Infrared spectra of sulphate ions trapped in rubidium and cesium

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Infrared spectra of sulphate ions trapped in rubidium and cesium selenate: harmonic frequencies and anharmonicity constants for antisymmetric SO4 stretching ...
Journal of Molecular Structure 482–483 (1999) 257–262

Infrared spectra of sulphate ions trapped in rubidium and cesium selenate: harmonic frequencies and anharmonicity constants for antisymmetric SO4 stretching vibrations Ljupcˇo Pejov*, Vladimir M. Petrusˇevski St. Cyril and Methodius University, Institute of Chemistry, P O Box 162, 91001 Skopje, Macedonia Received 24 August 1998; accepted 3 November 1998

Abstract Room and low temperature ( , 100 K) IR spectra of the sulphate doped Rb2SeO4 and Cs2SeO4 were recorded. The positions of the n3 and n4 fundamental mode components of the dopant anions, as well as of the n1 mode, were precisely measured. Nine (out of possible ten) second-order vibrational transitions of the dopant anions were detected. The anharmonicity constants and the harmonic eigenvalues were calculated for several second-order transitions on the basis of the second-order perturbation theory expressions. Comparison with our previous results show that the anharmonicity of practically all of the studied secondorder transitions decreases in the order (SO4/K2SeO4) . (SO4/Rb2SeO4) . (SO4/Cs2SeO4). According to the measured relative splitting of the n3 and n4 mode components, both angular and bond-length distortion of the dopant SO22 4 anions decrease in the same order. In all cases, the angular distortion seems to be smaller than the bond length one. The correlation of intensity of the bands due to the second order transitions vs. the corresponding anharmonicity constants suggests that the significance of the electrical anharmonicity increases in the order (SO4/K2SeO4) , (SO4/Rb2SeO4) , (SO4/Cs2SeO4). q 1999 Elsevier Science B.V. All rights reserved. Keywords: IR spectra of doped crystals; Isomorphously isolated ions; Sulphate ion distortion; Harmonic frequencies; Anharmonicity constants

1. Introduction The advantages of studying doped ions in an isomorphous matrix were well recognized [1–6], particularly when one is interested in the vibrational anharmonicity of the ionic species. In such cases, the interactions between identical oscillators (leading to dispersion of phonon curves and Davydov splittings), and the long-range electrostatic forces (leading to LO–TO splitting), for the dopant ions, may be * Corresponding author. Tel.: 1 389 91 117 055; fax: 1 389 91 226 865. E-mail address: [email protected] (L. Pejov)

neglected. This allows a prediction of the number of bands in the IR spectra only by site-group analysis. Continuing our studies [1,2] of the sulphate ions doped in selenates and chromates, we report here the IR spectra of sulphate ions doped in rubidium and cesium selenates, together with the calculated harmonic eigenvalues and anharmonicity constants of the S–O stretching modes. 2. Experimental details The sulphate doped Rb2SeO4 and Cs2SeO4 (with molar fractions of sulphate ions of 2 and 5%) were prepared by dissolving appropriate amounts of

0022-2860/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(98)00853-9

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Fig. 1. The region of appearance of the n3 (a), n1 (b) and n4 (c) fundamental modes in the LT FT-IR spectra of SO4 doped Rb2SeO4 (upper curve) and SO4 doped Cs2SeO4 (lower curve).

sulphate and selenate salts in water, followed by slow evaporation. The selenate compounds were prepared from H2SeO4 and corresponding carbonates. IR spectra of the sulphate doped selenates were recorded in Nujol mulls at room temperature (RT) and at low temperature (LT, , 100 K), on a Perkin Elmer FT-IR system 2000 interferometer. A variable-temperature cell (Graseby Specac) was used for the low-temperature measurements. Resolution of 2 cm 21 was used, taking 256 scans in order to obtain a good signal to noise ratio. Curve-fitting procedures and other spectra analyses were performed using the GRAMS32 program package [7]. 3. Results and discussion The regions of appearance of bands owing to the n1,

Fig. 2. The region of the second-order transitions (n3i 1 n3j ; n1 1 n3i ) in the LT FT-IR spectra of SO4 doped Rb2SeO4 (upper curve) and SO4 doped Cs2SeO4 (lower curve).

n3 and n4 modes as well as the region of the secondorder transitions due to the sulphate stretchings in the IR spectra of the SO4 doped Rb2SeO4 and Cs2SeO4 crystals are shown in Figs. 1 and 2. In Fig. 3, however, the spectral region of the second-order transitions in pure rubidium and cesium sulphates is shown. As seen in Fig. 3, this region looks rather complicated in cases of pure sulphate compounds. The bands in this spectral region, in fact, map the two-phonon density of states of the form n1 1 n3i and n3i 1 n3j , so no band can be assigned to any particular transition. However, the IR spectra of isomorphously isolated SO422 ions in selenate matrices are significantly simpler and may be subject to a straightforward assignment. Due to the true isomorphism between the corresponding sulphate and selenate compounds, however, the matrix influence on the doped sulphate ions closely resembles the one in pure sulphates,

Fig. 3. The region of the second-order transitions in the LT FT-IR spectra of Rb2SO4 (upper curve) and Cs2SO4 (lower curve).

