Internal Coordinate Green’s Function Analysis of Molecular Vibrations with Application to XY2Z Planar Molecules

Abstract

Abstract The Green’s function formalism for the analysis of molecular vibrations has been formulated for the internal or valence coordinate system. A general procedure for calculating isotopic frequencies and changes in force constants associated with the characterization of a perturbed molecule in terms of the unperturbed molecule is developed. It is shown that the internal molecular Green’s function can be constructed from the vibrational frequencies of the unperturbed molecule. Application is made to the XY2Z planar molecule. Exact formulae for the XY2Y(i) molecule are obtained. The shifts in the frequencies of an XY2Z planar molecule due to mass and bond length changes are obtained. It is shown that the A1 modes are unaffected by a change in the X–Z bond length while the B1 modes move to higher frequencies as the bond distance decreases. An explicit expression for the change in the valence bond bending force constant, fα, is obtained as an example of how force constant changes can be studied by means of the Green’s function procedure. Qualitative results for HBCl2 and HBBr2 are obtained which indicate that fα decreases in going from BCl3→ HBCl2.