Theoretical studies of vibrational spectra of [N\(CH3\)4

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Theoretical studies of vibrational spectra of [N(CH3)4]2ZnCl4-yBry compounds with y = 0, 2 and 4 a

a

a

b

K. Karoui , M. Ben Bechir , A. Ben Rhaiem , A. Bulou , F. b

a

Calvayrac & K. Guidara a

Faculty of Sciences, Laboratory of Condensed Matter, University of Sfax, Sfax, Tunisia b

LUNAM, CNRS UMR 6283, Institut des Molécules et Matériaux du Mans (IMMM), Université du Maine, Le Mans Cedex 09, France Published online: 07 Feb 2014.

To cite this article: K. Karoui, M. Ben Bechir, A. Ben Rhaiem, A. Bulou, F. Calvayrac & K. Guidara (2014) Theoretical studies of vibrational spectra of [N(CH3)4]2ZnCl4-yBry compounds with y = 0, 2 and 4, Phase Transitions: A Multinational Journal, 87:6, 613-628, DOI: 10.1080/01411594.2013.879588 To link to this article: http://dx.doi.org/10.1080/01411594.2013.879588

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Phase Transitions, 2014 Vol. 87, No. 6, 613–628, http://dx.doi.org/10.1080/01411594.2013.879588

Theoretical studies of vibrational spectra of [N(CH3)4]2ZnCl4yBry compounds with y ¼ 0, 2 and 4 K. Karouia*, M. Ben Bechira, A. Ben Rhaiema, A. Buloub, F. Calvayracb and K. Guidaraa a

Faculty of Sciences, Laboratory of Condensed Matter, University of Sfax, Sfax, Tunisia; bLUNAM, CNRS UMR 6283, Institut des Mol ecules et Mat eriaux du Mans (IMMM), Universit e du Maine, Le Mans Cedex 09, France


(Received 2 November 2013; accepted 27 December 2013) The infrared and Raman spectra of [N(CH3)4]2ZnCl4yBry, where y ¼ 0, 2 and 4, have been analyzed with ab initio calculations of the vibrational characteristics of constitutive polyhedra, tetramethylammonium [N(CH3)4]þ and [ZnCl4xBrx]2 (x ¼ 0, 1, 2, 3 and 4) tetrahedra. The optimized geometries, calculated vibrational frequencies, infrared intensities and Raman activities are calculated using Hartree– Fock and density functional theory B3LYP methods with 3-21G, 6-31G(d) and 6311Gþ(d,p) basis sets. Calculation of the root mean square difference drms between the observed and calculated frequencies allows to give scaling factors and to deduce that the best agreements are obtained by B3LYP/6-311Gþ(d,p) for [N(CH3)4]þ and B3LYP/3-21G for [ZnCl4xBrx]2. The present study establishes a strongly reliable assignment of the vibrational modes of [ZnCl4xBrx]2 tetrahedra based on comparison between experimental and ab initio calculations, both of the frequencies and the intensities of the Raman signals. Keywords: tetramethylammonium-dibromodichlorozincate; first-principles; Raman spectroscopy; HF; DFT; vibrational frequencies

1. Introduction Vibrational spectroscopy is one of the most widely used techniques for the determination of molecular structures, for the identification and characterization of molecules and for reaction control.[1] Infrared (IR) and Raman spectroscopy often give complementary information about molecular vibrations. Calculation of vibrational frequencies by ab initio molecular orbital or density functional methods can help in the interpretation of experimental spectra and is particularly useful for assignments of the fundamental vibrational frequencies. But it is known that vibrational frequencies obtained by ab initio calculations are typically larger than their experimental counterpart for organic cations; larger or smaller than their experimental counterparts for inorganic anions. Thus, empirical scaling factors are often used to better describe the experimental vibrational frequencies.[2] These scaling factors depend both, on the method, and on the basis sets used in calculations. They are determined from the mean deviation between the calculated and experimental frequencies.[3,4] *Corresponding author. Email: [email protected] Ó 2014 Taylor & Francis


