A novel implicit Newton-Raphson geometry optimization method for density functional theory calculations

A novel Newton–Raphson geometry optimization method for density functional theory calculation is presented. Contrary to the standard Newton–Raphson procedure, our method does not require the calculation of the full Hessian matrix. We use instead density functional perturbation theory to evaluate the effect of the Hessian on a given atomic displacement and invert the Hessian using a conjugate gradient method. The method uses Cartesian coordinates and is very robust. In a variety of tested molecular systems, it has an efficiency comparable with that of more established methods. In difficult condensed matter systems, it appears to be far superior