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Infrared and polarized Raman spectra of dixanthinium tetrachlorozincate single crystal

KALYANARAMAN, S., et al.

Abstract

Single crystal dixanthinium tetrachlorozincate has been grown from dilute chloridric acid.

Polarized Raman spectrum of the single crystalline sample, FT-Raman and FT-IR spectra of the polycrystalline samples have been examined and the bands assigned to the appropriate modes predicted by a factor group analysis for the space group Pmn21. The crystal structure has been confirmed by powder XRD measurements.

KALYANARAMAN, S., et al . Infrared and polarized Raman spectra of dixanthinium

tetrachlorozincate single crystal. Journal of Physics and Chemistry of Solids , 2007, vol. 68, no. 2, p. 256-263

DOI : 10.1016/j.jpcs.2006.11.004

Available at:

http://archive-ouverte.unige.ch/unige:3201

Disclaimer: layout of this document may differ from the published version.

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Journal of Physics and Chemistry of Solids](]]]])]]]]]]

Infrared and polarized Raman spectra of dixanthinium tetrachlorozincate single crystal

S. Kalyanaraman

a

, V. Krishnakumar

b,

, Hans Hagemann

c

, K. Ganesan

d

aDepartment of Physics, Sri Paramakalyani College, Alwarkurichi 627412, India

bDepartment of Physics, Periyar University, Salem 636011, India

cDepartment of Physical Chemistry, University of Geneva, Switzerland

dDepartment of Physics, T.B.M.L. College, Porayar 609307, India

Received 24 July 2006; received in revised form 5 November 2006; accepted 9 November 2006

Abstract

Single crystal dixanthinium tetrachlorozincate has been grown from dilute chloridric acid. Polarized Raman spectrum of the single crystalline sample, FT-Raman and FT-IR spectra of the polycrystalline samples have been examined and the bands assigned to the appropriate modes predicted by a factor group analysis for the space group Pmn21. The crystal structure has been confirmed by powder XRD measurements.

r2006 Published by Elsevier Ltd.

Keywords:A. Organometallic compounds; B. Crystal growth; C. Infrared Spectroscopy; C. Raman Spectroscopy

1. Introduction

Metal complexes of bi- and trivalent metal ions with adenine and guanine, the major purine bases present in DNA and RNA, have been described in a number of crystallographic studies and reviews[1,2] while much less structural data are available on compounds involving oxopurines such as hypoxanthine and xanthine. Xanthine is an intermediate product in the conversion of nucleic acid to uric acid. The failure of conversion of xanthine to uric acid results in the deposition of xanthine crystals in muscle tissues leading to a rare disorder, xanthiniuria [3–5].

Xanthine and its methyl derivatives had been widely studied due to their structural tautomerism, which is an intrinsic property of biological molecules and nucleic acids [6,7]. Vibrational spectral studies were undertaken by earlier workers on xanthine and its derivatives[8]. Though much work has been exposed in the biological field regarding metal xanthine complexes, not much work has been carried out on the physics and chemistry of the solid

in the condensed state. The present study is thus focused on the vibrational analysis of dixanthinium tetrachlorozincate.

Xanthine in its neutral free state involves three acidic protons, two of which are attached to the N(1), N(3) pyrimidine nitrogens, while the third is attached to the N(7) imidazole nitrogen [9,10]. In the interaction of metal ions with neutral xanthine the imidazole nitrogen atom N(9) would be the preferred metallation site and hydrogen atoms are attached at N(1), N(3) and N(7) [11]. In general, in purine derivatives the change of bond length and angles are more pronounced in the five membered imidazole ring than in the six membered pyrimidine ring. For example, upon protonation of N(7) and N(9) in the hypoxanthinium cations the double bond character of N(7)–C(8) was reduced while the double bond character of C(8)–N(9) was found to increase in addition to the change in their C–N–C bond angle[12]. Similar observation is also found in the case of 6- mercaptopurinium+complex[13]. This reveals the fact that when hydrogen atom is attached to nitrogen atom, purine derivatives show significant alterations in the ring geometry.

Xanthine binds the metal atom through N9 site when unidentate, through the more probable N7 and N9 combinations when bidentate and coordinating through N(3), N(7) and N(9) when tridentate [14,15]. The thermal

www.elsevier.com/locate/jpcs

0022-3697/$ - see front matterr2006 Published by Elsevier Ltd.

doi:10.1016/j.jpcs.2006.11.004

Corresponding author. Tel.: +91 427 2345766x214;

fax: +91 427 2345124.

