NEW ROTATION-VIBRATION HAMILTONIAN

Abstract

The conventional rotation-vibration Hamilonian is shown to be appropriate only for small enough atomic displacements. An exact rotation-vibration Hamiltonian appropriate for any atomic displacements is obtained in an explicit form. The method used is based on forming the matrix of derivatives of the set of coordinates describing separately translational, rotational, and internal motions of a molecule with respect to the set of atomic carlesion co-ordinates in the initial rest coordinate system. The new Hamiltonian can easily be represented in the form of a differential operator, which allows one to try to utilize methods other then the perturbation one for computation of molecular rotation-vibration spectra. The supposition of the existence of an equilibrium configuration of a molecule is shown to be quite enough for constructing the Hamiltonian, Eckart's conditions turning out to be unnecessary at all. The new rotation-vibration Hamiltonian can prove to be of special importance for computation of molecular spectra in the case of large rotation or vibration quantum numbers, in particular, for computation of spectra of molecules near their dissociative limits.