CC BY
32
имеет небольшое усиление по сравнению с усилением мод высших порядков (рис. 8, в). Мода под номером 9 имеет максимальное усиление в волокне с двумя активными сердцевинами (см. рис. 8, в, пустые квадраты). Мода с номером 14 имеет максимальное усиление в волокне с шестью активными сердцевинами (см. рис. 8, в, круги черного цвета). В микроструктурных волокнах динамика мод лазера будет определяться потерями и усилением лазера. При определенном соотношении между усилением и потерями можно добиться возбуждения только одной моды с максимальным значением мнимой части эффективного показателя Im(neff).
ЗАКЛЮЧЕНИЕ
Для исследования усиления в микро-структурных волокнах использовалось приближение комплексного показателя преломления. В таком приближении коэффициент усиления моды пропорционален мнимой части эффективного показателя преломления соответствующей моды. Показано, что в лазерах на основе микроструктурного волокна могут существовать оптимальные условия для генерации основной моды. Изменяя расположение активных областей в поперечном сечении волокна, можно выборочно влиять на усиление мод высших порядков.
Работа выполнена при финансовой поддержке гранта U.S. Civilian Research and Development Foun-
dation for the Independent States of the Former Soviet Union REC-006 и РФФИ (грант № 06-02-17343-a).
Библиографический список
1. Knight J.C., Arriaga J., Birks T.A., Ortigosa-Blanch A., Wadsworth W.J., Russell P.St.J. Anomalous Dispersion in Photonic Crystal Fiber // IEEE Photon. Technol. Lett. 12, 807809 (2000).
2. Fedotov A.B., Zheltikov A.M., Alfimov M.V., Ivanov A.A., Syrchin M.S., Tarasevitch A.P., Linde D. von der // Laser Physics. 2001. V.11. Р.1058-1068.
3. Limpert J., Liem A., Reich M., Schreiber T, Nolte S., Zell-mer H., Tunnermann A. Low-nonlinearity single-transversemode ytterbium-doped photonic crystal fiber amplifier // Opt. Express. 2004. V.12. Р.1313-1319.
4. Wadsworth W.J., Knight J.C., Reeves W.H., Russell P.St.J. Yb3+-doped photonic crystal fibre laser // Electron. Lett. 2000. V.36. Р.1452-1453.
5. Moenster M., Glas P., Steinmeyer G., Iliew R. Mode-locked Nd-doped microstructure fiber laser // Opt. Express. 2004. V.12. Р.4523-4527,
6. Moenster M., Glas P., Steinmeyer G. Femtosecond Neodymium-doped microstructure fiber laser // Opt. Express. 2004. V.13. Р.8671-8677.
7. Roy A., Leproux P., Roy P., Auguste J.-L., Couderc V. Supercontinuum generation in a nonlinear Yb-doped, double-clad, microstructured fiber // J. Opt. Soc. Amer. 2007. B24. Р.788-791.
8. Guobin R., Zhi W. Full-vectorial analysis of complex refrac-tive-index photonic crystal fibers // Opt. Express. 2004. V.12(6). Р.1126-1135.
9. Адамс M. Введение в теорию оптических волноводов. М.: Мир, 1984.
10. Broeng D., Mogilevstev S., Barkou E., Bjarklev A. Photonic Crystal Fibers: A New Class of Optical Waveguides // Opt. Fiber Technology. 1999. V.5. Р.305-330.
11. Снайдер A., Лав Дж. Теория оптических волноводов. М.: Радио и связь, 1987. С.656.
УДК 539.196,3
INVESTIGATION OF THE INFLUENCE OF THE HYDROGEN BONDING ON THE STRUCTURE AND VIBRATIONAL SPECTRA OF BIPHENYLMETHANOLS
L.M. Babkov, J. Baran*, N.A. Davydova**, K.E. Uspenskiy
Saratov State University E-mail: babkov@sgu.ru
* Institute of Low Temperature and Structure Research, PAS, Wroclaw E-mail: baran@int.pan.wroc.pl
** Institute of Physics, NAS of Ukraine, Kiev E-mail: davydova@iop.kiev.ua
Using density functional method (B3LYP/6-31G*), the structures of the biphenylmethanols, their h-bond complexes and methanol h-bond complexes, energies, dipole moments, polarizabilities, frequencies of normal vibrations (in harmonic approximation) and their intensities in vibrational spectra were simulated. The effect of methanol group location in the molecules of 2-, 3- and 4-biphenylmethanols and the influence of the hydrogen bonding on their geometry and vibrational spectra of the molecular systems due to H-bonding have been studied on the basis of molecular modeling.
