Knowledge Bank

The Hougen-Watson isomorphic Hamiltonian of a linear molecule (1,2) is related to skewed coordinates of a special kind allowing one to treat the linear molecule as a quasi-diatom”. Orientation of the quasi-diatom in space is determined by the vector (3) \[\stackrel{F}{\sim} =\sum m_{D} r_{zD}{^{0}}\stackrel{r}{\sim}_{D} ,\] where $r_{zD}{^{0}}$ are constants parametrizing a linear equilibrium configuration (2), $m_{D}$ and $\stackrel{r}{\sim}_{D}$ are respectively mass and the radius-vector of the D-th nucleus. Transverse projections of quasi-electrons perform vibrations with frequencies of bending modes. The local-mode picture is analogous to the separated-atom model of the hydrogen molecule (4) and the appropriate vibrational coordinates coicide with those introduced by Suzuki and Overend (5). The isomorphic Hamiltonian is derived by means of an imaginary particle in a state with zero angular momentum. The relationship of the derived Hamiltonian to the formalism developed by Pack and Hirschfelder (4) and to the variational procedure recently suggested by Carter and Handy (6) for the nonrotating acetylene molecule is analyzed.