  The presence of sharp peaks in the real part of the static dielectric
response function are usually accepted as indication of charge or spin
instabilities in a material. However, there are misconceptions that Fermi
surface (FS) nesting guarantees a peak in the response function like in
one-dimensional systems, and, in addition, response function matrix elements
between empty and occupied states are usually considered of secondary
importance and typically set to unity like in the free electron gas case. In
this work, we explicitly show, through model systems and real materials, within
the framework of density functional theory, that predictions about the peaks in
the response function, using FS nesting and constant matrix elements yields
erroneous conclusions. We find that the inclusion of the matrix elements
completely alters the structure of the response function. In all the cases
studied other than the one-dimensional case we find that the inclusion of
matrix elements washes out the structure found with constant matrix elements.
Our conclusion is that it is imperative to calculate the full response
function, with matrix elements, when making predictions about instabilities in
novel materials.
