Motif-based Hessian matrix for ab initio geometry optimization of nanostructures

A simple method to estimate the atomic degree Hessian matrix of a nanosystem is presented. The estimated Hessian matrix, based on the motif decomposition of the nanosystem, can be used to accelerate ab initio atomic relaxations with speedups of 2-4 depending on the size of the system. In addition, the programing implementation for using this method in a standard ab initio package is trivial.