Physics – Mathematical Physics
Scientific paper
2011-11-21
Physics
Mathematical Physics
17 pages, Accidentally missed superscript T (for transpose) on the matrix appearing at page 5, line 4 from above, added. One s
Scientific paper
In a molecule subjected to no external fields, motion of nuclei is governed by a function V of nuclear coordinates. This function (potential energy) is a sum of two terms: Coulomb repulsion between nuclei and the electronic effective potential E which results from the Born-Oppenheimer approximation. In this paper we have presented a group of coordinate transformations which are the symmetries of functions E and V. We showed that the formula for dynamical representation, which has fundamental importance in the symmetry analysis of normal modes of a molecule, follows from these symmetries. In addition, we proved that every molecule has at least one normal mode belonging to the totally symmetric irreducible representation of the point group of that molecule. Next, we used symmetries of V and E to analyze possible shapes of some molecule types applying both Abud-Sartori-Michel theorem and symmetry adapted approximate expressions for the electronic effective potential. Finally we derived approximate relation between the vibration frequency and the bond length in a diatomic molecule.
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