Synthesis and photochromic reactivity of diarylethene trimers bridged by ethenyl and ethynyl unit

Article abstract of DOI:10.1016/j.tet.2006.06.095

Two diarylethene trimers bridged by ethenyl and ethynyl groups were synthesized and their photochromic behaviors were examined. Upon irradiation of the trimers 2 and 4 with UV light, one-three photoinduced cyclization reactions occur. Each isomer was isol

Full text of DOI:10.1016/j.tet.2006.06.095

Tetrahedron 62 (2006) 9059–9065
Synthesis and photochromic reactivity of diarylethene trimers
bridged by ethenyl and ethynyl unit
Hyunbong Choi,a Il Jung,a Kyu Ho Song,a Kihyung Song,b Dong-Soo Shin,c
a,
Sang Ook Kanga, and Jaejung Ko
*
*
aDepartment of Chemistry, Korea University, Jochiwon, Chungnam 339-700, Republic of Korea
bDepartment of Chemistry, Korea National University of Education, Chongwon, Chungbuk 363-791, Republic of Korea
cDepartment of Chemistry, Changwon National University, Changwon, GN 641-773, Republic of Korea
Received 31 May 2006; revised 28 June 2006; accepted 29 June 2006
Available online 26 July 2006
Abstract—Two diarylethene trimers bridged by ethenyl and ethynyl groups were synthesized and their photochromic behaviors were exam-
ined. Upon irradiation of the trimers 2 and 4 with UV light, one–three photoinduced cyclization reactions occur. Each isomer was isolated and
analyzed by 1H NMR spectrum. The quantum yield of 2 and 4 is 0.52 and 0.311, respectively.
Ó 2006 Elsevier Ltd. All rights reserved.
1. Introduction
photochromic state of one photochrome will influence the
reactivity of another photochrome when they are covalently
joined. Among the various types of diarylethene dimers
connected with single bond,10 phenylene,11 ethynylene,12
and diyne,13 in most cases only one of the diarylethenes
can convert to the closed-ring form upon UV irradiation.
Even though some studies have been performed to clarify
the effect of substituents,14 a more general understanding
of the way in which one photochromic unit interacts with
another photochromic unit in a molecule is an important
issue for practical applications. We envisioned that the stra-
tegic placement of diarylethene units within a macromole-
cular framework would help to understand the interaction
between the diarylethene units. We now describe (i) the
synthesis of macromolecules having three diarylethene
units; (ii) their photochromic reactivities; (iii) the isolation
of photocyclized products; (iv) the effect of bridging unit.
Photochromic compounds undergo reversible transforma-
tion between two distinct chemical isomers with different
colors of light.1 The photoreaction can be accompanied by
changes in useful physical properties such as refractive
index,2 luminescence,3 electronic conductance,4 and optical
rotation.5 Photochromic diarylethene is very suitable for
these purposes, due to their thermal stability and high fatigue
resistance.6 Some of these photoswitching effects are based
on the changes in the extent of p-conjugation in diarylethene
upon photochromic reaction (Scheme 1). Any p-electrons
on the R groups can interact with each other through the
p-conjugation in the ring-closed state.7 The functionaliza-
tion of the photochromic unit is a major issue because of
some reasons, such as tuning the absorption wavelength or
creating a system that can be used for information storage.8
In substituted dithienylethenes some of the substituents
cause a strong decrease or even a complete loss of the
photochromic behavior.9 It has been assumed that the
2. Results and discussion
2.1. Synthesis
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UV
Vis
Diarylethene trimers 2 and 4 were prepared according to the
synthetic method shown in Schemes 2 and 3. Compound 2
was synthesized from 1,3,5-tris((E)-2-(tributylstannyl)-
vinyl)benzene15 in two steps. Stille cross coupling reac-
tion of the stannyl with 3,5-dibromo-2-methylthiophene,16
followed by the reaction of lithiated 1 with 4-(perfluoro-
cyclopent-1-enyl)-2-phenylthiophene,16 gave 2 in 50%
yield. Compound 4 was synthesized in two steps from
S
S
S
S
R
R
R
R
Scheme 1.
Keywords: Photoswitch; Macromolecule; Trimer; Diarylethene.
