Brief explanation of QM geometry optimization
Quantum mechanics packages are often tasked with optimizing a chemical structure. The problem is essentially this: Given a set of points in 3D space and potentials that are strongly correlated with chemical structure (bond lengths, bond angles, torsion angles), minimize the total potential with the points as degrees of freedom. Let's just assume you know who's bonded to who already. The potentials relate pairs of points that are bonded and nonbonded but the bonded ones are especially strong.
QM programs often use redundant internal coordinates for geometry optimization. For a single molecule, conformations can be parameterized nonredundantly in internal coordinates in a tree structure. The degrees of freedom are bond lengths, bond angles, and torsion angles. (Some chemical bonds may not have an explicit bond length parameter in this scheme.) Redundant internal coordinates have additional parameters that are not strictly necessary to describe the chemical topology, ex: nonbonded distances.
Redundant internal coordinates have apparently proven more efficient empirically, especially for systems that have bonded cycles.
The optimizations are typically done with BFGS.
Qualitatively, how can this be? Why would adding unnecessary information improve optimization efficiency?