Theoretic-information entropies analysis of nanostructures: ab initio study of PAMAM precursors and dendrimers G0 to G3

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Information theory in conjugated and in Hilbert spaces is employed to analyse the growing behaviour of nanostructures. Shannon entropies in position and momentum spaces require costly and time-consuming computations as the size of the molecules increases in contrast with information entropies in Hilbert space, which are shown to be highly advantageous for analysing large molecules. In this work, ab initio electronic structure calculations at the Hartree–Fock (HF), MP2 and B3LYP levels of theory were performed to analyse the initial steps towards growing nanostructured molecules of polyamidoamine (PAMAM) dendrimers, starting from the monomers, dimers, trimers and tetramers up to generations G0 (with 84 atoms), G1 (228 atoms), G2 (516 atoms) and G3 (1092 atoms). This was achieved by using selected physical descriptors such as the radius of gyration, the asphericity factor, the moments of inertia, the dipole moments, the total energies and chemical reactivity indices such as the hardness, softness and the electrophilicity index at the HF/3-21G* level of theory. For the chemical indices, higher level calculations at the B3LYP/6-311++ G** and MP2/6-311+ G* levels were also performed in order to account for the effects of electron correlation. Information-theoretic measures of the Shannon type in conjugated space were employed to characterise the G0–PAMAM precursors and G0. Hilbert space entropies of the Shannon and Kullback type were employed to provide theoretic-information evidence of the validity of the dense-core model of PAMAM precursors and dendrimers G0 to G3.