  A set of rules is defined to systematically number the groups and the atoms
of organic molecules and, particularly, of polypeptides in a modular manner.
Supported by this numeration, a set of internal coordinates is defined. These
coordinates (termed Systematic, Approximately Separable and Modular Internal
Coordinates, SASMIC) are straightforwardly written in Z-matrix form and may be
directly implemented in typical Quantum Chemistry packages. A number of Perl
scripts that automatically generate the Z-matrix files for polypeptides are
provided as supplementary material. The main difference with other
Z-matrix-like coordinates normally used in the literature is that normal
dihedral angles (``principal dihedrals'' in this work) are only used to fix the
orientation of whole groups and a somewhat non-standard type of dihedrals,
termed ``phase dihedrals'', are used to describe the covalent structure inside
the groups. This physical approach allows to approximately separate soft and
hard movements of the molecule using only topological information and to
directly implement constraints. As an application, we use the coordinates
defined and ab initio quantum mechanical calculations to assess the commonly
assumed approximation of the free energy, obtained from ``integrating out'' the
side chain degree of freedom chi, by the Potential Energy Surface (PES) in the
protected dipeptide HCO-L-Ala-NH2. We also present a sub-box of the Hessian
matrix in two different sets of coordinates to illustrate the approximate
separation of soft and hard movements when the coordinates defined in this work
are used.
