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We present a new numerical model called CAFE-PakalMPI with the capability tosolve the equations of classical magnetohydrodynamic (MHD) and to obtain themultispecies whose ionization states are calculated through statisticalequilibrium, using the approximation of non-local thermodynamic equilibrium(NLTE) in three dimensions with the multiprocessor environment. For this, wecouple the Newtonian CAFE MHD code introduced in Gonz\'alez-Avil\'es et al.(2015) with PakalMPI presented in De la Luz et al. (2010). In this model,Newtonian CAFE solves the equations of ideal MHD under the effects of magneticresistivity and heat transfer considering a fully ionized plasma. On the otherhand, PakalMPI calculates the density of ionization states using the NLTEapproximation for Hydrogen, electronic densities and H-, the other species arecomputed by the classical local thermodynamic equilibrium (LTE) approximation.The main purpose of the model focuses on the analysis of solar phenomena withinthe chromospheric region. As an application of the model, we study thestability of the C7 equilibrium atmospheric model with a constant magneticfield in a 3D environment. According to the results of the test, the C7 modelremains stable in the low chromosphere, while in the range $z\in$[1.5,2.1] Mmwe can observe the propagation of a wave produced by the changes in theionization rate of H.

CAFE-PakalMPI: a new model to study the solar chromosphere in the NLTE approximation