Reactivities of acridine compounds in hydride transfer reactions

Article abstract of DOI:10.1002/poc.1182

Reactivities of acridine derivatives (10-benzylacridinium ion, 1a ⁺, 10-methylacridinium ion, 1b⁺, and 10-methyl-9- phenylacridinium ion, 1c⁺) have been compared quantitatively for hydride transfer reactions with 1,3-dimethyl-2-substituted phenylbenzimidazoline compounds, 2Ha-h. Reactions were monitored spectrophotometrically in a solvent consisting of four parts of 2-propanol to one part of water by volume at 25 ± 0.1°C. Reduction potentials have been estimated for acridine derivatives by assuming that the equilibrium constants for the reductions of 1a⁺-c⁺ by 2Hb would be the same in aqueous solution and accepting -361 mV as the reduction potential of the 1-benzyl-3- carbamoylpyridinium ion. The resulting reduction potentials, E _red^o, are -47 mV for 1a⁺, -79 mV for 1b ⁺, and -86 mV for 1c⁺. Each of acridine derivatives gives a linear Bronsted plot for hydride transfer reactions. The experimental slopes were compared with those obtained by Marcus theory. This comparison shows that the kinetic data are consistent with a one-step mechanism involving no high-energy intermediates. Copyright

Full text of DOI:10.1002/poc.1182

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2007; 20: 484–490
Published online 9 May 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/poc.1182
Reactivities of acridine compounds in hydride
transfer reactions
*
In-Sook Han Lee, Hyun Joo Kil and Young Ran Ji
Department of Science Education, Kangwon National University, Chunchon 200-701, Korea
Received 1 February 2007; revised 8 March 2007; accepted 9 March 2007
ABSTRACT: Reactivities of acridine derivatives (10-benzylacridinium ion, 1aþ, 10-methylacridinium ion, 1bþ, and
10-methyl-9-phenylacridinium ion, 1cþ) have been compared quantitatively for hydride transfer reactions with
1,3-dimethyl-2-substituted phenylbenzimidazoline compounds, 2Ha–h. Reactions were monitored spectrophotome-
trically in a solvent consisting of four parts of 2-propanol to one part of water by volume at 25 ꢀ 0.1 8C. Reduction
potentials have been estimated for acridine derivatives by assuming that the equilibrium constants for the reductions of
1aþ–cþ by 2Hb would be the same in aqueous solution and accepting ꢁ361 mV as the reduction potential of the
1-benzyl-3-carbamoylpyridinium ion. The resulting reduction potentials, Eored, are ꢁ47 mV for 1aþ, ꢁ79 mV for 1bþ,
and ꢁ86 mV for 1cþ. Each of acridine derivatives gives a linear Brønsted plot for hydride transfer reactions. The
experimental slopes were compared with those obtained by Marcus theory. This comparison shows that the kinetic
data are consistent with a one-step mechanism involving no high-energy intermediates. Copyright # 2007 John Wiley
& Sons, Ltd.
KEYWORDS: acridine derivatives; hydride transfer reaction; Brønsted a; Marcus theory
INTRODUCTION
via a direct hydride transfer (one-step mechanism),12a,13
by electron transfer followed by hydrogen transfer, or by
sequential electron, proton, and electron transfer (step-
wise mechanism),7a–d depending on the structures of
acceptors and the reaction conditions.7e,f
For these reasons, further exploration of the reaction
kinetics of acridine derivatives is of interest. We report
here rate constants for the reactions of a series of 1,3-
dimethyl-2-substituted phenylbenzimidazolines, 2Ha–h
with three kinds of hydride acceptors: 10-benzylacridium
ion, 1aþ, 10-methylacridinium ion, 1bþ, and
10-methyl-9-phenylacridinium ion, 1cþ. These acceptors
differ in their substitution at N-1 and C-9. The hydride
donors differ in their substitution on the phenyl ring.