Исследование влияния водородной связи на структуру и колебательные спектры бифенилметанолов
Л.М. Бабков, Я. Баран, Н.А. Давыдова, К.Е. Успенский
С использованием метода теории функционала плотности (B3LYP/6-31G*) были рассчитаны структуры молекул метанола, бифенилметанолов и их Н-комплексов, энергии, дипольные моменты, поляризуемости, частоты нормальных колебаний в гармоническом приближении, их интенсивности в колебательных спектрах. На основе молекулярного моделирования изучено влияние положения группы метанола в молекулах 2-, 3- и 4-бифенилметанола, а также влияние водородной связи на их геометрические параметры и колебательные спектры.
I. INTRODUCTION
Recently, 2-biphenylmethanol (hereafter 2BPM) has been the object of our detailed investigations [1-6]. We have studied the IR transmittance spectra of crystalline, glassy, and supercooled liquid phases of 2BPM and their temperature dependencies [1-3]. Also, the crystal structure of the stable (triclinic) [4] and metastable (monoclinic) [6] modifications of 2BPM have been studied by X-ray crystallography at room temperature. It has been shown that the monoclinic structure with four molecules per unit cell can be described as hydrogen-bonded chains of molecules, while triclinic structure can be described as cyclic tetramers of hydrogen-bonded molecules.
In the work [1] the room-temperature Raman and IR spectra of 2BPM have been measured and the calculations of the frequencies of normal vibration and their intensities in the IR spectrum of the free 2BPM molecule by means of the method of fragments [7] realized in the complex of programs ‘LEV-100’, have been carried out. Also the interpretation of the vibrational spectra of the crystalline 2BPM was given, the conclusion about the formation of the H-bonds was made, and the most probable model of a molecular conformer at room temperature was proposed. In the next paper [4], the 6-31 + + G(d) basis set at the B3LYP level of the density functional theory [8] has been applied to the calculation of the structures and the vibrational spectra of the free molecules of 2BPM, biphenyl, methanol, and cyclic tetramer of hydrogen-bonded methanol molecules. These results were improved in [5], where hydrogen-bonded complex: tetramer of 2BPM molecules was optimized and the vibrational spectrum of tetramer
of hydrogen-bonded 2BPM molecules was calculated. On the basis of the analysis of the experimental and computer simulation results, an interpretation of the room-temperature vibrational spectra of the triclinic modification of 2B PM and the role of the H-bond in the structure formation were given.
In the present paper the further two biphenylmethanols: 3-biphenylmethanol and 4-bi-phenylmethanol (hereafter 3BPM and 4BPM), which are differ by the location of the methanol group (CH2OH) within the molecule, the IR spectra of which were reported in the set of data on vibrational spectra of the organic compounds [9], have called our attention. Our interest to biphenylmethanols has been stimulated by the fact, that the existence of the isomers provides a unique opportunity to study the influence of the substitution in the 2, 3 and 4 positions of the methanol group in molecules on the vibrational spectra.
It is the main goal of the present investigation to study the effect of methanol group location in isomers of biphenylmethanols on their vibrational spectra and to reveal the role of the H-bond on the structure formation and on the vibrational spectra on the basis of molecular modeling and experimental IR spectra [6, 9].
The molecular modeling of the investigated compounds was performed using density functional theory (B3LYP/6-31G(d)) basis set with the GAUSSIAN’03 software for Windows [8]. Earlier this method was used in [4, 5]. In the course of calculations, the energy minimization and geometry optimization were performed followed by the calculation of the electro optical and mechanical parameters, and the vibrational spectra of the free molecules of 2-, 3- and 4-B PM. Also, this procedure was performed for the H-complex (cyclic tetramers and fragments of the H-bonded chains of biphenylmethanols) calculation. Further we have optimized the geometry and performed the modeling of the vibrational spectra of the methanol molecules and their H-complexes. The discrepancy between calculated and experimental frequencies of the vibrational spectra does not exceed 4%. To re-movе of this discrepancy we used the frequency scaling procedure [10].