E-mail address:[email protected] (V. Krishnakumar).

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behavior of the present complex was investigated by earlier workers[16], suggesting that a small mass loss of 3.8% was observed while degradation of the compound, which may be

due to loss of adsorbed water molecule. However, the crystal structure determination of the compound excludes the existence of a water molecule of hydration.

The present study aims to cover the entire region of the Raman spectrum of the crystalline complex in order to reveal the complete phonon picture. Group theoretical method has been employed to ascertain the internal and external modes of the fundamental lattice vibrations of the crystal. From the IR and Raman spectra of the complex, the vibrational modes are observed and assigned. The number of modes assigned could always be less than the theoretical predictions due to the overlapping of a large number of vibrational frequencies in relatively limited spectral range[17].

2. Experimental

2.1. Synthesis of dixanthinium tetrachlorozincate

Colorless transparent crystals of dixanthinium tetra- chlorozincate were obtained according to the method described in the literature [18]. The crystals were kept in an airtight container since it was reported as slightly air sensitive. The formation of the title compound can be represented by the chemical equation

2C5N4H4O2ðaqÞ þZnCl2ðaqÞ

þ2HClðaqÞ ! ðC5N4H5O2þÞ2½ZnCl4ðsÞ:

2.2. Physical measurements

2.2.1. Powder X-ray diffraction analysis

The crystal dixanthinium tetrachlorozincate was characterized by powder X-ray diffraction analysis to confirm its crystal structure. The Riche Seifert SH-37/80 diffractometer with the CuKa1 radiation of 1.5406 A˚

Fig. 1. Powder XRD pattern of dixanthinium tetrachlorozincate.

Table 1

Lattice parameters of dixanthinium tetrachlorozincate

Parameters Dixanthinium

tetrachlorozincatea

Dixanthinium tetrachlorozincateb Crystal symmetry Orthorhombic Orthorhombic

Space group Pmn21 Pmn21

Z 2 2

a(A˚) 19.701 19.823

b(A˚) 6.583 6.611

c(A˚) 6.610 6.602

a(deg) 90 90

b(deg) 90 90

g(deg) 90 90

D 1.98 1.962

U(A˚3) 857.3 865.19

aRef[18].

bPresent.

Wavenumber (cm -1)

Raman Intensity [arb.units]

100 150 200 250 300 350 400 100 150 200 250 300 350 400 a(bb)a

c(aa)c

b(cc)b

c(ba)c

a(bc)a

b(ac)b

Fig. 2. Polarized Raman spectra of different geometries in the region 140–400 cm1. S. Kalyanaraman et al. / Journal of Physics and Chemistry of Solids](]]]])]]]]]]

2

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(scanning speed of 0.51per minute) was used to record the X-ray diffraction pattern.

2.2.2. Polarized Raman measurements

The Raman spectra were recorded at room temperature on a Kaiser Holospec monochromator f/1.8 equipped with a Princeton Instruments liquid nitrogen cooled CCD camera, using 488 nm radiation of argon ion laser at 100 MW power. According to Porto notation[19], the six different setups aðbbÞ¯a, cðaaÞ¯c, bðccÞ¯b, cðbaÞ¯c, aðbcÞ¯a and

bðacÞ¯b have been utilized by the arrangement of the polarizer and crystal. For observations at very low Raman shifts, measurements were done using a SPEX 1404 double monochromator with an excitation wavelength of 568 nm.

Additional experiments were performed at room tempera- ture using a Labram Raman microscope with an excitation wavelength of 532 nm in the back scattering geometry.

2.2.3. FT-Raman measurements

FT-Raman spectra of the samples were recorded in the range 70–3600 cm1 at room temperature using the BRU- KER RFS 100/s spectrophotometer (stokes shift), which employs 1064 nm laser excitation with 2 cm1resolution.

2.2.4. FT-IR measurements

The infrared spectra were recorded with a BRUKER IFS 66 V vacuum F.T. spectrophotometer in the range 450–4000 cm1with a KBr pellet and extended to far-IR in the range 70–650 cm1with CsI window.