Acridine derivatives, like most heterocyclic compounds,
have been long-standing synthetic objectives due to their
important biological activities.1 Substituted acridines
have been synthesized and reported to have antibacterial,2
antimalarial,3 anthelmintic,4 analeptic,5 and antineoplas-
tic6 activities. Acridine derivatives are also important in
the study of reaction mechanisms because they have often
been used as models of the coenzyme NADþ (nicotinamide
adenine dinucleotide) for hydride transfer reactions.7–10
The oxidized forms of acridines, namely acridinium
ions, undergo characteristic electrophilic addition reac-
tions at the highly electron-deficient 9-position in the
acridine ring and have served as hydride acceptors. On the
other hand, the reduced forms, namely acridans, have
served as hydride donors in model reactions for NADþ–
NADH interconversion.11 Among them, 10-methylacridi-
nium ion and the corresponding reduced form, 10-methyl-
acridan, have frequently been used as convenient NADþ
model compounds for kinetic and mechanistic studies for
hydride transfer reactions7,8 because they are easily
prepared, stable in solution, and suitable for spectroscopic
measurement due to their characteristic chromophores in
the visible region. When 10-methylacridan is treated with
hydride acceptors, it converts to 10-methylacridinium ion
Y
CH3
N
H
N
N
R
-
Z
ClO4
CH3
1+
2H
1a+, Y = H, R = C6H5CH2
1b+, Y = H, R = CH3
a, p-CH3
b, H
c, p-F
d, p-Cl
e, m-F
f, m-Cl
g, m-CF3
h, m,m'-Cl2
Z =
1c+, Y = C6H5, R=CH3
*Correspondence to: I.-S. Lee, Department of Science Education,
Kangwon National University, Chunchon 200-701, Korea.
E-mail: ishl@kangwon.ac.kr
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490

HYDRIDE TRANSFER REACTION
485
1,3-Dimethyl-2-phenylbenzimidazoline, 2Hb, has
been reported previously as a powerful reducing agent
whose corresponding oxidant, 1,3-dimethyl-2-phenyl-
benzimidazolinium ion, 2bþ has a reduction potential of
ꢁ471 mV.14 Benzimidazoline derivatives can be also
regarded as NADH analogs,15 and, depending on the
structures of acceptors, can undergo hydride transfer to
hydride acceptors by a one-step mechanism,14,16 or by a
mechanism involving successive single electron transfer
(SET) and hydrogen-atom transfer (HAT), which will be
called an SET–HAT mechanism.15
We estimated the reduction potentials for the oxidants
1aþ–cþ in order to compare their reactivity for hydride
transfer reactions. We analyze the kinetic results by using
Marcus theory, which is based on a one-step mechan-
ism.17 The Marcus equation provides a relationship
between the free energy of activation, the intrinsic barrier,
and the overall Gibbs free energy of reaction, and it
provides insight into the two-dimensional characteriz-
ation of the transition structure as well as the reaction
mechanism.
The overall free energy is related to the equilibrium
constant by
K ¼ expðꢁDGꢃ=RTÞ
(6)
where R is the gas constant and T is the temperature. The
free energy of activation is related to the rate constant by
ꢀ
ꢁ
kBT
h
ꢁDGꢂ
k ¼
exp
(7)
RT
where kB is Boltzmann’s constant and h is Planck’s constant.
As shown in Eqn (2), DGꢂ is assumed to be the sum of
two parts. The work term Wr is that part of DGꢂ that is
insensitive to the value of DG8. It has been found10 that
nonzero values of Wr are required even when the potential
energy surfaces from which they were calculated had no
metastable intermediates. For reactions of the type studied
here, it has been found12–14 that Wr is about ꢁ8 kJ/
mol,12–14 and we will use that value. The full explanation
of why part of the free energy of activation should
ultimately be sought in valence bond theory,21 but that is
beyond the scope of the present paper. However, the value
of ꢁ8 kJ/mol may be considered reasonable in light of the
charge-transfer interaction between the reactants.13 The
final conclusions of Marcus theory analysis are not overly
sensitive to Wr, as long as it is not too far from zero.13
The Brønsted a parameter, which equals d(lnk)/d(lnK),
can be obtained from Eqns (1–7), which yields
THEORY
Semiempirical Marcus theory18 has been applied with
considerable success to hydride transfer between NADþ
analogs, and this analysis demonstrates that such transfers
form a single, large family of reactions.12,13 In
semiempirical calculations of rate constants for hydride
transfer by Marcus theory, the rate constants for the
related symmetrical (or degenerate) reactions play a key
role.12,13
ꢀ
ꢁ
RT ln K
a ¼ x ꢀ 0:5ðt ꢁ 1Þ ꢅ 0:5
where
2ðt ꢁ 1Þ (8)
l
ꢀ
ꢁ
ðRT ln KÞ
x ¼ 0:5 1 ꢁ
(9)
l
A reaction series is defined by Eqn (1), where i and j
indicate the hydride acceptor and donor, respectively.
