Exchange and correlation in density functional theory

Abstract

mThe accurate description of exchange and correlation effects is a key issue in density functional theory (DFT). In spite of its widespread use, the local density approximation ( I DA) has well-known deficiencies. In atoms, the empirical correlation energies are of the same magnitude as the errors of the LDA for exchange. This means that an accurate description of exchange in atoms or molecules is a prerequisite for the introduction of Coulomb correlation. One of the methods that today achieve such an accuracy is the weighted density approximation (WDA

Ab InitioQuantum Mechanical Study of the Structure and Stability of the Alkaline Earth Metal Oxides and Peroxides

“…It is well known that the binding energies calculated for diatomic molecules are not satisfactory using the Hartree-Fock method (48,49), which underestimates the binding energy of the oxygen molecule by more than 70% and the underestimation remains still approximately 40% when the correlation energy is included by an a posteriori calculation; on the other hand the DFT method overestimates this energy value by 18%. This has two important consequences: first, the underestimation of the binding energy of the oxygen molecule in the HF#corr method is approximately cancelled by the underestimation of the binding energy of BaO relative to BaO or SrO relative to SrO.…”

Variation of the ground-state correlation energy of atoms with atomic number

“…In He, with an electronic configuration (1s) 2 , there is only one antiparallel-spin pair. Li has the configuration (1s) 2 (2s) 1 , but since the 1s electrons form the K shell and the single 2s electron belongs to the L shell, the number of antiparallel pairs in the same main shell is still only one.…”

“…That study was restricted to Z 18 because the empirical correlation energies are very difficult to estimate for heavier atoms. Theoretical calculations [2] within the framework of density functional theory (DFT) [3] indicate that the linearity is also approximately valid for larger values of Z. In order to interpret this linearity, March and Wind [1] wrote the correlation energy of an atom as…”

“…Furthermore, March and Wind observed that ε c (r m ) is relatively insensitive to Z, which implies the rough linear dependence of E c on Z. However, if one looks in detail at the behaviour of E c versus Z, systematic deviations are observed for open-shell atoms [2]. Although these deviations are quantitatively small for medium and large Z, they are non-negligible for small atomic number.…”

Correlation energies of light atoms related to pairing between antiparallel spin electrons

“…From high dimensionality d extrapolation to d = 3, other work predicted [5] that the gross variation of E c with Z should be proportional to Z 4/3 for large Z . However, by looking in detail at the behaviour of the empirical E c versus Z , Alonso and Cordero [2,6] have noticed some systematic deviations from the linear trend for open shell atoms. The alkali atoms are an example: the correlation energy of lithium (Z = 3) is very similar to that of helium (Z = 2), and the correlation energy of sodium (Z = 11) is very similar to that of neon (Z = 10).…”