X. Gonze, FIRST-PRINCIPLES RESPONSES OF SOLIDS TO ATOMIC DISPLACEMENTS AND HOMOGENEOUS ELECTRIC-FIELDS - IMPLEMENTATION OF A CONJUGATE-GRADIENT ALGORITHM, Physical review. B, Condensed matter, 55(16), 1997, pp. 10337-10354
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.