Eigenspace Update for Molecular Geometry Optimization in Nonredundant Internal Coordinate

An eigenspace update method is introduced in this article for molecular geometry optimization. This approach is used to obtain the nonredundant internal coordinate space and diagonalize the Hessian matrix. A select set of large molecules is tested and compared with the conventional method of direct diagonalization in redundant space. While all methods considered herein take on similar optimization pathways for most molecules tested, the eigenspace update algorithm becomes much more computationally efficient with increasing size of the molecular system. A factor of 3 speed-up in overall computational cost is observed in geometry optimization of the 25-alanine chain molecule. The contributing factors to the computational savings are the reduction to the much smaller nonredundant coordinate space and the O(N(2)) scaling of the algorithm.