compared in
Table 2. They are in very reasonable agreement. The discrep-
ancies do not exceed the probable errors of the experimental
values, and the calculated values reproduce the trend in the
experimental values almost exactly. This trend is an expression
of the Leffler-Hammond or parallel effect.18 It shows the
gradual change in transition state structures as the reactions
become more spontaneous.
Marcus theory values for the three Brønsted Rs can be
calculated using eqs 8 and 9 if values are available for Wr, τ,
and λ. As indicated, -2 kcal mol-1 has been used for Wr,
following earlier practice.2 The negative value is qualitatively
justified by the observation of charge transfer complexes
between NAD+ analogues and NADH analogues.17 In any
event, the value of Wr has little effect on the agreement between
theory and experiment as long as the value is small compared
to ∆G*, and it is used consistently. A more positive value of
Wr is simply compensated by a smaller value of λ. From related
hydride transfer reactions a value of 0.81 has been obtained for
τ,2 and it is used in the present work.
The parallel effects can also be demonstrated by plotting ln
k values for reduction of one oxidant against ln k for reduction
of another oxidant by the same set of 4H variants. This avoids
the use of the series of K values. The plots are shown in Figure
2. The slopes of these plots differ from unity because of the
parallel effect. They should be given by ratios of calculated R
values. The calculation requires one K value for each oxidant.
The experimental and calculated slopes are compared in Table
3. The agreement is almost exact.
With values of Wr and ∆G° in hand, λ was evaluated for the
reactions of 4Hb with 1, 2, and 3a, using eq 2. The values are
given in Table 2. From each of these a value of λ4b was
calculated, using eq 3. The three values should be the same.
The values of λ1 and λ2, needed for the calculation, are given
in Table 1 of ref 2. They are 95.1 and 93.5 kcal mol-1
,
The Hammett F values can also be used to demonstrate the
variation of transition state structure, in a similar way. In all
three series the ln k values show good linear correlations with
respectively. No value of λ3a is available, but it can be estimated
from λ3b, which is given, using eq 13 of ref 2. The value
(17) (a) Florkin, A.; Stotz, E. H. ComprehensiVe Biochemistry; Elsevier;
Amsterdam, 1967; Vol. 22, p 109. (b) Hajdu, J.; Sigman, D. S. J. Am. Chem.
Soc. 1976, 98, 6060-6061.
(18) (a) Leffler, J. E. Science 1953, 117, 340-341. (b) Hammond, G. S.
J. Am. Chem. Soc. 1955, 77, 334-338.

Rate and Equilibrium Constants for Hydride Transfer
J. Am. Chem. Soc., Vol. 119, No. 11, 1997 2727
+
+
+
Figure 3. ln kPy , ln kQ , and ln kPh as a funtion of σ.
+
+
Figure 5. The correlation of ln kPy (circles) and ln KPy (squares)
with -ln Ka of the corresponding benzoic acids.
that the rate constant would be about as sensitive to changes in
the donor bond strength as the equilibrium constant, since the
donor bond is completely broken in the transition state. Similar
logic suggests that the rate constant will be nearly insensitive
to changes in the acceptor bond strength in the case of a no-
bond transition state within an equilibrium constant not far from
unity. The R value should be close to 0.0 in that case. Equation
8 will provide such a value if the upper signs are used when
the structural changes are in the acceptor.
In the present series of reactions these effects are best
illustrated by the reactions of 4H with 2. The equilibrium
constants are much larger than unity, giving the value of 0.41
for ø, but the calculated value of R is 0.51, due to addition of
the tightness factor. The experimental result is in good
agreement with the calculation which includes the tightness
factor.
Figure 4. ln K as a function of σ.
Hammett parameter, σ,19 as shown in Figure 3, giving F values
of -1.92, -1.70, and -1.85 for 1, 2, and 3a, respectively after
dividing by 2.3 to put them on the usual scale. These F values
vary monotonically with typical ∆G° value of the series. As
shown in Table 3 the ratios of F are very similar to the slopes
of the related ln k - ln k plots (Figure 2). (They would be
identical if the correlations were perfect.) They are also very
similar to the ratios of the calculated R values. Since the
calculation anticipates the parallel effect, the agreement il-
lustrates its occurrence.
The ln K values are also correlated with σ as shown in Figure
4. The F value is -3.15 with the correlation coefficient of
0.996. For compound 1, both ln k and ln K are linearly
correlated with the ln Ka values of the corresponding benzoic
acids, as shown in Figure 5, giving the slopes of 1.50 and 2.41,
with correlation coefficients of 0.998 and 0.987, respectively.
Again, the slopes of the correlation lines have been divided by
2.3 to put them on the customary scale.
