Knowledge Bank

The invariants of the derived molecular polarizability tensor, $\partial \alpha ¯/\partial Qi$ and $|\partial \gamma /\partial Qi|$, which determine the cross section of the $ith$ vibrational Raman band, are usually calculated from the invariants $\partial \alpha ¯/\partial Sj$ and $|\partial \gamma /\partial Sj|$ using the L matrix obtained from the molecular force field analysis. Here, $3\alpha ¯$ and $\gamma$ are the trace and anisotropy of the molecular polarizability tensor, $Qi$ is the $ith$ normal coordinate and the $Sj$ are internal symmetry coordinates of the molecule. The $\partial \alpha ¯\partial Sj$ and $\partial \gamma /\partial Sj$ are often estimated using bond polarizability $theory.1$ We have recently measured the intensities of the Raman active vibrational bands of normal and deuterated acetylene. For this case, enough intensity data are available to allow us to perform the reverse calculation to that described above; i.e., to determine the force constants of the harmonic force field from the Raman intensities. The intensity relations for the isotopic species together with the relation between the L matrix and the Wilson G matrix, which depend only on molecular geometry and atomic amasses, here provide a sufficient number of equations to determine $\delta \alpha ¯/\delta Sj,\delta \gamma /\delta Sj$, and the elements of the L matrices for the isotopic species. The latter are then used with the harmonic frequencies to calculate the elements of the F matrix. The results of this calculation will be presented with an error analysis, and our results will be compared with recent $experimental2$ and ab initio (calculated)$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ harmonic force fields.