A general nuclear motion Hamiltonian and non-internal curvilinear coordinates

Abstract

An exact Hamiltonian for nuclear motions in general curvilinear coordinates is derived. It is demonstrated how this Hamiltonian transforms into well-established expressions, such as the Wilson Howard Hamiltonian or the Meyer Günthard Hamiltonian, if the general coordinates are restricted to be rectilinear or internal. Furthermore, a compact expression for the Hamiltonian expressed in non-internal curvilinear coordinates is provided, which makes this coordinate class available for applications in a simple way, since only the Jacobian matrix with respect to the rotating frame coordinates must be calculated. An example, employing a water model potential, exemplifies how different coordinate systems from all three coordinate classes (rectilinear, internal, and non-internal) lead to vibrational spectra, which are in excellent agreement. Thereby, the applicability of the general Hamiltonian is demonstrated and also its correctness is confirmed.