Structure and photochromism of 2-(N-acyl-N-arylaminomethylene)benzo[b] thiophen-3(2H)-ones

Article abstract of DOI:10.1007/s11172-005-0108-8

It was shown by electron absorption spectroscopy and X-ray diffraction analysis that steric strains in photochromic 2-(N-acyl-N-arylaminomethylene) benzo[b]thiophen-3(2H)-one molecules ortho-substituted in the N-phenyl ring increase the quantum yield of t

Full text of DOI:10.1007/s11172-005-0108-8

2248
Russian Chemical Bulletin, International Edition, Vol. 53, No. 10, pp. 2248—2252, October, 2004
✾
Structure and photochromism
of 2ꢀ(NꢀacylꢀNꢀarylaminomethylene)benzo[b]thiophenꢀ3(2Н )ꢀones
A. D. Dubonosov,a V. P. Rybalkin,aꢀ Ya. Yu. Vorob´eva,a V. A. Bren´,a V. I. Minkin,a
S. M. Aldoshin,b V. V. Tkachev,b and A. V. Tsukanova
aResearch Institute of Physical and Organic Chemistry, Rostov State University,
194/2 prosp. Stachki, 344090 RostovꢀonꢀDon, Russian Federation.
Еꢀmail: dubon@ipoc.rsu.ru
bInstitute of Problems of Chemical Physics, Russian Academy of Sciences,
1 prosp. Akad. Semenova, 142432 Chernogolovka, Moscow Region, Russian Federation.
Eꢀmail: sma@icp.ac.ru
It was shown by electron absorption spectroscopy and Xꢀray diffraction analysis that steric
strains in photochromic 2ꢀ(NꢀacylꢀNꢀarylaminomethylene)benzo[b]thiophenꢀ3(2Н )ꢀone molꢀ
ecules orthoꢀsubstituted in the Nꢀphenyl ring increase the quantum yield of the N→O photoꢀ
induced rearrangement in accord with an increase in the steric constant of the orthoꢀsubꢀ
stituent.
Key words: benzo[b]thiophene, ketoenamines, photochromic compounds, quantum yield,
steric constant.
Scheme 1
Photochromism of 2ꢀ(NꢀacylꢀNꢀarylaminomethylꢀ
ene)benzo[b]thiophenꢀ3(2Н )ꢀones (1) is based on photoꢀ
initiated Z/Eꢀisomerization relatively to the С=С bond
followed by the thermal N→O migration of the acyl group
(Scheme 1).1,2
Compounds of this type (λmax (1) > λmax (2)) are of
interest as systems with negative photochromism,3,4 whose
molecules can accumulate the light energy released durꢀ
ing the catalytically controlled process 2 → 1. A wide variꢀ
ability of their structures also predetermined a possibility
of using ketoenamines 1 as chemosensors for metal catꢀ
ions5,6 (1e), molecular switches of an optical signal7 (1f),
and fluorescent sensors for a change of the pH of a meꢀ
dium8 (1g) acting according to principle of the РЕТ efꢀ
fect.9 Reasons for the appearance of chiral properties of
ketoenamines 1 orthoꢀsubstituted in the Nꢀphenyl ring
were studied.10 The examples presented show that the
structure of a molecule of the type 1, in particular, spatial
interactions between the Nꢀaryl and Nꢀacyl substituents
and the heterocyclic moiety, can exert a determining efꢀ
fect on the spectral luminescence properties and photoꢀ
chromism of these compounds. Nevertheless, a relationꢀ
ship between steric interactions in the ground state in
molecules of this type and their spectral and photochemiꢀ
cal properties (λmax, εmax, λb,* ϕ1→2) has not been studied
up to date. It can be useful to establish such a relationship
for design of chiral chemosensors or switches of an optical
signal. According to this, the following tasks of the present
* Longꢀwave absorption boundary λ with ε ≈ 1.0 L mol–1 cm–1
.
b
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2151—2155, October, 2004.
1066ꢀ5285/04/5310ꢀ2248 © 2004 Springer Science+Business Media, Inc.

Photochromic benzo[b]thiophenones
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 10, October, 2004
2249
A
work were stated: (1) synthesis of a series of ketoenamines
1а—с orthoꢀsubstituted in the Nꢀphenyl ring; (2) estabꢀ
lishment of their structure and specific features of photoꢀ
initiated reactions (see Scheme 1) depending on a steric
constant υ of the orthoꢀsubstituent.
