Vibrational Analysis of the Absorption System of Sulphur Dioxide atλ3400−2600

Photographs of the bands of sulphur dioxide in the region of $\lambda 3400-2600$ have been taken under low, medium and high dispersion, both at room temperature and at 200°K; the pressure of the absorbing gas was varied from 0.3 mm to 480 mm. Thirty bands can be represented by the formula $\nu =29622+770\mathrm{}{v^{\prime }}_1+320\mathrm{}{v^{\prime }}_2+813\mathrm{}{v^{\prime }}_3-6\mathrm{}{v^{\prime 2}}_1-2.5\mathrm{}{v^{\prime 2}}_2-20\mathrm{}{v^{\prime }}_1{v^{\prime }}_2-25\mathrm{}{v^{\prime }}_2{v^{\prime }}_3-15\mathrm{}{v^{\prime }}_1{v^{\prime }}_3,$ where ${v^{\prime }}_1$, ${v^{\prime }}_2$, ${v^{\prime }}_3$, are the quantum numbers of the symmetrical valence, the deformation and the antisymmetrical vibrations respectively. The three fundamental frequencies for infinitesimal vibrations in the upper electronic state are ${v^{\prime }}_1=794\mathrm{}$, ${v^{\prime }}_2=345\mathrm{}$ and ${v^{\prime }}_3=833\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. In addition, twelve bands have been identified that correspond to transitions from excited vibrational levels in the normal state. The relatively long ${v^{\prime }}_1$ and ${v^{\prime }}_2$ progressions indicate that both the bond distance and the angle have changed considerably in the transition to the excited electronic state. The vibrationless transition at 29622 ${\mathrm{cm}}^{-1\mathrm{}}$ is weak, as one would have expected from considerations of the Franck-Condon principle. Substituting the three fundamental frequencies in the formula based on a valence force model, one obtains a value of 100° for the apex angle in the excited state, as compared with 120° in the normal state. The absence of any regularity in the rotational structure supports the resulting conclusion that the molecule in its upper state has become a more asymmetrical top.