Geometry optimization of large biomolecules in redundant internal coordinates

We present an improved version of our recent algorithm [B. Paizs, G. Fogara si, and P. Pulay, J. Chem. Phys. 109, 6571 (1998)] for optimizing the geome tries of large molecules. The approximate Cholesky factorization technique has been generalized to the case of redundant coordinates, and an alternati ve approach involving use of the B daggerB matrix in the iterative coordina te back transformation is described. The generalized full Cholesky factors of B daggerB are very sparse and the corresponding force and geometry trans formations are fast and numerically stable, permitting us to apply this tec hnique for internal coordinate geometry optimization of molecules containin g thousands of atoms. As an example we present optimization data on alpha-h elical alanine polypeptides, and various globular proteins. Results for the alanine polypeptides indicates that internal coordinate optimization is cl early superior to the first-order Cartesian optimization techniques general ly used in force field calculations. The largest system investigated is alp ha-helical Ac-(Ala)(999)-NH2 containing 9999 atoms, which was successfully optimized using less than a megaword of memory. Optimization of various glo bular proteins shows that our procedure can easily deal with highly redunda nt (including full primitive) coordinate sets. (C) 2000 American Institute of Physics. [S0021-9606(00)30839-X].