Three-dimensional visualization sphere model

Diffraction of light in two-dimensional lattices and their calculations were known in Laue s time an additional information. They have been the basis for Laue s calculation of three-dimensional diffraction lattices from X-ray experiments as a result he formulated a model of a spatial symmetrical structure of ions in a salt crystal abstract mental model. Laue proposed the use of realistic models in order to better visualize the concepts - but needed irrelevant items like balls, sticks and glue, in order to construct closest packings of spheres or spatial lattice models concrete models. 

As described earlier in this chapter, polymers are long chains of atoms linked together. They may be flexible and bendable. To explain this, one may visual them as ball-and-stick model. In chemistry, the ball-and-stick model is a molecular model of a chemical substance which aims to display both the three-dimensional position of the atoms and the bonds between them. The atoms are typically represented by spheres, connected by rods which represent the bonds. Double and triple bonds are usually represented by two or three curved rods, respectively. The chemical element of each atom is often indicated by the sphere s color and size. The top of Figure 1.6 shows a drawing of a ball-and-stick model of a molecule. Figure 1.6 also indicates that there is free rotation around the single bonds. If there was a double or triple bond, there would not be any rotation possible around those bonds. 

Chemistry is dehned as a study of the elements and their properties. Most of the time chemists are interested not so much in the elements themselves but rather in molecules, which are combinations of elements into discreet units. The organic chemist normally thinks of a molecule by reference to a rather simple model, usually of the ball-and-stick type. Such models are extremely useful for aiding in the visualization of three-dimensional interactions between molecules and between parts of molecules. But they are also a little bit misleading. A real molecule is not static, the way the usual mechanical model is. Rather, it is undergoing rapid motions, both internally and externally. Molecular structure can be defined at different levels, which are useful for different kinds of purposes. As we go past the ball-and-stick model, to the hard sphere model (space-filling model), and then to the soft sphere model (computational chemistry), we obtain an increasingly accurate description of the molecule and its properties. 

Symmetry is an important aspect of molecular shape. Intuitively, we recognize diat a sphere and cube are highly symmetrical bodies. In this section are described the structural features, called SYMMETRY ELEMENTS, which make a molecule symmetrical. The search for symmetry elements sharpens one s ability to visualize the various structures. The use of three-dimensional models is strongly recommended for developing the ability to recognize and visualize symmetry elements. Once the models have been studied, the three-dimensional projectional formulas can be more easily understood. The symmetry elements that we shall consider are planes and points. ... 

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