Frequency standards electronic perturbation

There are several possible ways of deriving the equations for TDDFT. The most natural way departs from density-functional perturbation theory as outlined above. Initially it is assumed that an external perturbation is applied, which oscillates at a frequency co. The linear response of the system is then computed, which will be oscillating with the same imposed frequency co. In contrast with the standard static formulation of DFPT, there will be special frequencies cov for which the solutions of the perturbation theory equations will persist even when the external field vanishes. These particular solutions for orbitals and frequencies describe excited electronic states and energies with very good accuracy. 

The magnitudes of perturbation matrix elements are seldom tabulated in compilations of molecular constants. If deperturbed diagonal constants are listed, then the off-diagonal perturbation parameters should be listed as well, even though they cannot, without specialized narrative footnotes, be accommodated into the standard tabular format of such compilations. Without specification of at least the electronic part of the interaction parameters, it is impossible to reconstruct spectral line frequencies or intensities thus the deperturbed diagonal constants by themselves have no meaning. 

In this appendix we discuss a very convenient method to calculate electron-phonon coupling effects for stable-moment compounds, i.e., with integer 4f occupation. It is based on diagrammatic perturbation theory and will be used extensively in sect. 2. It is especially suitable for the calculation of finite-frequency phenomena like quadrupolar excitons and their mixing with phonons (sect. 2.7). In this pseudofermion method invented by Abrikosov (1965) and then adapted to CEF problems (Fulde and Peschel 1972) the transition operators = n) (ml that form the standard basis for operators acting within a given CEF system are replaced by pseudofermion operators/ according to Unlike the L... 

The photoabsorption spectrum a(co) of a cluster measures the cross-section for electronic excitations induced by an external electromagnetic field oscillating at frequency co. Experimental measurements of a(co) of free clusters in a beam have been reported, most notably for size-selected alkali-metal clusters [4]. Data for size-selected silver aggregates are also available, both for free clusters and for clusters in a frozen argon matrix [94]. The experimental results for the very small species (dimers and trimers) display the variety of excitations that are characteristic of molecular spectra. Beyond these sizes, the spectra are dominated by collective modes, precursors of plasma excitations in the metal. This distinction provides a clear indication of which theoretical method is best suited to analyze the experimental data for the very small systems, standard chemical approaches are required (Cl, coupled clusters), whereas for larger aggregates the many-body perturbation methods developed by the solid-state community provide a computationally more appealing alternative. We briefly sketch two of these approaches, which can be adapted to a DFT framework (1) the random phase approximation (RPA) of Bohm and Pines [95] and the closely related time-dependent density functional theory (TD-DFT) [96], and (2) the GW method of Hedin and Lundqvist [97]. 

---