Choice of internal coordinates:

One has to distinguish between the coordinates used for QM geometry optimizations and the ones defining bonded interactions in force fields: For geometry optimizations the choice of the coordinate system does not influence the result of the calculation but it can have a dramatic effect on the number of computational steps needed to reach the equilibrium geometry. In many cases redundant internal coordinates are a far better choice than cartesian coordinates [Pulay 1977]. Many QM packages have built in methods for automatic generation of internal coordinates. In Gaussian this is requested by the Opt=Redundant keyword.

For the determination of force constants the choice of coordinates depends on the type of force field. The task is to find a set of internal coordinates that implies low coupling between them and that facilitates transferability. Furthermore molecular compounds should be easy to combine into new molecules. The coordinates chosen in the topology files of CHARMM and AMBER force fields denote a good compromise between these requirements. First, all covalent bonds of a molecule are defined. Then, unless specified explicitely in the topology file, the the angles and dihedrals are autogenerated, i.e. all possible angles and dihedrals that can be constructed from the given bonds are generated.

However, in some cases it can be better to remove linear bends if they exist from the angle list because the force constant denotes the curvature of the potential energy function along the steepest gradient but the geometry can change two dimensions. Linear bends are included in the autogeneration so you must delete them manually if you don't want them. Examples for such linear bends are the ones between opposite ligands and the central atom in octahedral transition metal complexes.

The force constants from the Hessian matrix are based on the local harmonic approximation of the potential surface with respect to the given coordinate. Consequently the description of the potential energy is only correct in the vincinity of the equilibrium geometry. For covalent bonds and bond angles the geometry is not deviated to far from the equilibrium by typical thermal energies. However, for bond torsions the situation is different. Many torsional barriers are low enough that rotation around 360 degrees or at least a large deviation from equilibrium is possible.