  We present a new numerical model called CAFE-PakalMPI with the capability to
solve the equations of classical magnetohydrodynamic (MHD) and to obtain the
multispecies whose ionization states are calculated through statistical
equilibrium, using the approximation of non-local thermodynamic equilibrium
(NLTE) in three dimensions with the multiprocessor environment. For this, we
couple 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 magnetic
resistivity and heat transfer considering a fully ionized plasma. On the other
hand, PakalMPI calculates the density of ionization states using the NLTE
approximation for Hydrogen, electronic densities and H-, the other species are
computed by the classical local thermodynamic equilibrium (LTE) approximation.
The main purpose of the model focuses on the analysis of solar phenomena within
the chromospheric region. As an application of the model, we study the
stability of the C7 equilibrium atmospheric model with a constant magnetic
field in a 3D environment. According to the results of the test, the C7 model
remains stable in the low chromosphere, while in the range $z\in$[1.5,2.1] Mm
we can observe the propagation of a wave produced by the changes in the
ionization rate of H.
