J. E. Alvarellos

Kinetic energy density study of some representative semilocal kinetic energy functionals

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.

Fully nonlocal kinetic energy density functionals: a proposal and a general assessment for atomic systems.

Following some recent ideas on the construction of kinetic energy density functionals that reproduce the linear response function of the homogeneous electron gas, a family of them with a nonlocal term based on the von Weizsacker functional and with a dependence on the logarithm of the density is presented. As localized systems are the most difficult to study with explicit kinetic functionals, in this paper we apply to atomic systems a number of families of fully nonlocal kinetic functionals. We have put our attention in both the total kinetic energy and the local behavior of the kinetic energy density, and the results clearly show the quality of these fully nonlocal functionals. They make a good description of the local behavior of the kinetic energy density and maintain good results for the total kinetic energies. We must remark that almost all the functionals discussed in the paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, with a quasilinear scaling for the computational cost.

Electron density, exchange-correlation density, and bond characterization from the perspective of the valence-bond theory. II. Numerical results

In this work we have analyzed the bond character of a series of representative diatomic molecules, using valence bond and the atoms in molecules points of view. This is done using generalized valence-bond calculations. We have also employed more exigent levels, as configuration interaction with single and double excitations and complete active space self-consistent field calculations, in order to validate the generalized valence-bond results. We have explored the possibility that the known delocalization index, and a parameter that measures the excess or defect population within a given atomic basin, can be considered as indicators of the character of bond interaction. We conclude that for a proper description of the bond character, the global behavior of both the charge and two-electron densities should be considered.

Electron density, exchange-correlation density, and bond characterization from the perspective of the valence-bond theory. I. Two simple analytical cases

In this work, using a valence-bond wave function we obtain analytical expressions for the first- and second-order reduced density matrices of two simple, but quite representative, cases of diatomic molecular systems, namely, H2 and LiH. A detailed study of their exchange-correlation density is performed for both equilibrium and nonequilibrium internuclear distances, discriminating the parallel- and antiparallel-spin contributions. The results show that the behavior of the exchange-correlation density clearly changes with the character of the bond, making it possible to obtain a good deal of information regarding the type of the bond interaction.

Local behavior of the first-order gradient correction to the Thomas–Fermi kinetic energy functional

The first-order gradient correction to the Thomas-Fermi functional proposed by Haq et al. [Chem. Phys. Lett. 111, 79 (1984)] has been tested by evaluating both the total kinetic energy and the local kinetic energy density. For the kinetic energy density, we have evaluated its deviation from the exact orbital-based result through a quality factor that reflects the quality of the functionals in a better way than their relative errors. The study is performed on two different systems: Light atoms (up to Z=18) and a noninteracting model of fermions confined in a Coulombic-type potential, a system that provides useful insights about the performance of the functionals when the ground state is degenerate. It is found that this approximation gives very low relative errors and a better local behavior than any other kinetic energy density functional.

Kinetic-energy density functionals with nonlocal terms with the structure of the Thomas-Fermi functional

We study two families of approximate nonlocal kinetic-energy functionals that include a full von Weizsaecker functional, and that have nonlocal terms with the mathematical structure of the Thomas-Fermi functional. The functionals recover the exact kinetic energy and the linear response function of a homogeneous electron system. The first family is a generalization of a successful previous nonlocal functional. The second family is proposed in the paper, and is designed to obtain functionals suitable for use in both localized and extended systems. Furthermore, this family has been designed to be evaluated by a single integration in momentum space when a constant reference density is used. The atomic total kinetic energies are in good agreement with the exact calculations. The kinetic-energy density corresponding to each functional has been assessed to control its quality. The results show that, in general, these functionals behave better than both the Thomas-Fermi and all semilocal generalized gradient approximation functionals when describing the kinetic-energy density of atoms, providing a better description of the nonlocal effects of the kinetic energy of electron systems.

All-electrical production of spin-polarized currents in carbon nanotubes: Rashba spin-orbit interaction

We study the effect of the Rashba spin-orbit interaction in the quantum transport of carbon nanotubes with arbitrary chiralities. For certain spin directions, we find a strong spin-polarized electrical current that depends on the diameter of the tube, the length of the Rashba region and on the tube chirality. Predictions for the spin-dependent conductances are presented for different families of achiral and chiral tubes. We have found that different symmetries acting on spatial and spin variables have to be considered in order to explain the relations between spin-resolved conductances in carbon nanotubes. These symmetries are more general than those employed in planar graphene systems. Our results indicate the possibility of having stable spin-polarized electrical currents in absence of external magnetic fields or magnetic impurities in carbon nanotubes.

Defect-enhanced Rashba spin-polarized currents in carbon nanotubes

A.L. acknowledges the financial support of FAPERJ through Grants No. E-26/102.272/2013 and No. E-26/202.953/2016, CNPq, and INCT em Nanomateriais de Carbono. L.C. acknowledges support from Spanish MINECO through Grant No. FIS2015-64654-P, and helpful conversations with Jorge I. Cerda. H.S. is grateful for financial support from the Brazilian CAPES.