3. Results and discussion

The recorded X-ray spectrum of dixanthinium tetra- chlorozincate, shown inFig. 1, exhibits the high degree of crystallinity of the compound. The lattice parameters Wavenumber (cm-1)

Raman Intesnity [arb.units]

200 400 600 800 1000 1200 1400 1600 1800 2000 2200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 a(bb)a

c(aa)c

b(cc)b

a(bc)a

b(ac)b c(ba)c

Fig. 3. Polarized Raman spectra of different geometries in the region 300–2000 cm1.

20kcps

15

10

5

0

-200 -100 0 100 200 300 cm-1

Raman Shift [cm -1]

Raman Intensity [a.u.]

ZZ+ZX

YX+YX

YZ YX

Fig. 4. Low frequency Raman spectrum in the range 0–300 cm1.

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derived from the diffraction pattern are in good agreement with the literature values (Table 1), confirming that the dixanthinium tetrachlorozincate obtained in this work has the same crystalline structure of the one described earlier [18]. Polarized Raman spectra are recorded in the range 140–1700 cm1 as shown in Figs. 2 and 3. The low frequency Raman spectrum is shown in Fig. 4. The FT- Raman spectra corresponding to the various regions are depicted inFigs. 5 and 6. The unpolarized Raman spectra have been taken to support the inadequacy in the low frequency and high frequency region of the polarized Raman spectrum. The mid-IR and far-IR spectra are shown inFigs. 7 and 8, respectively.

3.1. Factor group analysis

(C5N4H5O2+)2[ZnCl4] crystallizes in the orthorhombic system with the space group Pmn21 (C72v) [18]. The primitive cell contains two formula units with the cations and anions occupying sites of Cssymmetry. Application of a factor group analysis predicts the nature of the k¼0 vibrational modes and their distribution among the irreducible representations of the factor group C72v.The representation corresponding to the total degrees of freedom is given by GN¼74A1þ37A2þ37B1þ74B2

from where acoustic modes GT¼A1þB1þB2 may be removed giving a combination describing the optic modes Go¼73A1þ37A2þ36B1þ73B2 which are all Raman active. Specification of the unit-cell modes can be performed as follows:

Translational lattice modes:

GT¼6A1þ3A2þ3B1þ6B2; Rotational lattice

modes:

GB¼3A1þ6A2þ6B1þ3B2; Internal modes of the

ZnCl4systems:

Gn¼6A1þ3A2þ3B1þ6B2; Internal modes of the

xanthine:

Gn¼42A1þ42A2þ42B1þ42B2.

The notations GN, Go, GT, GB and Gn are irreducible representations correspond to total modes, optic modes, translational modes, rotational modes and internal modes, respectively. All the optical modes are Raman active, while the modes A1, B1, B2are infrared active also. The A2 phonons are not infrared active. The polarization modes A1, B1, B2 are parallel to z-, x-, y-axes (crystal- lographic c-, a-, b-axes), respectively. It is possible to determine the symmetry species of various vibrations by recording the Raman spectra using suitable scattering geometries. The geometries employed and the associated polarizability tensor [20] components contributing to the Raman spectrum are given inTable 2. The correlation scheme for the internal modes of xanthine and ZnCl4systems are given inTables 3 and 4. The summary of the factor group analysis is listed in Table 5.

The complete vibrational assignment of dixanthinium tetrachlorozincate single crystal has been depicted in Table 6.

0 200 400 600 800 1000 1200 1400 1600 1800 0.000

0.001 0.002 0.003 0.004 0.005

Raman Intensity [arb.units]

Wavenumber (cm-1)

Fig. 5. Unpolarized Raman spectra in the range 70–2000 cm1.

3000 3100 3200 3300 3400 3500 0.0000

0.0002 0.0004 0.0006 0.0008

wavenumber (cm-1)

Raman Intensity [arb.units]

Fig. 6. Unpolarized Raman spectra in the range 3000–3500 cm1. S. Kalyanaraman et al. / Journal of Physics and Chemistry of Solids](]]]])]]]]]]

4

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3.2. Analysis of spectra 3.2.1. 3300–3100 cm1region

The IR and far-IR vibrational frequencies of the free ligand xanthine have been taken for band assignments and to verify the shift in their frequencies with the present compound[21–23]. The strong band at 3271 cm1in IR has been assigned ton(OH) which was absent in the free ligand.

