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We performed an investigation on (alpha)-Al(_{2})O(_{3}): Mn(^{3+}) material based on first-principles calculations without referring to any experimental parameter for the first time. In order to estimate the lattice relaxation effect due to Mn(^{3+}) substitution, we carried out a geometry optimization using Cambridge Serial Total Energy Package (CASTEP) code. Next, the molecular orbitals (MO) were calculated using the discrete variational-X(alpha) (DV-X(alpha)) method while the multiplet energies were calculated discrete variational multi-electron (DVME) method. Since, the multiplet energies are generally overestimated, here we also used the energy corrections to improve the accuracy. We thus compared our calculated results with the observed data reported by McClure et. al., (1962). The results shows that by considering both of the lattice relaxation effect and the energy corrections, the agreement between our calculated results and the observed data is improved.