0.6
7
6
Results and Discussion
0.4
5
Compounds 1а—с were synthesized by the condensaꢀ
tion of 3ꢀhydroxybenzo[b]thiopheneꢀ2ꢀcarbaldehyde with
the corresponding amines in acetonitrile followed by the
acylation of ketoenamines 3a—c that formed with acetyl
chloride in the presence of triethylamine. According
to the data of IR and 1Н NMR spectroscopies, they
have a structure of Nꢀacylated ketoenamines and exist
in the Z form. Their IR spectra contain absorption
bands of the amidic (1710—1715 cm–1) and exocyclic
(1675—1680 cm–1) carbonyl groups. In the 1Н NMR specꢀ
tra in CDCl3, the signal of the methinic proton lies in the
region characteristic of Z structures (δ 8.9).10 The elecꢀ
tronic absorption spectra (EAS) exhibit bands in a region
of 423—429 nm typical of Zꢀketoenamine isomers of the
type 1. In toluene, which is characterized by a low solvent
polarity EТ,11 the position of λmax and the intensity εmax of
the longꢀwave absorption maximum depend weakly on
the steric constant of the orthoꢀsubstituent υ.12 However,
in DMSO, which is a solvent with high ЕТ, the following
regularity is observed: λmax and especially εmax increase in
parallel with υ (Table 1). The quantum yields of photoꢀ
initiated transformations increase in the same direction
(see Scheme 1). The highest quantum yield ϕ = 0.41 is
observed for ketoenamine 1d with the bulkiest orthoꢀsubꢀ
stituent, viz., iodine atom. Evidently, maximum steric
interactions affect the simple and double bond lengths
and interatomic distances in molecule 1d. These interꢀ
actions also determine the shape and intensity of the
absorption band of the Оꢀacetyl isomers of ketoꢀ
enamines 2а—d, which are formed in the photoinitiated
process (see Scheme 1). For the least bulky substituent in
1
4
3
2
0.2
1
7
350
400
500 λ/nm
Fig. 1. Electronic absorption spectra of 2ꢀ[NꢀacetylꢀNꢀ
(2ꢀfluorophenyl)aminomethylene]benzo[b]thiophenꢀ3(2Н )ꢀone
(1а) in toluene before (1) and after irradiation for 5 (2), 10 (3),
20 (4), and 40 s (5) and 1 (6) and 2 min (7), λrad = 436 nm, с =
2.5•10–5 mol L–1
.
the orthoꢀposition of the phenyl ring R = F, the absorpꢀ
tion maximum of isomer 2а is typical of bands of this
type2 and comparable in intensity with a shorterꢀwave
maximum of 313 nm (Fig. 1), whereas in the case of
R = I, steric interactions result in the situation when this
band experiences a hypsochromic effect and appears as an
additional inflection of the shorterꢀwave band at 317 nm
(Fig. 2). All these data indicate strong steric interactions
and the acoplanarization of structures 1d and 2d.
To verify this assumption, we carried out the Xꢀray
diffraction study of 2ꢀ[NꢀacetylꢀNꢀ(2ꢀiodophenyl)aminoꢀ
methylene]benzo[b]thiophenꢀ3(2Н )ꢀone (1d) containꢀ
ing an orthoꢀsubstituent with the highest steric conꢀ
stant υ = 0.78.12
The general view of a molecule of ketoenamine 1d is
shown in Fig. 3. The main distances and angles in the
molecule are presented in Table 2. In crystal, the acetyl
group at the nitrogen atom exists in the sꢀtransꢀposition
relatively to the С(1)—С(9) bond. The aryl group occuꢀ
pies the sꢀcisꢀposition relatively to this bond, and steric
interactions appeared between the sulfur atom and the
С(13) and С(17) atoms of the orthoꢀiodophenyl moiety
result in the mutually perpendicular arrangement of the
benzothiophene and aryl rings, which decreases steric
hindrances as much as possible. The dihedral angle beꢀ
tween planes of these rings is 92.7°. Note that this is the
maximum value of a dihedral angle of all values earlier
determined by Xꢀray diffraction analysis for this type
of compounds. For instance, this angle is 71° in
Table 1. Spectral and photochemical characteristics of ketoꢀ
enamines 1 (R1 = 2ꢀR3C6H4, R2 = Me)
Comꢀ R3
pound
υ
Solꢀ
vent
EAS, λmax/nm
ϕ
1→2
(ε •10–4/L mol–1 cm–1
)
max
1а
1b
1c
1d
F
0.27 Toluene
DMSO
307 (2.44), 423 (1.24)
310 (1.31), 428 (0.62)
307 (2.22), 425 (1.10)
311 (1.68), 429 (0.80)
308 (2.40), 423 (1.21)
311 (1.86), 429 (0.94)
309 (2.52), 427 (1.28)
312 (2.08), 431 (1.10)
0.14
0.29
0.35
0.41
Cl 0.55 Toluene
DMSO
Br 0.65 Toluene
DMSO
I
0.78 Toluene
DMSO
Note: υ is the steric constant, and ϕ
is the quantum yield.