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Hybrid materials have attracted considerable interest because of their structural phase transitions and several remarkable physical properties. In particular, the [N (CH3)4]2ZnCl4, [N(CH3)4]2Cu0.5Zn0.5Cl4 and [N(CH3)4][N(C2H5)4]ZnCl4 compounds are characterized by the occurrence of many phase transitions below room temperature, including incommensurate and ferroelectric ones.[5–12] In this paper, we report on the chemical quantum calculation studies of the structure and vibrational characteristics of the components of [N(CH3)4]2ZnCl4yBry compounds where y ¼ 0, 2 and 4, with the purpose to analyze the experimental results. Several basis sets are considered to obtain a better insight into the choices of the theoretical methods on their optimized chemical structure and their calculated vibrational frequencies. At room temperature, the [N(CH3)4]2ZnCl4yBry compounds crystallize in the orthorhombic system, with Pnma space group, whatever y. The unit cell dimension change from a ¼ 12.276 A, b ¼ 8.998 A and c ¼ 15.541 A, for y ¼ 0, to a ¼ 12.681 A, b ¼ 9.239 A and c ¼ 16.025 A, for y ¼ 4.[13,14] The structure of [N(CH3)4]2ZnCl4yBry compounds contains two isolated entities: tetramethylammonium (TMA) cation [N (CH3)4]þ and inorganic tetrahedra.[15] [N(CH3)4]2ZnCl2Br2 actually contains five kinds of inorganic polyhedra: [ZnCl4]2 and [ZnBr4]2 ideal tetrahedra with Td symmetry, [ZnCl2Br2]2 with C2v symmetry and [ZnCl3Br]2 and [ZnClBr3]2 with C3v symmetry. Their local symmetry in the crystal is in addition lowered to Cs for the case y ¼ 0 or y ¼ 4, and to C1 for y ¼ 2. The correlations between these point groups have been already reported by van Loosdrecht and Janner.[16]

2. Experimental details The [N(CH3)4]2ZnCl4yBry (y ¼ 0, 2 and 4) compounds were prepared by the reaction with stoichiometric quantities of N(CH3)4X and ZnX2 (X ¼ Cl, Br) in aqueous solution. In this way, good-quality transparent crystals were obtained from a solution with a known bromide concentration (y). Figure 1 shows the X-ray powder diffraction pattern of [N(CH3)4]2ZnCl4yBry compounds (y ¼ 0, 2 and 4) at room temperature using λKa1 ¼ 1.5418 A wavelength. The refined unit cell parameters obtained (a ¼ 12.248 A , b ¼ 8.956 A , c ¼ 15.543 A for y¼ 0; a ¼ 12.491 A , b ¼ 9.130 A , c ¼ 15.772 A for y ¼ 2; a ¼ 12.678 A , b ¼ 9.250 A , c¼ 16.002 A for y ¼ 4 in the orthorhombic system with Pnma space group) are consistent with the values reported in the literature.[1,2,15] Since these compounds are characterized by several phase transitions as a function of temperature, the vibrational measurements for the three compounds have been performed at room temperature in order to preserve the orthorhombic structure. The Raman spectra were excited by the 514.5 nm wavelength radiation of an Ar/Kr laser, and collected with a T64000 Raman spectrometer (Horiba-Jobin-Yvon) in subtractive triple monochromator geometry, using an 1800 tr/mm grating, in the 10–3500 cm1 range; the typical spectral resolution is 1.5 cm1. The experiments, performed under microscope using X50 long working distance objective in backscattering geometry, were done on single crystals optically oriented with polarized light. The spectra were collected in all polarizations, but only those obtained in the Z(XX)Z and Z(XY)Z polarizations are presented with regard to their best signal-to-noise ratio. The IR absorption spectra of the crystallized powders in KBr were recorded on a Perkin-Elmer FT-IR 1000 spectrometer in the 400–4000 cm1 range. The spectral resolution was better than 4 cm1.


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Fig. 1. X-ray diffractograms of the [N(CH3)4]2ZnCl4, [N(CH3)4]2ZnCl2Br2 and [N(CH3)4]2ZnBr4 compounds at room temperature with wavelength λKa1 ¼ 1.5418 A.

3. Computations Ab initio calculations have been performed using the Gaussian 98 program at room temperature.[17] Hartree–Fock (HF) and B3LYP density functional theory (DFT) methods with 3-21G, 6-31G(d) and 6-311Gþ(d,p) basis sets were used to obtain equilibrium geometry and fundamental vibrational frequencies and spectroscopic intensities of the isolated polyhedra [(N(CH3)4]þ and [ZnCl4xBrx]2 with x ¼ 0, 1, 2, 3 and 4.

