Preparation and magnetic properties of radical anion salts derived from styrylpyryliums and the corresponding photo-dimers

Article abstract of DOI:10.1246/bcsj.76.1245

The preparation and magnetic properties of organic radical anion salts derived from styrylpyrylium derivatives 1a and 2a are described and compared to those of the corresponding photo-dimers. The magnetic properties of the radical anions for TCNQ salt 1b

Full text of DOI:10.1246/bcsj.76.1245

Ó 2003 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 76, 1245–1250 (2003) 1245
Preparation and Magnetic Properties of Radical Anion Salts Derived
from Styrylpyryliums and the Corresponding Photo-Dimers#
ꢀ
Shin0ichi Nakatsuji, Yuya Ogawa, Hiroki Akutsu, and Jun-ichi Yamada
Department of Material Science, Graduate School of Science, Himeji Institute of Technology,
3-2-1 Kouto, Kamigori, Hyogo 678-1297
(Received November 22, 2002)
The preparation and magnetic properties of organic radical anion salts derived from styrylpyrylium derivatives 1a
and 2a are described and compared to those of the corresponding photo-dimers. The magnetic properties of the radical
anions for TCNQ salt 1b and TCNQF4 salt 1c are rather different, showing antiferromagnetic interactions based on the 1-
D Heisenberg model in the former, and ferromagnetic interactions in the latter. This difference is considered to be a
result of the fairly large difference in their crystal structures. A considerable change in the magnetic properties was
found between the radical anion salts of monomers and the corresponding photo-dimers, in which magnetic susceptibil-
ities are largely diminished.
The search for novel spin systems with multiple properties
is of current interest in the field of molecular-based magnetic
materials to examine the synergy between magnetic properties
and other properties such as conduction, optical, liquid crystal-
line, and other physical properties.1 As for the development of
organic spin systems with optical properties, several groups
have recently developed intriguing organic photo-responsive
spin systems. Iwamura, Matsuda et al. reported in 1998 an
azobenzene derivative carrying two nitronyl nitroxide radicals,
and observed it’s UV as well as it’s EPR spectral change upon
irradiation in solution.2 Matsuda, Irie et al. have succeeded in
switching the intramolecular spin-spin interactions efficiently
in their elaborate diarylethene systems.3 Veciana and his col-
laborators have reported on interesting photo-dimerization in
an iminoferrocene derivative with a triphenylmethyl radical.4
In this case, although no reverse reaction was reported, pho-
to-induced intramolecular isomerization and the successive di-
merization were observed to give this diradical. Interesting ex-
amples of 2-D photochromic molecular based magnets, such as
(spiropyran)MCr(ox)3, that show a change in their hysterisis
loops upon irradiation have also been reported recently by
Pei Yu et al.5
In the course of our studies in the development of organic
multifunctional spin systems,6 including heat-responsive sys-
tems,7 we have also been interested in developing spin systems
with photo-responsive properties to observe the alteration of
intermolecular spin–spin interactions based on the structural
change.
We have hitherto reported norbornadiene de-
rivatives,8 spiropyran derivatives8 and anthracene derivatives9
with TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy) substi-
tuents as spin sources. In the studies on the anthracene and
the corresponding dimer systems with TEMPO substituents,
we dealt with intermolecular photo-dimerization reactions,
and found that the signs and the magnitudes of intermolecular
magnetic interactions could be changed, in principle, by outer
stimuli such as light, heat, or appropriate solvents in a reversi-
ble system derived from 9-methylanthracene with 4-amino-
TEMPO.9 Since that time, except the anthracene and the
corresponding dimer systems, only one example of an imino-
ferrocene derivative with triphenylmethyl radical4 has been
found in which intermolecular photo-dimerization reaction
was used to change the magnetic properties. We then have
Chart 1.
# This paper is dedicated to Emeritus Professor Soichi Misumi on
the occasion of his 77th birthday.

1246 Bull. Chem. Soc. Jpn., 76, No. 6 (2003)
Radical Anions of Styrylpyryliums & Dimers
Scheme 1.
sought other possible candidates. It was reported that some
styrylpyrylium salts give the corresponding photo-dimers in
an intermolecular manner which, in turn, dissociate by heating
in solution to the starting salts.10 We have been interested in
introducing a spin center to this attractive reversible system.
