Fragment mode analysis and its application to the vibrational normal modes of boron trichloride–ammonia and boron trichloride–pyridine complexes

Abstract

A method for expressing quantitatively the vibrational normal modes of a molecule in a basis set consisting of the normal vibrations (plus translations and rotations) of its constituent fragments is presented. The method is illustrated by describing the vibrational modes of BCl 3–NH 3 and BCl 3–pyridine electron donor–acceptor complexes in terms of motions of BCl 3 and either NH 3 or pyridine. These complexes show examples of mixing between modes located on different fragments, mixing between modes of one fragment due to symmetry lowering, and the transformation of six fragment translations/rotations into vibrations of the complex. Although perturbation theory has been proposed to explain such examples of mode mixing, calculations imply that interactions between fragments of both complexes are too strong for perturbation theory to be generally applicable. In addition, the transformation of fragment rotations and/or translations into vibrations of the composite molecule will always occur and cannot be understood in detail by using perturbation theory. For the BCl 3–pyridine complex, a band observed at 1107 cm −1 is re-assigned as a combination of CH in-plane bending and a ring-breathing mode of the pyridine fragment.