Once a displacement vector s has been chosen, either for a geometry optimization step or for the iterative Hessian diagonalization scheme described in section 2.3, the molecular geometry must be updated. This process is trivial when using Cartesian coordinates, as the displacement vector can simply be added to the current Cartesian coordinate vector x to update the molecular geometry. In redundant internal coordinates, however, the point in coordinate space specified by q + s may not correspond to a physically possible combination of internal coordinates. This is because the set of all physically possible coordinate vectors forms a (3n -6)-dimensional manifold embedded in the larger m-dimensional redundant internal coordinate space. Moreover, this manifold has curvature that arises from the coupling between the internal coordinates. As a result, even if the starting point q lies on the manifold and the displacement vector s lies tangent to the manifold at q, the point q + s will generally not lie on the manifold of physically allowed configurations.