# Understanding nuclear motions in molecules: A new ro-vibrational Hamiltonian

## Viktor Szalay

### (Wigner RCP SZFKI)

Time: Tue Feb 24 13:00:00 2015

Location: Building 1, Auditorium

The rotational-vibrational Hamiltonian is one of the basic notions in spectroscopy and molecular reaction dynamics. Its derivation is famously difficult due to the use of a rotating reference frame. To make the idea of vibrational and rotational motions meaningful on must choose the reference frame according to the Eckart conditions. A ro-vibrational Hamiltonian with exact kinetic energy operator, \hat{K}, and accounting for the Eckart conditions has been derived in terms of normal coordinates. Its simplest form is known as the Watsonian. For polyatomic molecules, except for triatomics, no Hamiltonian with analytical, exact \hat{K} is known in the Eckart frame when curvilinear internal coordinates are employed. Although a general expression of the ro-vibrational Hamiltonian with exact \hat{K} has been set up without taking into account the Eckart conditions when employing curvilinear internal coordinates, these general formulas become extremely complicated when applied to particular molecules. In this communication a new expression of the ro-vibrational Hamiltonian with analytical, exact \hat{K} is presented. It is in the Eckart frame and it is nearly as simple as the Watsonian. The vibrational coordinates employed are not normal coordinates. At the first sight they have no immediate geometrical significance either, but a simple argument shows that they are related to a radial coordinate and 3N-7 angle coordinates (different from both the polyspherical and hyperspherical coordinate systems). Not only is analytical, simple and exact, but the potential energy surface is simpler to calculate in terms of these coordinates, than in any other vibrational coordinate sets.