A variational method for density functional theory calculations on metallic systems with thousands of atoms

A new method for finite-temperature density functional theory calculations which significantly increases the number of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic system, described in terms of a set of non-orthogonal, localized functions which are optimized in situ using a periodic-sinc basis set, equivalent to plane waves. Most parts of the calculation, including the demanding operation of building the Hamiltonian matrix, have a computational cost that scales linearly with the number of atoms in the system. Also, this approach ensures that the Hamiltonian matrix has a minimal size, which reduces the computational overhead due to diagonalization, a cubic-scaling operation that is still required. Large basis set accuracy is retained via the optimization of the localized functions. This method allows accurate simulations of entire metallic nanostructures, demonstrated with calculations on a supercell of bulk copper with 500 atoms and on gold nanoparticles with up to 2057 atoms.