A theory of high-energy optical conductivity of La0.7Ca0.3MnO3 has been proposed previously. The proposed theory works to explain the temperature-dependence of the optical conductivity for the photon energy region above ∼0.5 eV for up to ∼22 eV, but fails to capture the correct physics close to the dc limit in which metal-insulator transition occurs. The missing physics at the low energy has been acknowledged as mainly due to not incorporating phonon degree of freedom and electron-phonon interactions. In this study, we aim to complete the above theory by proposing a more complete Hamiltonian incorporating additional terms such as crystal field, two modes of Jahn-Teller vibrations, and coupling between electrons and the two Jahn-Teller vibrational modes. We solve the model by means of dynamical mean-field theory. At this stage, we aim to derive the analytical formulae involved in the calculation, and formulate the algorithmic implementation for the self-consistent calculation process. Our final goal is to compute the density of states and the optical conductivity for the complete photon energy range from 0 to 22 eV at various temperatures, and compare them with the experimental data. We expect that the improved model preserves the correct temperature-dependent physics at high photon energies, as already captured by the previous model, while it would also reveal ferromagnetic metal - paramagnetic insulator transition at the dc limit.