An analysis of two local measures of the electronic localization: a comparison with the ELF and the exchange-correlation density results

In this work we have explored the performance of two functions, recently proposed by Ayers [J. Chem. Sci., 2005, 117, 441], with the purpose of quantifying local electron localization. The first function, ζ(h), measures the total fluctuation per electron in the number of electrons at a given position r(1), while the second one, ζ(R), is a local representation of the minimum fluctuation criterion for electron localization. The study is carried out through a set of diatomic molecules that covers a wide range of covalent/polar character. Additionally, we have also calculated the electron localization function and the exchange-correlation hole along the internuclear axis. We have found that, for all the studied molecules, the numerical integration involved in computing ζ(h) did not converge. We think that this is so because the hole correlation calculations are not able to yield its correct asymptotic decaying behavior for large absolute values of the internuclear distances. On the other hand, the calculation of ζ(R) has proved to be feasible, and the information obtained from it has been concluded to be compatible to that rendered by the electron localization function (ELF) and the exchange-correlation density. Moreover, it has been also found that the results for ζ(R) allow to quantify the relative degree of electron localization within different molecular regions.     

Generalized nonlocal kinetic energy density functionals based on the von Weizsäcker functional

We generalize the ideas behind the procedure for the construction of kinetic energy density functionals with a nonlocal term based on the structure of the von Weizs?cker functional, and present several types of nonlocal terms. In all cases, the functionals are constructed such that they reproduce the linear response function of the homogeneous electron gas. These functionals are designed by rewriting the von Weizs?cker functional with the help of a parameter β that determines the power of the electron density in the expression, a strategy we have previously used in the generalization of Thomas-Fermi nonlocal functionals. Benchmark calculations in localized systems have been performed with these functionals to test both their relative errors and the quality of their local behavior. We have obtained competitive results when compared to semilocal and previous nonlocal functionals, the generalized nonlocal von Weizs?cker functionals giving very good results for the total kinetic energies and improving the local behavior of the kinetic energy density. In addition, all the functionals discussed in this paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, resulting in a quasilinear scaling for the computational cost.     

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.