* Corresponding authors. Tel.: +82 41 860 1337; fax: +82 41 867 5396;
e-mail: jko@korea.ac.kr
0040–4020/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tet.2006.06.095

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H. Choi et al. / Tetrahedron 62 (2006) 9059–9065
F
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S
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Br
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SnBu3
(i)
(ii)
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Bu3Sn
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F
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Br
SnBu3
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Br
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1
2
Scheme 2. (i) 3,5-Dibromo-2-methylthiophene, Pd(PPh3)2Cl2, CsF in toluene; (ii) 4-(perfluorocyclopent-1-enyl)-2-phenylthiophene, n-BuLi in THF.
F
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S
F
Br
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S
(i)
(ii)
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F
S
S
F
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Br
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F
3
4
Scheme 3. (i) 3,5-Dibromo-2-methylthiophene, Pd(PPh3)4, CuI, NEt3; (ii) 4-(perfluorocyclopent-1-enyl)-2-phenylthiophene, n-BuLi in THF.
1,3,5-triethynylbenzene.17 Sonogashira coupling of 1,3,5-
triethynylbenzene with 3,5-dibromo-2-methylthiophene
1.0
followed by the reaction of lithiated 3 with 4-(perfluoro-
cyclopent-1-enyl)-2-phenylthiophene yielded 4. Spectro-
0.8
scopic data for 2 and 4 are completely consistent with
their proposed structures. One resonance at 1.97 ppm for 2
and 4 in the H NMR spectrum for the methyl group is
observed. The mass spectra of 2 and 4 showed a molecular
ion at m/z 1482 and 1476, respectively.
0.6
1
0.4
0.2
2.2. Photochromism of trimer 2 in chloroform
0.0
Figure 1 shows the absorption spectra of 2 in chloroform
upon photoirradiation. Upon irradiation of 2 with 365 nm
300
400
500
600
700
800
light, the colorless solution of the open-ring form turned
blue, in which initial maximum was observed at 594 nm. It
grew with shifting of the absorption maximum, and reached
the photostationary state after 6 min. Upon visible light
irradiation (l>532 nm) for 2 h, the colored solution was
Wavelength, nm
Figure 1. Absorption spectral change of the trimer 2 in chloroform upon
0
irradiation with 365 nm light: ( ) before irradiation, (-$-$) after UV light
irradiation for 2 min, (- - -) for 4 min, (/) for 8.

H. Choi et al. / Tetrahedron 62 (2006) 9059–9065
9061
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S
365 nm
532 nm
365 nm
532 nm
365 nm
532 nm
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F
2 (OOO)
Scheme 4. The photochromic reactivity of 2.
2 (COO)
2 (CCO)
2 (CCC)
completely bleached, indicating return to the initial open-
ring isomer. In first 2 min of irradiation, an absorption
band centered at 594 nm rapidly grows in as most of the 2
is converted from the colorless-open form 2 (OOO) to the
blue-closed form 2 (COO) (Scheme 4). The presence of an
isosbestic point at 342 nm indicates that 2 (OOO) is cleanly
converted to a second photocyclized product. The closed-
ring isomer 2 (COO) was isolated from the above blue
colored solution by HPLC (silica gel, eluent hexane/ethyl
acetate (10:1)) in 74% yield. Further irradiation (2 min) of
2 (COO) with 365 nm light afforded the anticipated red-shift
of the absorption maximum at 602 nm that would have
resulted from the two closed-ring isomers 2 (CCO). The
photoirradiated product 2 (CCO) was analyzed with HPLC
from the above solution. The fully closed-ring isomer 2
(CCC) can be achieved after an 8 min irradiation period of
2 (OOO) using 365 nm light in 52% yield. Absorption maxi-
mum of 2 (CCC) at 610 nm is shifted to longer wavelength
by 8 nm in comparison with that of 2 (CCO) due to the
extension of p-conjugation. The photogenerated ring-closed
isomers 2 (COO), 2 (CCO), and 2 (CCC) were stable at room
temperature. Figure 2 shows the 1H NMR spectrum of
methyl proton of 2 (OOO) in CDCl3 before photoirradiation
and in the ring-closed form 2 (COO), 2 (CCO), and 2 (CCC).
In the 1H NMR spectrum of 2 (OOO), one methyl resonance
was observed at 1.97 ppm. In the blue isomer 2 (COO), one
distinct new band appeared at 2.16 ppm, together with one
singlet at 1.97 ppm. The integral ratio of the two signals
was 1:2, indicating that the colored isomer is 2 (COO).
