By Miguel A.L. Marques, Neepa T. Maitra, Fernando M.S. Nogueira, E.K.U. Gross, Angel Rubio
Time-dependent density practical conception (TDDFT) relies on a suite of principles and theorems rather special from these governing ground-state DFT, yet emphasizing related strategies. this day, using TDDFT is speedily growing to be in lots of parts of physics, chemistry and fabrics sciences the place direct resolution of the Schrödinger equation is simply too not easy. this can be the 1st accomplished, textbook-style advent to the correct fundamentals and strategies.
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Extra info for Time-Dependent Density Functional Theory
Below we systematically derive a set of identities that are commonly used for dealing with such functions and will be used extensively in the following sections. Most of the relations are well known [Langreth 1976], while others, equally important [Wagner 1991], are not. Our aim is to provide a self-contained derivation of all of them. A table at the end of the section summarizes the main results. For those who are not familiar with the Keldysh contour, we strongly recommend to scan what follows with pencil and paper.
To calculate observables from the Green function we must of course take all matrix elements into account. 39), we introduced the electronic self-energy functional Σ, which accounts for the eﬀects of the electron interaction. The self-energy is a functional of the Green function, and will have to be approximated in practical calculations. Diagrammatic techniques provide a natural scheme for generating approximate self-energies and for systematically improving these approximations. There are no general prescriptions for how to select the relevant diagrams, which means that this selection must be guided by physical intuition.
32. The equations of motion for the Green function, known as the Kadanoﬀ-Baym equations, are explained in Sect. 5. While in TDDFT we take exchange and correlation eﬀects into account through vxc [n], the corresponding quantity in Green function theory is the self-energy Σ[G]. Just like vxc , the self-energy functional must be approximated. For a given functional Σ[G], it is important that the resulting observables obey the macroscopic conservation laws, such as the continuity equation. These approximations are known as conserving, and will be discussed brieﬂy in Sect.