Gradient corrections to the local spin density approximation for the exchange-correlation energy Exc are increasingly useful in quantum chemistry and solid state physics. We present elementary physical arguments which explain the qualitative dependencies of the exchange and correlation energies upon the local density, local spin polarization, and reduced density gradient. The nearly local behavior of the generalized gradient approximation for Exc at valence-electron densities, due to strong cancellation between the nonlocalities of exchange and correlation, is shared by the exact linear response of the uniform electron gas. We further test and develop our rationale for the chemical and solid-state consequences of gradient corrections. We also partially explain the “conjointness” between the exchange energy and the noninteracting kinetic energy, whose generalized gradient approximation is tested here. An appendix presents the full expression for the gradient-corrected correlation potential.
The size effect on the electronic density of states and spin susceptibility $\ensuremath{\chi}$ of small metal particles and thin films is evaluated to order (area/volume) within the spin-density functional formalism. Conditions are given under which the size effect arises only in the surface region. Size-effect parameters and magnetization profiles, as well as surface energies and work functions, are calculated self-consistently for the jellium surface using the random-phase approximation and the local spin-density approximation (LSDA) for exchange and correlation. The jellium surface is also used to test two approximations for $\ensuremath{\chi}$ which require only spin-unpolarized calculations. One of them, the Vosko-Perdew (VP) approximation, is found to agree closely with the full spin-polarized calculation within the LSDA. The VP theory, which gives lower bounds for the bulk and surface susceptibilities and does not necessarily require the LSDA, is used to discuss the possibility of a giant surface effect, i.e., a giant enhancement of the surface susceptibility, in any metal that is nearly ferromagnetic. The giant surface effect is illustrated by an LSDA calculation for a low-density jellium, and by two other instructive models.
We use the two-electron wavefunctions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function for a uniform electron gas. We find excellent agreement with Quantum Monte Carlo simulations in the short-range region, for a wide range of electron densities. We are thus able to estimate the value of the second-order coefficient of the small interelectronic-distance expansion of the pair-distribution function. The results are generalized to the partially polarized gas.
Very accurate surface energies and work functions for a semi-infinite jellium can be calculated from a simple and transparent analytic model. The model is a modified version of one proposed by Smith and refined by Ma and Sahni which employs the gradient expansion for the kinetic energy and a one-parameter trial density profile; the modifications are use of a more-realistic profile and a less-profile-sensitive expression for the work function. This model is used to explore the qualitative effects of exchange and correlation on the metal surface properties, as well as the significant quantitative effects of different choices for the bulk correlation energies ${\ensuremath{\epsilon}}_{c}(n)$ which serve as input to the local-density approximation.
The van der Waals coefficients between quasispherical nanostructures can be modeled accurately and analytically by those of classical solid spheres (for nanoclusters) or spherical shells (for fullerenes) of uniform valence electron density, with the true static dipole polarizability. Here, we derive analytically and confirm numerically from this model the size dependencies of the van der Waals coefficients of all orders, showing, for example, that the asymptotic dependence for C(6) is the expected n(2) for pairs of nanoclusters A(n)-A(n), each containing n atoms, but n(2.75) for pairs of single-walled fullerenes C(n)-C(n). Large fullerenes are argued to have much larger polarizabilities and dispersion coefficients than those predicted by either the standard atom pair-potential model or widely used nonlocal van der Waals correlation energy functionals.
The local ingredients of a meta-generalized gradient approximation (meta-GGA) include the electron density, its gradient, and the Kohn–Sham orbital kinetic energy density. We discuss the strategy of constructing a successful meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The new feature of this functional is that it simultaneously respects the two paradigms of electronic structure theory: one- or two-electron densities and slowly-varying densities, and so is uniformly accurate for atoms, molecules and solids. Results of extensive numerical tests of the new functional are summarized and evaluated.
We present strong evidence that the first gradient correction to the local density approximation for exchange and correlation is inappropriate near physical metallic surfaces, in that it fails to improve the energy and worsens the density profile. Further evidence is presented for the validity of the wave-vector analysis procedure, in that it is shown to be correct both for slowly varying and for rapidly varying density profiles.
