An efficient direct method for geometry optimization of large molecules in internal coordinates

Abstract

A new efficient procedure has been developed for geometry optimization of large molecules using internal coordinates. The method stores only the nonzero elements of the large transformation matrices, in the spirit of direct methods in electronic structure theory. Matrix inversion has been replaced by iterative solution of linear systems of equations by the preconditioned conjugate gradient method. A new incomplete Cholesky preconditioner proved essential to accelerate the conjugate gradient procedure. The geometries of several alpha helical alanine polypeptides, up to 50 alanine units, have been optimized by the new method, using the SYBYL force field. For larger systems, the number of energy/gradient evaluations is reduced by a factor of 6–10, compared to Cartesian optimization, and the cost of the optimization is small compared to the energy calculation. We expect this method to be useful in molecular mechanics and in mixed quantum mechanics/molecular mechanics calculations.