Moreover, the photo-dimerization of a methanesulfonate salt
of p-methoxy 1a to the corresponding dimer 3a (Chart 1) is
known to be a typical example of a single-crystal-to-single-
crystal reaction.11 In this paper, we wish to report on the prep-
aration, the structures, and the magnetic properties of some
styrylpyrylium derivatives, and the corresponding photo-di-
mers with radical anions from TCNQ or TCNQF4 as spin
sources.12
ions of the dimers were exchanged with LiTCNQ or
LiTCNQF4 to give the desired radical anion salts of the dimers
(3b, 3c, 4b, and 4c).
Magnetic Properties of Radical Anion Salts of Styrylpyr-
ylium Derivatives and X-ray Analysis of 1b. The magnetic
susceptibility of each radical anion salt was measured by a
SQUID susceptomer in the temperature region 2 K to 300 K.
The temperature dependence data of ꢀT-values for the TCNQ
radical anion salt of p-methoxy derivative (1b) is shown in
Fig. 1 (left), from which the existence of antiferromagnetic in-
teractions is apparent. It has also been found from the data of
the ꢀ-values shown in Fig. 1 (right) that the behavior can be
well expressed using the one dimensional (1-D) antiferromag-
netic Heisenberg model13 with a J-value of ꢁ5:42 K. In addi-
tion, the spins of TCNQ radical anions have been found to re-
main unchanged without any appreciable decrease in the ꢀ-
values. The magnetic behavior is rather similar to that of
the radical anion salts of cyanine derivatives reported by
Takagi et al.,14 which provides another example of a typical
S ¼ 1=2 Heisenberg antiferromagnetic (AFM) chain, although
the J-value is smaller in the present system.
The molecular structures of each component in 1b obtained
by X-ray analysis are shown in Fig. 2 (left) and its crystal
structure in Fig. 2 (right), respectively. It was apparent from
the analysis that the styrylpyrylium as well as TCNQ mole-
cules have relatively high planarity in the salt and that they
are stacked along the b-axis to form alternate columns. This
packing feature is quite different from that of the trifluoro-
methanesulfonate salt of the same styrylpyrylium derivative,
in which the styrylpyrylium molecules are stacked almost in
a segregate manner.12 Since the salt has the space group
P21=m, the distance between a styrylpyrylium and a TCNQ
Results and Discussion
Preparation of Radical Anion Salts of Styrylpyrylium
and the Corresponding Dimers. The trifluoromethanesulfo-
nate salts of styrylpyrylium derivatives (R = p-MeO: 1a and R
= p-Me: 2a) were prepared by the condensation of 2,6-di-t-bu-
tyl-4-methylpyrylium trifluoromethanesulfonate with p-anisal-
dehyde or p-tolualdehyde in acetic acid according to the meth-
od described by Hesse and Hunig.11 The anion exchange of
¨
the trifluoromethanesulfonate salts was carried out by using
LiTCNQ or LiTCNQF4 in a mixed solvent of acetonitrile
and water to give the corresponding radical anion salts (1b,
1c, 2b, and 2c) in moderate yields (Scheme 1).
We then tried to prepare photo-dimers of the styrylpyrylium
radical anion salts by irradiation under various conditions in
solution or in the solid-state. Unfortunately, however, no fruit-
ful result was obtained for the direct photo-dimerization reac-
tion by the irradiation of each radical anion salt with a mercury
lamp or other light sources such as a Xe lamp. Instead, the
corresponding radical anion salts of photo-dimers could be
obtained by indirectly way. So, at first, the trifluoromethane-
sulfonate salts of the dimers (3a, 4a) were prepared by irradia-
tion of the corresponding salts of monomers and then the an-
ꢀ
molecule is estimated to be 3.43 A, and that of a couple of
ꢀ
TCNQ molecules to be 6.87 A. The 1-D Heisenberg AFM be-
havior found in the salt is considered to be based on the inter-
actions between the spins in the TCNQ radical anions along

S. Nakatsuji et al.
Bull. Chem. Soc. Jpn., 76, No. 6 (2003) 1247
Fig. 1. (Left) Temperature dependence of ꢀT values for 1b. (Right) Temperature dependence of ꢀ values for 1b. The calculated
data are indicated as the solid line.