This may be due to the strong hydrogen bonding interaction N(1)–H(1)yO(2) that exists between the two symmetry-related xanthinium cations. However, Raman spectra does not show the n(OH) vibrations, as these vibrations are usually very weak in Raman. No significant spectral changes were observed in the nCH and nNH regions, which is quite obvious since no direct metal–ligand coordination is found. However, more number lines are

observed in this region, which may be due to the presence of N–H+ band in the protonated form. All the ring nitrogen atoms are attached to hydrogen atoms by protonation of the title compound since it is prepared under acidic condition. This is revealed by the group of lines in the region 2377–2060 cm1in both IR and Raman spectrum corresponds to combinational bands, however, not included in the assignments.

3.2.2. 1700–1500 cm1region

There is no appreciable shift in the double bonded bands of C(2) and C(6) with oxygen atoms both in IR and Raman, ruling out the possibility of coordination through the exocyclic oxygen atoms, but show more substantial shifts of the nCQC and nCQN ligand absorptions in both IR and Raman. Occasional splitting was also found in Raman. The appreciable shift in frequency and modifica- tion of intensity in the CQC and CQN band region, clearly indicates that all ring nitrogen atoms are proto- nated, leading to a change in their bond length (double bond) and bond angles[18]. In the region of the carbonyl stretching mode, the IR and Raman spectrum shows strong peaks at 1689, 1720 cm–1and 1677, 1682, 1689, 1691 cm–1, respectively. Though the polarized Raman measurements at different geometries in this region show subtle variation of 3–4 cm1, there is a marked variation in their intensities.

3.2.3. 1500–600 cm1region

The region 1500–950 cm1 has been assigned to ring vibrations, single bonded C–N stretching vibrations and NH bending vibrations. The marginal frequency shift in this region may be due to the less pronounced ring vibrations, NH bending and C–N stretching vibrations.

This is well supported by the smaller change in the bond 100.0

95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0.0

4000.0 3600 3200 2800 2400 2000 1800 1600 1400 1000 800 600 450.0

Wavenumber cm-1

% Transmittance

1200

Fig. 7. FT-IR spectrum of dixanthinium tetrachlorozincate.

0 100 200 300 400 500 600 700

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

Intensity [arb.units]

Wavenumber (cm-1)

Fig. 8. Far-IR spectrum of dixanthinium tetrachlorozincate.

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length (single bond) and bond angles compared to the other purine bases. The region 900–600 cm1 has been assigned to ring vibrations, NH asymmetric stretching vibrations and CH bending vibrations. There was sig- nificant alteration in the ring geometry in the imidazole moiety when compared to the pyrimidine ring especially a widening of the C(8)–N(9)–C(4) and C(5)–N(7)–C(8) bond angles due to protonation at N(9). This could be the reason for the shift in the band frequencies in the NH asymmetric stretching and CH bending vibrations when compared to the neutral xanthine. Polarized Raman in these regions has shown additional lines providing assignment of the ligand Xanthine.

3.2.4. 600–120 cm1region

These bands identified in this region are mainly due to ring vibrations. The vibrational frequencies found at 351,

304, 274, 226, 149 and 122 cm1in polarized Raman, 337, 283, 152, 122 cm1 in unpolarized Raman and 345, 303, 265, 148 and 111 cm1 in IR were assigned to tetrachlor- ozincate ion. These assignments are in good agreement with characteristic bands of tetrachlorozincate ion[24–27].

But in free xanthine several absorption bands found in this region are mainly due to out-of-plane ring vibrations[22].

The additional bands observed in the title crystal when compared to that of free xanthine was due to the addition of tetrachlorozincate ion with xanthine. The extent of distortion produced in the tetrahedral geometry of the tetrachlorozincate ion when compared to the free ion depends on the N–HyCl hydrogen bonding in the present case. As the N–HyCl hydrogen bonding is very weak in this case, the deviation in the tetrahedral geometry is expectedly very small. This was confirmed by the measured tetrahedral angle for the title compound[18].