2
→
1

2250
0.6
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 10, October, 2004
Dubonosov et al.
A
Table 2. Main bond lengths (d) and bond angles (ω) in ketoꢀ
enamine 1d
7
Bond
d/Å
Angle
ω/deg
I—C(17)
S—C(4)
S—C(1)
O(1)—C(2)
O(2)—C(10)
N—C(9)
2.088(3)
1.754(3)
1.765(3)
1.219(4)
1.195(4)
1.370(4)
1.413(4)
1.438(4)
1.482(4)
1.337(4)
1.476(4)
1.385(4)
1.380(4)
1.392(4)
1.369(5)
1.406(6)
1.375(5)
C(4)—S—C(1)
91.0(1)
118.5(3)
120.5(2)
120.9(2)
118.7(3)
112.2(2)
129.1(2)
124.8(3)
126.1(3)
109.1(2)
113.2(2)
125.9(3)
120.8(3)
120.3(3)
114.3(2)
125.4(2)
118.8(3)
121.1(3)
119.7(3)
119.4(3)
130.5(3)
120.5(3)
C(9)—N—C(10)
C(9)—N—C(12)
C(10)—N—C(12)
C(9)—C(1)—C(2)
C(2)—C(1)—S
6
5
0.4
0.2
1
N—C(10)
N—C(12)
C(1)—C(2)
C(1)—C(9)
C(2)—C(3)
C(3)—C(4)
C(3)—C(8)
C(4)—C(5)
C(5)—C(6)
C(6)—C(7)
C(7)—C(8)
C(10)—C(11) 1.496(5)
C(12)—C(13) 1.385(4)
C(12)—C(17) 1.388(4)
C(13)—C(14) 1.376(5)
C(14)—C(15) 1.385(6)
C(15)—C(16) 1.369(5)
C(16)—C(17) 1.385(4)
C(9)—C(1)—S
4
O(1)—C(2)—C(1)
O(1)—C(2)—C(3)
C(3)—C(2)—C(1)
C(4)—C(3)—C(2)
C(8)—C(3)—C(2)
C(8)—C(3)—C(4)
C(3)—C(4)—C(5)
C(3)—C(4)—S
3
2
1
7
C(5)—C(4)—S
350
400
500 λ/nm
C(6)—C(5)—C(4)
C(5)—C(6)—C(7)
C(8)—C(7)—C(6)
C(7)—C(8)—C(3)
C(1)—C(9)—N
Fig. 2. Electronic absorption spectra of 2ꢀ[NꢀacetylꢀNꢀ
(2ꢀiodophenyl)aminomethylene]benzo[b]thiophenꢀ3(2Н )ꢀone
(1d) in toluene before (1) and after irradiation for 5 (2), 10 (3),
20 (4), and 40 s (5) and 1 (6) and 2 min (7), λrad = 436 nm, с =
2.5•10–5 mol L–1
.
