An accurate total energy calculation is essential in materials computation. To date, many tight-binding (TB) approaches based on parameterized hopping can produce electronic structures comparable to those obtained using first-principles calculations. However, TB approaches still have limited applicability for determining material properties derived from the total energy. That is, the predictive power of the TB total energy is impaired by an inaccurate evaluation of the repulsive energy. The complexity associated with the parametrization of TB repulsive potentials is the weak link in this evaluation. In this study, we propose a new method for obtaining the pairwise TB repulsive potential for crystalline materials by employing the Chen-Möbius inversion theorem. We show that the TB-based phonon dispersions, calculated using the resulting repulsive potential, compare well with those obtained by first-principles calculations for various systems, including covalent and ionic bulk materials and two-dimensional materials. The present approach only requires the first-principles total energy and TB electronic band energy as input and does not involve any parameters. This striking feature enables us to generate repulsive potentials programmatically.