Thermodynamics and kinetics of formation of intramolecular naphthalene dimer radical cation studied by near-IR transient absorption spectroscopy

Article abstract of DOI:10.1246/bcsj.77.1443

Thermodynamics and kinetics for formation of an intramolecular dimer radical cation of a series of α,ω-di(2-naphthyl)alkanes in solutions were quantitatively investigated by near-IR transient absorption spectroscopy, which allows one to observe dimer radical cations directly. The standard enthalpy (-ΔH°) for the formation of the intramolecular dimer radical cation increased as the chain length between the two naphthyl moieties increased, and was smaller than that of the intermolecular dimer radical cation of 2-ethylnaphthalene. This shows that -ΔH° depends on the strain required for the chain to form the ring-closure configuration. Destabilization due to repulsion between the two naphthyl moieties in the intramolecular dimer radical cation was evaluated to be ca. 20 kJ mol^-1. This value is smaller than that of the naphthalene excimer, indicating that the separation distance and/or the overlap between the two naphthyl moieties are not as restricted as those of the excimer. The activation energy for the formation of the intramolecular dimer radical cation was comparable to the energy for local motions of a few methylene units linking the two naphthalene moieties.

Full text of DOI:10.1246/bcsj.77.1443

ꢀ 2004 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 77, 1443–1448 (2004) 1443
Headline Articles
Thermodynamics and Kinetics of Formation of Intramolecular
Naphthalene Dimer Radical Cation Studied by Near-IR Transient
Absorption Spectroscopy
ꢀ
Toshiki Fushimi, Yusuke Fujita, Hideo Ohkita, and Shinzaburo Ito
Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University,
Katsura, Nishikyo, Kyoto 615-8510
Received February 16, 2004; E-mail: sito@photo.polym.kyoto-u.ac.jp
Thermodynamics and kinetics for formation of an intramolecular dimer radical cation of a series of ꢀ,!-di(2-naph-
thyl)alkanes in solutions were quantitatively investigated by near-IR transient absorption spectroscopy, which allows one
to observe dimer radical cations directly. The standard enthalpy (ꢁꢀHꢂ) for the formation of the intramolecular dimer
radical cation increased as the chain length between the two naphthyl moieties increased, and was smaller than that of
the intermolecular dimer radical cation of 2-ethylnaphthalene. This shows that ꢁꢀHꢂ depends on the strain required
for the chain to form the ring-closure configuration. Destabilization due to repulsion between the two naphthyl moieties
in the intramolecular dimer radical cation was evaluated to be ca. 20 kJ molꢁ1. This value is smaller than that of the naph-
thalene excimer, indicating that the separation distance and/or the overlap between the two naphthyl moieties are not as
restricted as those of the excimer. The activation energy for the formation of the intramolecular dimer radical cation was
comparable to the energy for local motions of a few methylene units linking the two naphthalene moieties.
Bichromophoric molecules are useful model compounds for
investigating intramolecular interactions between two aromatic
groups such as excimers, exciplexes, and dimer radical cati-
ons.1–19 Among them, formation of intramolecular excimers
has been most extensively studied since the first report of intra-
molecular excimers in diphenyl and triphenyl alkanes by
Hirayama.4 This is because the fluorescent properties of exci-
mers and exciplexes enable one to discuss the kinetics4–7,9–13
and thermodynamics7,10,11,13 for the geometrical arrangement
quantitatively by fluorescence spectroscopy with high sensitiv-
ity and time resolution. Many studies have been done so far us-
ing bichromophoric molecules in which two chromophores are
connected by a chain with various lengths,7–11 composi-
tions,11–13 and diastereoisomeric forms.13 For example, we
found that ꢀ,!-di(2-naphtyl)alkanes (DNpn, the length of the
methylene chain between the two naphtyl groups n ¼ 3{12)
formed an intramolecular excimer only at n ¼ 3, and that the
standard enthalpy and the activation energy for the formation
of the excimer are 18 and 14 kJ molꢁ1, respectively.7 On the
other hand, Zachariasse et al. found that dipyrenyl compounds
formed intramolecular excimers in a wide range of chain
lengths. They discussed the standard enthalpy, the activation
energy for the formation of the intramolecular excimers, and
dependence of formation yield on the chain length.8,11 These
results show that the formation of excimers strongly depends
on the length of the chain.