4. Results and discussion 4.1. Optimized geometries The geometrical parameters of [N(CH3)4]þ, ZnCl42, ZnBr42, ZnCl3Br2, ZnCl2Br22 and ZnClBr32 calculated after optimization of the structure under HF and DFT methods, and the experimental ones measured in [N(CH3)4]2ZnCl4 and [N(CH3)4]2ZnBr4 are given in Table 1. Whatever the method, the calculated bond lengths of ZnCl42 and ZnBr42 are slightly longer than the experimental values, and the bond lengths calculated by the HF method are always higher than the B3LYP one. The best agreements with the experimental values are obtained with B3LYP/6-31G (d) for ZnBr42- where the difference is 0.009A (0.004), and with B3LYP/3-21G for ZnCl42 and [N(CH3)4]þ where the differ ences are 0.096A (0.043) and about 0.13 A for N–C bond, respectively.

4.2. Vibrational frequencies Table 2 and Table 3 lists the frequencies and intensities of [N(CH3)4]þ polyhedra and Table 4 those of the ZnCl4xBrx for x ¼ 0–4 calculated with HF and B3LYP methods using 3-21G, 6-31G(d) and 6-311Gþ(d,p) basis sets, and experimentally measured in [N(CH3)4]2ZnCl4yBry for y ¼ 0, 2 and 4.

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Table 1. Experimental and calculated bond lengths (A) and bond angle ( ) of [N(CH3)4]þ and ZnCl4x Brx2 (x ¼ 0, 1, 2, 3 and 4). Calculated HF Entities

Bond lengths (A)

3-21 G

6-31 G

N(CH3)4 ZnCl4 ZnBr4 (ZnCl3Br)

N–C Zn–Cl Zn–Br Zn–Cl

1.516 2.391 2.537 2.39

1.495 2.388 2.494 2.39

1.52 2.392 2.550 2.38

1.530 2.346 2.484 2.34

1.51 2.361 2.454 2.36

1.507 1.66–1.77 [14] 2.368 2.25 [13] 2.523 2.445 [14] 2.36

2.53 2.39 2.53 2.39 2.53

2.48 2.40 2.48 2.39 2.48

2.59 2.36 2.56 2.37 2.57

2.48 2.34 2.48 2.34 2.48

2.43 2.38 2.44 2.37 2.44

2.55 2.34 2.53 2.35 2.54

Zn–Br Zn–Cl Zn–Br (ZnCl2Br2) Zn–Cl Zn–Br (ZnClBr3)


Calculated B3LYP

Bond angle ( ) Cl–Zn–Cl 109.2 (ZnCl3Br) Cl–Zn–Br 109.7 (ZnClBr3) Cl–Zn–Cl 109.0 Cl–Zn–Br 109.7 Cl–Zn–Cl 108.9 (ZnCl2Br2) Br–Zn–Br 110.2 Br–Zn–Br 109.4

108.9 110.0 108.9 109.9 108.4 110.7 109.4

6-311 Gþ(d,p)

108.8 109.0 109.7 109.2 108.9 110.0 109.4

3-21 G

109.3 109.6 109.0 109.9 108.8 110.0 109.4

6-31 G(d)

108.7 110.2 108.7 110.0 108.0 111.0 109.4

6-311 Gþ(d,p) Experimental

109.7 109.2 109.6 109.3 109.0 110.0 109.4

Table 2. Experimental (Raman and infrared) and calculated frequencies (cm1) of [N(CH3)4]þ using HF and DFT methods with several basis sets. Calculated HF

Calculated B3LYP

Experimental

No.

3-21G

6-31G (d)

6-311Gþ (d,p)

3-21G

6-31G (d)

6-311Gþ (d,p)

Raman

Infrared

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

282 338 427 684 898 1069 1164 1268 1442 1466 1480 1485 1504 2896 2906 2981 2983 2989

281 344 434 703 915 1048 1150 1280 1413 1439 1450 1471 1478 2898 2909 2988 2989 2996

286 383 487 697 892 1077 1134 1413 1429 1438 1453 1463 1488 2871 2910 2962 2981 3003

302 336 422 674 875 1032 1164 1223 1402 1437 1443 1459 1482 2906 2912 2995 2997 3001

277 339 429 693 885 1019 1150 1233 1377 1410 1424 1428 1452 2912 2920 3003 3004 3009

281 340 430 696 890 1023 1134 1238 1377 1404 1418 1428 1446 2915 2923 3004 3006 3011

