Using redundant internal coordinates to optimize equilibrium geometries and transition states

TLDR

The authors construct a redundant internal coordinate system comprising all bonds, valence angles, and dihedral angles, then eliminate redundancies using the generalized inverse of the G matrix and apply constraints via a projector. Using redundant coordinates markedly speeds up geometry optimizations compared to Cartesian or nonredundant internal coordinates, particularly for flexible and polycyclic molecules, and also enhances transition‑state searches when combined with a quadratic synchronous transit initial step. © 1996 John Wiley & Sons, Inc.

Abstract

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach. © 1996 by John Wiley & Sons, Inc.