In this paper the deposition and surface growth of chromium nanoparticles (CrNPs) coatings on a commercial steel substrate by electrodeposition at a constant current, is presented; both theoretically through a theoretical-computational model applying a modified Schrödinger equation, energy potentials and electrochemistry and phitosynthesis of Cr Nanoparticles . For the simulation process, the finite element method (FEM) was used considering the equation of electric potential and electroneutrality with and without the inclusion of a quantum leap. The theoretical results are in accordance with the experimental results, considering a three-level multifactorial experiment design with current, voltage and ion concentration as factors and the formation and growth of the coatings as a response function. The results obtained indicate the presence of electro-diffusion at the substrate-coating interface. The developed model has the predictive ability of 97±2 % for the electrochemical deposition of CrNPs on a steel substrate.