A GF-Matrix Approach to the End-to-End Coupling in Ethane-like Molecules

Abstract

We examine the effect of end-to-end coupling on the degenerate vibrational deformations of ethane-like molecules by considering the form of the dependence of the elements of the G and F matrices on the internal rotation angle γ. This can be done by simple geometrical considerations, in a basis of internal vibrational coordinates. After transformation to symmetry coordinates belonging to different species of the G36(EM) extended molecular group, the product G(0)F(0) of the γ-independent parts of the G and F matrices is diagonalized. The resulting zero-order normal modes and their conjugate momenta are used in building up the vibration-torsion Hamiltonian, including the γ-dependent terms. We find that (i) in the case of a low barrier hindering the internal rotation the most convenient sets of degenerate normal coordinates are either Gs (in the case of a weak effect of the end-to-end coupling on the relative deformations) or E1d, E2d; (ii) degenerate vibrational coordinates whose top and frame components have at the least one common atom lead to E1d, E2d normal modes regardless of the barrier height; (iii) "unpaired" degenerate vibrational coordinates, such as the skeletal bending of dimethylzinc, always contribute an E1d normal mode; and (iv) in the case of high or moderate barriers, Gs normal modes are unlikely to occur, and the most probable normal mode symmetries are E1d, E2d.