– 365 455 755 950 1119 1171 1292 1405 – – 1448 1486 2823 2923 2955 2978 3026

– – – – 952 – – 1286 1416 – – – 1481 – – 2958 – 3023

Assignment d2s (E) N–C d4as (F) N–C v1s (A) N–C v3as (F) N–C vR (E) CH3 vR (F) CH3 ds (E) CH3

das (E) CH3 vs (A) C–H vs (A) C–H vas (T) C–H

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Table 3. Values of infrared (IR) absorption and Raman activities of [N(CH3)4]þ calculated with for B3LYP method using 3-21G, 6-31G(d) and 6-311Gþ(d,p) basis sets. B3LYP


Basis

3-21G

6-31G(d)

6-311Gþ(d,p)

No.

IR absorption

Raman activity

IR a bsorption

Raman activity

IR absorption

Raman activity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0 0 0 0 23 0 0 0.3 19 0 0 0 74 0.3 0 0 0 0.4

0 0.5 0.1 16 9 0 7 0.6 5 0.3 0 56 0 0.3 275 0 5.6 94

0 0 0.3 0 21 0 0 1.4 6 0 0 0 55 1.3 0 0 0 1

0 0.43 0.1 14 8 0 6 0.3 3.6 0.4 0 43 0 0 312 0 8 100

0 0 0 0 22 0 0 0.5 3.4 0 0 0 52 0.6 0 0 0 1

0 0.9 0.4 18 7 0 2.7 0.05 0.9 0.2 0 21 0 0 407 0 9 90

The attributions of the experimental spectra are described in Sections 4.2.1 and 4.2.2 on the basis of these calculations and on results from literature. Figure 2 shows plots of the calculated versus experimental vibrational frequencies of (1) [N(CH3)4]þ and (2) ZnCl42 and ZnBr42. Whatever the basis sets, the calculated values are slightly different from the experimental ones (dashed lines), but they are well described by a linear-fitting; the values for [N(CH3)4]þ are slightly above, and those for the inorganic anions slightly below. For [N(CH3)4]þ, the calculated scaling factors are 0.94 for B3LYP/3-21G and 6-31G(d), and 0.96 for B3LYP/6-311Gþ(d,p) basis. For HF method, the scaling factors are 0.89 for 321G and 6-31G(d), and 0.90 for 6-311Gþ(d,p). These values are close to those reported in the literature.[18–21] For the ZnCl42 and ZnBr42 entities (Figure 2(b)), the linear fitting with B3LYP/3-21G is below the correlation line with unit slope but it is very close to it (scaling factor equal to 0.99). This basis will be chosen for attribution of the vibrational modes of the ZnCl4xBrx2 polyhedra. 4.2.1. Vibrations of [N(CH3)4]þ cation The IR and Raman lines of the organic [N(CH3)4]þ polyhedron appear almost at the same positions in the mixed and the pure compounds. The internal modes for this cation that extends from about 300–3000 cm1 can be divided into three groups. The first group, below about 1000 cm1, corresponds to the stretching mode of the N–C vibrations. The second group in the 1000–1500 cm1 frequency range is identified as vibrational modes of the CH3 groups and a third group above 2800 cm1 corresponds to the stretching

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Table 4. Calculated frequencies (cm1) and Raman intensities (Ra) of [ZnCl4xBrx]2 where x ¼ 0, 1, 2, 3 and 4 in the framework of HF and DFT methods using 3-21G, 6-31G(d) and 6-311Gþ(d,p) basis sets. Experimental values and proposed assignments. Calculated HF 3-21 G vi

Si

6-31 G(d) vi

Si

Calculated B3LYP

6-311 Gþ(d,p) vi

Si

3-21 G vi

Si

6-31 G(d) vi

Si

Experimental

6-311 Gþ(d,p) vi

Si

Raman results ni Symmetry Assignment


[ZnBr4]2 50 0.8 54 0.6 46 0.7 49 1.2 51 1.0 46 1.4 56

E

v2(ZnBr4)

82 1.3 78 0.8 73 0.8 86 1.9 79 1.4 74 1.4 87 145 1.2 144 2.6 131 2.1 160 2.8 153 5.5 134 4.6 170 196 0.0 177 0.0 158 0.0 214 0.1 189 0.2 165 0.9 204

T2 A1 T2

v4(ZnBr4) v1(ZnBr4) v3(ZnBr4)

