Knowledge Bank

By modifying the vibration-rotation Hamiltonian to include mass dependent changes in the rotational constants and band center, we have been able to fit the lines arising from the several tellurium isotopes simultaneously to one Hamiltonian expression. This has been done for the $2\nu 1$ band of the prolate molecule HDTe and the $2\nu 1\leftrightarrow \nu 1+\nu 3$ and $\nu 1+\nu 2\leftrightarrow \nu 2+\nu 3$ Coriolis coupled bands of the oblate molecule $H2$Te. The results agree very well with a first order approximation to the expressions derived by Steenbeckcliers for isotopic mass dependencies of the constants of the rotational Hamiltonian. The mass dependencies of the rotational constants determined in the fit were as follows: $\xi A=0.000296$ $cm-1$ $\xi B=0.000327$ $cm-1$, $\xi c=0.000221$ $cm-1$ for HDTe and $\xi A=0.000726$ $cm-1$ and $\xi C=0.000190$ $cm-1$ for $H2$Te, where $AM=A130+\xi A(130-M)$, etc. Linear plus marginally significant quadratic mass dependencies of the band center were determined in the fit to be: $$0.1091(130 - M)\kern-7pt= + 0.00094(130 - M)^{2} \hbox{ for } 2\nu_{1}\mbox{ of HDTe},$$ $$0.1093(130 - M) + 0.00091(130 - M)^{2} \hbox{ for } 2\nu_{1} of H_{2}{Te},$$ $$0.08097(130 - M) + 0.00062(130 - M)^{2} \hbox{ for } \nu_{1} + \nu_{2}\mbox{ of }H_{2}{Te},$$ $$0.033(130 - M) + 0.0009(130 - M)^{2} \hbox{ for } \nu_{2} + \nu_{3}\mbox{ of } H_{2}{Te},$$ $$0.1109(130 - M) + 0.0008(130 - M)^{2} \hbox{ for } \nu_{1} + \nu_{3}\mbox{ of } H_{2}{Te},$$ (in $cm-1$).