Fig. 2. (Left) Molecular structures of the pyrylium cation and TCNQ in 1b. (Right) Crystal structure of 1b viewed almost along the
a-axis. The hydrogen atoms and the methyl groups in t-butyl groups are omitted for clarity because of occurrence of the disorder
by the rotation of the methyl groups in the latter case.
the stacking direction through the intercalated styrylpyrylium
molecules, as significant intercolumnar interactions would be
almost impossible in the present case. Owing to the remote
spin centers, the J-value (ꢁ5:4 K) observed in the salt is small-
er than that of the radical anion salt MEM-(TCNQ)2, which is
reported to be a typical one-dimentional S ¼ 1=2 Heisenberg
antiferromagnet with J=kB ¼ ꢁ53 K.15 From the point of
view of photochemical dimerization, the alternated stacking
feature of the salt is considered to be unsuitable for the reac-
tion in the solid-state, and, as the consequence, the photochem-
ical dimerization was unsuccessful not only in the solid-state
but also in solution.
tive (1c) is rather different from the TCNQ salt, as shown in
Fig. 3 (left). Ferromagnetic interactions (FM) are apparent
in the lower temperature range and the behavior is well ex-
pressed by the 1-D ferromagnetic Heisenberg model with
small interactions (J ¼ þ0:65 K) (Fig. 3, right). Thus, distinct
changes in the magnetic behavior have been found in the styr-
ylpyrylium salts by changing counter radical anions.
The molecular structures of the salt 1c and its crystal struc-
ture obtained by X-ray analysis are shown in Fig. 4 (left). The
alternate stacking feature observed in the previous salt 1b has
also been found in the TCNQF4 salt 1c. The styrylpyrylium
and TCNQF4 molecules are stacked along the c-axis with
ꢀ
two types of intermolecular distances (3.35 A and 3.38 A) be-
tween the styrylpyrylium and TCNQF4 molecules. Short con-
ꢀ
tacts of ca. 3.5 A are also found between the F and N atoms in
ꢀ
Magnetic Properties of Radical Anion Salts of Styrylpyr-
ylium Derivatives and X-ray Analysis of 1c. The magnetic
behavior of the TCNQF4 radical salt of the p-methoxy deriva-

1248 Bull. Chem. Soc. Jpn., 76, No. 6 (2003)
Radical Anions of Styrylpyryliums & Dimers
Fig. 3. (Left) Temperature dependence of ꢀT values for 1c. (Right) Temperature dependence of ꢀ values for 1c. The calculated
data are indicated as the solid line.
Fig. 4. (Left) Molecular structures of the pyrylium cation and TCNQ in 1c. (Right, upper) Crystal structure of 1c viewed along the
a-axis. The hydrogen atoms are omitted for clarity. (Right, lower) Selected TCNQF4 molecules of 1c with indication of the in-
teractions between fluorine and nitrogen atoms (broken lines).
the TCNQF4 molecules, as shown in Fig. 4 (right/lower),
which are supposed to be relevant to the observed 1-D ferro-
magnetic interactions in this radical anion salt. When the spin
polarization effect is taken into account through the short con-
tacts between F and N atoms, the spin-spin interactions be-
tween the nearest TCNQF4 radical anions in the neighboring
columns are antiferromagnetic, while those between the
TCNQF4 radical anions in the stacked direction are
ferromagnetic. Therefore, the occurrence of 1-D ferromagnet-
ic interactions is thought to be possible in this case. Thus, the
difference in the magnetic properties found in 1b and 1c can be
derived from the apparent difference in their crystal structures.
On the other hand, similar magnetic behavior has been
found in TCNQ and TCNQF4 radical anion salts of p-methyl

