Connection between the su(3) algebraic and configuration spaces: bending modes of linear molecules

Abstract

ABSTRACTAn approach to connect the dynamical group – used to describe the bending modes of linear molecules – with configuration space is discussed. The group may be seen as a consequence of adding a scalar boson to the space of two degenerate harmonic oscillators. The resulting group becomes the dynamical group for 2D systems The connection of the model with configuration space however is not obvious. Our approach is based on establishing a mapping between the algebraic and configuration states. The identification in the algebraic space of coordinates and momenta leads to a new identification of the group chains: they are associated with energy, coordinate and momentum representations. In addition an analysis of local-to-normal mode transition is presented. This provides a criterion to decide between a local or normal mode descriptions in an spectroscopic description. As an example we consider the situation of the bending modes of acetylene taking a Hamiltonian up to quartic order. The different results for the force constants obtained from the local and normal mode treatments leads to the conclusions that previous applications of the bending modes of acetylene dealing with a local mode treatment is on the verge of applicability.