Another key feature of 2 (COO) is the presence of four
new thienyl signals at 7.28, 7.10, 6.70, and 6.42 ppm. The
two new resonances at 6.70 and 6.42 ppm are significantly
shifted up-field as would be expected for the ring-closed iso-
mer. Such an up-field shift was observed in covalently linked
double 1,2-dithienylethenes10–13 and macromolecules18
incorporating four dithienylethene units. The dissymmetric
nature of the photogenerated product indicates that one of
three thienyl units has cyclized to form 2 (COO). Figure 2c
shows the 1H NMR spectrum of methyl protons of 2 (CCO)
separated from the photogenerated product by HPLC after
the photoirradiation of 2 (OOO) for 4 min. Two distinct
bands appeared at 2.16 and 1.97 ppm. The integral ratio of
the two signals was 2:1, which indicates that the colored
isomer is 2 (CCO). Figure 2d shows the 1H NMR spectrum
of methyl protons of 2 (CCC). One distinct band appeared at
2.16 ppm, demonstrating that 2 (OOO) was completely con-
verted into the closed form 2 (CCC).
2.3. Photochromism of trimer 4 in chloroform
Figure 3 shows the absorption spectrum of trimer 4 in chlo-
roform upon UV light irradiation. Irradiation of chloroform
solution of 4 at 365 nm light resulted in an immediate
increase in the absorption intensity at 607 nm. It grew with
shifting of the absorption maximum to red-shifted region.
Upon visible light irradiation (l>532 nm) for 6 h, the blue
colored solution was completely bleached. After the irradia-
tion of 4 (OOO) for 2 min, the photogenerated products were
analyzed with HPLC (silica gel, eluent hexane/ethyl acetate
(9:1)). The elution peaks were detected at the isosbestic
point of 342 nm. The open-ring form 4 (OOO) was eluted
at 14 min. The photogenerated solution gave two peaks at
Figure 2. 1H NMR methyl signals of the (a) 2 (OOO) trimer; (b) 2 (COO) trimer; (c) 2 (CCO) trimer; and (d) 2 (CCC) trimer.

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0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
300
400
500
600
700
800
Wavelength, nm
Figure 3. Absorption spectral change of the trimer 4 in chloroform upon
0
irradiation with 365 nm light: ( ) before irradiation, (-$-$) after UV light
irradiation for 2 min, (- - -) for 8 min.
Figure 4. 1H NMR methyl signals of the (a) 4 (OOO) trimer; (b) 4 (COO)
trimer; and (c) 4 (CCO) trimer.
11 and 14 min. As the peak at 14 min can be assigned to be
4 (OOO), the peak at 11 min can be assigned as a photo-
cyclized product. The H NMR spectrum is demonstrated
1
2.20 ppm, together with one singlet at 1.97 ppm. The inte-
gral ratio of the two signals was 1:2, indicating that the
colored isomer is 4 (COO). Figure 4c shows the H NMR
spectrum of methyl protons of 4 (CCO). The methyl protons
show two resonances at 2.20 and 1.97 ppm with the integral
ratio of 2:1. This indicates that two closed-ring forms 4
(CCO) are included in the trimer.
to be 4 (COO) (Scheme 5). Further irradiation (2 min) of 4
(COO) with 365 nm light gave the deep blue solution. The
photogenerated products were analyzed with HPLC (silica
gel, eluent hexane/ethyl acetate (9:1)). When monitored at
the isosbestic point of 342 nm, two peaks were observed.
