Equivalent delocalized internal coordinates

It is shown that a new set of internal coordinates called the equivalent delocalized internal coordinates can be defined through a linear combination of conventional equivalent internal coordinates. The equivalent internal coordinates are isolated in the delocalized internal coordinates by a Gram-Schmidt orthogonalization. Then, the new coordinates are obtained from the linear combinations of the delocalized internal coordinates. With this approach an unified scheme for the calculation of equivalent and constant delocalized internal coordinates is obtained. It is shown that the new set of coordinates permits a better description of the concerted movement of atoms thereby allowing a more efficient geometry optimization in complex systems. Examples for the application of equivalent and constant delocalized internal coordinates are given.