Non-universality of commonly used correlation-energy density functionals

The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient and meta-gradient density functionals. The results are compared with the exact correlation energies, showing that while several of the more recent density functionals reproduce the exact correlation energies of the helium isoelectronic sequence rather closely, none is satisfactory for Hooke's atom isoelectronic sequence. It is argued that the uniformly acceptable results for the helium sequence can be explained through simple scaling arguments that do not hold for Hooke's atom sequence, so that the latter system provides a more sensitive testing ground for approximate density functionals. This state of affairs calls for further effort towards formulating correlation-energy density functionals that would be truly universal at least for spherically-symmetric two-fermion systems.Comment: To appear in J. Chem. Phy

Structural and electronic properties of Si/Ge nanoparticles

Results of a theoretical study of the electronic properties of (Si)Ge and (Ge)Si core/shell nanoparticles, homogeneous SiGe clusters, and Ge$|$Si clusters with an interphase separating the Si and Ge atoms are presented. In general, (Si)Ge particles are more stable than (Ge)Si ones, and SiGe systems are more stable than Ge$|$Si ones. It is found that the frontier orbitals, that dictate the optical properties, are localized to the surface, meaning that saturating dangling bonds on the surface with ligands may influence the optical properties significantly. In the central parts we identify a weak tendency for the Si atoms to accept electrons, whereas Ge atoms donate electrons.Comment: To appear in Phys. Rev.

Quasi-pinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank-eight approximation we find well-defined families of saturation conditions.Comment: 22 pages, 6 figures, minor changes, references adde

Electronic polarization in quasilinear chains

Starting with a finite $k$-mesh version of a well-known equation by Blount, we show how various definitions proposed for the polarization of long chains are related. Expressions used for infinite periodic chains in the 'modern theory of polarization' are thereby obtained along with a new single particle formulation. Separate intracellular and intercellular contributions to the polarization are identified and, in application to infinite chains, the traditional sawtooth definition is found to be missing the latter. For a finite open chain the dipole moment depends upon how the chain is terminated, but the intracellular and intercellular polarization do not. All of these results are illustrated through calculations with a simple H\"uckel-like model.Comment: 5 page