Unconstrained minimization approach for electronic computations that scales linearly with system size

Abstract

We present a method for the calculation of total energies and forces that scales linearly with the number of atoms in the system. The key points are (i) an unconstrained conjugate gradient minimization of the electronic energy that avoids the need of explicit orthonormalization, and (ii) description of the electrons in terms of localized wave functions, truncated beyond a radius ${\mathit{R}}_{\mathit{c}}$. The method is variational, giving an upper bound to the exact total energy, and is exact as ${\mathit{R}}_{\mathit{c}}$\ensuremath{\rightarrow}\ensuremath{\infty}. We test the method for a model tight-binding Hamiltonian, and in full ab initio molecular-dynamics calculations.