On the contrary, there is no quantitative study on intramolec-
ular dimer radical cations formed in a series of bichromophoric
compounds with various chain lengths. There are only qualita-
tive studies on the formation of intramolecular dimer radical
cations formed in bichromophoric compounds linked by short
alkane chains.14–18 The lack of a quantitative study is probably
due to difficulties in the evaluation of the numbers of monomer
and dimer radical cations. In general, monomer radical cations
show absorption overlapping that of dimer radical cations in the
UV–visible region, which is covered by conventional transient
absorption spectroscopy. Near-IR transient absorption spec-
troscopy is a powerful tool for observing characteristic absorp-
tion bands originating from inter- and intramolecular interac-
tions between aromatic molecules, which correspond to the
photon energy in the near-IR region. Dimer radical cations have
a characteristic absorption band in the near-IR region, which is
called the charge resonance (CR) band. It originates from
charge delocalization between two aromatic molecules.16–21
On the other hand, most radical cations of aromatic molecules
have absorption bands in the UV–visible region. Thus, the num-
bers of monomer and dimer radical cations can be quantitative-
ly evaluated by absorption spectroscopy from the UV–visible to
the near-IR wavelength regions, even if the ratio of dimer radi-
cal cations to monomer radical cations is low. In addition, ob-
servation of CR bands allows one to evaluate the stabilization
energy due to the charge delocalization (CR stabilization).16–21
Published on the web August 6, 2004; DOI 10.1246/bcsj.77.1443

1444 Bull. Chem. Soc. Jpn., 77, No. 8 (2004)
HEADLINE ARTICLES
Here, we investigated an intramolecular dimer radical cation
in a series of DNpn in solutions by near-IR transient absorption
spectroscopy. We discuss quantitatively for the first time the ki-
netics and thermodynamics for the formation of the intramolec-
ular dimer radical cation in DNpn and its dependence on the
length of the chain between the naphthyl (Np) moieties.
(a)
(b)
1
2
3
5
µ
µ
µ
µ
s
s
s
s
0.08
0.04
Experimental
0
0.2
0.1
0
Materials. 1,3-Di(2-naphthyl)propane (DNp3) was synthe-
sized from Wolff–Kishner reduction of 1,3-di(2-naphthyl)propan-
1-one, which was prepared by the hydrogenation of the product ob-
tained from the condensation of 2-naphthaldehyde and 2-aceto-
naphthone in an alkaline ethanol solution.5 1,5-Di(2-naphthyl)pen-
tane (DNp5) was synthesized from the reduction of 1,5-di(2-naph-
thyl)pentan-3-one, which was prepared by the hydrogenation of the
product obtained from the condensation of 2-naphthaldehyde and
acetone. 1,7-Di(2-naphthyl)heptane (DNp7) and 1,12-di(2-naph-
thyl)dodecane (DNp12) were synthesized from the reduction of
the corresponding ꢀ,!-di(2-naphthoyl)alkanes, which were pre-
pared by the Grignard reactions of 2-naphthonitrile and the corre-
sponding ꢀ,!-dibromoalkanes. The detailed synthesis of this
DNpn series has been described elsewhere.7 The monomeric com-
pound of 2-ethylnaphthalene (EtNp) was purchased from Tokyo
Kasei Kogyo Co. and was used without further purification. o-Di-
cyanobenzene (o-DCNB) used as an electron acceptor was pur-
chased from Tokyo Kasei Kogyo Co. and was used after several
recrystallizations. Acetonitrile (spectroscopic grade) was pur-
chased from Nacalai Tesque and was used without further purifica-
tion. The sample solutions in 1-cm quartz cells were degassed by
the freeze–pump–thaw method. The concentration of the naphtha-
lene compounds was adjusted to 0.3 mM where intermolecular for-
mation of a Np dimer radical cation is negligible. The concentra-
tion of o-DCNB was 0.1 M.
