This study permits to explore the interactions involved in Lewis acid $\left(\mathrm{AlH}_3\right)$ and Lewis bases: $\mathrm{CO} ; \mathrm{H}_2\mathrm{O} ; \mathrm{NH}_3 ; \mathrm{PH}_3 ; \mathrm{PCl}_3 ; \mathrm{H}_2 \mathrm{S} ; \mathrm{CN}^{-} ; \mathrm{OH}^{-} ; \mathrm{O}_2^{-2} ; \mathrm{F}^{-} ; \mathrm{N}\left(\mathrm{CH}_3\right)_3 ; \mathrm{N}_2 ; \mathrm{N}_2 \mathrm{H}_4 ; \mathrm{N}_2 \mathrm{H}_2 ; \mathrm{C}_5 \mathrm{H}_5 \mathrm{N} ; \mathrm{C}_6 \mathrm{H}_{5^{-}}\mathrm{N}\mathrm{H}_2$. By means of DFT theory calculations with B3LYP functional using $6-31 \mathrm{G}(\mathrm{d}, \mathrm{p})$ basis set and in order to check the effects of both the donor and the acceptor in the establishment of the different adducts we focused mainly on the calculation of the energetic gap $\Delta E_{\text {HOMO-LUMO }}$, Gibbs energies $\Delta \mathrm{G}$, the angle ($\Delta \Theta$) in $\mathrm{Al}\mathrm{H}_3$ - base and the interaction energy values ${E}_{inter}$. The several parameters of the reactivity (electrophilicity index $\left(\omega\right)$, nucleophilicity $\left({N}\right)$, chemical potential $\left(\mu\right)$, hardness $\left(\eta\right)$, and polarizability $\left(\alpha\right)$) are also calculated to define the weak interaction as well as to distinguish between the nucleophilicity and basicity of different Lewis bases. The results showed that the electronic charge transfer is estimated to be important in the systems where the interaction is established between $\mathrm{Al}$ and anionic bases, and the electron donor power is predictable for $\mathrm{O}^{-2}, \mathrm{F}^{-}, \mathrm{OH}^{-},$ and $\mathrm{CN}^{-}$. The pseudo-tetrahedral adduct arrangements depend on the parameter geometries (bond length interaction and $\Theta$ angle) and Gibbs energies $\Delta \mathrm{ G}$ characterizing the main stability.
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