O(2)—C(10)—N
O(2)—C(10)—C(11) 123.2(3)
N—C(10)—C(11) 116.4(3)
C(13)—C(12)—C(17) 119.7(3)
O(1)
C(2)
O(2)
C(13)—C(12)—N
C(17)—C(12)—N
119.4(3)
120.9(2)
C(10)
C(9)
C(8)
C(3)
C(11)
C(14)—C(13)—C(12) 120.2(3)
C(13)—C(14)—C(15) 119.8(3)
C(16)—C(15)—C(14) 120.4(3)
C(15)—C(16)—C(17) 120.2(3)
C(16)—C(17)—C(12) 119.7(3)
N
C(1)
C(7)
C(12)
I
C(4)
C(5)
C(16)—C(17)—I
C(12)—C(17)—I
119.0(2)
121.3(2)
S
C(6)
C(17)
C(16)
C(13)
C(14)
C(15)
Н(9)...О(1) distance is equal to 2.47 Å in this case. When
a plane is passed through the С(1)...С(11), N, and O(1)
atoms, all atoms listed lie in a rootꢀmeanꢀsquare plane
with an accuracy of 0.03 Å, and the S and O(2) atoms
shift from this plane to opposite directions by 0.12 and
0.14 Å. The iodine atom and six carbon atoms of the
phenyl ring lie in the same plane with an accuracy
of 0.01 Å.
The distribution of bond lengths in the planar part of
molecule 1d indicates that the electron density is delocalꢀ
ized in this part. The O(1)—C(2) bond length of 1.219 Å
corresponds to a standard double bond in ketones of
1.23 Å, and the О(2)—С(10) bond (1.195 Å) is much
shorter. The C(1)—C(9) bond of 1.337 Å is elongated and
coincides with the lengths of similar С=С bonds in
transꢀdiarylethylenes, and the N—C(9) bond (1.371 Å) is
shortened, being medium between the ordinary N—C
(1.472 Å) and double N=C (1.27 Å) bonds. The ordinary
Fig. 3. Molecular structure of 2ꢀ[NꢀacetylꢀNꢀ(2ꢀiodopheꢀ
nyl)aminomethylene]benzo[b]thiophenꢀ3(2Н )ꢀone (1d).
orthoꢀmethylphenylꢀsubstituted ketoenamine (υ = 0.52)12
studied previously. However, even for this arrangement,
the С(1)—С(9)—N bond angle is increased to 130.5(3)°,
which allows the interatomic distances S...C(12) (3.05 Å),
S...C(13) (3.30 Å), and S...C(17) (3.43 Å) to remain comꢀ
parable with standard intramolecular contacts between
valenceꢀunbonded atoms. Other atoms in the molecule,
including those of the acetyl group, are virtually coplanar
to the plane of the benzothiophene ring and form a planar
conjugated molecular system. This is also favored by a
hydrogen bond between the methylene Н(9) hydrogen
atom and carbonyl О(2) oxygen atom (2.27 Å), and the

Photochromic benzo[b]thiophenones
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 10, October, 2004
2251
Acylated ketoenamines 1a—d were synthesized according to
a previously described procedure.14
С(1)—С(2) bond (1.481 Å) is also shortened. The conꢀ
figuration of bonds at the nitrogen atom is almost planar
(the sum of angles at the nitrogen atom is equal to 359.9°),
favoring the efficient conjugation of the free electron pair
of the nitrogen atom with the rest πꢀsystem.
Thus, steric interactions of the orthoꢀsubstituent in
the Nꢀphenyl ring of 2ꢀ(NꢀacylꢀNꢀarylaminomethylꢀ
ene)benzo[b]thiophenꢀ3(2Н )ꢀones with adjacent groups
have been shown for the first time to change remarkably
the spectral characteristics and increase the quantum yield
of phototransformation of these compounds into the
Оꢀacetyl isomers in accord with an increase in the steric
constant of the orthoꢀsubstituent.
2ꢀ[NꢀAcetylꢀNꢀ(2ꢀfluorophenyl)aminomethylene]benꢀ
zo[b]thiophenꢀ3(2Н )ꢀone (1a). The yield was 94%, m.p.
178—179 °С. Found (%): С, 65.06; Н, 3.92; N, 4.37.
C17H12FNO2S. Calculated (%): С, 65.16; Н, 3.86; N, 4.47. IR,
1
ν/cm–1: 1710, 1680, 1600, 1560, 1255. Н NMR, δ: 2.60 (br.s,
3 H, Me); 7.20—7.90 (m, 8 H, Ar); 8.90 (br.s, 1 H, СН).
2ꢀ[NꢀAcetylꢀNꢀ(2ꢀchlorophenyl)aminomethylene]benꢀ
zo[b]thiophenꢀ3(2Н )ꢀone (1b). The yield was 83%, m.p.
