A new proof of the molecular Hamiltonian in Radau coordinates for triatomic molecules based on tensor form

Abstract

A generalized coordinates molecular Hamiltonian for polyatomic molecules has been obtained. Using this Hamiltonian in Radau coordinates as the orthogonal coordinates, the molecular Hamiltonian is derived for triatomic molecules. An exact derivation is presented of the molecular Hamiltonian in different axis embedding such as bond embedding, bisector embedding, and the linear combination of Radau vector coordinates. In addition, the symmetrized Radau coordinates are considered as an example for this general formulation. This new approach is greatly simplified. Also presented are simple and explicit expressions without cross-terms in Radau coordinates as vibrational variables.

On the determination of the intramolecular potential energy surface of polyatomic molecules: Hydrogen sulfide and formaldehyde as an illustration

“…On the other hand, the introduced coordinates, R N , are not the Radau coordinates because (see, for example Eq. (6) in [41]) the Radau coordinates are simple sums of Dr N coordinates with coefficients depending on the nuclear masses. At the same time, as is seen from Eq.…”

“…4 It should be mentioned that the introduced vibrational coordinates are very close to the curvilinear coordinates. Dr. and the Radau coordinates (see, for example [40,41]). However they are considerably different from both the curvilinear and Radau coordinates as can be clearly seen from Eq.…”

A general rigorous quantum dynamics algorithm to calculate vibrational energy levels of pentaatomic molecules

“…We have derived 21 sets of coordinate systems using four orthogonal Jacobi [4,5,50,68,[91][92][93], Radau [7,8,[11][12][13][14]18,35,66,94,95] and/or orthogonal satellite [35,96,97] vectors for a five atom molecule ABCDE. The coordinates are depicted in Fig.…”

A simple method for derivation of the rovibrational Hamiltonian: application to orthogonal radau coordinate systems as special cases

“…This method has been extended to cover large amplitude motions by solving completely the vector i f Z for various kinds of coordinate systems [9][10][11]. In this article, we have applied a general definition of internal coordinates and obtained the rovibrational Hamiltonian in this coordinate system.…”