and
Aþi þ DjH ! AiH þ Dþj
(1)
dðln kiÞ
t ꢁ 1 ¼
(10)
dðln KꢃÞ
If the reactants and products are structurally related and
of the same charge type, it is assumed that the free energy
required for forming an encounter complex or a precursor
where K8 is the equilibrium constant of the reaction of Aiþ
with a standard hydride donor. We can write
ꢀ
ꢁ
19,20
ꢁDGꢃꢃ
structure
from the separated reactants, Wr, is the
Kꢃ ¼ exp
(11)
same as the free energy for forming a successor structure
from the separated products, Wp. In that case, the Marcus
relations10,18 predict that the free energy of activation is
given by13,18
RT
where DG8i8 is the overall Gibbs free energy of reaction
for the reaction of Aþi with a standard hydride donor. The
upper signs are used in Eqn (8) if the structural variation is
in the acceptor, and the lower signs are used if the
structural variation is in the donor.12 For the present work,
each system has the structural variation in the hydride
donor so we used the lower signs consistently.
2
DGꢂ ¼ Wr þ ð1 þ DGꢃ=lÞ ꢄ l=4
(2)
where DG8 is the Gibbs free energy of reaction, and l is
the intrinsic barrier given by
l ¼ ðli þ ljÞ=2
(3)
The parameter x is called the resemblance parameter
and it accounts for the parallel effect, also called the
Leffler–Hammond effect.22 The parameter t is called the
tightness parameter and it accounts for the perpendicular
effect, also called the Thornton effect.23
For consistency with previous work,12a 10-methyl-
acridan, 1Hb, has been used as the standard donor. Using
where li and lj are free energies of activation for the
related symmetrical reactions shown as Eqns (4, 5).
Aꢂi þ þ AiH
Dꢂj þ þ DjH
!
!
Aꢂi H þ Aþi
Dꢂj H þ Dþj
(4)
(5)
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc

486
I.-S. HAN LEE, H. J. KIL AND Y. R. JI
Eqn (10), the variation in rate constants of symmetrical
reactions with Ko can be used to evaluate the parameter t.
Or, conversely, the effect of changes in hydride affinity
of Aþi on the value of li can be evaluated from the change
in DG8i8, which is measurable. For hydride transfer
between NADþ analogs, t was found to be reasonably
constant with an average value of 0.8113 and this value is
used in the present work. The third term in Eqn (8) is
negligible in most cases because (RT/l)2 will usually be
very small. It has been shown, however, that both of the
first two terms in Eqn (8) are required for a satisfactory
estimate of a.12–14
Note that t was originally defined as the sum of the
bond orders of the in-flight hydrogen at the critical
configuration,12a but, more generally, it is a phenomen-
ological parameter related to the distance between the end
groups as well as the partial charge on the in-flight atom
or group.10 Theoretical work suggests18 that it is
approximately constant over a long range of K values,
as long as the end atoms are unchanged.
exchange reaction with NaClO4. Compound 1cþ was
prepared by addition of Grignard reagent to 1bþ followed
by oxidation reaction with p-chloranil and perchloric
acid.12b All the acridine compounds were identified by
their physical and spectroscopic properties. Compounds
2Ha–h were prepared by the method of Craig et al.24 with
a small modification.
A typical synthetic procedure is as follows: A mixture
of substituted benzoic acid (1.2 eq), o-phenylendiamine
(1 eq), and polyphosphoric acid (three times of weight of
acid) was heated with stirring at 175 8C for 1.5 h and then
cooled to room temperature. An aqueous solution
of NH4OH (7%) was added to neutralize unreacted acids
(benzoic acid and polyphosphoric acid). The solid was
filtered and thoroughly rinsed with the NH4OH solution to
give 2-substituted phenylbenzimidazole. The yields were
generally over 90%. Without further purification, the
product was treated with methyl iodide (3 eq) in methanol
containing NaOH (1 eq). The reaction mixture was heated
at 110 8C overnight in a pressure tube. The crude product
was recrystallized from absolute ethanol to give 2þ
(yields, over 80%). To a solution of 2þ (1 eq) in methanol
(25 ml/g), NaBH4 (3 eq) was slowly added . The reaction
mixture was stirred vigorously for 1 h under N2. After
removal of the solvent under reduced pressure the solid
was recrystallized from EtOH–H2O (2:1, v/v) to give a
colorless crystalline product, 2H (yields, over 70%).
