On the gradient for metallic systems with a local basis set

The analytical gradient for periodic systems is presented, for the case of metallic systems. The total energy and the free energy are computed on the Hartree–Fock or density functional level, with the wave function being expanded in terms of Gaussian type orbitals. The expression for the gradient is similar to the case of insulating systems, when no thermal broadening is applied. When the occupation of the states is according to the Fermi function, then the gradient is consistent with the gradient of the free energy. By comparing with numerical derivatives, examples demonstrate that a reasonable accuracy is achieved.