78 120 235 255

1.0 1.3 1.4 0.0

74 116 210 208

1.1 1.3 2.4 0.0

74 110 212 209

1.3 1.1 2.0 0.2

79 127 262 282

1.6 2.1 4.6 0.5

70 115 214 217

1.8 2.2 7.2 0.5

74 110 220 221

2.4 2.0 5.7 1.0

113 130 276 294

E T2 A1 T2

v2(ZnCl4) v4(ZnCl4) v1(ZnCl4) v3(ZnCl4)

60 66 101 102 103 172 199 247 254

1.0 1.9 1.5 1.2 1.3 0.7 0.0 0.6 0.0

62 67 97 98 99 165 185 203 206

0.8 0.9 1.0 1.2 1.1 1.8 0.0 0.0 0.8

55 62 91 92 94 143 149 219 223

0.9 1.0 0.9 1.1 1.2 1.5 0.0 0.6 0.3

60 66 104 107 108 182 218 276 283

1.5 1.4 2.2 2.0 2.0 2.2 0.1 1.7 0.4

60 65 100 101 102 178 201 211 217

1.3 1.4 1.7 1.9 2.0 4.4 0.1 0.6 2.2

55 61 92 93 97 150 159 228 235

1.5 1.7 1.4 2.0 2.2 3.8 0.3 1.9 1.6

59 A1 v2 90 A2 v2 94 B1 v4 99 A1 v4 106 B2 v4 190 ns(ZnBr2) 213 B2 nas(ZnBr2) 279 A1 ns(ZnCl2) 302 B1 nas(ZnCl2)

70 109 111 185 241 253

1.0 1.3 1.4 0.5 0.9 0.0

70 107 108 178 205 210

0.9 1.3 1.2 1.3 1.2 0.0

65 98 102 143 213 216

1.1 1.2 1.1 0.8 1.2 0.2

69 114 116 201 267 278

1.5 2.0 2.1 1.6 2.7 0.4

68 109 110 191 211 219

1.6 2.0 2.1 3.9 2.9 0.5

65 99 101 153 219 224

1.9 2.3 1.8 2.4 3.2 0.3

... ... ... 200 276 289

E A1 E A1 A1 E

v2 v4 v4 ns(ZnBr) ns(ZnCl3) nas(ZnCl3)

56 90 94 157 196 249

0.9 1.5 1.3 1.0 0.0 0.3

59 85 91 155 181 203

0.7 0.9 1.0 2.2 0.0 0.4

51 79 85 138 153 225

0.9 0.8 1.1 1.9 0.0 0.5

55 93 97 173 214 276

1.3 2.1 1.9 2.5 0.1 0.9

57 87 94 164 196 213

1.2 1.6 1.7 4.8 0.1 1.5

51 80 86 143 164 232

1.5 1.3 1.8 4.6 0.5 1.7

... ... ... 181 213 283

E A1 E A1 A1 E

v2 v4 v4 ns(ZnBr3) nas(ZnBr3) ns(ZnCl)

[ZnCl4]2

[ZnCl2 Br2]2

[ZnCl3 Br]2

[ZnCl Br3]2

619


Phase Transitions

Fig. 2a. (a) Hartree–Fock (HF) and DFT (B3LYP) – in the framework of three different basis sets – calculated vibrational frequencies (s (cm1)) of [N(CH3)4]þ (full square black) internal modes versus the experimental values measured at room temperature in [N(CH3)4]2ZnCl4yBry compounds such that y ¼ 0, 2 and 4; linear fitting of the results (solid lines) compared with exact correlation (dashed lines). (b) HF and DFT (B3LYP) – in the framework of three different basis sets – calculated vibrational frequencies (s (cm1)) of [ZnCl4]2 (full square black) and [ZnCl4]2 (full square red) versus the experimental value measured at room temperature in [N(CH3)4]2ZnCl4 and [N(CH3)4]2ZnBr4 compounds, respectively; linear fitting of the results (solid lines) compared with exact correlation (dashed lines).

vibrational modes of the C–H bonds. These later are difficult to interpret in terms of selection rules.[22,23] The assignments of the internal vibrational modes in the IR and Raman spectra of [N(CH3)4]þ cation (Figure 3(a) and 3(b)) are based on the calculated frequencies

K. Karoui et al.


620

Fig. 2b. (Continued)

