  A formalism for electronic-structure calculations is presented that is based
on the functional renormalization group (FRG). The traditional FRG has been
formulated for systems that exhibit a translational symmetry with an associated
Fermi surface, which can provide the organization principle for the
renormalization group (RG) procedure. We here advance an alternative
formulation, where the RG-flow is organized in the energy-domain rather than in
k-space. This has the advantage that it can also be applied to inhomogeneous
matter lacking a band-structure, such as disordered metals or molecules. The
energy-domain FRG ({\epsilon}FRG) presented here accounts for Fermi-liquid
corrections to quasi-particle energies and particle-hole excitations. It goes
beyond the state of the art GW-BSE, because in {\epsilon}FRG the Bethe-Salpeter
equation (BSE) is solved in a self-consistent manner. An efficient
implementation of the approach that has been tested against exact
diagonalization calculations and calculations based on the density matrix
renormalization group is presented.
  Similar to the conventional FRG, also the {\epsilon}FRG is able to signalize
the vicinity of an instability of the Fermi-liquid fixed point via runaway flow
of the corresponding interaction vertex. Embarking upon this fact, in an
application of {\epsilon}FRG to the spinless disordered Hubbard model we
calculate its phase-boundary in the plane spanned by the interaction and
disorder strength. Finally, an extension of the approach to finite temperatures
and spin S = 1/2 is also given.