In this paper we consider three reaction series: when
the structural variation for hydride transfer reaction is in
the hydride donor as shown by Eqns (12–14),
1aþ þ 2H ! 1Ha þ 2þ
1bþ þ 2H ! 1Hb þ 2þ
1cþ þ 2H ! 1Hc þ 2þ
(12)
(13)
(14)
the Brønsted a parameter can be obtained by using Eqn
(8) with the lower signs. Using the same donors for all
three systems makes the comparison possible in terms of
the Brønsted a, x, and t. The perpendicular effect, t, on a
is the same for all three systems and the magnitude of the
variation of a depends entirely on x. Ratios of a values
are given by
KINETICS 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 8C to facilitate comparison with a
large body of analogous results already available in this
solvent system.13 2-Propanol and water were distilled
before use. Reactions of 1aþ and 1bþ with 2H had
half-lives less than 1 s. The reaction rate constants were
determined with a stopped-flow apparatus (Hi-Tech
Scientific, SFA-20) attached to the spectrophotometer
(Beckmann DU-7500) by monitoring the decay of the
absorption of 1aþ and 1bþ at 420 nm. Reactions of 1cþ
with 2H were slow enough to monitor the decay of its
absorption at 420 nm. These reactions went to completion
in the presence of excess of 2H (>2.5 ꢇ 10ꢁ3 M). All
kinetic experiments were carried out with at least 25-fold
excess of the spectroscopically inactive constituent, 2H.
Therefore, kobs was obtained from the first-order rate
law:26
a1aþ
½dðln k1aþÞ=dðln k1bþÞꢆ
¼
(15)
a1bþ ½dðln K1aþÞ=dðln K1bþÞꢆ
The numerator in Eqn (15), the derivative involving
rate constants, is accessible experimentally by measuring
the rate constants, k, for the three reaction systems, and
the denominator, the derivative involving equilibrium con-
stants, is unity for the present system because the same
hydride donors, 2Ha–h, are used with each of the three
acceptors. These ratios demonstrate the Leffler–Ham-
mond or parallel effect. They are much less dependent on
the accuracy of the K values than the individual values.
Therefore, these ratios are very useful in comparing the
experimental results with Marcus theory.
ꢀ
and the second-order rate constants, k, were given by kobs
ꢁ
Ao ꢁ A1
At ꢁ A1
kobs ¼ tꢁ1 ln
(16)
SYNTHESIS
/
C, where C is the concentration of the substance in excess.
All kinetic experiments were performed at least four
times, in separate experiments. More than 20 experiments
were performed for fast reactions of 1aþ and 2bþ,
Compounds 1aþ and 1bþ were prepared by benzylation
and methylation of acridine using benzyl bromide and
methyl iodide, respectively,9 and followed by an ion
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc

HYDRIDE TRANSFER REACTION
487
Table 1. Rate constants and equilibrium constant for hydride transfer reactions
Reductant
Oxidant, k (Mꢁ1 sꢁ1
)
2H
1aþ
1bþ
1cþ
Ka
ꢁ1
ꢁ1
ꢁ2
ꢁ2
ꢁ2
ꢁ2
ꢁ2
ꢁ3
a
b
c
d
e
f
1.37 ꢇ 103
9.80 ꢇ 102
7.17 ꢇ 102
5.35 ꢇ 102
3.21 ꢇ 102
2.15 ꢇ 102
1.55 ꢇ 102
5.90 ꢇ 10
4.11 ꢇ 102
2.94 ꢇ 102
1.61 ꢇ 102
1.12 ꢇ 102
6.71 ꢇ 10
5.47 ꢇ 10
4.05 ꢇ 10
1.60 ꢇ 10
2.91 ꢇ 10
1.92 ꢇ 10
8.35 ꢇ 10
7.17 ꢇ 10
5.80 ꢇ 10
4.87 ꢇ 10
2.15 ꢇ 10
9.53 ꢇ 10
6.58 ꢇ 10
3.60 ꢇ 10
1.72 ꢇ 10
4.46
2.52
1.65
g
h
1.17b
1.12 ꢇ 10ꢁ1
a The equilibrium constant for the reaction of 1-benzyl-3-carbamoylpyridinium ion with 2H in Ref. 14.