Measurements. A nanosecond laser pulse (308 nm, ꢃ0:5
mJ cmꢁ2, fwhm 17 ns) from a XeCl excimer laser (Lambda Physik
EMG101MSC) was used as an excitation light source. For meas-
urement of transient absorption decay, a pulsed 500-W xenon flash
lamp was used as a monitor light source. The monitor light in the
direction normal to the excitation light was passed through a mon-
ochromator (Ritsu, MC-10N) before detection. A photomultiplier
tube (Hamamatsu Photonics, R5188) was used as a detector. The
temperature of a sample cell set in a quartz Dewar vessel was con-
trolled by precooled nitrogen gas. For measurement of transient ab-
sorption spectra, a steady-state 150-W xenon lamp was used as a
monitor light source. A photomultiplier tube (Hamamatsu Photon-
ics, R1477) and an InAs photovoltaic detector (Hamamatsu Pho-
tonics, P838) were used for the detection in the visible region from
400 to 850 nm and in the near-IR region from 780 to 2000 nm,
respectively.
1
2
3
5
µ
µ
µ
µ
s
s
s
s
6W00 av70e0le8n0g0th10/0n0m
500
2000
Fig. 1. Transient absorption spectra for radical cations of
6 mM EtNp in acetonitrile solutions with 0.1 M o-DCNB
1, 2, 3, and 5 ms after laser excitation at (a) 295 K and
(b) 233 K.
at 675 nm disappeared completely, while the two broad absorp-
tion bands due to the dimer radical cation remained, as shown
in Fig. 1b. The molar absorption coefficients are reported to be
4500 Mꢁ1 cmꢁ1 at 675 nm for the absorption of the monomer
radical cation and 4400 Mꢁ1 cmꢁ1 at 1100 nm for the CR band
of the dimer radical cation.19 Thus, we can evaluate the concen-
trations of the dimer radical cation [Dþ] as well as the monomer
radical cation [Mþ] from these characteristic absorption bands.
The dimer radical cation of Np formed not only intermolec-
ularly, but also intramolecularly. A sharp absorption band at
675 nm and a broad absorption band around 1250 nm were
observed in the transient absorption spectrum of DNp5 at 295
K in an acetonitrile solution with 0.3 mM DNp5 and 0.1 M
o-DCNB.19 The sharp and the broad absorption bands were as-
cribed to the monomer radical cation and the intramolecular di-
mer radical cation of DNp5, respectively. Figure 2 shows the
time evolution of the ratio of dimer radical cations [Dþ] to
monomer radical cations [Mþ] formed in DNp5 at various tem-
peratures. The ratio was evaluated from the absorbance at 675
and 1050 nm. There are two characteristic time domains in the
time evolution of the ratio. The ratio increased in the earlier
time domain and saturated in the later time domain. The rise
in the ratio in the earlier time domain shows dynamic formation
of the intramolecular dimer radical cation. From the data ob-
tained in the earlier time domain, we will discuss the kinetics
and the activation energy ED for the formation of the intramo-
lecular dimer radical cation in the latter half of this paper. From
the data obtained in the later time domain, we will discuss the
standard enthalpy ꢁꢀHꢂ for the formation in the next section.
Thermodynamics of the Formation of the Dimer Radical
Cation of DNpn. Figure 3 shows the van’t Hoff plots for the
formation of the dimer radical cation in DNp5, 7, 12, and EtNp.
Each ꢁꢀHꢂ evaluated from the slopes is listed in Table 1, with
the experimental error, which was less than 4 kJ molꢁ1 for all
compounds. The standard enthalpy ꢁꢀHꢂ for the dimer radical
Results and Discussion
Figures 1a and 1b show the transient absorption spectra for
radical cations of EtNp at 295 and 233 K, respectively, formed
in an acetonitrile solution with 6 mM EtNp and 0.1 M o-DCNB
1, 2, 3, and 5 ms after laser excitation. At 295 K, three charac-
teristic absorption bands were observed, as shown in Fig. 1a.
The sharp absorption band at 675 nm is ascribed to the mono-
mer radical cation of EtNp.16,17 The broad absorption bands
around 590 and 1100 nm are ascribed to the local excitation
(LE) and charge resonance bands of the intermolecular dimer
radical cation of EtNp.16,17 At 233 K, the sharp absorption band

T. Fushimi et al.
Bull. Chem. Soc. Jpn., 77, No. 8 (2004) 1445
2
b)
K243
233 K
hνCR
a)
+
+
1
K253
K273
ER
ECR
c)
253 K
273 K
+
−∆H°
(
)
0
0
1000 2000 3000 4000
Scheme 1. Schematic energy diagrams for ꢁꢀHꢂ, ECR, and
ER. a) The two Np moieties are far from each other and the
charge is localized on either of the Np moieties. b) The mu-
tual configuration of the two Np moieties is the same as that
of the dimer radical cation, but the charge is localized. c)
The mutual configuration is the same as that of b), and
the charge is delocalized between the Np moieties.
