Internal- and rho-axis systems of molecules with one large amplitude internal motion: The geometry of rho

The internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) is determined by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, simple methods are devised for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator. The parameter ρ so calculated agrees exactly with that one obtained by the Floquet method as shown in the example of acetaldehyde. Geometrical interpretation of ρ is given. The advantageous property of the RAS over the IAS in retaining simple periodic boundary conditions is numerically demonstrated.