FIRST-PRINCIPLES RESPONSES OF SOLIDS TO ATOMIC DISPLACEMENTS AND HOMOGENEOUS ELECTRIC-FIELDS - IMPLEMENTATION OF A CONJUGATE-GRADIENT ALGORITHM

The changes in density, wave functions, and self-consistent potentials of solids, in response to small atomic displacements or infinitesimal homogeneous electric fields, are considered in the framework of the d ensity-functional theory. A variational: principle for second-order de rivatives of the energy provides a basis for efficient algorithmic app roaches to these linear responses, such as the state-by-state conjugat e-gradient algorithm presented here in detail. The phase of incommensu rate perturbations of periodic systems, that are, like phonons, charac terized by some wave vector, can be factorized: the incommensurate pro blem is mapped on an equivalent one presenting the periodicity of the unperturbed ground state. The singularity of the potential change asso ciated with an homogeneous field is treated by the long-wave method. T he efficient implementation of these theoretical ideas using plane wav es, separable pseudopotentials, and a nonlinear exchange-correlation c ore correction is described in detail, as well as other technical issu es.