  Based on the variational Gutzwiller theory, we present a method for the
computation of response functions for multiband Hubbard models with general
local Coulomb interactions. The improvement over the conventional random-phase
approximation is exemplified for an infinite-dimensional two-band Hubbard model
where the incorporation of the local multiplet-structure leads to a much larger
sensitivity of ferromagnetism on the Hund coupling. Our method can be
implemented into LDA+Gutzwiller schemes and will therefore be an important tool
for the computation of response functions for strongly correlated materials.