The first peak of the isomer had an absorption maximum
at 615 nm. The product was proven to be 4 (CCO) based
1
1
on the H NMR. Further irradiation of 4 (CCO) (4 min)
2.4. Quantum yield
with 365 nm light did not afforded the anticipated red-shift
of the absorption maximum that would have resulted from
the fully ring-closing isomer. Instead, the increase in the
absorbance levels off. The 1H NMR spectroscopy is a useful
tool that determines the exact ratio between the open and
closed forms. The most suitable signals, showing the largest
shifts upon cyclization, are those of the methyl groups on the
The quantum yield of the macromolecules 2 and 4 are mea-
sured using 1,2-bis(2-methyl-3-thienyl)perfluorocyclopen-
tene (TF6) as a reference.19 The cyclization quantum yield
of 2 from the all open-ring form 2 (OOO) to the isomer 2
(COO), from 2 (COO) to the 2 (CCO), and 2 (CCO) to the
all closed-ring form 2 (CCC) was determined to be 0.23,
0.18, and 0.11, respectively. The total cyclization quantum
yield is 0.52, which is much higher than that of tridithienyl-
ethene array.12 The quantum yield of 4 was determined to be
0.311. The cycloreversion quantum yield of 2 (CCC) and
1
thiophene rings. Figure 4 shows the H NMR spectrum of
methyl protons 4 (OOO) in CDCl3 before photoirradiation
and in the ring-closed form 4 (COO) and 4 (CCO). In the
1H NMR spectrum of 4 (OOO), only one methyl signal
1
was observed at 1.97 ppm. In the H NMR spectrum of
blue isomer 4 (COO), a new methyl signal appeared at
4 (CCO) was measured to be 8.4ꢀ10ꢁ4 and 8.2ꢀ10ꢁ4
,
respectively.
F
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F
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S
S
S
F
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S
S
S
365 nm
532 nm
365 nm
532 nm
F
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S
S
F
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S
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S
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4 (OOO)
Scheme 5. The photochromic reactivity of 4.
4 (COO)
4 (CCO)

H. Choi et al. / Tetrahedron 62 (2006) 9059–9065
9063
2.5. MO calculation
cyclization reaction occurs. Each isomer was isolated and
analyzed by H NMR spectrum. The quantum yield of 2
1
Our interests are focused on examining the electronic com-
munication between three intimately connected 1,2-dithi-
enylethene photochromes in 2 and 4. It is assumed that the
photochromic state of one photochrome will influence the
reactivity of another when they are covalently joined. In
compounds 2 and 4, we wondered why three dithienylethene
units in 2 (OOO) are converted into the all closed-ring form 2
(CCC), and on the other hand, only two dithienylethene units
in 4 (OOO) are partially converted into 4 (CCO). To clarify
the effect of bridged unit in 2 and 4, we have carried out
ab initio calculations. Molecular orbital calculation for the
compounds 2 and 4 were performed using Gaussian 03 pro-
gram at the B3LYP/3-21G* level. Geometry was optimized
at this level. The HOMO in 2 (CCC) is delocalized over the
p-conjugated systems via the two thienylethene unit (Fig. 5,
2a). The LUMO in 2 (CCC) is delocalized through three
dithienylethene units. On the other hand, the HOMO in 4
(CCC) is localized on a dithienyl unit (Fig. 5, 4a) and the
LUMO in 4 (CCC) is delocalized through two dithienyl
units. Examination of the HOMO and the LUMO of 2
(CCC) and 4 (CCC) indicates that the photochromic state
of one photochrome in 2 bridged by ethenyl unit influences
well the reactivity of another, compared with 4 bridged by
ethynyl unit resulting in the all closed-ring form.
and 4 are 0.52 and 0.311, respectively. The formation of
all closed-ring form 2 (CCC) is due to the delocalization
of the p-conjugated systems through the three dithienyl-
ethene units.
3. Experimental
3.1. General
All reactions were carried out under an argon atmosphere.
Solvents were distilled from appropriate reagents. Per-
fluorocyclopentene was purchased from Fluorochem.
1,3,5-Tris((E)-2-(tributylstannyl)vinyl)benzene,15 3,5-di-
bromo-2-methylthiophene,16 and 4-(perfluorocyclopent-1-
enyl)-2-phenylthiophene16 were synthesized using previous
1
references. H and 13C NMR spectra were recorded on a
Varian Mercury 300 spectrometer. The absorption was re-
corded on a Perkin–Elmer Lambda 2S UV–vis spectrometer.
3.2. Determination of quantum yields
The quantum yield of the photochromic ring-cyclization of 2
and 4 was determined from the absorption changes at lmax in
UV spectra upon excitation with a UV light for ring closure
and visible light for ring opening reaction. Conversion and
the number of absorbed photons were determined at a given
radiation power and absorbance of the sample. Then,
In summary, we have prepared two macromolecules incor-
porating three dithienylethene units. Upon irradiation of 2
(OOO) with UV light, one, two, and three photoinduced
Figure 5. Representation of (a) HOMO and (b) LUMO of 2 (CCC); (a) HOMO and (b) LUMO of 4 (CCC) based on Gaussian 03 program at the B3LYP/3-21G*
level.