(Table 2), calculated intensities (Table 3) and on the literature.[23–25] The calculated rms deviation (drms) for [N(CH3)4]þ in the [(N(CH3)4)]2ZnCl4 crystal has the following order (Table 5): HF/6-31G(d) > HF/3-21G > HF/6-311Gþ(d,p) > B3LYP/3-21G >B3LYP/6-31G(d) > B3LYP/6-311Gþ(d,p). It is observed that the frequencies calculated by B3LYP are closer to the experimental frequencies than those calculated using HF method, and that the B3LYP/6-311Gþ(d,p) basis leads to the weaker value of drms. This basis is therefore used for the attribution modes of [N(CH3)4]þ entity in the [(N(CH3)4)þ]2ZnBr2Cl2 crystal. [N(CH3)4]þ is a symmetrical quasi-tetrahedral structure and has four main frequencies associated with N–C vibrations: totally symmetrical N–C stretching vibration v1, doubly

621


Phase Transitions

Fig. 3a. (a) Infrared spectra of [N(CH3)4]2ZnCl4yBry (y ¼ 0, 2, and 4) in the main vibrational range. (b) Raman spectrum of [N(CH3)4]2ZnCl2Br2 in the 350–3200 cm1 spectral range for two different polarizations.


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degenerate C–N–C bending vibration ds, and two triply degenerate vibrations, v3 (asymmetric stretching) and das (asymmetric bending).[23] These modes are observed in the Raman spectrum (Figure 3(b)) at 755, 365, 950 and 455 cm1, respectively, and are calculated at 696, 340, 890 and 430 cm1. Among them, only v3 is observed in the IR spectrum at 952 cm1 (Figure 3(a)), which is consistent with the calculated intensities in Table 3. Somewhat weaker lines appear at 1171, 1292, 1405 and 1448 cm1 in Raman spectrum and have been calculated at 1122, 1238, 1377 and 1428 cm1. These are not fundamental modes of the C–N vibration: they represent deformation (symmetric and asymmetric) and the pendulum oscillation frequencies of the CH3 vibrations. The IR spectrum presents mostly three modes in this region at 1286, 1416 and 1481 cm1, as expected from the calculated intensities (Table 3). The mode at 1481 cm1 is calculated at 1446 cm1 and assigned to the deformation of the CH3 vibration. This mode is observed in the Raman spectrum at 1486 cm1. Finally, stretching (symmetric and asymmetric) modes of the C–H vibrations are seen in the region of 2800–3100 cm1. The observed modes at 2823 and 2923 cm1 corresponding to vs(A)C–H are calculated at 2915 and 2923 cm1. The modes that appear at 2955, 2978 and 3026 cm1 in the experimental spectrum are calculated at 3004, 3006 and 3011 cm1; these modes correspond to the vas(T)C–H vibrations. In the IR spectrum, only the modes at 2955 and 3026 cm1 are clearly seen.

4.2.2. Vibrations of [ZnCl4-xBrx]2 anions [N(CH3)4]2ZnCl2Br2 contains five different inorganic tetrahedra ZnCl4-xBrx with x ¼ 0–4. Each of them has up to nine fundamental vibrations. For x ¼ 0 and 4, the point group is

623


Phase Transitions

Fig. 4a. (a) Low frequency Raman spectra of the [N(CH3)4]2ZnCl4yBry (y ¼ 0, 2 and 4) compounds. (b) Deconvolution of the Raman spectra of [N(CH3)4]2ZnCl4yBry (y ¼ 0, 2 and 4) compounds. The broad signal at very low frequency is introduced to represent the lattice mode contribution to the Raman signal.

Td, and there are four vibrations with symmetries Gvib ¼ A1 þ E þ 2T2. For x ¼ 1 and 3, where the symmetry is C3v, the normal modes are Gvib ¼ 3A1 þ 3E (six modes). Finally, for x ¼ 2, the point group is C2v and the nine normal modes belong to the following symmetries: Gvib ¼ 4A1 þ A2 þ 2B1 þ 2B2.[16]


