Knowledge Bank

{Makarewicz}$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ has shown that the rovibrational Hamiltonian of a symmetrical triatomic molecule takes a simple form when expressed in terms of Radau’s coordinates $r1,r2$ and 0, very similar to the two valence and bond angle coordinates. This Hamiltonian can be further simplified if the two coordinates $r1$ and $r2$ are frozen. Taking then a simple model potential function, the eigenvalues of this simplified Hamiltonian can be determined exactly for each K $value.2$ In this paper a trial rovibrational Hamiltonian for triatomic molecules has been derived starting from the one proposed by $Makarewicz.2$ However, $\Delta K>0$ matrix elements arising from the rotational Hamiltonian were treated rigorously and phenomenological distortion-like parameters were introduced. The Hamiltonian thereby obtained can account for the rotational levels up to $J=15$ of $ H_{2}O$ in its ground vibrational $state3$ with an R.M.S. deviation of 4.9 $\times 10-3cm-1$, using 30 parameters. In the first excited vibrational state $v2=1$ of the same $molecule,4$ the rotational levels up to J = 9 are reproduced with an R.M.S. deviation of $1.4\times 10-3cm-1$, using 22 parameters. These results will be discussed and we hope to be able to achieve a better understanding of the four-fold clustering.