Geometry optimization in redundant internal coordinates

The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton–Raphson–type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy-free internal coordinates. This procedure, already used for the geometry optimization of porphine, C20N4H14, is illustrated here at the ab initio self-consistent-field level for the four-membered ring azetidine, for bicyclo2.2.2octane, and for the four-ring system C16O2H22, the skeleton of taxol.