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Table 1 Band frequencies, integrated intensities (I, in arbitrary units) and anharmonicity constants for SO422 ions doped in Rb2SeO4 and Cs2SeO4 at LT (primes refer to 34SO422 species) Mode n4a 0 n4a n4b n4c n1 n3a 0 n3b 0 n3a n3b n3c 2n1 n1 1 n3a n1 1 n3b n1 1 n3c 2n3a n3a 1 n3b 2n3b n3a 1 n3c n3b 1 n3c 2n3c a

K2SeO4 a n (cm 21)

I (au)

610.0 613.5 617.0 623.0 980.5 1089.5 1096.5 1103.5 1115.5 1142.0 — 2073.0 2086.0 2113.0 2199.0 2215.5 2224.3 2245.5 2257.0 2274.0

0.8500 0.7000 0.6200 — 0.0310 0.0730 3.2000 4.3000 4.5000 — 0.0330 0.0350 0.0340 0.0045 0.0100 0.0085 0.0018 0.0022 0.0110

Xij (cm 21)

Rb2SeO4 n (cm 21)

I (au)

2 11.0 2 10.0 2 9.50 2 4.00 2 3.50 2 3.35 0.00 2 0.50 2 5.00

607.4 611.1 615.2 619.3 971.7 1084.9 1093.4 1099.2 1108.1 1127.8 — 2063.2 2072.7 2093.1 2190.1 2203.9 2209.4 2227.6 2236.1 2246.7

0.0896 0.1251 1.1894 0.9774 — 0.3436 0.7077 3.4591 4.2357 4.9415 — 0.1244 0.1314 0.1394 0.0342 0.0708 0.0342 0.0071 0.0065 0.0436

Table 2 Harmonic eigenvalues (at LT) for the SO422 stretching vibrations calculated on the basis of the anharmonicity data K2SeO4 a

v 0/cm 21 Rb2SeO4

Cs2SeO4

1118.75 1129.30 1157.50

1112.75 1120.05 1139.50

1102.90 1106.45 1125.30

Mode

a

2 7.70 2 7.10 2 6.40 2 4.15 2 3.40 2 3.40 0.60 0.20 2 4.45

Cs2SeO4 n (cm 21)

I (au)

608.0 611.9 614.2 965.2 1075.4 1085.1 1089.9 1096.3 1115.2 — 2047.8 2054.9 2074.6 2171.3 2183.4 2186.6 2206.2 2212.6 2222.1

1.0307 0.9273 1.0933 — 0.2577 0.5106 8.0420 8.8453 9.9745 — 0.0723 0.0686 0.0583 0.0066 0.0391 0.0184 0.0023 0.0037 0.0187

Xij (cm 21)

2 7.30 2 6.60 2 5.80 2 4.25 2 2.80 2 3.00 1.10 1.10 2 4.15

Data from Ref. [2].

allowing data regarding the anharmonicity constants and the harmonic eigenvalues to be transferred to pure Rb2SO4 and Cs2SO4 [2]. The band frequencies, intensities and the anharmonicity constants calculated from the experimental data for doped samples are compiled in Table 1. The Cs symmetry of the sites occupied by the SO422 ions leads to a complete removal of the degeneracy of the E and F2 modes. As for the sulphate doped K2SeO4 and K2CrO4 [1,2], the bands due to the n3 and n4 modes split into three components (denoted as nia ,

n3a n3b n3c

Xij (cm 21)

Data from Ref. [2].

nib and nic ; i [ {3,4}). However, in the region of the second-order transitions only bands due to the n3i 1 n3j overtones/combinations and n1 1 n3i combinations were detected. Nine (out of possible ten) second-order transitions of the dopant anions were detected. No bands due to the n1 overtone, nor to the stretching 1 bending combinations appear. As the geometry of the SO422 ions in these compounds deviates only slightly from the ideal Td one (see the discussion later), the absence of the 2n1 band and the extremely low intensity of the n1 mode are self-understood. This low SO4 site-symmetry also allows the usage of the formulae for non-degenerate case, in the calculation of the harmonic vibrational frequencies (eigenvalues) on the basis of the anharmonicity data [8]. The harmonic eigenvalues for the SO4 stretching vibrations are presented in Table 2. In addition to the n3i fundamentals originating from the 32 16 S O4 species, bands due to the n3i modes from the 34 16 S O4 species were detected in the same spectral region (see Table 1). The assignment of these bands is supported by our previous normal coordinate

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Fig. 4. The dependencies of the intensities of the second-order transitions on the anharmonicity constants for a) SO4 doped K2SeO4; b) SO4 doped Rb2SeO4; c) SO4 doped Cs2SeO4.