2. RESULTS AND DISCUSSION
In Fig.1 experimental room-temperature IR spectra of the stable and metastable modifications of 2BPM obtained in our earlier publication [6] are compared with experimental IR spectra of 2-, 3- and 4-BPM reported in Ref. [9] (curves 1', 1” and 1a, 1b, 1c, correspondingly). It should be noted that to our knowledge, no information about the structures of biphenylmethanols studied in [9] is available in the literature. The existence of strong absorption bands in the region 3450-3150 cm-1 with anomalously large width suggests the presence of the H-bonds in these crystals. These wide bands are usually related to the OH stretching vibrations. The comparison of the OH bands observed in the spectra of 2-, 3- and 4-BPM reported in [9] (Fig.
1, curves 1 a, 1 b and 1 c) with the OH band observed in the spectrum of monoclinic modification of 2BPM (Fig.1, curve 1”) shows their similarity. On the other hand, there is a fairly large difference between the frequency of the OH stretching band observed in the spectrum of monoclinic modification (curve 1'') and triclinic
modification (curve 1'). The curve 1'' is red-shifted on 60 cm-1 as compared to the curve 1'. The similarity of the IR spectra of the compounds investigated in [9] with that of the monoclinic modification of 2BPM [6] allowed us to conclude, that the cores of the H-complexes in these compounds are similar and close to the monoclinic structure. This suggestion was of fundamental importance for modeling of the 2-, 3- and 4BPM compounds.
According to our previous results [4, 5] the free molecule of 2BPM can be realized in two c onformers A and B, which are differed by the angles between planes of the phenyl rings and by the orientation angles of the methanol group with respect to the nearest phenyl ring. There is a difference in the orientation angles of the O-H bond relative to the CH2 in the methanol group. They are equal to 5.2° for conformer A and 77.9° for conformer B. On the basis of the modeling it has been found that the free molecules of 3BPM and 4BPM can be realized only in one conformer. The calculated values of the O-H bond length in the 3BPM and 4BPM molecules
Figure 1. IR spectra of biphenylmethanols in the 3500-3000 cm-1 spectral region: experimental spectra of the triclinic, i' and monoclinic, 1", modification of 2BPM; experimental spectra [9] of the crystalline 2BPM, 1a; 3BPM, ib; 4BPM, 1c; calculated IR spectrum of the dimer, 2, and cyclic tetramer,J
are equal to 0.969 A; the values of the angles between phenyl rings are: 38.3° for 3BPM and 40.9° for 4BPM; the values of the orientation angles of methanol group relative to the plane of the nearest phenyl ring (CCCO) are: 27.2° for 3BPM and 27.9° for 4BPM; dihedral angles between the planes CCO and COH (CCOH) of the methanol group are: 10.0° for 3BPM and 10.5° for 4BPM.
The comparison of the calculated IR spectra of 2-, 3- and 4BPM molecules (Fig.2, Table 1) allowed us to estimate the influence of the position of the methanol group in the molecule on the vibrational spectra. The fragments of the IR spectra are shown in Fig.2, and the assignments of their normal vibrations are given in Table 1. In the spectral region 1500-1400 cm-1 there is a sequence of vibrations, which are related to the deformational vibrations of the phenyl rings in biphenyl.
The absorption band of moderate intensity centered at 1479 cm-1 in the spectrum of 2BPM is by 6 cm-1 and by 12 cm-1 red shifted as compared to its position in the spectra of 3BPM (1485 cm-1) and 4BPM (1491 cm-1), correspondingly. At the same time, the intensity of the band centered at 1479 cm-1 slightly increases.
The low-frequency band in the spectrum of 2BPM is by 20 cm-1 blue shifted as compared to its position in the spectrum of 3BPM, while moving from 3BPM to 4BPM the position of this band does not change. At the same time, the intensity of this band slightly decreases.
