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14.3 Internal Coordinate Concepts

Given the positions of any three atoms, the position of a fourth atom can be defined in relative terms (internal coordinates) with three values: a distance, an angle, and a dihedral specification. Where many atoms are connected in a long sequence (as in proteins) it is easiest to consider four atoms in a chain. If the positions of one end of the chain is known, it is possible to find the positions of all of the remaining atoms with a series of internal coordinate values. But in the more general case, where some central portion of a molecule is known it is necessary to be able work in both directions. This lead to the present form of the internal coordinate data structure (five values for four atoms) where if either endpoint is unknown and the other three atoms are determined, the position of the end atom can be found. The improper type of internal coordinate data structure was created for branching structures (as opposed to simple chains). Since there are roughly five values in the data structure for every atom it is clear that the positions are overspecified Keep this in mind when externally editing IC files. The program will use the first acceptable value when building a structure and ignore any redundancies. The EDIT commands will always modify all occurrences of each edited parameter.