C. R. Proetto

Universal correction for the Becke–Johnson exchange potential

The Becke-Johnson exchange potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form, the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge-invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.

Exact Conditions in Finite-Temperature Density-Functional Theory

Density-functional theory (DFT) for electrons at finite temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite temperature, including the adiabatic connection formula. We discuss consequences for functional construction.

Lower bounds on the exchange-correlation energy in reduced dimensions.

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Position-dependent exact-exchange energy for slabs and semi-infinite jellium

The position-dependent exact-exchange energy per particle

Becke-Johnson-type exchange potential for two-dimensional systems

\varepsilon_x(z)

Correlation energy of finite two-dimensional systems: Toward nonempirical and universal modeling

(defined as the interaction between a given electron at

Localized versus extended systems in density functional theory: Some lessons from the Kohn-Sham exact exchange potential

z

Exact-exchange Kohn-Sham potential, surface energy, and work function of jellium slabs

and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove analytically and numerically that in the vacuum region far away from the surface

Parameter-free density functional for the correlation energy in two dimensions

\varepsilon_{x}^{\text{Slab}}(z \to \infty) \to - e^{2}/2z

Virial theorem and exact properties of density functionals for periodic systems

, {\it independent} of the bulk electron density, which is exactly half the corresponding exact-exchange potential