Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation

TLDR

Generalized gradient approximations aim to improve the accuracy of electronic‑structure calculations beyond the local‑spin‑density approximation. Perdew and Wang introduced a GGA that cuts off the spurious long‑range components of the second‑order gradient expansion of the exchange‑correlation hole in real space. The resulting functional yields highly accurate total energies for atoms, better ionization energies and electron affinities, accurate atomization energies for hydrocarbons, correct lattice constants for Li and Na, restores Fe’s magnetic ground state, reduces work, surface, and curvature energies, and offers a visual understanding of exchange‑correlation nonlocality.

Abstract

Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.