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The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ = 2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model. [ABSTRACT FROM AUTHOR]

We describe a new algorithm for the generation of 3D grids for the numerical evaluation of multicenter molecular integrals in density functional theory. First, we use the nuclear weight functions method of Becke [A. D. Becke, J. Chem. Phys. 88, 2547 (1988)] to decompose a multicenter integral ∫F(r) dr into a sum of atomic-like single-center integrals. Then, we apply automatic numerical integration techniques to evaluate each of these atomic-like integrals, so that the total integral is approximated as ∫F(r) dr≊∑iωiF(ri). The set of abscissas ri and weights ωi constitutes the 3D grid. The 3D atomic-like integrals are arranged as three successive monodimensional integrals, each of which is computed according to a recently proposed monodimensional automatic numerical integration scheme which is able to determine how many points are needed to achieve a given accuracy. When this monodimensional algorithm is applied to 3D integration, the 3D grids obtained adapt themselves to the shape of the integrand F(r), and have more points in more difficult regions.The function F(r), which, upon numerical integration, yields the 3D grid, is called the generating function of the grid. We have used promolecule densities as generating functions, and have checked that grids generated from promolecule densities are also accurate for other integrands. Our scheme is very reliable in the sense that, given a relative tolerance ε, it generates 3D grids which are able to approximate multicenter integrals with relative errors smaller than ε for all the molecules tested in this work. Coarser or finer grids can be obtained using greater or smaller tolerances. For a series of 21 molecules, the average number of points per atom for ε=2.0·10-3, ε=2.0·10-4, ε=2.0·10-5, ε=2.0·10-6, and ε=2.0·10-7 is respectively 3141 (2.9·10-4), 10271 (2.4·10-5), 27184 (3.1·10-6), 72266... [ABSTRACT FROM AUTHOR]

The competition between Na + and K + with a protein for water was investigated by using Density Functional Theory (DFT) calculations. The optimized potential energy curves have been made in the DFT, together with balanced basis sets of split valence Def2-SV(P). Initially, calculations were done in order to know the organization of the hydration shell of the sodium and potassium ions, when up to sixteen molecules of water are added. The results indicate the structure and stability of these cations with water clusters. Then, this knowledge was used for the analysis of the hydrated protein when potassium or sodium cations approach them, showing that cation has a dehydration process more favorable energetically, and indicating for which cation, potassium or sodium is the competition with the protein for water more favorable. [ABSTRACT FROM AUTHOR]