Time / ns
Fig. 2. Time evolution of [Dþ]/[Mþ] for DNp5 after laser
excitation at several temperatures. The circle, rectangle,
and triangle indicate the value of [Dþ]/[Mþ] at 273, 253,
and 233 K, respectively.
methylene chain (DNp12) < the intermolecular dimer radical
cation (EtNp). These results indicate that the strain in shorter
methylene chains prevents formation of a stable dimer radical
cation. The chain length is too short for DNp5 and DNp7 to
form a dimer radical cation that is as stable as the intermolec-
ular Np dimer radical cation of EtNp, but is long enough for
DNp12 to do so. This tendency corresponds to that of the CR
stabilization energy ECR, which has been discussed else-
where.19
DNp12
EtNp
2
1
8
7
6
5
0
DNp7
DNp5
-1
The CR stabilization energy ECR of the dimer radical cation
formed in DNpn can be evaluated from the CR bands, whose
peak wavelength corresponds to about half of the energy re-
quired for the CR transition.16–21 The ECR due to the charge de-
localization was larger than the thermodynamical stabilization
energy ꢁꢀHꢂ for all the DNpn. The difference between ECR
and ꢁꢀHꢂ is equal to the repulsion energy ER, which is due
to the electronic repulsion between a neutral Np moiety and a
Np radical cation in a configuration where a dimer radical cat-
ion could be formed. Scheme 1 shows the relationship among
ꢁꢀHꢂ, ECR, and ER; i.e., ER ¼ ECR ꢁ ðꢁꢀHꢂÞ. The dimer for-
mation would be conveniently divided into two steps: 1) cycli-
zation to a conformation where the two Np moieties have the
same mutual configuration as the dimer radical cation, but the
charge is localized in one of the two Np moieties; 2) charge de-
localization without any conformational changes. These values
are summarized in Table 1. The experimental error in ECR orig-
inating from the evaluation of the peak wavelength of the CR
bands was less than 2 kJ molꢁ1, which corresponds to a devia-
tion of ca. 50 nm in the peak wavelength. The values of ER are
about 20 kJ molꢁ1 for the intramolecular dimer radical cation of
all the DNpn as well as for the intermolecular dimer radical cat-
3.4 3.6 3.8
4
4.2
1000 T −1 / K −1
Fig. 3. van’t Hoff plots for the formation of the dimer radi-
cal cation of DNpn (n ¼ 5, 7, and 12) and EtNp. The open
circle, closed circle, closed rectangle, and open rectangle
indicate the value of ln K for DNp5, 7, 12, and EtNp at var-
ious temperatures, respectively.
Table 1. Values of ꢁꢀHꢂ, ECR, ER, kD, and Ea for the Dimer
Radical Cation of DNpn (n ¼ 5, 7, and 12) and EtNp
ꢁꢀHꢂ
ECR
ER
kD
Ea
/kJ molꢁ1 /kJ molꢁ1 /kJ molꢁ1 /106 sꢁ1a) /kJ molꢁ1
DNp5
DNp7
27 ꢄ 2
27 ꢄ 3
47 ꢄ 2
49 ꢄ 2
53 ꢄ 2
54 ꢄ 2
20 ꢄ 4 3:7 ꢄ 0:4 15 ꢄ 2
22 ꢄ 5 2:0 ꢄ 0:2 15 ꢄ 2
DNp12 30 ꢄ 4
23 ꢄ 6
19 ꢄ 3
19 ꢄ 2
13 ꢄ 2
EtNp
36 ꢄ 1
—
—
a) At 248 K.
cation of Np was larger than that of the excimer of Np and com-
parable to that of the excimer of pyrene.7 This is one of the rea-
sons why the intramolecular dimer radical cation of Np can be
formed for all of DNpn, while the intramolecular excimer of Np
cannot be formed apart from DNp3. The standard enthalpy
ꢁꢀHꢂ increased in the following order: the intramolecular di-
mer radical cation with a shorter methylene chain (DNp5,
DNp7) < the intramolecular dimer radical cation with a longer
ion of EtNp. This is smaller than that of ER for the Np excimer,
22
which is reported to be about 30 kJ molꢁ1
.