S. Nakatsuji et al.
Bull. Chem. Soc. Jpn., 76, No. 6 (2003) 1249
Table 1. Magnetic Data of Radical Anion Salts of Monomersa)
Experimental
Salts
J-value/K
Magnetic Interaction
Materials. LiTCNQ and LiTCNQF4 were prepared from LiI
and TCNQ or TCNQF4. p-Methoxystyrylpyrylium trifluorometh-
ane sulfonate 1a and p-methylstyrylpyrylium trifluoromethane
1b
1c
2b
2c
ꢁ5:42
0.64
antiferromagnetic
ferromagnetic
antiferromagnetic
antiferromagnetic
sulfonate 2a were prepared as described by Hesse and Hunig.11
ꢁ2:95
¨
ꢁ2:80
Instrumentation. Melting points were measured on a YA-
MATO MP-21 apparatus and are uncorrected. MS data was taken
using a JEOL JMS-AX 505 mass spectrometer. EPR spectra were
obtained on a JEOL JES-FE3XG spectrometer and each g-value
was determined using a Mn2þ/MgO maker as an internal
standard. Magnetic susceptibility measurements were carried
out on a QUNTUM DESIGN MPMS-5 SQUID susceptometer
using ca. 10 mg for each powdered sample, correcting diamagnet-
ic contributions in the usual way.17
X-ray Structure Determination. X-ray diffraction data were
collected at room temperature on a Rigaku RAXIS4 diffractome-
ter with Mo-Kꢁ radiation for 1b and on a Brucker AXS SMART
1000 diffractometer with Mo-Kꢁ radiation for 1c, respectively.
The structures were solved by direct methods and expanded using
Fourrier techniques. The non-hydrogen atoms were refined
anisotropically. Hydrogen atoms were included but not refined.
All calculations were performed using the teXsan (Molecular
Structure Corporation) and the crystals (Chemical Crystallography
Laboratory, Oxford University) crystallographic software pack-
ages.
a) Fitting for 1-D Heisenberg model.
Table 2. Magnetic Data of Radical Anion Salts of Dimersa)
Curie constant/
emu K molꢁ1
Weiss
temperature/K
Magnetic
Interaction
Salts
3b
3c
4b
0.058
0.072
0.058
ꢁ0:83
ꢁ0:11
ꢁ0:15
antiferromagnetic
antiferromagnetic
antiferromagnetic
a) Fitting for Curie-Weiss law.
derivatives (2b, 2c) that are well expressed by 1-D Heisenberg
AFM interactions with small J-values, as shown in Table 1
together with those of 1b, 1c.
Magnetic Properties of Radical Anion Salts of Dimers.
From the magnetic data of the radical anion salts of dimers
3b, 3c, and 4b shown in Table 2, it is apparent that the Curie
constants of the radical anions of the dimers decrease greatly
compared with those of the salts of monomers, presumably be-
cause of the singlet formation between the radical anions irre-
spective of the sort of radical anions. It is thus obvious that the
magnetic properties of a radical anion salt can be significantly
changed, in principle, by photo-dimerization, and the distinct
difference in magnetic behaviors found in each monomer/di-
mer pair provides a potential switching system of magnetic
properties by external photo stimuli. However, the mono-
mer/dimer pairs of the radical anions could not be directly ex-
changed photochemically in this case, indicating the limita-
tions of the usage of TCNQ or TCNQF4 radical anion salts
for this photochemical reaction.16
Preparation of Radical Anion Salts of Styrylpyrylium
Derivatives. A typical procedure is exemplified for 1b and is
as follows; To a stirred solution of 1a (56 mg, 0.12 mmol) in a
solvent (10 mL) of acetonitrile and water (1:1) was added
LiTCNQ (25 mg, 0.12 mmol) in a mixed solvent as above at am-
bient temperature. A dark solid precipitated immediately and was
collected by the filtration under reduced pressure and then recrys-
tallized from acetonitrile to give 1b as black needles (39 mg,
60%), mp 209–211 ꢂC. Found: C, 77.11; H, 6.42; N, 9.86%.
Calcd for C34H33N4O2: C, 77.10; H, 6.28; N, 10.58%. EPR (ace-
tone): 1 line, g ¼ 2:010. In a similar manner, other radical anion
salts (1c, 2b, 2c) were prepared and the data are as follows;
ꢂ
1c: black needles, mp 248–251 C. Found: C, 68.03; H, 4.93;
N, 9.40%. Calcd for C34H29F4N4O2: C, 67.88; H, 4.86; N, 9.31%.
Conclusion
EPR (acetone): 1 line, g ¼ 2:010.
ꢂ
2b: black needles, mp 210–211 C. Found: C, 79.90; H, 6.38;
N, 10.66%. Calcd for C34H33N4O: C, 79.50; H, 6.48; N, 10.91%.
