Knowledge Bank

It would be desirable to extend the Direct Numerical Diagonalization (DND) calculations1 to handle the large amplitude vibrations that occur in molecules at very high temperatures approaching disassociation. Many important advances have occurred recently in the formulation of the full rotation-vibration kinetic energy for the quantum mechanical Hamiltonian of a general polyatomic molecule. These new approaches generally utilize curvilinear internal coordinates rather than the rectilinear internal coordinates associated with the traditional $form2$ of the kinetic energy. In applying a new technique like DND, there are different requirements on the form of the Hamiltonian than has been usual for perturbation approaches. These formulations are compared with DND calculations in mind, and a valence coordinate Hamiltonian which satisfies the Eckart conditions is derived for comparison. The balance between the range of applicable domain and the minimization of off-diagonal matrix elements will be discussed. Future DND calculations using the most promising Hamiltonians should reveal the optimum approach for the calculation of the large amplitude properties of triatomic molecules.