This difference
suggests that the separation distance and/or the overlap of
the two Np moieties in the dimer radical cation is not as restrict-
ed as those of the Np excimer. This is probably because the CR
interaction is less dependent on the separation distance and/or
the overlap between two aromatic moieties than the exciton in-

1446 Bull. Chem. Soc. Jpn., 77, No. 8 (2004)
HEADLINE ARTICLES
teraction. For example, an intramolecular dimer radical cation
is formed in trans-1,2-di(N-carbazolyl)cyclobutane,16 where
no intramolecular excimer is formed.14 Consequently, the over-
lapping structure for the Np dimer radical cation is slightly
distorted from the symmetrical sandwich structure to avoid
the ꢁ-electron repulsion between the two aromatic moieties.
Yamamoto et al. reported that the Np dimer radical cation with
a sandwich structure is less stable than that with a partially
overlapping structure.17 Badger and Brocklehurst obtained a
similar result from their calculations.21 These reports support
our interpretation.
from Scheme 2.
d½Mþꢅ
dt
d½Dþꢅ
dt
¼ ꢁkD½Mþꢅ ꢁ kR½Aꢁꢅ½Mþꢅ þ kDꢁ1½Dþꢅ
ð1Þ
ð2Þ
¼ kD½Mþꢅ ꢁ kDꢁ1½Dþꢅ ꢁ kR0 ½Aꢁꢅ½Dþꢅ:
A boundary condition holds over the entire time range.
½Aꢁꢅ ¼ ½Mþꢅ þ ½Dþꢅ:
The initial conditions are as follows:
ð3Þ
½Mþꢅ ¼ ½Mþꢅ0 at t ¼ 0
½Dþꢅ ¼ 0
ð4Þ
ð5Þ
Kinetic Study for the Formation of the Dimer Radical
Cation of DNpn. In this section, we discuss the kinetics for
the formation of the intramolecular dimer radical cation of
DNpn in the time domain before the equilibrium is established.
In this paragraph, we explain a model for analyzing the kinetics
and demonstrate the validity of the model. We assume a kinetic
scheme for the formation of the intramolecular dimer radical
cation, as shown in Scheme 2. The monomer radical cation
of DNpn and the counter anion are generated by photoinduced
electron transfer from one Np moiety in the excited state to a
dopant electron acceptor. The intramolecular dimer radical cat-
ion of DNpn is formed by the charge delocalization between the
monomer radical cation and the neutral Np moiety in a DNpn
molecule. Both monomer and dimer radical cations return to
the neutral state through charge recombination with an acceptor
at t ¼ 0:
We assumed that the charge recombination reactions are diffu-
0
sion-controlled. Thus, we can set kR ¼ kR . Under such initial
and boundary conditions and the assumption, the system of the
differential equations can be solved.
½Mþꢅ0½kDꢁ1 þ kD expfꢁðkD þ kDꢁ1Þtgꢅ
½Mþꢅ ¼
½Dþꢅ ¼
½Aꢁꢅ ¼
ð6Þ
ð7Þ
ð8Þ
ðkD þ kDꢁ1Þð1 þ ½Mþꢅ0kRtÞ
½Mþꢅ0½kD ꢁ kD expfꢁðkD þ kDꢁ1Þtgꢅ
ðkD þ kDꢁ1Þð1 þ ½Mþꢅ0kRtÞ
½Mþꢅ0
:
1 þ ½Mþꢅ0kRt
0
anion. The kinetic parameters, kD, kDꢁ1, kR, and kR for each
The time evolution of the absorbance at 675 and 1050 nm were
fitted with Eqs. 6 and 7, respectively. The values of [Mþ]0, kD,
and kR were evaluated from the fitting. For example, Fig. 4
shows the time evolution of the absorbance at 675 and 1050
nm for DNp7 at 248 K with the fitting curves drawn by solid
lines. The values of [Mþ]0, kD, and kR were evaluated from
DNpn represent the rate constants for the formation of the di-
mer radical cation, the dissociation of the dimer radical cation,
the recombination of the monomer radical cation with an ac-
ceptor radical anion, and the recombination of the dimer radical
cation with an acceptor radical anion, respectively. [Mþ], [Dþ],
and [Aꢁ] represent the concentrations of the monomer radical
cation, the dimer radical cation, and an acceptor radical anion,
respectively. The following differential equations are derived
the fitting to be 2:5 ꢆ 10ꢁ5
M
ꢁ1, 2:0 ꢆ 106 ꢁ1, and 6:5 ꢆ
s
109 Mꢁ1sꢁ1, respectively. The fitting curves agreed well with
the experimental data. This agreement demonstrates that our
model can explain the kinetics of the formation. The value of
M+
D+
+
kD
0.12
+
)
a) at 675 nm
0.08
(
A−
−
−1
A−
kD
−
0.04
0
0.06
0.04
0.02
kR
,
hv
kR
b) at 1050 nm
0
A
0
200 400 600 800
Scheme 2. Kinetic scheme for the intramolecular dimer radi-
0
cal cation. The parameters, kD, kDꢁ1, kR, and kR represent
Time / ns
the rate constants for the formation of the dimer radical cat-
ion, the dissociation of the dimer radical cation, the recom-
bination of the monomer radical cation with an acceptor
radical anion, and the recombination of the dimer radical
cation with an acceptor radical anion, respectively.
