  This article presents a new and efficient alternative to well established
algorithms for molecular geometry optimization. The new approach exploits the
approximate decoupling of molecular energetics in a curvilinear internal
coordinate system, allowing separation of the 3N-dimensional optimization
problem into an O(N) set of quasi-independent one-dimensional problems. Each
uncoupled optimization is developed by a weighted least squares fit of energy
gradients in the internal coordinate system followed by extrapolation. In
construction of the weights, only an implicit dependence on topologically
connected internal coordinates is present. This new approach is competitive
with the best internal coordinate geometry optimization algorithms in the
literature and works well for large biological problems with complicated
hydrogen bond networks and ligand binding motifs.