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H. Choi et al. / Tetrahedron 62 (2006) 9059–9065
quantum yield was determined according to the method
described in Ref. 19.
The product was extracted with ether. The organic layer
was dried over MgSO4. The pure product 4 was obtained
by chromatographic work-up (1:5 ethyl acetate/hexane, Rf ¼
1
3.2.1. Compound 1. To a mixture of 1,3,5-tris((E)-2-(tri-
butylstannyl)vinyl)benzene (0.1 g, 0.1 mmol), Pd(PPh3)2Cl2
(7 mg, 10 mol %), and CsF (0.027 g, 0.66 mmol) in toluene
(30 mL) was added 3,5-dibromo-2-methylthiophene
(84.4 mg, 0.33 mmol). The solution was refluxed for 20 h.
After cooling the solution, H2O (10 mL) and brine were
added to the solution. The organic layer was separated and
dried in MgSO4. The solvent was removed in vacuo. The
pure product 1 was obtained by chromatographic work-up
(1:3 ethyl acetate/hexane, Rf ¼0.5) as a yellow solid in
0.5) as a blue solid in 50% yield. Mp: 136 ꢂC. H NMR
(CDCl3): d 7.60 (s, 3H), 7.55 (d, J¼7.1 Hz, 6H), 7.39 (t,
J¼7.2 Hz, 6H), 7.33 (s, 3H), 7.32 (d, J¼7.2 Hz, 3H), 7.29
(s, 3H), 1.97 (s, 18H).13C{1H} NMR (CDCl3): d 144.1,
142.6, 141.4, 133.8, 133.3, 132.3, 129.1, 128.5, 128.1,
125.7, 125.6, 125.3, 123.7, 122.3, 121.1, 119.5, 116.2,
113.8, 92.1, 83.2 14.6. MS: m/z 1476 [M+]. Anal. Calcd for
C75H42F18S6: C, 60.97; H, 2.87. Found: C, 60.62; H, 2.72.
3.2.5. Closed-ring isomer of 2 (COO). 1H NMR (CDCl3):
d 7.55 (d, J¼8.1 Hz, 6H), 7.42 (s, 3H), 7.39 (t, J¼6.2 Hz,
6H), 7.31 (t, J¼7.1 Hz, 3H), 7.28 (s, 2H), 7.20 (d,
J¼16.2 Hz, 3H), 7.10 (s, 2H), 6.81 (d, J¼16.2 Hz, 3H),
6.70 (s, 1H), 6.42 (s, 1H), 2.16 (s, 6H), 1.97 (s, 12H).
1
70% yield. Mp: 176 ꢂC. H NMR (CDCl3): d 7.37 (s, 3H),
7.11 (d, J¼16.2 Hz, 3H), 6.89 (s, 3H), 6.79 (d, J¼16.2 Hz,
3H), 2.40 (s, 9H).13C{1H} NMR (CDCl3): d 137.5, 134.8,
133.6, 130.7, 129.2, 127.6, 126.8, 109.7, 14.5. MS: m/z
683 [M+]. Anal. Calcd for C27H21Br3S3: C, 47.59; H, 3.11.
Found: C, 47.46; H, 3.06.
1
3.2.6. Closed-ring isomer of 2 (CCO). H NMR (CDCl3):
d 7.55 (d, J¼8.1 Hz, 6H), 7.42 (s, 3H), 7.39 (t, J¼6.2 Hz,
6H), 7.31 (t, J¼7.1 Hz, 3H), 7.28 (s, 1H), 7.20 (d,
J¼16.2 Hz, 3H), 7.10 (s, 1H), 6.81 (d, J¼16.2 Hz, 3H),
6.70 (s, 2H), 6.42 (s, 2H), 2.16 (s, 12H), 1.97 (s, 6H).