Fig. 4. Time evolution of absorbance at (a) 675 and (b)
1050 nm for DNp7 after laser excitation at 248 K. The dots
and solid lines show the experimental data and the fitting
curves, respectively.

T. Fushimi et al.
Bull. Chem. Soc. Jpn., 77, No. 8 (2004) 1447
kR obtained from the fitting was similar to that evaluated from
the viscosity of the solvent under the diffusion-controlled con-
dition.23 This agreement proves that our assumption is valid:
the charge recombination reactions are diffusion-controlled.
We obtained these kinetic parameters for the series of DNpn
at 248 K: kD > 108 sꢁ1 for DNp3, kD ¼ 3:7 ꢆ 106 sꢁ1 for
DNp5, kD ¼ 2:0 ꢆ 106 sꢁ1 for DNp7, kD ¼ 1:9 ꢆ 107 sꢁ1 for
DNp12. The experimental error for kD originating from noise
in the time evolution was ca. ꢄ10 percent. We will discuss
the dependence of kD on the length of the methylene chain n
in the next paragraph.
17
16
15
14
DNp12
DNp5
DNp7
The rate constant for the formation of the intramolecular
dimer radical cation was largest at n ¼ 3. The values of kD de-
creased by two orders of magnitude at n ¼ 5 and 7, and by one
order of magnitude at n ¼ 12. The kD for DNp3 was roughly
estimated to be more than 108 sꢁ1 in the range of temperature
measured from 233 to 295 K because the time constant for the
rapid rise of the CR band corresponded to the width of the laser
pulse (FWHM = 20 ns) even at 233 K, where the value of kD
should be smallest. The rapid formation is because the propane
chain is favorable for formation of dimer radical cations in a
parallel configuration, which is consistent with the Hirayama
rule.4 The value of kD is larger than that for the intramolecular
excimer at n ¼ 3, which is 1:9 ꢆ 107 sꢁ1 at 233 K and 4:8 ꢆ
107 sꢁ1 at 253 K.7 That the formation of the intramolecular di-
mer radical cation is faster than the intramolecular excimer may
be due to the less restricted separation distance and/or the over-
lap between the two Np moieties required for the formation of
the dimer radical cation than those for the excimer. On the con-
trary, the dimer radical cation of DNp5 and DNp7 were formed
slowly, in several microseconds. This is one of the reasons why
DNp5 and DNp7 cannot form an intramolecular excimer: the
lifetime of Np in the excited state is as short as 55 ns.7 The di-
mer radical cation of DNp12 was formed about 10 times faster
than those of DNp5 and DNp7. This dependence of kD can be
explained in terms of the ring-closure probability of the DNpn
molecules. The ring-closure probability of DNp5, DNp7, and
DNp12 corresponds to that of alkane chains with 8, 10, and
15 methylene units, respectively, because two aromatic groups
forming a dimer radical cation can be considered as three meth-
ylene units forming a half part of a cyclohexane ring in the chair
conformation.8,19 The observed dependence is enhanced com-
pared with the ring-closure probability of alkane chains. The
probability predicts that alkane chains with 8 to 13 methylene
units are virtually unclosed, while those with more than 14
methylene units can take closed conformations.24 Sisido and
his co-worker calculated the distribution of the end-to-end dis-
tances r for DNpn molecules (n ¼ 3{16).25 They found that no
conformation leads to an end-to-end distance of r < 0:5 nm for
all the DNpn molecules in the ground state. Thus, the enhance-
ment of the dimer formation results from the large stabilization
energy of the charge delocalization in the dimer radical cation,
which allows the DNpn cation to form closed conformations
more easily than the corresponding neutral molecules.
