Adiabatic density-functional perturbation theory

Xavier Gonze

Research output: Contribution to journalArticlepeer-review

415 Citations (Scopus)


The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Greens function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a parallel-transport-gauge and a diagonal-gauge perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.

Original languageEnglish
Pages (from-to)1096-1114
Number of pages19
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 1995
Externally publishedYes


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