A couple of styrylpyrylium derivatives (1a, 2a) were pre-
pared as trifluoromethanesulfonate salts, from which TCNQ
and TCNQF4 salts (1b, 1c, 2b, 2c) were derived by anion ex-
change reactions. The magnetic properties of the radical an-
ions for 1b and 1c are rather different, showing antiferromag-
netic interactions based on the 1-D Heisenberg model in the
former, and ferromagnetic interactions in the latter. This,
and the fairly large difference in their crystal structures is con-
sidered to be responsible for the difference in the magnetic
properties. Although the direct photo-dimerization of the
monomers was unsuccessful, the corresponding radical anion
salts of the dimers were obtained in an indirect way through
the anion exchange from the triflates of the photo-dimers.
The radical anion salts of dimers show largely diminished
magnetic susceptibilities, presumably because of the singlet
formation between the radical centers. Thus, although the
monomer/dimer pairs of radicals anions could not be directly
exchangeable, distinct differences in the magnetic behavior
found in each pair provides some potentially attractive exam-
ples of photo-responsive spin systems.
EPR (acetone): 1 line, g ¼ 2:011.
ꢂ
2c: black needles, mp 241–243 C. Found: C, 69.97; H, 5.03;
N, 9.59%. Calcd for C34H29F4N4O: C, 69.73; H, 4.99; N, 9.57%.
EPR (acetone): 1 line, g ¼ 2:011.
Preparation of Radical Anion Salts of Dimers. In a vessel
(200 mL) for photochemical reactions with a pyrex filter was
placed an acetic acid solution (15 mL) of 1a (2.3 g, 4.9 mmol)
and irradiated with high-pressure Hg-lamp (400 W) under nitro-
gen at ambient temperature. The resulting precipitates was fil-
tered and then dried to give dimer 3a11 (1.8 g, 78%). The dimer
thus obtained was dissolved in a solvent (10 mL) of acetonitrile
and water (1:1) and then LiTCNQ (66 mg, 0.32 mmol) in a mixed
solvent as above was added at ambient temperature. A dark green
solid formed immediately and was collected by the filtration under
reduced pressure to give 3b as a dark green powder (0.15 g, 86%),
mp 96–99 ꢂC. Found: C, 76.77; H, 6.44; N, 9.40%. Calcd for
C68H66N8O4: C, 77.10; H, 6.28; N, 10.58%. EPR (acetone): 1 line,
g ¼ 2:011. In a similar manner, other radical anion salts (3c, 4b,
4c) were prepared and the data are as follows;

1250 Bull. Chem. Soc. Jpn., 76, No. 6 (2003)
Radical Anions of Styrylpyryliums & Dimers
ꢂ
3c: black needles, mp 138–140 C. Found: C, 68.03; H, 4.93;
N, 9.40%. Calcd for C68H58F8N8O4: C, 67.88; H, 4.86; N, 9.31%.
EPR (acetone): 1 line, g ¼ 2:011.
K. Matsuda and M. Irie, J. Am. Chem. Soc., 122, 8309 (2000).
e) K. Matsuda, M. Matsuo, and M. Irie, Chem. Lett., 2001, 436.
f) K. Matsuda and M. Irie, Chem. Eur. J., 7, 3466 (2001). g) K.
Matsuda, M. Matsuo, and M. Irie, J. Org. Chem., 66, 8799 (2001).
4b: dark green powders, mp 110–112 ꢂC. Found: C, 79.90; H,
6.38; N, 10.66%. Calcd for C68H66N8O2: C, 79.50; H, 6.48; N,
10.91%. EPR (acetone): 1 line, g ¼ 2:011.
4
I. Ratera, D. Ruiz-Molina, J. Vidal-Gancedo, K. Wurst, N.
`
Daro, J.-F. Letard, C. Rovira, and J. Veciana, Angew. Chem., Int.
Ed., 40, 919 (2001).
ꢂ
4c: dark green powders, mp 123–124 C. Found: C, 69.62; H,
´ `
a) S. Benard, E. Riviere, P. Yu, K. Nakatani, and J. F.
Delouis, Chem. Mater., 13, 159 (2001). b) K. Nakatani and P.
Yu, Adv. Mater., 13, 1411 (2001).
5.12; N, 9.94%. Calcd for C68H58F8N8O2: C, 69.73; H, 4.99; N,
9.57%. EPR (acetone): 1 line, g ¼ 2:011.
5
Crystal Structure Determination of Compounds 1b and 1c.