Between the low-frequency and high-frequency components of this sequence, a doublet of two weak bands is observed. While moving from 2BPM to 4BPM, the redistribution of intensities of the components of the doublet is observed. The overall intensity of the doublet
Yf
1500
—I----------r
1400
1100
1000 800 750
250 200 v, cm-1
a
b
Figure 2. Fragments of the calculated IR spectra of the free molecules: 2BPM (a); 3BPM (b); 4BPM (c)
Table 1
The influence of the substituent location on the IR spectra of biphenylmethanols
Abbreviations. Q - stretching vibration of C-C or C-O bonds, x - out of plane deformational vibrations (torsion, deviation of the C-H out of phenyl ring, deformation of the phenyl ring), P and a - variation of the angle formed by two CC or C-H bonds. The atoms of the phenyl ring with the substituent are signed with A index, the atoms of the phenyl ring without the substituent are signed with B index, the atoms of the methanol group are signed with R index.
in the spectra of 3BPM is larger as compared to that of 2BPM. In the spectra of 4BPM, the intensity of the high-frequency component of the doublet is close to zero, while its low-frequency component is rather strong. The distance between the components of the doublet increases, too.
According to our computer simulation in the spectral region 1040-1070 cm-1 the vibra-
tions of the C-C bond in the phenyl ring are observed. In the spectra of 2BPM one strong band centered at 1052 cm-1 is observed (Fig. 2a), while in the spectra of 3BPM a clear doublet of two bands centered at 1064 and 1044 cm-1 is seen (Fig. 2b). In the spectra of 4BPM only one intense band centered at 1051 cm-1 is observed (Fig. 2c).
Weak absorption band observed in the spectral region 830-760 cm-1 is assigned to the out-of-plane vibration of the C-H bond of the phenyl ring. The position of this band is blue shifted for 3BPM (794 cm-1) and for 4BPM (825 cm-1) as compared to its position in the spectra of 2BPM (772 cm-1). The intensity of this band is practically the same in the spectra of 2BPM and 3BPM, while it increases in 4BPM spectra.
The O-H vibration band in the low-frequency region is related to O-H banding vibration. This band centered at 248 cm-1 in the spectra of 2BPM is blue shifted on 15 cm-1 and on 8 cm-1 as compared to its position in the spectra of 3BPM (263 cm-1) and 4BPM (256 cm-1), respectively. The intensity of these bands is comparable.
The optimized structures of the fragments of the H-bonded chains of biphenylmethanols are shown in Fig. 3 (5, 6, 7). Fig. 3 also shows the fragments of the H-bonded chains: dimer (i), trimer (2), tetramer (3); and cyclic tetramer (4) of methanol molecules.
The calculated data needed for the analysis of the influence of the H-bonding on the IR spectra are summarized in Table 2. In the triclinic modification cyclic tetramer of 2BPM molecules has a Ci symmetry and builts up of two pairs of similar molecules [5]. One pair contains the molecules, which structure is close to that calculated for the conformer A. The second pair contains the molecules, in which structure is intermediate between the structures of A and B conformers. The lengths of the O-H bonds in this tetramer are equal to 0.993 and 0.994 Á. The lengths of the H-bonded bridges (O-H--- O) are 2.726 and 2.700 Á (Table 2). The number of the normal vibrations in the cyclic tetramer is equal to 306 (in the free molecules of biphenylmethanols this number is equal to 72). They are divided into two blocks according to Ci group: 153 ag + 153 au. The vibrations of the ag type are
2BPM 3BPM 4BPM Assignment
V, cm-1 I, km/mole V, cm-1 I, km/mole V, cm-1 I, km/mole
1491 3.4 1494 0.7 1494 4.0 a ( Hr Cr Hr ), X ( Ca Ca Cr Hr )
1479 17.8 1484 29.3 1491 27.3 в ( Ca Ca Ha ), a ( Hr Cr Hr )
1453 6.5 1455 12.9 1451 3.5 в ( Cb Cb Hb ), в ( Ca Ca Ha )
1436 8.4 1437 10.5 1429 35.2 в ( Cb Cb Hb ), Q ( Cb Cb )
1424 23.0 1405 23.8 1403 17,4 в ( Ca Cr Hr ), в ( Cr Or Hr )
1112 10.3 1095 3.9 1117 2.5 в ( Ca Ca Ha ), Q( Cr Or )
1052 7.0 1064 40.9 1041 5.1 Q ( Ca Ca ), в ( Ca Ca Ha )
1046 63.5 1044 25.9 1051 64.1 Q ( Cr Or ), Q ( Cb Cb )
1035 1.5 1022 1.3 1018 1.0 Q ( Cb Cb ), в ( Cb Cb Hb )