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treatment (NCT) calculations [2]. However, a more detailed ab initio Hartree–Fock (HF) and density functional theory (DFT) quantum chemical study of the spectral properties of these species is in progress [9]. As in the case of the previously studied SO4 doped K2SeO4, the X13i anharmonicity constants are several times larger than the X3i3j ones. This finding has already been explained as being due to the larger anharmonicity of the symmetric stretching mode n1 (cubic terms in the potential energy expansion survive) compared to that of the n3 ones [1,2]. The following trends in the values of the X13i and the X3i3j anharmonicity constants are observed (including the results for the SO4 doped K2SeO4 [2]): 2X13i …SO4 =K2 SeO4 † . 2X13i …SO4 =Rb2 SeO4 † . 2X13i …SO4 =Cs2 SeO4 †; and 2X3i3j …SO4 =K2 SeO4 † . 2X3i3j …SO4 =Rb2 SeO4 † . 2X 3i3j …SO4 =Cs2 SeO4 †;

…for i ± j†

while for the X3i3i values: 2X3a3a …SO4 =K2 SeO4 † , 2X3a3a …SO4 =Rb2 SeO4 †

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mode in this system is 1.33%, thus indicating smaller angular than bond length distortion. The corresponding relative splittings of the n3 and n4 mode components in the SO4 doped Cs2SeO4 are 2.30% and 1.01% respectively. Both angular and bond length distortions, thus decrease in the series: …SO4 =K2 SeO4 † . …SO4 =Rb2 SeO4 † . …SO4 =Cs2 SeO4 †: In order to test the relative significance of the mechanical versus the electrical anharmonicity in the studied systems, the intensities of bands due to the second-order transitions were correlated with the corresponding anharmonicity constants. The results of the linear regression analysis show that the correlation coefficient decreases in the order: SO4/K2SeO4 . SO4/ Rb2SeO4 . SO4/Cs2SeO4 (the corresponding values being 0.928, 0.801 and 0.687; Fig. 4(a)–(c)). According to the simple quantum theoretical basis proposed in [2], the higher correlation between these two quantities implies a larger predominance of the mechanical vs. the electrical anharmonicity. One is thus led to the conclusion that the relative significance of the electrical anharmonicity increases in the order: …SO4 =K2 SeO4 † , …SO4 =Rb2 SeO4 † , …SO4 =Cs2 SeO4 †:

, 2X3a3a …SO4 =Cs2 SeO4 †; 2X3b3b …SO4 =Cs2 SeO4 † , 2X3b3b …SO4 =K2 SeO4 † , 2X3b3b …SO4 =Rb2 SeO4 †; (the values being very close to each other in the latter case), and 2X3c3c …SO4 =K2 SeO4 † . 2X3c3c …SO4 =Rb2 SeO4 † . 2X3c3c …SO4 =Cs2 SeO4 †: Conclusions regarding the degree of distortion of the SO422 dopant ions may be derived from the observed splitting of the n3 and n4 mode components. The splitting of the n3(SO4) mode components in sulphate doped Rb2SeO4 is 28.6 cm 21 at LT, which compared to the corresponding centro-frequency (n c ˆ 1111.7 cm 21) yields 2.57% as a value for the relative splitting (Dn /n c) of the antisymmetric stretching vibration. The relative splitting for the n4

4. Conclusions The present IR study of the SO4 doped Rb2SeO4 and Cs2SeO4 shows that the anharmonicity of practically all studied second-order transitions of the dopant SO422 anions decreases in the order (SO4/K2SeO4) . (SO4/Rb2SeO4) . (SO4/Cs2SeO4). According to the relative splitting of the n3 and n4 normal mode components, both the angular and bond length distortions of the dopant SO422 anions decrease in the same order, the last one being predominant in all of the studied systems. The harmonic eigenvalues, which are of key importance in lattice dynamics and force constant calculations, are reported too. On the basis of the spectral data it is suggested that the electrical anharmonicity becomes more important as the radius of the metal cation increases.

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References [1] V. Petrusˇevski, W.F. Sherman, J. Mol. Struct. 219 (1990) 171. [2] V. Petrusˇevski, W.F. Sherman, Bull. Chem. Technol. Macedonia 13 (1994) 69. [3] S. Lewis, W.F. Sherman, Spectrochim. Acta 35A (1979) 613. [4] P. Tarte, G. Nizet, Spectrochim. Acta 20 (1964) 503. [5] H.J. Becher, F. Friedrich, H. Willner, Z. Anorg. Allg. Chem. 395 (1973) 134.

[6] B. Ha´jek, O. Smrcˇkova, P. Zaruba, Collection Czechoslovak. Chem. Commun. 49 (1984) 1756. [7] GRAMS/32 Spectral Notebase, Version 4.10, Galactic Industries Corporation, 1996. [8] G. Herzberg, Molecular Spectra and Molecular Structure: II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, New York, 1956. [9] Lj. Pejov, V.M. Petrusˇevski, in preparation.