As indicated in the previous section, there are two groups of parameters to be determined, the electronic ones (pseudoatomic orbitals and electron density) and the repulsive potentials for each pair of chemical elements. These parameters are subject to optimization in order to reproduce certain desired properties, such as the electronic band structure, and atomization energies, among others. Following the work of van den Bossche et al. only the 2s valence electron is considered for Li, meanwhile, the 3s and 3p valence electrons were considered for Si. Figure shows a comparison of DFTB computed band structures using the set of parameters B with DFT computed band structures for four systems: Li BCC, level and a small degree of compression when approaching the Fermi level. Given that in general, the repulsive term is capable of correcting small imperfections in the electronic part quite effectively, we decided to continue with the parameterization using these confinement parameters. This criterion is supported also by the good results that we present below. We proceed to parameterize the pair repulsion of the DFTB model by using each of the two energy band terms obtained as starting point. This gives us two different sets of DFTB parameters, say A and B, obtained by using the weight optimization procedure described in the method section. The ξs coefficients obtained for each set, A and B, are reported in table 2. It is interesting that for set A, the algorithm reduces the relative weight of pure Li and Si crystals, and increases the weights of the different alloys. On the contrary, for set B, the optimal weights are lower for the alloys and higher for the pure crystals. We rationalize this behavior by noticing that the band energy term of set A is built using pure element structures while the same term for set B uses an alloy. It seems reasonable that the pair repulsion term, which attempts to compensate for the energy residue given by all the other energy contributions, will be less important for those structures used for fitting the band energies and more important for the others. In this sense, optimal ξs coefficients seem to be able to sense this situation and try to compensate for it by focusing the parameterization on the structures that need it most.