CHAPTER 14 - THE THEORETICAL ANALYSIS OF MOLECULAR VIBRATIONS

Abstract

Publisher Summary This chapter focuses on the theoretical analysis of molecular vibrations. Normal modes of vibration are reviewed in the chapter. A nonlinear molecule has 3N — 6 normal modes of vibration. The chapter discusses how the frequencies and forms of the normal modes of vibration are calculated mathematically. The chapter further reviews internal coordinates, normal coordinates, and symmetry coordinates. Internal coordinates characterize the change in the shape of a molecule from its equilibrium shape without regard for its position or orientation as a whole in space. Four general types of internal coordinates are illustrated in the chapter. If the molecules have some symmetry, the solution of the secular determinant is simplified by the use of symmetry coordinates. Symmetry coordinates are linear combinations of the internal coordinates. One can frequently select symmetry coordinates intuitively by taking combinations of symmetry related internal coordinates. The symmetry coordinates picked out are not necessarily unique but must have definite properties. They must be normal and orthogonal, and they must transform properly.