VIBRATIONAL BAND INTENSITIES \& MOLECULAR CONSTANTS PART 1-INFRARED INTENSITY AND CHARGE ON CENTRAL ATOM IN TETRAHEDAL SYSTEMS
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Date
1981
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Ohio State University
Abstract
The halfwidth and infrared absorption intensity of $\nu_{3}(F_{2})$ vibration of a series of tetrahedral ions, viz. $WO_{4}^{2-}, MO_{4}^{2-}, MnO_{4}^{-}, TeO_{4}^{-}, ClO_{4}^{-}, ReO_{4}^{-},OsO_{4}, PO_{4}^{3-},CrO_{4}^{2-},TiO_{4}^{4-}, VO_{4}^{3-}$ and $SO_{4}^{2-}$ have been employed to study dipole moment derivatives, $\partial\mu/\partial R$ and thereby to derive the charge on central atom, $qx^{\prime}$, using group theoretical approach and fixed charge model. An alternative model based on Raman intensities has also been adopted to the calculation of $qx^{\prime}$ values such that the total charge on the ion is concentrated to the central atom governed by the equation $qx^{\prime} - 4qy^{\prime} - z$ for an $X\eta_{4}^{z-}$ system. It has been found that in oxyanions $PO_{4}^{3-}, SO_{4}^{2-} \& ClO_{4}^{-}$ the $qx^{\prime}$ values decrease according to the trend: $PO_{4}^{3-}(1.58)>SO_{4}^{2-}(1.56)>ClO_{4}^{-}$(1.53) showing that the extent of $d_\pi - p_\pi $ bonding is minimum for $PO_{4}^{3-}$. Also, although halfwidth are related to the formal charge on the ions, the same is not true with the charge on the central atoms. In case of $PO_{4}^{3-}$ while $Larson^{1}$ evaluated $qp^{\prime} = -0.14$, our values differ to become +2.907 (fixed charge model) and 1.589 (polarizability model). Estimation of $K\alpha$ satellites in X-ray $spectroscopy^{2}$ results $q_{p}^{\prime} = +1.35$ and preliminary ab initio calculation by Johansen $^{3}$ suggest a value of $qp^{\prime} = +1.2$. Similar calculation by CNDO-method predicts $qp^{\prime}$ to be either +1.08 or -0.38. This clearly supports our results obtained by polarizability model. In case of $CrO_{4}^{2-}$, the $qCr^{1}$ = 1.07 compares fairly well with ZDO calculations $^{4}$ ($qCr^{\prime$} = +0.78). In general the computed $qx^{\prime}$ values for all the twelve ions were found compatible with those obtained by quantum theoretical methods. $^{1}$ R. Larson, Chemica Scripta, 5, 145 (1974). $^{2}$ L. Popula, W. Strehl \& H.U. Chun, Thioret. Chim. Acta, 22, 304 (1971). $^{3}$ B.J. Mc. Aloon \& P.G. Perkins. Theoret. Chim. Acta, 22, 304 (1971). $^{4}$ L. Oberai, G. de Michelis \& L. Disipio, Mol. Phys., 10, 111 (1966).
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