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Deconvolution and Raman spectra of [N(CH3)4]2ZnCl4yBry compounds (y ¼ 0, 2 and 4) at low frequencies are shown in Figure 4 (a) and 4(b). The low frequency vibrational spectra of these compounds and of the two entities, ZnCl3Br and ZnClBr3, have been studied by van Loosdrecht and Janner [16] on the basis of phenomelogical valence force model, whereas the calculations in the present work are performed ab initio and include predictions of the Raman and IR intensities. As already mentioned, we focused on the frequency range of the internal ZnCl41xBrx2 tetrahedra modes v1, v2,v3 and v4, (10–350 cm1). There are two regions of interest in the spectra. The first one (10– 150 cm1) contains the external modes and the v2 and v4 internal ZnCl41xBrx2 modes, whereas the second one (150–350 cm1) contains the v1 and v3 internal modes of the ZnCl41xBrx2 tetrahedral. The root mean square deviation (drms) for the case of the pure [N(CH3)4]2ZnBr4 and [N(CH3)4]2ZnCl4 compounds is shown in Table 5. It can be used to evaluate the

Phase Transitions

625

Table 5. Root mean square deviation (drms) for [N(CH3)4]þ and [ZnCl4xBrx]2 (x ¼ 0 and 4) molecular ions after the scaling factor. Method Basis


drms [N(CH3)4]þ drms [ZnBr4]2 drms [ZnCl4]2

HF

B3LYP

3-21G

6-31G(d)

6-311Gþ(d,p)

3-21G

6-31G(d)

6-311Gþ(d,p)

69.3 6.0 5.2

72.7 5.6 18.3

67.7 8.8 17.9

40.1 5.6 3.2

40.0 3.9 20.0

34.2 10.6 19.3

discrepancy between the calculated and the observed vibrational frequencies. It appears that B3LYP/3-21G is the common basis giving the best drms. The n1(A1), n2(E), n3(T2) and n4(T2) vibrational modes of ZnCl42 are calculated at 262, 79, 282 and 127 cm1, respectively, whereas the experimental frequencies are 277, 111, 294 and 129 cm1, respectively. For ZnBr42, they are calculated at 160, 49, 214 and 86 cm1 and observed at 170, 54, 202 and 86 cm1, respectively. The weak difference between the observed and calculated frequencies for the different modes detected especially at low frequency (n2) can be attributed at least to the perturbation by its environment (in the crystal). Anyway, the agreement between the observed and calculated frequencies of ZnCl42 and ZnBr42 entities with 3-21G basis is fairly good. This approach can be though reliable to calculate those of the ZnCl2Br2, ZnCl3Br and ZnClBr3 entities. In the 150–350 cm1 range, the Raman spectra of [N(CH3)4]2ZnCl2Br2 exhibit lines at the same frequency as in pure [N(CH3)4]2ZnBr4 (170 and 204 cm1) and pure [N (CH3)4]2ZnCl4 (276 and 294 cm1). The low frequency band shows also at least three additional lines at 181, 189 and 202 cm1. In view of the calculated frequencies and Raman activities, these lines can be attributed to vibrations of ZnClBr32, ZnCl2Br22 and ZnCl3Br2, respectively, predicted at 173, 182 and 201 cm1 using B3LYP/3-21G. The presence of such entities unambiguously establishes that the compound is a true solid solution and not just a mixture of the two pure chloride and bromide crystals. As a consequence, it can be predicted that the unresolved band in the vicinity of 274 cm1 is composed of seven components associated with vibrations of ZnCl4 (calculated at 262 cm1 and found at 272 cm1 in pure [N(CH3)4]2ZnCl4), ZnCl3Br, predicted at 267 cm1, and ZnCl2Br2 and ZnClBr3, both predicted at 276 cm1 (Table 3). The three modes experimentally observed at 276, 279 and 283 cm1, therefore, are assigned to such entities, respectively. The above attributions based on frequencies of the highest predicted intensities can be also checked in view of the relative intensities. As a matter of fact, in [N (CH3)4]2ZnCl2Br2, the ZnBr4, ZnBr3Cl, ZnBr2Cl2, ZnBrCl3 and ZnCl4 entities are expected with probabilities 1/16, 4/16, 6/16, 4/16 and 1/16, respectively, in case of random distribution of the halogens. The intensities therefore should be proportional to such probabilities and the Raman activities (Si) as given by the ab initio calculations reported in Table 6 (note that their relative values are close to the number of Zn–Br bonds involved in the vibrational modes in the 170–210 cm1 band, and those of the Zn–Cl bonds involved in the band centered at 274 cm1). Indeed, the relative calculated intensities weighted by such probabilities appear fairly close to the experimental ones (Table 6). Figure 5 shows the experimental relative intensities normalized by the Raman activities for the five different polyhedra: it appears that the relative populations are close to those expected in case of random distribution of the halogen in different polyhedra.

