Model Hessian for accelerating first-principles structure optimizations

We present two methods to accelerate first-principles structural relaxations, both based on the dynamical matrix obtained from a universal model of springs for bond stretching and bending. Despite its simplicity, the normal modes of this model Hessian represent excellent internal coordinates for molecules and solids irrespective of coordination, capturing not only the long-wavelength acoustic modes of large systems, but also the short-wavelength low-frequency modes that appear in complex systems. In the first method, the model Hessian is used to precondition a conjugate gradients minimization, thereby drastically reducing the effective spectral width and thus obtaining a substantial improvement of convergence. The same Hessian is used in the second method as a starting point of a quasi-Newton algorithm (Broyden’s method and modifications thereof), reducing the number of steps needed to find the correct Hessian. Results for both methods are presented for geometry optimizations of clusters, slabs, and biomolecules, with speed-up factors between 2 and 8.