Internal Coordinate Definition

For any one atom, i, this consists of an interatomic distance in Ångstroms from an already-defined atom, j, an interatomic angle in degrees between atoms i and j and an already defined k, (k and j must be different atoms), and, finally, a torsional angle in degrees between atoms i, j, k, and an already defined atom l (l cannot be the same as k or j). See also Torsion or Dihedral Angle Coherency. If the geometry contains PDB atom-label information, atom numbers can be replaced by PDB or JSmol definitions.

 

Exceptions:

  1. Atom 1 has no internal coordinates at all. The coordinates of atom 1 are, by definition, Cartesian. Normally, the coordinates of atom 1 are (0,0,0), but can be set to any value desired.
    2.  
  2. Atom 2 must be connected to atom 1 by an interatomic distance only. If atom 1 is not at the origin, then the care must be taken in defining atom 2: if internal coordinates are used, then the connectivity must be given. If the connectivity is not specified, then the coordinate of atom 2 is, by definition, Cartesian.
    3.  
  3. Atom 3 can be connected to atom 1 or 2, and must make an angle with atom 2 or 1 (thus 3-2-1 or 3-1-2); no dihedral is possible for atom 3. Again, if the connectivity is not given, the coordinate is defined as Cartesian.