We present a new formalism for the explanation of the curvature of the Arrhenius self-diffusion plots on the basis of mono-vacancy diffusion mechanism. The temperature dependence of the diffusion coefficient appears from the concentration dependence of the vacancy formation energy and without any additional assumption about a particular diffusion mechanism. This method gives a possibility to estimate different parameters of the self-diffusion process from first principles in an assumption that vacancies form a random solid solution of holes in the bulk of the crystal. We apply this formalism to the analysis of the curvature of the Arrhenius plot as well as to the estimation of other parameters of self-diffusion in bcc Cs. The numerical evaluations are based on the Full Potential Linearized Muffin-Tin Orbitals method of the calculation of total energies.