b This value was obtained by extrapolation of a plot of lnK as a function of s in Ref. 14.
because the stopped-flow apparatus required small
volumes, which give rise to greater-than-usual uncertain-
ties in the concentrations. The average deviations from
mean values of kobs were about 5–8% for compounds 1aþ
and 1bþ and 5% for compound 1cþ.
The parallel effects for the reactions between NADþ
analogs are shown in Fig. 2. The correlation of lnk with s
for the reactions in Eqns (12–14) is shown in Fig. 3.
DISCUSSION
As shown in Table 1, the order of reactivity of the oxidants
is 1aþ > 1bþ > 1cþ. The oxidant 1aþ is more reactive
than 1bþ due to the greater inductive effect of benzyl as
compared to methyl; sI for phenyl, which distinguishes
the two substitutes, is 0.1.28 However, the introduction of
a phenyl group at the 9-position of the acridine ring,
which is the reactive site, decreases the reaction rate by
more than a factor of 103, resulting in 1cþ being much less
reactive than 1bþ. These trends are consistent with those
observed for the reactions of 1-benzyl-1,4-dihydroni-
cotinamide with 1bþ and 1cþ in acetonitrile at 20 8C,
where 1bþ reacts 31 times faster than 1cþ as a hydride
acceptor.29 It is believed that the steric effect of the phenyl
group predominates the inductive effect for 1cþ. This
reactivity trend is also consistent with the values of pKR
listed in Table 2 because logk may be linearly correlated
with pKR.9
RESULTS
Rate constants for hydride transfer reactions are listed in
Table 1. We also list the equilibrium constants for the
reaction of 1-benzyl-3-carbamoylpyridinium ion with 2H
in Table 1. Equilibrium constants, Brønsted a parameters,
and Hammett r parameters for hydride transfer reactions
are listed in Table 2 along with the values of l (kJ/mol),
Eored (ꢁmV), and pKR. The parameters required for
analyzing the parallel effect for hydride transfer reaction
are listed in Table 3. The correlation of lnk with lnK for
the reactions shown in Eqns (12–14) is shown in Fig. 1.
Table 2. Equilbrium constants, Brønsted as, and Hammett
rs for hydride transfer reactions
Parameter
1aþ
1bþ
1cþ
Another way to compare the reactivity of the oxidant is
to measure the magnitude of reduction potential. By using
a ladder procedure with the value of K for the reaction of
1bþ with 2Hb and previously reported values of K (the
equilibrium constants for the reactions of 1aþ and 1bþ
with 3-methyl-2-phenylbenzothiazoline, respectively),12d
Ka
x
1.45 ꢇ 1012b
1.23 ꢇ 1011c
7.81 ꢇ 1010c
0.41
383
0.42
385
0.43
456
l (kJ/mol)
a (expt.)
a (calc.)e
r
0.50 ꢀ 0.03d
0.51 ꢀ 0.02d
0.52 ꢀ 0.05d
0.51
0.52
0.53
ꢁ1.57 ꢀ 0.11d ꢁ1.62 ꢀ 0.08d ꢁ1.63 ꢀ 0.15d
Eored (ꢁmV)
47
79f
85
pKR
6.66g (8.92)h 7.60i (10.00)h 8.57j (11.03)k
Table 3. Demonstration of the parallel effect
a Equilibrium constants for reactions of each oxidant with 2Hb.
b Determined by the ladder procedure.
Ratio
of rs
Calculated
ratio of as
c Values obtained from Ref 25.
Slopea,b
d The uncertainty is a probable error.
oxidant
e Values obtained from Eqn (8).
