Generalized variational density functional perturbation theory

We present an implementation of variational perturbation theory in the fram ework of density functional theory. We use an ab initio pseudopotential sch eme with a plane wave basis set and expand the energy functional up to seco nd order in the perturbation. The approach is fairly general and does not r ely on the representativeness of the perturbation through a Hamiltonian ope rator and does not require the use of canonical orbitals. Instead, a functi onal formulation is used to characterize the perturbation. Several types of applications are presented which illustrate the variety of linear response phenomena that can be treated with our method (vibrational modes, Raman sc attering, and nuclear magnetic resonance chemical shift computations). In c ombination with advanced gradient correction formulas, an accurate descript ion of second order effects in periodic and isolated systems can be achieve d. (C) 2000 American Institute of Physics. [S0021-9606(00)30641-9].