The magnitude of R, within the Marcus formalism, depends
on the location of the structural variation. In the present system
the structural variation is in the hydride donor. When the
structural variation is in the hydride donor, the perpendicular
effect (τ - 1) should be subtracted from ø. Since (τ - 1) is
negative in the present case, this gives a larger value of R than
ø by itself. The logic of this is best appreciated by considering
the extreme case, where the bonds to the transferring atom or
group are both completely broken in the transition state. In
that case τ is zero, (τ -1) is -1.0, and eq 8 would give an R
value close to 1.0 for reactions with equilibrium constants not
too far from unity. That value is consistent with the intuition
The present system demonstrates the parallel effect through
the comparison of reactions of quite different reactivity. The
equilibrium constants cover a range of over 1012. Parallel effects
are seldom reliably observed due to difficulty of experimental
measurement of equilibrium constants over a sufficiently wide
range. Even in the present case, with such a wide range of
equilibrium constants, the sums of the uncertainties in the
experimental R’s nearly equals the differences between them,
which show the effect. It is only the consistency of the
experimental results with the theoretical expectations which
gives confidence that the parallel effect has really been observed.
Marcus formalism provides a useful indication of the range of
reactivity needed to demonstrate a parallel effect on the Brønsted
R, and a neccessary confirmation that it has been observed.
The F value for the pKa’s of benzoic acids in the present
solvent system is 1.27 with correlation coefficient of 0.986. The
substituent effect is larger in the mixed solvent than in water.
This is consistent with prior observations.20 As expected, the
plot of ln K Vs. ln Ka in Figure 5 has a negative slope, because
the reacting site at C-2 on the benzimidazole ring of 4H develops
a positive charge in the transition state, while benzoic acid
develops a negative charge in the process of dissociation. In
our previous study of the reaction of 1-benzyl-3-cyanoquino-
linium ions, substituted in the benzyl group, with 10-
methylacridan,5a the value of the slope of the plot of ln K vs. ln
Ka for the corresponding benzoic acid was +1.75. In that case
the positive charge on the quinoline ring diminishes in the course
of reaction due to hydride transfer from 10-methylacridan. And
the magnitude of the slope in the previous case is smaller than
that in the present system (2.41). The reacting site in the
(19) Leffler, J. E.; Grunwald, E. Rates and Equilibria or Organic
Reactions; Wiley: New York, 1963; p 173.
(20) Nummert, V.; Palm, V. Organic ReactiVity (English Edition) 1980,
17, 292-311.

2728 J. Am. Chem. Soc., Vol. 119, No. 11, 1997
Lee et al.
previous system has a methylene group between the phenyl ring
and quinoline ring, while the substituted phenyl group is directly
connected to the reacting site in the present case.
Wr. It would make a large, positive contribution, close to the
overall free energy of activation, because the reaction produces
a radical and a radical ion from paired-electron reactants. We
would expect to require a large, positive value for Wr and small
values for λ. This is not observed.
For the reaction of acridan with the acridinium ion in
acetonitrile, radical and radical ion intermediates are definitively
excluded by comparing the reduction potentials, determined by
Saveant and co-workers,21 with the measured rate of the
symmetrical reaction.2 The present reactions are similar, and
we believe that our results exclude high energy intermediates
in these cases, also.
The foregoing results are consistent with the conclusion that
1,3-dimethyl-2-substituted phenylbenzimidazolines transfer hy-
dride ion to NAD+ analogues without high energy intermediates,
just as previously concluded for similar reactions.2 If a multistep
mechanism (electron transfer followed by proton transfer
followed by another electron transfer) were used, the proton
transfer step presumably would be rate limiting for the reactions
of 4H with 1, for which the K values are not far from unity.
However the first electron transfer would probably become rate
limiting for the reactions of 4H with 2, since these reactions
have equilibrium constants which are 11 powers of 10 larger.
Because of the additional bottleneck the rate constants for the
more spontaneous reactions would be smaller than those
obtained by Marcus theoretical calculation, since Marcus theory
is based on a one step model. The value of λ4b calculated from
the rate constant for the reaction of 4H with 2 would be much
smaller than the value calculated from the reaction of 4H with
1. In fact, these two values of λ4b are in perfect agreement.
If the rate limiting step did not change, the standard free
energy of the first electron transfer would be incorporated in
Acknowledgment. This work was supported by the U.S.
National Science Foundation through Grant NSF/CHE-9208746
to the University of Minnesota and by the Basic Science
Research Institute Program of the Ministry of Education of the
Republic of Korea (BSRI-95-3401).
JA963768L
(21) Hapiot, P.; Mairoux, J.; Saveant, J.-M. J. Am. Chem. Soc. 1990,
112, 1337-1343.