In this study, we compute all of the dynamically relevant vibrational quantum states of benzene, using an "exact" quantum dynamics (EQD) methodology. Benzene (C6H6), in addition to being a very large molecule for EQD (12 atoms, 30 vibrational modes), also has a very large number of vibrational states-around 106 in all, lying within 6500 cm-1 of the ground state. The EQD methodology developed here uses a phase space picture to optimize the truncation of a harmonic oscillator basis-not only with respect to the molecular system of interest but also with respect to the targeted spectral range. By employing several such EQD calculations, targeted to different spectral ranges, a "hybridized" data set is constructed that provides the most accurate results everywhere. In particular, more than 500 000 states are converged to 15 cm-1 or better.