Time-dependent current-density-functional theory (TDCDFT) provides an in principle exact scheme to calculate efficiently response functions for a very broad range of applications. However, the lack of approximations valid for a range of parameters me
t in experimental conditions has so far delayed its extensive use in inhomogeneous systems. On the other side, in many-body perturbation theory (MBPT) accurate approximations are available, but at a price of a higher computational cost. In the present work the possibility of combining the advantages of both approaches is exploited. In this way an exact equation for the exchange-correlation kernel of TDCDFT is obtained, which opens the way for a systematic improvement of the approximations adopted in practical applications. Finally, an approximate kernel for an efficient calculation of spectra of solids and molecular conductances is suggested and its validity discussed.
Measurable spectra are theoretically very often derived from complicated many-body Greens functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct effective potenti
als and kernels for the direct calculation of electronic spectra. In particular, the potential that yields the spectral function needed to describe photoemission turns out to be dynamical but {it local} and {it real}. As example we illustrate this ``photoemission potential for sodium and aluminium, modelled as homogeneous electron gas, and discuss in particular its frequency dependence stemming from the nonlocality of the corresponding self-energy. We also show that our approach leads to a very short derivation of a kernel that is known to well describe absorption and energy-loss spectra of a wide range of materials.