181—182 °С. Found (%): С, 61.79; Н, 3.98; N, 4.12.
C
17H12ClNO2S. Calculated (%): С, 61.91; Н, 3.86; N, 4.25. IR,
ν/cm–1: 1715, 1680, 1600, 1570, 1250. Н NMR, δ: 2.20 (br.s,
3 H, Me); 7.15—7.84 (m, 8 H, Ar); 8.9 (br.s, 1 H, СН).
2ꢀ[NꢀAcetylꢀNꢀ(2ꢀbromophenyl)aminomethylene]benꢀ
zo[b]thiophenꢀ3(2Н )ꢀone (1с). The yield was 94%, m.p.
170—171 °С. Found (%): С, 54.50; Н, 3.97; N, 3.54.
1
Experimental
С
17Н12BrNO2S. Calculated (%): С, 54.56; Н, 3.23; N, 3.74. IR,
ν/cm–1: 1710, 1680, 1605, 1260. 1Н NMR, δ: 2.20 (br.s, 3 H,
Me); 7.15—7.84 (m, 8 H, Ar); 8.90 (br.s, 1 H, СН).
Electronic absorption spectra of compounds 1а—d were reꢀ
corded on a Specord Mꢀ40 spectrophotometer. Solutions were
irradiated with a DRShꢀ250 mercury lamp using a set of changeꢀ
able filters. Quantum yields for reactions in toluene were deterꢀ
mined using potassium ferrioxalate.13 IR spectra in Nujol were
recorded on an Specord 75IR instrument, and 1Н NMR spectra
were measured on a Varian Unityꢀ300 instrument (300 MHz) in
CDCl3 using Me4Si as the standard.
Synthesis of 2ꢀ[Nꢀ(2ꢀhalophenyl)aminomethylene]benꢀ
zo[b]thiophenꢀ3(2Н )ꢀones (3a—d) (general procedure). A soluꢀ
tion of the corresponding aniline (0.01 mol) in acetonitrile was
added to a warm solution of 3ꢀhydroxybenzo[b]thiopheneꢀ2ꢀ
carbaldehyde (0.01 mol) in acetonitrile. The mixture was heated
in the presence of acetic acid (1 mL) for 30 min. A precipitate
that formed on cooling was filtered off, washed with cold methaꢀ
nol, and crystallized from an appropriate solvent.
2ꢀ[NꢀAcetylꢀNꢀ(2ꢀiodophenyl)aminomethylene]benꢀ
zo[b]thiophenꢀ3(2Н )ꢀone (1d). The yield was 82%, m.p.
183—184 °С. Found (%): C, 48.91; Н, 2.70; N, 3.92.
C
17H12INO2S. Calculated (%): C, 48.47; Н, 2.87; N, 3.32. IR,
ν/cm–1: 1710, 1675, 1590, 1550, 1245. Н NMR, δ: 2.05 (br.s,
3 H, Me); 7.10—8.10 (m, 8 H, Ar); 8.94 (br.s, 1 H, СН).
Xꢀray diffraction study. Unit cell parameters of a crystal of
1d and a threeꢀdimensional array of intensities were obtained on
a KMꢀ4 fourꢀcircle automated diffractometer (MoꢀKα raꢀ
diation, graphite monochromator). The yellow transparent
crystals of 1d were monoclinic, C17H12INO2S, М = 421.24;
a = 10.389(4), b = 8.405(2), с = 18.538(1) Å, β = 97.10(5)°,
1
V = 1606.3(7) Å3, Z = 4, ρ
= 1.742 g cm–3, µ(MoꢀКα) =
calc
2.13 mm–1, space group P21/n.
Intensities of 3289 reflections were measured in an interval
of angles 2θ ≤ 52.2° using an ω/2θ scan mode from a single
crystal 0.4×0.4×0.5 mm in size. After systematically extinguished
reflections were excluded and intensities of equivalent reflecꢀ
tions were averaged, the working array of measured F 2(hkl) and
σ(F 2) was 3190 independent reflections of which 2814 reflecꢀ
tions with F 2 > 4σ(F 2) were used in subsequent calculations.