3.2.2. Compound 2. To a stirred THF solution (50 mL)
of 1 (0.31 g, 0.45 mmol) was added n-BuLi (1.43 mL,
2.29 mmol, 1.6 M in hexane) at ꢁ78 ꢂC under argon atmo-
sphere, and stirred for 1.5 h at the temperature. 4-(Perfluoro-
cyclopent-1-enyl)-2-phenylthiophene (0.84 g, 2.29 mmol)
in THF (5 mL) was slowly added to the solution at ꢁ78 ꢂC
and stirred for 3 h at the temperature. The reaction mixture
was quenched by the addition of H2O (1 mL). The product
was extracted with ether. The organic layer was dried over
MgSO4. The pure product 2 was obtained by chromato-
graphic work-up (1:5 ethyl acetate/hexane, Rf ¼0.3) as
1
3.2.7. Closed-ring isomer of 2 (CCC). H NMR (CDCl3):
d 7.55 (d, J¼8.1 Hz, 6H), 7.39 (t, J¼6.2 Hz, 6H), 7.31
(t, J¼7.1 Hz, 3H), 7.20 (d, J¼16.2 Hz, 3H), 6.81 (d,
J¼16.2 Hz, 3H), 6.70 (s, 3H), 6.42 (s, 3H), 2.16 (s, 18H).
3.2.8. Closed-ring isomer of 4 (COO). 1H NMR (CDCl3):
d 7.60 (s, 3H), 7.55 (d, J¼7.1 Hz, 4H), 7.42 (d, J¼7.1 Hz,
2H), 7.39 (t, J¼7.2 Hz, 6H), 7.33 (s, 2H), 7.32 (d,
J¼7.2 Hz, 3H), 7.29 (s, 2H), 6.68 (s, 1H), 6.50 (s, 1H),
2.19 (s, 6H), 1.97 (s, 12H).
1
a blue solid in 70% yield. Mp: 143 ꢂC. H NMR (CDCl3):
d 7.55 (d, J¼8.1 Hz, 6H), 7.42 (s, 3H), 7.39 (t, J¼6.2 Hz,
6H), 7.31 (t, J¼7.1 Hz, 3H), 7.28 (s, 3H), 7.20 (d,
J¼16.2 Hz, 3H), 7.10 (s, 3H), 6.81 (d, J¼16.2 Hz, 3H),
1.97 (s, 18H).13C{1H} NMR (CDCl3): d 142.3, 141.4,
140.7, 137.6, 136.4, 133.4, 129.4, 128.8, 128.4, 127.7,
126.8, 125.9, 125.7, 124.1, 122.9, 122.1, 119.7, 116.3,
112.9, 111.1, 14.8. MS: m/z 1482 [M+]. Anal. Calcd for
C75H48F18S6: C, 60.72; H, 3.26. Found: C, 60.45; H, 3.13.
1
3.2.9. Closed-ring isomer of 4 (CCO). H NMR (CDCl3):
d 7.60 (s, 3H), 7.55 (d, J¼7.1 Hz, 2H), 7.42 (d, J¼7.1 Hz,
4H), 7.39 (t, J¼7.2 Hz, 6H), 7.33 (s, 1H), 7.32 (d,
J¼7.2 Hz, 3H), 7.29 (s, 1H), 6.68 (s, 2H), 6.51 (s, 2H),
2.19 (s, 12H), 1.97 (s, 6H).
3.2.3. Compound 3. To a degassed mixture of 1,3,5-tri-
ethynylbenzene (0.576 g, 3.9 mmol), Pd(PPh3)4 (0.67 g,
0.58 mmol), and CuI (0.044 g, 0.24 mmol) in Et3N
(50 mL) was added 3,5-dibromo-2-methylthiophene (5 g,
19.5 mmol). The mixture was stirred at 45 ꢂC for 7 h. The
solvent was evaporated under reduced pressure. The pure
product 3 was obtained by chromatographic work-up (1:10
ethyl acetate/hexane, Rf ¼0.5) as a pale yellow solid in
7.08 (s, 3H), 2.41 (s, 9H).13C{1H} NMR (CDCl3): d 137.2,
134.7, 133.7, 123.7, 120.2, 109.3, 91.9, 83.3, 15.1. MS:
m/z 675 [M+]. Anal. Calcd for C27H15Br3S3: C, 48.02; H,
2.24. Found: C, 47.75; H, 2.14.
Acknowledgements
This work was supported by the KOSEF through National
Research Laboratory (NRL 2005) program awarded to J.K.
References and notes
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