Table 2

Various illumination–observation geometries and the associated polarizability tensor components contributing to the Raman spectrum Axis along

incident light

Axis along polarization of incident light

Axis along polarization of scattered light

Axis along scattered light

Contributing polarizability tensors

Symmetry

a b b ¯a ayy A1(Z)

c a a ¯c axx A1(Z)

b c c ¯b azz A1(Z)

c b a ¯c ayx A2

a b c ¯a ayz B2(Y)

b a c ¯b axz B1(X)

Table 3

Internal vibrations of xanthinium cation Free ion

symmetry Cs

Site

symmetry Cs

Factor gr oup symmetry C2v

42 A1 42 A1 21A1

42 A11 42 A11 21A2

21B1

21B2

Table 4

Internal vibrations of ZnCl42

Free ion symmetry

Td

Site gr oup symmetry

Cs

Factor gr oup symmetry C2v

2 A1 2 A1 6 A1

2 A1 3 A2

4 E 2 A11 3 B1

8 A1 6 B2

12 F 4 A11

18 18 18 S. Kalyanaraman et al. / Journal of Physics and Chemistry of Solids](]]]])]]]]]]

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Table 6

Vibrational assignment of dixanthinium tetrachlorozincate

aðbbÞa cðaaÞc bðccÞb cðbaÞc aðbcÞa bðacÞb Symmetry IR Unpolarized Raman Assignments

60 60 A1(Z)+B1(X) Lattice

82 80 78 82 A1(Z)+A2+B2(Y)+B1(X) Lattice

100 101 101 100 A1(Z)+A2+B2(Y)+B1(X) 111 100 Lattice

122 122 122 122 A1(Z)+A2+B2(Y)+B1(X) 122 n2(ZnCl4)

143 143 145 143 145 145 A1(Z)+A2+B1(X)+B2(Y) 148 n4(ZnCl4)

149 A1(Z) n4(ZnCl4)

155 156 156 157 157 A1(Z)+A2+B1(X)+B2(Y) 152 n4(ZnCl4)

225 225 226 226 227 226 A1(Z)+A2+B1(X)+B2(Y) 226 n(Xanthine)

271 271 274 273 274 273 A1(Z)+A2+B1(X)+B2(Y) 265 283 n3(ZnCl4)

288 288 A1(Z) n3(ZnCl4)

304 303 304 303 304 304 A1(Z)+A2+B1(X)+B2(Y) 303 n1(ZnCl4)

347 349 351 350 350 350 A1(Z)+A2+B1(X)+B2(Y) 345 n(Xanthine)

358 A1(Z) 356

394 394 397 393 396 395 A1(Z)+A2+B1(X)+B2(Y) 390 n(Xanthine)

494 496 A1(Z) 494 487 n(Xanthine)

531 533 531 A2+B2(Y)+B1(X) 528 541 Ring vibrations

616 616 581 A1(Z)+B2(Y) 572,612

642 641 644 641 644 644 A1(Z)+A2+B1(X)+B2(Y) 650,667 648 Ring vibrations

697,742 g(NH)+d(CH)

786,838,

918

942 943 941 944 944 944 A1(Z)+A2+B1(X)+B2(Y) 942 955 Ring vibrations

1000 1003 1004 1004 1000 A1(Z)+A2+B1(X)+B2(Y) 999 988 Ring vibrations

1106 1107 1106 1107 1108 A1(Z)+A2+B1(X)+B2(Y) 1109 Ring vibrations+

1133 1133 1133 1134 1131 1134 A1(Z)+A2+B1(X)+B2(Y) 1172 n(C–N)+dNH

1249 1252 1249 1252 1250 1252 A1(Z)+A2+B1(X)+B2(Y) 1253 1263 ,,

1280 1283 1279 1283 1281 1284 A1(Z)+A2+B1(X)+B2(Y) ,,

1301 1302 1298 1300 1299 1300 A1(Z)+A2+B1(X)+B2(Y) 1303 1302,1327 ,,

1384 1384 1385 1386 1386 A1(Z)+A2+B1(X)+B2(Y) ,,

1416 1415 1412 1413 1412 1413 A1(Z)+A2+B1(X)+B2(Y) 1420 1424 ,,

1458 1458 1454 1458 1455 1456 A1(Z)+A2+B1(X)+B2(Y) 1444 1440,1462 ,, 1519 1517 1517 1517 1516 1519 A1(Z)+A2+B1(X)+B2(Y) 1523 1496,1528 d(NH)

1592 1589 1592 A1(Z)+B1(X) 1594 1556,1595, 1615 nðCQCÞ þnðCQNÞ;dðNHÞ

1650 1649 1645 1649 1646 1649 A1(Z)+A2+B1(X)+B2(Y) 1652 1642,1659 nðCQCÞ þnðCQ

1691 1689 1677 1683 1677 1682 A1(Z)+A2+B1(X)+B2(Y) 1689 1687 nðC2QOÞþ

1720 1723,1762 nðC6Q

2894,2920 2961 nNH+nCH

3004

3115,3176 3130 nC8–H

3271 n(OH)

n, stretching;r, rocking;d, deformation.