1aþþ–1bþþ
1bþ–1cþ
1a –1c
0.97 ꢀ 0.05
0.96 ꢀ 0.07
0.93 ꢀ 0.08
0.97
0.99
0.96
0.98
0.98
0.96
f This value was obtained from Ref. 12d.
g An estimated value from extrapolation of a plot of pKR in our solvent
system (2-propanol: H2O, 4:1 v/v) against pKR in H2O.
h Values obtained in H2O from Ref. 9.
i This value was obtained from Ref. 31 (This value was reported as 7.74 due
to a systematic computational error in the literature.)
j The value was obtained from Ref. 12c.
a The slopes of the plots of lnk in one series as a function of lnk in another
series for the same hydride donors, 2Ha–h, with a different hydride
acceptor, 1R.
k The value was obtained from Ref. 27.
b The uncertainty is a probable error.
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc

488
I.-S. HAN LEE, H. J. KIL AND Y. R. JI
Figure 3. The correlation of lnk with s for the reactions in
Eqns (12–14). The slopes of plots, which are the values of r,
are ꢁ1.57 (r ¼ 0.970) for 1aR (~), ꢁ1.62 (r ¼ 0.984) for 1bR
(&), and ꢁ1.63 (r ¼ 0.944) for 1cR (^), respectively. The
slopes are divided by 2.3 to convert them to r values
Figure 1. The correlation of lnk with lnK for the reactions
shown in Eqns (12–14). The slopes of plots (the Brønsted a)
are 0.50 (r ¼ 0.974) for 1aR (~), 0.51 (r ¼ 0.987) for 1bR
(&), and 0.52 (r ¼ 0.945) for 1cR (^), respectively
we can calculate that the equilibrium constant for the
reaction of 1aþ with 2Hb is 1.45 ꢇ 1012. The equilibrium
constants for the reactions of 1Ha with 1bþ and 1Hc with
1bþ in the same solvent system can be also obtained by
another ladder, which yields 8.48 ꢇ 10ꢁ2 for 1aþ and
6.35 ꢇ 10ꢁ1 for 1cþ.25 With these values of K, reduction
potentials, Eored, of ꢁ47 mV for 1aþ and ꢁ85 mV for 1cþ,
are obtained by
where F is the Faraday constant and n is the number of
electrons transferred (two in this case).31
For all the systems, Brønsted plots were made by
plotting the values of lnk against the values of lnK for the
reactions shown in Eqns (12–14). The equilibrium
constants are obtained from the reactions of
1-benzyl-3-carbamoylpyridinium ion with 2H.14 It is
assumed that since the structural variations are in the
donors (2H), the equilibrium constants for the present
system are proportional to those for the reactions of
RT ln K ¼ nFDEꢃ
(17)
Figure 2. The parallel effects for hydride transfer reactions between NADþ analogs. The slopes are 0.97 (r ¼ 0.982), 0.96
(r ¼ 0.967), and 0.93 (r ¼ 0.954) for I, II, and III, respectively. They are in good agreement with the ratios of calculated a values, as
shown in Table 3
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc

HYDRIDE TRANSFER REACTION
489
1-benzyl-3-carbamoylpyridinium ion with 2H.14 All
three plots are quite reasonably linear, as shown in
Fig. 1. According to Eqn (8), their slopes are the Brønsted
a values; these are given in Table 2, along with the
probable errors of the slopes. The values of slopes are
0.50 ꢀ 0.03 for 1aþ, 0.51 ꢀ 0.02 for 1bþ, and 0.52 ꢀ 0.05
for 1cþ, respectively. Since the same values of K were
used for all three plots, errors in a values due to errors in K
values (about 10%)14 are completely compensated when
ratios of a values are taken. In other words, differences in
a are almost unaffected by errors in the K values and such
ratios are much more reliable than would be suggested by
the probable errors of the values of a themselves.
The calculated values of a in Table 2 can be obtained
from the Marcus theory in Eqns (8, 9) if the values of Wr,
t, l, are available (the values of Wr (ꢁ8 kJ/mol) and t
(0.81) were described above). With the values of DGꢂ,
DG8, and Wr in hand, l and x were evaluated from Eqns
(8, 9). They are listed in Table 2. The intrinsic barrier of
2Hb, l2Hb, has been reported as 413 kJ/mol.14 With this
value we can estimate the individual values of l by
applying to Eqn (3), giving 353 (kJ/mol) for l1aþ, 357 (kJ/
mol) for l1bþ, and 502 (kJ/mol) for l1cþ, respectively.