Among the radical anions prepared, single crystals suitable for X-
ray diffraction were obtained for 1b and 1c and their crystal data
are as follows;
6
a) S. Nakatsuji and H. Anzai, J. Mater. Chem., 7, 2161
(1997). b) S. Nakatsuji, Adv. Mater., 13, 1719 (2001). c) S.
Nakatsuji, in ‘‘Recent Research Developments in Organic &
Bioorganic Chemistry,’’ ed by S. G. Pandalai, Transworld
Research Network, Trivandrum (2001), Vol. 5, pp. 1–26.
Crystal Data for 1b: C34H33N4O2, Mr ¼ 529:66, monoclinic,
ꢀ
ꢀ
ꢀ
a ¼ 14:257ð8Þ A, b ¼ 6:8727ð7Þ A, c ¼ 15:853ð4Þ A, ꢂ ¼
ꢂ
ꢀ 3
97:95ð4Þ , V ¼ 1538:4ð8Þ A , T ¼ 295 K, space group P21=m ,
Z ¼ 2, Dc ¼ 1:143 g cmꢁ3. R ¼ 0:099, wR ¼ 0:097 [2560 ob-
served reflections and 245 parameters, I > 3ꢃðIÞ].
7
Cf. a) S. Nakatsuji, M. Mizumoto, H. Ikemoto, H. Akutsu,
and J. Yamada, Eur. J. Org. Chem., 2002, 1912. b) S. Nakatsuji,
H. Ikemoto, H. Akutsu, J. Yamada, and A. Mori, J. Org. Chem.,
68, 1708 (2003).
Crystal Data for 1c: C34H29N4O2F4, Mr ¼ 601:62, orthor-
ꢀ
ꢀ
ꢀ
ohmbic, a ¼ 16:494ð2Þ A, b ¼ 28:275ð4Þ A, c ¼ 6:7405ð9Þ A,
8
a) S. Takeuchi, Y. Ogawa, A. Naito, K. Sudo, N. Yasuoka,
ꢀ 3
V ¼ 3143ð1Þ A , T ¼ 295 K, space group Pna21, Z ¼ 4,
H. Akutsu, J. Yamada, and S. Nakatsuji, Mol. Cryst. Liq. Cryst.,
345, 167 (2000). b) S. Nakatsuji, Y. Ogawa, S. Takeuchi, H.
Akutsu, J. Yamada, A. Naito, K. Sudo, and N. Yasuoka, J. Chem.
Soc., Perkin Trans. 2, 2000, 1969.
Dc ¼ 1:271 g cmꢁ3. R ¼ 0:063, wR ¼ 0:038 [767 observed reflec-
tions and 396 parameters, I > 2ꢃðIÞ].
The X-ray crystallographic data (bond lengths and angles,
atomic coordinates, and anisotropic thermal parameters) for 1b
and 1c are deposited at the Editorial Office which will be available
upon request.
9
a) T. Ojima, H. Akutsu, J. Yamada, and S. Nakatsuji,
Chem. Lett., 2000, 918. b) T. Ojima, H. Akutsu, J. Yamada, and
S. Nakatsuji, Polyhedron, 20, 1335 (2001). c) S. Nakatsuji, T.
Ojima, H. Akutsu, and J. Yamada, J. Org. Chem., 67, 916 (2002).
10 K. Hesse and S. Hunig, Liebigs Ann. Chem., 1985, 715.
11 K. Navak, V. Enkelmann, G. Wegner, and K. B. Wagner,
Angew. Chem., Int. Ed. Engl., 32, 1614 (1993).
12 A portion of this paper was presented at the 15th Interna-
tional Conference on Organic Solid State (ICOSS 15) held in
Mainz, July 2001 and the proceedings has been published; Y.
Ogawa, T. Ojima, H. Akutsu, J. Yamada, and S, Nakatsuji, Mol.
Cryst. Liq. Cryst., 390, 97 (2003).
¨
We thank Prof. Hayao Kobayashi of The Institute for Mole-
cular Sciences and Prof. Masao Hashimoto of Kobe University
for kindly providing us the opportunity to use the X-ray
facilities. This work was supported by a Grant-in-Aid for Sci-
entific Research (No. 13440213) from the Ministry of Educa-
tion, Culture, Sports, Science and Technology, which is grate-
fully acknowledged.
13 Cf. J. C. Bonner and M. E. Fisher, Phys. Rev. A, 135, 640
(1964).
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