Ii (area)

11155.8 50044.2 16207.6 5664.8 900.8 519.5 15897.4 6538.6 912.8 4612.3 748.4 382.7 1178.7

vi (cm1)

170 181 190 200 204 213 272 276 279 283 289 294 302

Ii

0.0292 0.0236 0.0188 0.0126 0.0009 0.0012 0.0223 0.0129 0.0079 0.0042 0.0021 0.0023 0.0017

Experimental values

160 173 182 201 214 218 262 267 276 276 278 282 283

vi (cm1) 2.865 (4/4) 2.579 (3/4) 2.233 (2/4) 1.630 (1/4) 0.129 0.175 4.686 (4/4) 2.768 (3/4) 1.741 (2/4) 0.959 (1/4) 0.490 0.543 0.422

Si (estimated relative value of Si )

% (percent according to the estimated values) 25 (25) 100 (75) 100 (100) 33 (25) 0 0 42 (25) 100 (75) 100 (100) 33 (25) 0 0 0

Si Pi (Si P according to the estimated values) 0.179 (4/4 16) 0.644 (9/4 16) 0.837 (12/4 16) 0.407 (4/4 16) 0.008 0.065 0.293 0.692 0.653 0.239 0.122 0.034 0.158

3-21G

Calculated values (B3LYP)

v1(ZnBr4) ZnBr3Cl:vs(ZnBr3) ZnBr2Cl2:vs(ZnBr2) ZnBrCl3:vs(ZnBr) v3(ZnBr4) ZnBr2Cl2:vas(ZnBr2) v1(ZnCl4) ZnCl3Br:vs(ZnCl3) ZnCl2Br2:vs(ZnCl2) ZnClBr3:vs(ZnCl) ZnCl3Br:vas(ZnCl3) v3(ZnCl4) ZnBr2Cl2:vas(ZnCl2)

Attribution

1/16 4/16 6/16 4/16 1/16 6/16 1/16 4/16 6/16 4/16 4/16 1/16 6/16

Pi

Table 6. Experimental frequencies (vi) and intensities (Ii ) of the Raman lines associated with stretching of the Zn–X bonds. Theoretical frequencies (vi) and intensities (Si ) calculated using B3LYP/3-21G. Attribution, probabilities (Pi ) and Raman line intensities (Si Pi) due to the ZnCl1xBrx polyhedra (with x ¼ 0, 1, 2, 3 and 4) as predicted in [N(CH3)4]2ZnCl2Br2 in case of random distributions of Cl and Br. Estimated values of the Raman intensities according to the number of Zn– X bonds involved.


626 K. Karoui et al.

Phase Transitions

627


Figure 5. Theoretical (full lines) and experimental (dashed lines) probabilities of the different ZnCl x Br(1x) polyhedra in[N(CH3)4]2ZnCl2Br2 from the experimental intensities of the lines arising from the tetrahedral breathing mode.

Below 150 cm1, in addition to the n2(E)/n4(T) modes of ZnBr4 (at 56/87 cm1) and ZnCl4 (113/130 cm1) as found in the pure compounds (Figure 4(a), Table 4), one observes bands at 90, 94, 99, 104, 106 and 119 cm1. They can be supposed to be due to the internal modes of ZnBr3Cl, ZnBr2Cl2 and ZnBrCl3 polyhedra (Table 4). However, these modes are set in the range of the external modes of the crystal, so that no reliable attribution can be proposed.

5. Conclusions IR, Raman spectroscopy and theoretical calculations, using HF and B3LYP methods with 3-21G, 6-31G(d) and 6-311Gþ(d,p) basis sets, are applied to analyze [(N (CH3)4)]2ZnCl4yBry synthesized compounds with y ¼ 0, 2 and 4 to calculate the geometric parameters and the vibrational frequencies of the [N(CH3)4]þ organic cation and [ZnCl4-xBrx]2 inorganic anions with x ¼ 0–4. For the inorganic polyhedra, the optimized bond lengths and bond angles obtained by B3LYP/3-21G method show the best agreement with the experimental values. For the organic cation, the best basis is B3LYP/6-311Gþ(d, p). The calculated intensities for the different modes appear in the mixed compound confirm the random distribution of the halogen in different polyhedra.

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