3.9
4
4.1
4.2
4.3
1000 T−1/K−1
Fig. 5. Arrhenius plots for the formation of the intramolec-
ular dimer radical cation of DNpn. The open circle, rectan-
gle, and triangle indicate the value of ln kD for DNp5, 7,
and 12 at various temperatures, respectively.
kJ molꢁ1 for DNp5, DNp7, and DNp12, respectively. The ex-
perimental error for Ea originating from the evaluation of kD
was less than 2 kJ molꢁ1. The values of the activation energy
ED for the formation of the dimer radical cation were 8, 8,
and 6 kJ molꢁ1 for DNp5, DNp7, and DNp12, respectively, be-
cause the activation energy E of acetonitrile is reported to be 7
ꢂ
kJ molꢁ1
.
26 These values of ED are smaller than those of ER for
all the DNpn molecules. This difference in energy demonstrates
that a transition state of the intramolecular dimer formation is
more stable than the state shown in Scheme 1b. In other words,
the positive charge is delocalized over the two aromatic moiet-
ies at an early stage of the formation process where the two ar-
omatic moieties are not as close as the geometry of the dimer
radical cation. Considering the experimental errors, we con-
clude that these observed values of ED are independent of the
chain length n and are rather comparable to or less than that
of the activation energy required for the conformational transi-
tion of methylene chains. Thus, we conclude that the formation
of the dimer radical cation is controlled by local motions of a
few methylene units linking two aromatic moieties as well as
by the hydrodynamic force of solvents. The dependence of
kD on the chain length results from a frequency factor for en-
counter of the two Np moieties, not from the activation energy
ED, because motions required to form the dimer radical cation
are probably so local that only a few units from the Np moieties
participate in the dimer formation.
Conclusion
The thermodynamics and the kinetics for the formation of
the intramolecular dimer radical cation in the series of DNpn
in acetonitrile solutions were quantitatively investigated by
transient absorption measurement in the wavelength region of
the UV–visible to the near-IR, where characteristic absorption
bands for the monomer radical cation and the dimer radical cat-
ion are observed. The standard enthalpy ꢁꢀHꢂ evaluated from
the van’t Hoff plots has a good relation with the charge reso-
nance energy ECR, which increased with a decrease in the strain
of the methylene chain for the formation of the intramolecular
dimer radical cation. The value of the repulsion energy ER was
evaluated to be ca. 20 kJ molꢁ1 for all DNpn, which is smaller
We measured the formation rate kD for a series of DNpn over
a temperature range from 233 to 253 K. Figure 5 shows the
Arrhenius plots for the formation of the intramolecular dimer
radical cation of DNpn. The values of the apparent activation
energy Ea obtained from the slopes were 15, 15, and 13

1448 Bull. Chem. Soc. Jpn., 77, No. 8 (2004)
HEADLINE ARTICLES
than that of the Np excimer by ca. 10 kJ molꢁ1. This difference
indicates that the separation distance and/or the overlap be-
tween the two Np moieties in the dimer radical cation are not
as restricted as those in the Np excimer. The rate constants
for the formation of the dimer radical cation kD was evaluated
from the time evolution of the absorption bands for the mono-
mer and the dimer radical cation. Compared with the ring-clo-
sure probability of methylene chains, the dependence of kD on
the chain length was enhanced by the stabilization energy of the
charge delocalization in the dimer radical cation. The activation
energy ED for the formation of the dimer radical cation of
DNpn was comparable to the energy for local motions of a
few methylene units linking the two Np moieties. These find-
ings provide quantitative understanding of the behavior of in-
tramolecular dimer formation, such as dependence of dimer
formation yield on temperature and on the length of a chain
linking two chromophores.
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This work was supported by Grants-in-Aid for Encourage-
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