Geometry optimization of large biomolecules in redundant internal coordinates

We present an improved version of our recent algorithm B. Paizs, G. Fogarasi, and P. Pulay, J. Chem. Phys. 109, 6571 (1998) for optimizing the geometries of large molecules. The approximate Cholesky factorization technique has been generalized to the case of redundant coordinates, and an alternative approach involving use of the B†B matrix in the iterative coordinate back transformation is described. The generalized full Cholesky factors of B†B are very sparse and the corresponding force and geometry transformations are fast and numerically stable, permitting us to apply this technique for internal coordinate geometry optimization of molecules containing thousands of atoms. As an example we present optimization data on alpha-helical alanine polypeptides, and various globular proteins. Results for the alanine polypeptides indicates that internal coordinate optimization is clearly superior to the first-order Cartesian optimization techniques generally used in force field calculations. The largest system investigated is alpha-helical Ac-(Ala)999-NH2 containing 9999 atoms, which was successfully optimized using less than a megaword of memory. Optimization of various globular proteins shows that our procedure can easily deal with highly redundant (including full primitive) coordinate sets.