The compound 1cþ has the highest reaction barrier
among them, leading to the lowest reactivity. The
introduction of phenyl group at C-9 on the acridine ring
for 1cþ gives a significant steric effect which overcomes
the electronic effect, resulting in the reduction of the
reactivity. This provides additional support for the order
of reactivity.
as described in the Section ‘Theory’. This method can
avoid the use of the series of K values by cancellation of
the ratio of K in denominator in Eqn (15). The plots are
shown in Fig. 2. The slopes of these plots slightly differ
from unity because of the parallel effect. This effect for
the present system may not be as significant as the earlier
observation14 due to a narrow range of K values compared
to the previous system which had a much wide range of K
values (1012), but it is still appreciable as shown in
Table 3. They should be given by ratios of calculated a
values according to Eqn (15). They are also in good
agreement.
The Hammett parameter32 can be also used for
mechanistic study by comparing r values in a similar
way. The correlations of lnk with Hammett parameter, s,
show a good linearity for all three series as shown in
Fig. 3, giving r values of ꢁ1.57, ꢁ1.62, and ꢁ1.63 for
1aþ, 1bþ, and 1cþ, respectively, after dividing by 2.3 to
put them on the usual scale. As expected, the values of r
are negative because the reacting site at C-2 on the
benzimidazole ring of 2H develops a positive charge in
the transition state. The ratios of r are very similar to the
slopes shown in Fig. 2 as well as the ratios of the
calculated a values. All the selectivity parameters
indicate that the reactivity-selectivity principle (RSP)
holds, so that rates of the hydride transfer are more
dependent on basicities rather than on intrinsic barriers.
The foregoing results are consistent with the mechan-
ism that the present system undergoes direct hydride
transfer from 2H to 1aþ-cþ without high-energy
intermediate.
The equilibrium constants are much larger than unity
for the present system, giving x values of 0.41, 0.42, and
0.43 for 1aþ, 1bþ, and 1cþ, respectively. But the
calculated values of a are 0.51, 0.52, and 0.53 for 1aþ,
1bþ, and 1cþ, respectively, as shown in Table 2. The
experimental and calculated a values are in fairly good
agreement. The calculated values reproduce the trend in
the experimental values almost exactly. This trend is an
expression of the Leffler–Hammond or parallel effect. It
shows the gradual change in transition state structures as
the reactions become more spontaneous even though the
difference is not large. It should be pointed out that most a
values for the present system are greater than 0.5 even
though the values of K are much greater than unity,
although conventionally one would expect them to be less
than 0.5.22 This is explained by the perpendicular effect,
that is, by the second term in Eqn (8).30 The structural
variation is in the hydride donor in the present system and
the perpendicular effect (0.5(t – 1)) should be subtracted
from x in Eqn (8). As mentioned in the Section ‘Theory’,
t is 0.81, leading to the contribution of the perpendicular
effect of ꢁ0:5ð0:81 ꢁ 1Þ ¼ þ0:1 on the Brønsted a in the
present case. This leads to the value of a greater than x by
itself.
CONCLUSIONS
The introduction of phenyl group on the acridine ring
affects the reactivity and the reactivity depends on its
location. The order of reactivity for the acridine
compounds is 1aþ > 1bþ and > 1cþ and their reduction
potentials, Eored, are ꢁ47 mV for 1aþ, ꢁ79 mV for 1bþ,
and ꢁ85 mV for 1cþ, respectively. The Brønsted a for the
present system can be calculated with the aid of Marcus
theory which is based on a one-step mechanism and the
calculated and experimental a values are in good
agreement. Within Marcus formalism the present system
can also demonstrate the Leffler–Hammond or parallel
effect by introducing the same structural variation in the
hydride donor, 2H.
Acknowledgements
Plotting of lnk values for reduction of one oxidant as a
function of lnk for reduction of another oxidant by the
same donors, 2Ha–h, can demonstrate the parallel effect
This work was supported by Korea Science and Engin-
eering Foundation (R01-2004-10279). The authors thank
Professors D. G. Truhlar and M. M. Kreevoy in the
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc

490
I.-S. HAN LEE, H. J. KIL AND Y. R. JI
University of Minnesota for valuable comments and
discussion as well as for proofreading the manuscript.
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Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 484–490
DOI: 10.1002/poc