The phonovoltaic (pV) cell is similar to the photovoltaic. It harvests nonequilibrium (hot) optical phonons (E p,O ) more energetic than the bandgap (∆E e,g ) to generate power in a p-n junction.We examine the theoretical electron-phonon and phonon-phonon scattering rates, the Boltzmann transport of electrons, and the diode equation and hydrodynamic simulations to describe the operation of a pV cell and develop an analytic model predicting its efficiency. Our findings indicate that a pV material with E p,O ≃ ∆E e,g ≫ k B T , where k B T is the thermal energy, and a strong interband electron-phonon coupling surpasses the thermoelectric limit, provided the optical phonon population is excited in a nanoscale cell -enabling the ensuing local nonequilibrium. Finding and tuning a material with these properties is challenging. In Part II (this issue), we tune the bandgap of graphite within density functional theory through hydrogenation and the application of uniaxial strains. The bandgap is tuned to resonate with its energetic optical phonon modes and calculate the ab initio electron-phonon and phonon-phonon scattering rates. While hydrogenation degrades the strong electron-phonon coupling in graphene such that the figure of merit vanishes, we outline the methodology for a continued material search.