Density-functional approach to nonlinear-response coefficients of solids

We propose a general scheme, within the density-functional theory, for an accurate computation of a large class of nonlinear-response coefficients of solids. The scheme is applicable to all kinds of adiabatic perturbations of the crystal ground state, such as the application of mechanical strains, static electric fields of any wavelength, or individual atomic displacements, and allows the study of coefficients which describe anharmonicities or coupling of simultaneously applied disturbances. Total-energy changes as a function of the perturbation wavelength, as needed to obtain phonon group velocities, can also be considered. The formalism, which avoids the use of supercells and large-matrix inversions, contains as a special case the treatment of linear-response coefficients recently suggested by Baroni, Giannozi, and Testa. The central ingredient in our scheme is an efficient use of the ``2n+1'' theorem of the perturbation theory, which allows us to obtain the third-order derivatives of the total energy by using only byproducts of a first-order perturbation calculation.