Normal geometrical arrangement

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. 

Crystallites above about 50 nm (and smaller for electron diffraction) are large enough to yield broadened but characteristic diffraction patterns. By characteristic it is meant that the symmetry and geometric arrangement of the structure will be clearly reflected in the diffraction pattern. The normal way in which this is represented is via the crystallographic structure factor ... 

Fig. 2.2 Geometrical arrangements being necessary in photoemission experiments using dichroic effects. Left CDAD. Middle MCDAD. Right MLDAD. q denotes the photon propagation direction, Oph the angle of the incoming photon beam, the photoelectron momentum, n the surface normal, and M the magnetization direction...

Fig. 2.3 Geometrical arrangement of a normal incidence monochromator. The important directions of the experiment are additionally shown...

Positive and negative ions will normally exist together, in the gas phase, in solution, or in the regtdar geometrical arrangement of a crystal lattice, in numbers such that electrical neutrality is preserved. We then speak of electrovalent chemical compounds. Such compounds possess the well-known property of electrical conductivity. They are in fact only compounds to the extent that the positive and negative ions are present in fixed proportions they are not bound together in any more profound sense than this. 

Furthermore, for each of the stereoisomers in the second-last line of Figure 1, two alternative geometric arrangements arise from rotation about a single bond, as shown in Figure 2. Stereoisomers of this kind, called conformers, are often not distinguished, since they usually interconvert under normal conditions and therefore cannot be isolated. 

---