1015 1.4 1012 2.3 1013 4.5 X ( Ca Ca Cr Hr ), x ( Hr Cr Or Hr )
772 10.3 795 14.6 801 2.5 x ( Ca Ca Ca Ha ), X ( Hb Cb Cb Cb )
749 58.8 753 57.2 757 47.6 X ( Ca Ca Ca Ha ), X ( Hb Cb Cb Cb )
731 0.3 716 1.9 720 6.3 X ( Ca Ca Ca Ca ), X ( Ca Ca Ca Ha )
718 3.5 699 5.4 699 7.8 X ( Ca Ca Ca Ca ), X ( Ca Ca Ca Ha )
303 1.9 284 0.7 332 3.1 X ( Ca Ca Ca Ca ), X ( Cb Ca Ca Ca )
276 6.4 269 15.6 274 1.9 X ( Hr Cr Or Hr ), X ( Ca Cr Or Hr )
248 87.3 263 71.7 256 106.7 X ( Ca Cr Or Hr ), X ( Hr Cr Or Hr )
217 14.9 222 24.4 206 3.7 X ( Ca Cr Or Hr ), X ( Hr Cr Or Hr )
172 16.6 180 16.3 177 11.1 X ( Ca Ca Ca Cr ), X ( Hr Cr Or Hr )
Figure 3. Structure of the H-complexes, optimized at the B3LYP level. Fragments of the H-bonded chains of methanol molecules: a - two molecules; b - three molecules; c - four molecules; d - cyclic tetramer of methanol molecules. Dimers of biphenyl-methanol molecules: e - 2BPM; f-3BPM; g -4BPM
active in the Raman and au are active in IR. Under packing of the molecules into tetramers some normal vibration frequencies of the free molecule are splitting into four components. The largest value of the splitting is 152 cm-1 for OH stretching vibration. This value is determined by the difference of the normal vibration frequencies with the symmetry ag, which are inactive in the IR spectrum. The position of the quartet is substantially red shifted on 380 cm-1. The difference between the frequencies of the two normal vibrations, which are active in the IR spectrum (au), is equal to 45 cm-1. These two normal vibrations substantially contributed to the corresponding band in the IR spectrum.
From the analysis of the calculated parameters for the chain fragments (dimers) of 2-, 3-
and 4BPM (Table 2) it follows that the H-bond energy in these cases is smaller than in the case of cyclic tetramers of 2BPM. Moreover, the red shift of the O-H stretching vibration frequency in the case of chain structures is smaller as compared to that of cyclic tetramer of 2BPM (Table
2, Fig. 1, a, b, c, 2, 3). The value of the O-H stretching band splitting caused by formation of the H-bonded chain is comparable with this value in the cyclic tetramer. In the case of H-bonded chain, all vibrations are active, thus the corresponding band is wider as compared to that of cyclic tetramer. This is clearly illustrated by the modeling results of the cyclic tetramer of methanol molecules and the fragments of the chains of methanol molecules: dimer, trimer and tetramer (Table 2, Fig. 4).
a
e
b
c
g
d
Table 2
Calculated parameters of biphenylmetanols, methanol, and their H-bond complexes
Object RqH, Â Rqh-q, Â Voh, cm-1 Av, cm 1 AH, kcal/mole I ir, km/mole H-, d
2BPM 0.968 3575 18.3 1.707
3085 490 6.36 0.0
tetramer 0.993 2.726 3161 414 5.80 3036.3 0.000
0.994 2.700 3203 3226 372 349 5.47 5.27 2709.0 0.0
dimer 0.977 0.971 2.838 3432 3549 143 3.04 845.7 24.2 4.134
3BPM 0.969 - 3572 - - 16.3 1.651
dimer 0.978 0.972 2.838 3418 3541 154 3.20 1015.4 20.9 3.710
4BPM 0.969 - 3571 - - 15.3 1.730
dimer 0.978 0.971 2.848 3427 3544 144 3.06 961.8 4.294
Methanol 0.969 - 3568 - - 11.2 1.695
chain fragment (2 mol.) 0.976 0.969 2.850 3450 3575 118 2.65 383.0 21.7 2.885
chain fragment (3 mol.) 0.976 0.976 0.976 2.755 2.741 3395 3448 3481 173 120 3.46 2.68 590.0 739.7 27.9 3.152
chain fragment (4 mol.) 0.976 0.976 0.976 0.976 2.740 2.721 2.780 3377 3416 3427 3487 191 152 141 3.69 3.17 3.01 1370.0 42.5 864.8 25.4 8.930
0.993 2.716 3091 477 6.27 0.0
cyclic tetramer 0.993 2.734 3192 376 5.50 2005.3 0.000
0.993 2.716 3199 369 5.44 1798.7
0.993 2.734 3237 331 5.12 0.0
methanol molecules allowed us to make fairly correct conclusions without the modeling of the huge fragments of the chain of biphenylmethanol molecules. According to the modeling results (Table 2), the length of the free O-H bond in dimers makes up 0.971 A for 2BPM and 4BPM, and 0.972 A for 3BPM. The length of the O-H bond in the H-bonded bridge is 0,977 A for 2BPM, and 0,978 A for 3BPM and 4BPM; the
length of the H-bonded bridge О-Н......O is 2.838
A for 2BPM and 3BPM, and 2.848 A for 4BPM; the hydrogen atom in 2BPM does not lie
on the strait line, which is a prolongation of the O-H bond, but deviates from it by the angle of 3°.
