Geometry optimization methods for modeling large molecules

Geometry optimization is an essential part of quantum chemical applications. The diversity of the scaling of different methods from linear to exponential implies that there are different requirements for a chosen optimization method. The proposed method aims to meet two requirements, good scaling with size and reliability, which would be a good match for redundant internal coordinate system-based optimization techniques with linear scaling coordinate transformation. The new optimization algorithm uses screened Cholesky decomposition for coordinate transformations and an iterative subspace optimization method. The iterative subspace appears in the course of any optimization. However, few methods are available for using such information efficiently. The Geometry Optimization using Direct Inversion in the Iterative Subspace method is known to have good scaling and efficiency, but poor reliability. Building a Hessian-like matrix in the iterative subspace allows one to take advantage of the reliability offered by Rational Function Optimization, Eigenvector Following and Trust Radius Method (TRM), but still avoid a consequent computational penalty. Also, the new approach steps away from the regular quadratic approximation related to the Newton methods by assuming a simple linear connection between gradient and coordinate changes