Table 5

Summary of factor group analysis of dixanthinium tetrachlorozincate Factor froup

species

C5H5N4O2) xanthinium cation 1

(C5H5N4O2) xanthinium cation 2

ZnCl4 General Cssites Optic

modes

Acoustic modes

C2v Cs site Cs site Cs site

Int Ext Int Ext Int Ext C H N O Cl Zn

A1(IR,R) 21 2T,1R 21 2T,1R 6 2T,1R 20 20 16 8 8 2 73 1

A2(R) 21 1T,2R 21 1T,2R 3 1T,2R 10 10 8 4 4 1 37

B1(IR,R) 21 1T,2R 21 1T,2R 3 1T,2R 10 10 8 4 4 1 36 1

B2(IR,R) 21 2T,1R 21 2T,1R 6 2T,1R 20 20 16 8 8 2 73 1

84 6 6 84 6 6 18 6 6 60 60 48 24 24 6 219 3

Int corresponds to internal modes.

Ext corresponds to external modes.

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3.2.5. External vibrations

Group theory predicts 9A1, 9A2, 9B1and 9B2 external modes, which are Raman active. Experimentally, fewer modes are observed. One of the possible explanations is that some of the lattice modes are either too weak to appear or (accidentally) degenerate. The librational modes of ZnCl24 ions will probably be weak since the ZnCl24 tetrahedron exhibits approximate spherical symmetry in the crystal. The region below 200 cm1contains few strong peaks and a set of weak to medium peaks in both IR and Raman. Usually they are assigned to lattice translation and rotation, however, precise assignment is doubtful to decide among the two. Often translational modes are difficult to get identified as they involve motions of metal ions. There are few methods such as the metal isotopic substitution method is available to distinguish whether it belongs to translation or rotation. The translational mode was found to be mass-sensitive, whereas the librational mode was mass invariant [28,29] and hence a comparison of the spectrum after isotopic substitution would reveal us to choose between the two. Another simple tool is the Raman spectrum where the rotational modes are often stronger than their counterpart translational modes and the complimentary is true with IR [30]. Based on these facts and available literature, assignments were made.

4. Conclusion

Good quality single crystals of dixanthinium tetrachlor- ozincate were grown from dilute chloridric acid by slow evaporation technique at room temperature. The polarized single-crystal Raman spectra of dixanthinium tetrachlor- ozincate are in close agreement with the factor group analysis predictions based on the Pmn21 space group, providing further support for the assignment of the given space group. Most of the anticipated n1, n2 n3 and n4

internal optic mode components (14 out of 18) of tetrachlorozincate [ZnCl4]2 were found and assigned.

However, in the external optic modes, only seven out of 36 were observed and assigned due to lack of inadequate low frequency Raman data. In the case of xanthinium cation more number of internal modes (90 out of 168) were detected, still a lot more could not be identified due to overlapping of vibrational frequencies. However, more modes could be resolved with polarized Raman spectra at low temperature.

Acknowledgments

The authors are thankful to University of Geneva, Switzerland, IISC, Bangalore, IIT Madras, Chennai, and IGCAR, Kalpakkam for making available their spectral facilities. One of the authors (S. Kalyanaraman) is indebted to the University Grants Commission, Government of India, New Delhi for the award of teacher fellowship under the Faculty Improvement Program.

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[28] P. Tarte, M. Liegeois-Duyckaerts, Spectrochim. Acta Part A 28 (1972) 2029.

[29] N. Mohan, A. Mueller, K. Nakamoto, Advances in Infrared and Raman Spectroscopy, vol. 1, Heyden, London, 1975 (Chapter 5).

[30] R. Bhattacharjee, J. Raman Spectrosc. 21 (1990) 491.

S. Kalyanaraman et al. / Journal of Physics and Chemistry of Solids](]]]])]]]]]]

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