A study of accurate exchange-correlation functionals through adiabatic connection

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial GGA functionals, this has culminated into the recently proposed SCAN(Strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals -the GGA hybrid functionals B3LYP and PBE0, and the meta-GGA functional SCAN- from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as scaling parameter times Vee with this parameter varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density.Comment: 8 Pages, 3 Figures and 8 Table

Exchange and correlation energy functionals for two-dimensional open-shell systems

We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation holes, respectively, and assuming proportionality between their characteristic sizes. The electron current and spin are explicitly taken into account, so that the resulting functionals are suitable to deal with systems exhibiting orbital currents and/or spin polarization. Our numerical results show that in finite systems the proposed functionals outperform the standard two-dimensional local spin-density approximation, still performing well also in the important limit of the homogeneous two-dimensional electron gas

Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions

The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate technique to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas (2D-HEG). The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory which indicates why these are suitable for two-dimensional quantum systems.Comment: 8 pages, 1 figur

Functional relations for the density functional exchange and correlation functionals connecting functionals at three densities

It is shown that the DFT exchange and correlation functionals satisfy an expression that couples exchange and correlation functionals and functional derivatives evaluated at three different densities and for two particle numbers. This equation can be used as a stringent test to check the internal self-consistency of approximations to the exchange and correlation functionals.Comment: 5 page

Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem

Popular density functionals for the exchange-correlation energy typically fail to reproduce the degeneracy of different ground states of open-shell atoms. As a remedy, functionals which explicitly depend on the current density have been suggested. We present an analysis of this problem by investigating functionals that explicitly depend on the Kohn-Sham orbitals. Going beyond the exact-exchange approximation by adding correlation in the form of the Colle-Salvetti functional we show how current-dependent terms enter the Colle-Salvetti expression and their relevance is evaluated. A very good description of the degeneracy of ground-states for atoms of the first and second row of the periodic table is obtained

Exact time-dependent density functional theory for impurity models

We employ the density matrix renormalization group to construct the exact time-dependent exchange correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely long-ranged exchange correlation potential which is built up {instantly} after switching on the voltage. Our result demonstrates the fundamental difficulties of transport calculations based on time-dependent density functional theory. While formally the approach works, important information can be missing in the ground-state functionals and may be hidden in the usually unknown non-equilibrium functionals

Reference-State One-Particle Density-Matrix Theory

A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by a constrained search. The correlation-energy functionals are not universal; they depend on the external potential. Nevertheless, model systems can still be used to derive universal energy-functionals. In addition, the correlation-energy functionals can be partitioned into individual terms that are -- to a varying degree -- universal; yielding, for example, an electron gas approximation. Variational and non-variational energy functionals are introduced that yield the target-state energy when the reference state -- or its corresponding one-particle density matrix -- is constructed from Brueckner orbitals. Using many-body perturbation theory, diagrammatic expansions are given for the non-variational energy-functionals, where the individual diagrams explicitly depend on the one-particle density-matrix. Non-variational energy-functionals yield generalized Hartree--Fock equations involving a non-local correlation-potential and the Hartree--Fock exchange; these equations are obtained by imposing the Brillouin--Brueckner condition. The same equations -- for the most part -- are obtained from variational energy-functionals using functional minimizations, yielding the (kernel of) correlation potential as the functional derivative of correlation-energy functionals. Approximations for the correlation-energy functions are introduced, including a one-particle-density-matrix variant of the local-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP) functional.Comment: 68 Page, 0 Figures, RevTeX 4, Submitted to Phys.Rev.A (on April 28 2003