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##### Response Functions in TDDFT: Concepts and Implementation

**Authors**: D. A. Strubbe, L. Lehtovaara, A. Rubio, M.A.L. Marques, and S. G. Louie

**Ref.**: in "Fundamentals of Time-Dependent Functional Theory", edited by M.A.L. Marques, N. Maitra, F. Nogueira, E.K.U. Gross, and A. Rubio, chapter 7 (Springer-Verlag, Berlin), 139-166 (2012)

**Abstract**: Many physical properties of interest about solids and molecules can be considered as
the reaction of the system to an external perturbation, and can be expressed in terms
of response functions, in time or frequency and in real or reciprocal space. Response
functions in TDDFT can be calculated by a variety of methods. Time-propagation
is a non-perturbative approach in the time domain, whose static analogue is the
method of finite differences. Other approaches are perturbative and are formulated
in the frequency domain. The Sternheimer equation solves for the variation of the
wavefunctions, the Dyson equation is used to solve directly for response functions,
and the Casida equation solves for the excited states via an expansion in an electron
hole basis. These techniques can be used to study a range of different response
functions, including electric, magnetic, structural, and k · p perturbations. In this
chapter, we give an overview of the basic concepts behind response functions and
the methods that can be employed to efficiently compute the response properties
within TDDFT and the physical quantities that can be studied.

**Citations**: 6 (Google scholar)