5.7.1 Relation Between Theory and Experiment

The linear response theory can also be applied, within the DFT framework, to the case of the interaction between the cluster and a time dependent electric field characterized by a potential

(5.27)

This leads to the time dependent Density Functional Theory [83 85]. The external field induces a time dependent perturbation of the electron density

(5.28)

with Fourier components Sn( r; ?). The key quantity to calculate the response of the system in the linear regime is the dynamical susceptibility ?( r, r'; ?), which relates the individual components of the induced density to those of the external potential

(5.29)

Again the main interest arises in the case of a dipole field. The dynamical polarizability ?( ?), which is the ratio between the induced dipole moment and the intensity of the applied field, becomes

(5.30)

The dynamical polarizability reduces to the static one of Eq. (5.24) for ? = 0. Dissipation results in ?n( r; ?) being a complex function, and its imaginary part represents the power absorption of the cluster, that is due to electronic excitations. Using the Golden Rule, one obtains the photoabsorption cross section

(5.31)

where c is the velocity of light and Im ?( ?) is the imaginary part of the dynamical polarizability.

Experiments have been performed to measure the photoabsorption spectrum. The experimental configuration [64, 86] is shown in Fig.