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.

Silicon Nanocrystal Functionalization: Analytic Fitting of DFTB Parameters.

A density functional tight binding (DFTB) scheme has been applied to functionalized silicon nanocrystals. Using an analytic functional representation of DFTB parameters, the scheme has been used to compute the adsorption energies in the organic functionalization of reconstructed Si(100) and H-terminated Si(111) surfaces of hundreds-of-atoms nanocrystals. We adopt an ONIOM(QM:QM') approach that corrects the overbinding of DFTB, obtaining nice agreement with high-level reaction energies and structural configurations.

Time-Dependent Density Functional Tight Binding: New Formulation and Benchmark of Excited States.

A new formulation of time-dependent density functional tight binding (TD-DFTB) is reported in this paper. It is derived from the application of the linear response theory to the ground state DFTB Hamiltonian, without the introduction of additional parameters for the description of the excited states. The method is validated for several sets of organic compounds, against the best theoretical estimates from the literature, density functional theory, semiempirical methods, and experimental data. The comparison shows that TD-DFTB gives reliable results both for singlet and triplet excitation energies. In addition, the application of TD-DFTB to open-shell systems shows promising results.

Effects of electronic and lattice polarization on the band structure of delafossite transparent conductive oxides.

We use hybrid functionals and restricted self-consistent GW, state-of-the-art theoretical approaches for quasiparticle band structures, to study the electronic states of delafossite Cu(Al,In)O2, the first p-type and bipolar transparent conductive oxides. We show that a self-consistent GW approximation gives remarkably wider band gaps than all the other approaches used so far. Accounting for polaronic effects in the GW scheme we recover a very nice agreement with experiments. Furthermore, the modifications with respect to the Kohn-Sham bands are strongly k dependent, which makes questionable the common practice of using a scissor operator. Finally, our results support the view that the low energy structures found in optical experiments, and initially attributed to an indirect transition, are due to intrinsic defects in the samples.