One of the most important open challenges in modern Kohn-Sham (KS) density-functional theory (DFT) is the correct treatment of systems involving fractional electron charges and spins. Approximate exchange-correlation functionals struggle with such systems, leading to pervasive delocalization and static correlation errors. We demonstrate how these errors, which plague density-functional calculat...

The self-consistent theory of Singwi, Tosi, Land and Sjolander (STLS), which accounts for exchange and short-range correlation effects through an effective potential depending on the structure factor, is generalized to the Visscher and Falicov model of the layered electron gas. The complete numerical solution of the STLS self-consistent equations provides information about intraplane and inter...

We consider the two-electron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree-Fock AHF(α) and BHF(β) for He and the first-row atoms are investigated, with particular attention to the effects of Pauli exchange. The...

Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital ener...

Current-spin-density-functional theory CSDFT provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin and orbital degrees of freedom. Unlike in the usual spindensity-functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, exp...

The equation of motion for the first-order density matrix ~1DM! is constructed for interacting electrons moving under the influence of given external scalar and vector potentials. The 1DM is coupled there to the 2DM by means of the electron-electron interaction. This equation is then employed to obtain the differential virial equation for interacting electrons moving in a magnetic field of arbi...