Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets.

The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem.

Exact exchange plane-wave-pseudopotential calculations for slabs.

The exact exchange of density functional theory is applied to both free-standing graphene and a Si(111) slab, using the plane-wave pseudopotential (PWPP) approach and a periodic repetition of the supercell containing the slab. It is shown that (i) PWPP calculations with exact exchange for slabs in supercell geometry are basically feasible, (ii) the width of the vacuum required for a decoupling of the slabs is only moderately larger than in the case of the local-density approximation, and (iii) the resulting exchange potential vx shows an extended region, both far outside the surface of the slab and far from the middle of the vacuum region between the slabs, in which vx behaves as -e(2)/z, provided the width of the vacuum is chosen sufficiently large. This last result is corroborated by an analytical analysis of periodically repeated jellium slabs.

Random-phase-approximation-based correlation energy functionals: benchmark results for atoms.

The random phase approximation for the correlation energy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the Kohn-Sham Hamiltonian.

Time-dependent density functional calculation of e-H scattering.

Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H- ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact exchange yields an excellent approximation to the ground-state Kohn-Sham potential, while the adiabatic local density approximation yields good singlet and triplet phase shifts.

Kohn-Sham perturbation theory: simple solution to variational instability of second order correlation energy functional.

The orbital-dependent correlation energy functional resulting from second order Kohn-Sham perturbation theory leads to atomic correlation potentials with correct shell structure and asymptotic behavior. The absolute magnitude of the exact correlation potential, however, is greatly overestimated. In addition, this functional is variationally instable, which shows up for systems with nearly degenerate highest occupied and lowest unoccupied levels like Be.

Second-order Kohn-Sham perturbation theory: correlation potential for atoms in a cavity.

Second-order perturbation theory based on the Kohn-Sham Hamiltonian leads to an implicit density functional for the correlation energy E(c) (MP2), which is explicitly dependent on both occupied and unoccupied Kohn-Sham single-particle orbitals and energies. The corresponding correlation potential v(c) (MP2), which has to be evaluated by the optimized potential method, was found to be divergent in the asymptotic region of atoms, if positive-energy continuum states are included in the calculation [Facco Bonetti et al., Phys.