Third generation photovoltaic cells promise to overcome the Schockley-Quessier limit of solar cell energy conversion. In the Multiple Exciton Generation (MEG) pathway quantum confined highly energetic electron-hole pairs relax by emitting additional electron-hole pairs. The overall utility of this process is undermined, however, by the very fact that quantum confinement pushes the gap of nanoparticles (NPs) out of the solar spectrum. Here we propose that Si and Ge NPs with core structures made out of exotic high-pressure phases of bulk Si and Ge have lower gaps, more intense absorption and higher MEG rates than those of made out of the cubic diamond phase. Some of these exotic phases have already been proven to exist in colloidal NPs or on laser treated surfaces, therefore, our findings may open the door for promising solar applications of such exotic nanoparticle systems.