Frequency spectra of sphere-, cube-, and tetrahedron-shaped Si nanoparticles with sizes ranging from $0.732\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4.223\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, evaluated using molecular mechanics, are reported. A consistent size dependence of the traction-free vibration frequencies was found. The frequency-radius product $\ensuremath{\omega}R$ exhibits a linear variation with the size of the particles for small particles. This is in contrast to both the constant behavior that has been reported for other nanoparticles and to the frequency scale invariance that holds for continuum solids. The size dependence of the molecular mechanics frequencies depends on the nanoparticle geometry.