Knowledge Bank

The halfwidth and infrared absorption intensity of $\nu 3(F2)$ vibration of a series of tetrahedral ions, viz. $WO42-,MO42-,MnO4-,TeO4-,ClO4-,ReO4-,OsO4,PO43-,CrO42-,TiO44-,VO43-$ and $SO42-$ 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 $X\eta 4z-$ system. It has been found that in oxyanions $PO43-,SO42-\&ClO4-$ the $qx\prime$ values decrease according to the trend: $PO43-(1.58)>SO42-(1.56)>ClO4-$(1.53) showing that the extent of $d_\pi - p_\pi $ bonding is minimum for $PO43-$. 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 $PO43-$ while $Larson1$ 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 $spectroscopy2$ results $qp\prime =+1.35$ and preliminary ab initio calculation by Johansen $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ 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 $CrO42-$, the $qCr1$ = 1.07 compares fairly well with ZDO calculations $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ ($qCr^\{\backslash prime$} = +0.78). In general the computed $qx\prime$ values for all the twelve ions were found compatible with those obtained by quantum theoretical methods. $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ R. Larson, Chemica Scripta, 5, 145 (1974). $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ L. Popula, W. Strehl & H.U. Chun, Thioret. Chim. Acta, 22, 304 (1971). $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ B.J. Mc. Aloon & P.G. Perkins. Theoret. Chim. Acta, 22, 304 (1971). $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ L. Oberai, G. de Michelis & L. Disipio, Mol. Phys., 10, 111 (1966).