Polyatomic linear molecules, chemical

Molecules consist of atoms which have a certain mass and which are connected by elastic bonds. As a result, they can perform periodic motions, they have vibrational deitrees of freedom All motions of the atoms in a molecule relative to each other are a superposition of so-called normal vibrations, in which all atoms are vibrating with the same phase and normal frequency. Their amplitudes are described by a normal coordinate. Polyatomic molecules with n atoms possess 3n - 6 normal vibrations (linear ones have 3n - 5 normal vibrations), which define their vibrational spectra. These spectra depend on the masses of the atoms, their geometrical arrangement, and the strength of their chemical bonds. Molecular aggregates such as crystals or complexes behave like super molecules in which the vibrations of the individual components are coupled. In a first approximation the normal vibrations are not coupled, they do not interact. However, the elasticity of bonds does not strictly follow Hooke s law. Therefore overtones and combinations of normal vibrations appear. 

The valence-bond treatment of polyatomic molecules is closely tied to chemical ideas of structure. One begins with the atoms that form the molecule and pairs up the unpaired electrons to form chemical bonds. There are usually several ways of pairing up (coupling) the electrons. Each pairing scheme gives a VB structure. A Heitler-London-type function (called a bond eigenfunction) is written for each structure i, and the molecular wave function is taken as a linear combination 2, c,4>, of the bond eigenfunctions. The variation principle is then applied to determine the coefficients c,. The VB wave function is said to be a resonance hybrid of the various structures. 

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