Geometry optimization in delocalized internal coordinates: An efficient quadratically scaling algorithm for large molecules

Using a Z-matrix-like approach for generating new Cartesian coordinates fro m a new geometry defined in terms of delocalized internal coordinates, we e liminate the costly O(N-3) iterative back-transformation required in standa rd geometry optimizations using delocalized (or natural/redundant) internal s, replacing it with a procedure which is only O(N). By replacing the gradi ent transformation with an iterative solution of a set of linear equations, we also reduce this step from O(N-3) to roughly O(N-2). This allows a very efficient method for geometry optimization of large molecules in internal coordinates. Several optimizations on systems containing up to 500 atoms ar e presented, comparing the performance of the new algorithm with its predec essor, and demonstrating the practical utility and efficiency of our approa ch. (C) 1999 American Institute of Physics. [S0021-9606(99)30211-7].