Small changes in the dielectric response of a material result in substantial variations in the Hamaker coefficient of the van der Waals interactions, as demonstrated in a simplified approximate model as well as a realistic example of amorphous silica with and without an exciton peak. Variation of the dielectric response spectra at one particular frequency influences all terms in the Matsubara summation, making the total change in the Hamaker coefficient depend on the spectral changes not only at that frequency but also at the rest of the spectrum, properly weighted. The Matsubara terms most affected by the addition of a single peak are not those close to the position of the added peak, but are distributed doubly non-locally over the entire range of frequencies. A possibility of eliminating van der Waals interactions or at least drastically reducing them by spectral variation in a narrow regime of frequencies thus seems very remote.
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