**7**

Computing properties

**7.1 Adiabatic density-functional perturbation theory: Hessian, polarizability, NMR**

**7.1.1 Introduction**

The total energy and charge density are basic quantities of density functional theory and give access to a wide range of experimental observables. Most of these quantities can be obtained as derivatives of the energy or density with respect to external perturbations, as collected in Table 7.1 for a selection of relevant response properties. As a simple example, the force exerted on a given nucleus is given by the negative derivative of the total energy of the system with respect to the position of this nucleus. The calculation of such energy derivatives can be done by finite-difference methods. The total energy is computed ...

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