The structure was solved by the direct method and refined by
the fullꢀmatrix leastꢀsquares method against F 2 using the
SHELXLꢀ97 program for nonꢀhydrogen atoms. The most
part of H atoms were localized in the Fourier synthesis of difꢀ
ference electron density, and positions of several H atoms
were calculated and further refined in the isotropic approximaꢀ
tion. The final refinement parameters: R1 = 0.031, wR2 = 0.085
against 2814 observed reflections with I ≥ 2σ(I ); R1 = 0.0386,
2ꢀ[Nꢀ(2ꢀFluorophenyl)aminomethylene]benzo[b]thiophenꢀ
3(2Н )ꢀone (3а). The yield was 83%, m.p. 178—179 °С.
Found (%): С, 66.30; Н, 3.61; N, 5.23. C15H10FNOS. Calcuꢀ
lated (%): С, 66.41; Н, 3.72; N, 5.16. IR, ν/cm–1: 1650, 1620,
1450, 1410, 1375. 1Н NMR, δ: 7.00—7.60 (m, 7 H, Ar); 7.84 (d,
14 H, СН, J = 12.0 Hz); 8.00 (d, 1 H, Ar, J = 9.0 Hz); 12.44
(br.d, 1 Н, NН, J = 12.0 Hz).
2ꢀ[Nꢀ(2ꢀChlorophenyl)aminomethylene]benzo[b]thiophenꢀ
3(2Н )ꢀone (3b). The yield was 76%, m.p. 165—166 °С.
Found (%): С, 62.49; Н, 3.89; N, 4.80. C15H10СlNOS. Calcuꢀ
lated (%): С, 62.61; Н, 3.50; N, 4.87. IR, ν/cm–1: 1690, 1600,
1450, 1400, 1360. 1Н NMR, δ: 7.01—7.92 (m, 8 H, Ar); 8.6
(br.d, 1 H, СН, J = 8.0 Hz); 12.62 (br.d, 1 H, NH, J = 8.0 Hz).
2ꢀ[Nꢀ(2ꢀBromophenyl)aminomethylene]benzo[b]thiophenꢀ
3(2Н )ꢀone (3с). The yield was 79%, m.p. 176—177 °С.
Found (%): С, 54.28; Н, 3.12; N, 4.36. C15H10BrNOS. Calcuꢀ
lated (%): С, 54.23; Н, 3.03; N, 4.22. IR, ν/cm–1: 1675, 1650,
wR2
= 0.087 against all 3190 measured reflections,
GOOF = 1.096.
The full Xꢀray diffraction data, including coordinates of
atoms and thermal parameters, were deposited at the Cambridge
Structural Database.
1
1600, 1560, 1410, 1375. Н NMR, δ: 6.81—7.92 (m, 8 H, Ar);
8.58 (br.d, 1 H, СН, J = 12.0 Hz); 12.52 (br.d, 1 H, NH,
J = 8.0 Hz).
2ꢀ[Nꢀ2ꢀ(Iodophenyl)aminomethylene]benzo[b]thiophenꢀ
3(2Н )ꢀone (3d). The yield was 69%, m.p. 198—199 °С.
Found (%): С, 47.71; Н, 2.58; N, 3.56. C15H10NOS. Calcuꢀ
lated (%): С, 47.56; Н, 2.68; N, 3.69. IR, ν/cm–1: 1625, 1575,
1450, 1400, 1370. 1Н NMR, δ: 6.81—7.92 (m, 9 H, Ar); 12.36
(br.d, 1 H, NH, J = 8.0 Hz).
This work was financially supported by the Russian
Foundation for Basic Research (Project No. 02ꢀ03ꢀ
32527), the Ministry of Industry, Science, and Technoloꢀ
gies (Grant NShꢀ945.2003.3), the American Civilian Reꢀ
search and Development Foundation (CRDF), and the

2252
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 10, October, 2004
Dubonosov et al.
N. N. Tkalina, A. V. Tsukanov, and E. N. Shepelenko,
Zh. Org. Khim., 2002, 38, 1755 [Russ. J. Org. Chem., 2002,
38, 1698 (Engl. Transl.)].
8. V. A. Bren´, A. D. Dubonosov, V. I. Minkin, L. L. Popova,
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Received March 19, 2004;
in revised form May 17, 2004