The length of the H-bonded bridge ОН....O in the H-bonded chain involving three
and four molecules of methanol is slightly In Ref. [4], the applicability of such model- smaller as compared to that of cyclic tetramer of
ing was justified for the analysis of the high- methanol molecules. An increase in the number
frequency region (3150-3450 cm-1) of the IR of the molecules in the chain changes the length
spectrum of 2BPM, because the structure of the of the О-Н......O bridge. Namely, for the chain
cores of the H-complexes formed by 2BPM and with two molecules this length is equal to 2.809
methanol molecules are very similar. The results A, while for the chain with three molecules it
of the modeling of the fragments of the chain of decreases and becomes equal to 2.605 A. In the
Figure 4. Fragments of the calculated IR spectra of the H-bonded chains of methanol molecules: 1 - two molecules; 2 - three molecules; 3 - four molecules; 4 - cyclic tetramer of methanol molecules
case of the chain of four molecules there are three bridges. The lengths of the two bridges are equal to 2.605 À, while the length of the third bridge is equal to 2.710 À, due to the formation of the weak bond О•••" H-C.
The frequencies of the OH stretching bands in methanol molecules and in 2-, 3- and 4BPM are similar (Figs. 1, 4; Table 2). The H-bond energy (AH) in the cyclic tetramers of biphenylmethanol molecules, which was estimated using the empirical formula obtained by Iogansen [11] are approximately 6 kcal/mol and are similar to the H-bond energy in the cyclic tetramer of methanol molecules [4]. The H-bond energy in the H-complexes formed by 2-, 3- and 4BPM and methanol are also similar and are approximately equal to 3 kcal/mol (Table 2). This means that the investigated biphenylmethanols are the molecular crystals with the H-bond energy of a moderate strength.
3. CONCLUSION
On the basis of the analysis of the experimental IR spectra and the results of computer modeling it was established, that the location of the methanol group in 2, 3 and 4 positions in biphenylmethanol molecule influence on the vibrational spectrum. This influence appears as negligible shifts of some bands related to the vibrations of the phenyl ring and as a essential redistribution of the intensities among these bands.
It was established that the experimental vibrational spectrum of 2BPM, studied in [9], belongs to a monoclinic crystalline modification. This modification consists of H-bonded chains. The similarity of the IR spectra of 2-, 3- and 4BPM in the region 3450-3150 cm-1 allowed us to conclude, that the 3BPM and 4BPM, studied in [9], also belong to the monoclinic modification. The results of the modeling are in accordance with the X-ray data for the triclinic and monoclinic modifications of 2BPM [6] and with the experimental IR spectra of 2-, 3- and 4BPM compounds [6, 9].
In the case of tetramer two closely spaced O-H vibration bands, which are related to O-H asymmetric stretching vibrations, which are active in the IR spectrum, determine the shape of the corresponding band in the IR spectrum of the triclinic modification. In the case of the
H-bonded chains all stretching vibrations of the O-H bond are active and form a zone. This zone determines the width of the corresponding band in the IR spectrum of the monoclinic modification, which turns out to be wider relative to that in the IR spectrum of the triclinic modification.
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