  It is shown that the lowest excitation energies of a quantum many-fermion
system in the random phase approximation (RPA) can be obtained by minimizing an
effective classical energy functional. The minimum can be found very
efficiently using generalized Lanczos technique. Application of the new
technique to molecular spectra allows to compute excited states at the expense
comparable to the ground-state calculations. As an example, the first-principle
RPA excitation spectrum of C60 molecule is computed taking into account all 240
valence electrons in the full valence space of the molecule. The results match
linear absorption experiment within percents.
