Normal Coordinate Analysis

Abstract

Abstract The chapter summarizes important concepts from the theory of molecular vibrations of which normal coordinate analysis is a part. Section 2 describes how molecular vibrations or, more precisely, harmonic oscillators are treated in classical mechanics and how normal coordinates are defined. The quantum mechanics of coupled harmonic oscillators, which is based on normal coordinates, is developed in section 3, together with the selection rules for infrared and Raman spectroscopy. It is followed by excursions into some applications of symmetry concepts and into the domain of real molecules where harmonic oscillators are satisfactory approximations at best (anharmonicity and large‐amplitude internal motions). Section 4 introduces the commonly used internal and symmetry coordinates, the transformations between them and the Cartesian and normal coordinates, Wilson's GF method of normal coordinate analysis, and discusses redundant sets of internal coordinates. A short survey of force fields past and present (central, valence, and Urey‐Bradley force fields and force fields from semiempirical and ab initio calculations) is given in section 5. The invariance of internal coordinates, the transformation from internal to Cartesian coordinates, and some aspects of redundant coordinates are detailed in appendices.