Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations.

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

Graphene nanoribbon electrical decoupling from metallic substrates.

We address the structural and electronic properties of graphene nanoribbons (GNRs) covalently immobilized on a metallic substrate by means of an organic layer. The GNR-organic layer and organic layer-metal interfaces can be thought of as constituents of a nanodevice and have been accurately studied using large-scale density functional theory calculations. Our results demonstrate the possibility of combining nanopatterned metal-organic layer substrates with selected GNRs to obtain well ordered and stable structures while preserving the GNR energy band gap, an essential requirement for any switching nanodevice.

Spin channels in functionalized graphene nanoribbons.

We characterize the transport properties of functionalized graphene nanoribbons using extensive first-principles calculations based on density functional theory (DFT) that encompass both monovalent and divalent ligands, hydrogenated defects, and vacancies. We find that the edge metallic states are preserved under a variety of chemical environments, while bulk conducting channels can be easily destroyed by either hydrogenation or ion or electron beams, resulting in devices that can exhibit spin conductance polarization close to unity.

A first-principle study of the adsorption of 1-amino-3-cyclopentene on the (100) silicon surface.

The adsorption of 1-amino-3-cyclopentene on the (100) silicon surface has been studied by methods rooted in the density-functional theory using both delocalized (plane waves, PWs) and localized (Gaussian-type orbitals, GTOs) basis functions. The results obtained by modeling the surface by silicon clusters of different sizes are quite similar, thus confirming that the reaction is quite localized. Furthermore, PW and GTO computations give comparable results, provided that the same density functional and carefully chosen computational parameters (contraction of GTO, pseudopotentials, etc.) are used. Slab computations performed in the PW framework show that the cluster results are retrieved when low-coverage adsorption on the surface is considered. On these grounds, we are quite confident that reaction parameters obtained by the more reliable hybrid density functional (PBE0) are essentially converged, our best estimates of reaction and activation free energies are thus -40 and 6 kcal/mol, respectively.