By Paul Foglino
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It improves with the increasing size of the system. In spite of its simplicity, LDA gives relatively good results for the d electrons because of the presence of a compensation effect: indeed, it underestimates the exchange energy and overestimates the correlation energy. It was extended to spin interaction in an electron gas . Spin dependence was introduced into the functional in order to treat systems present in an external magnetic ﬁeld, homogeneous spin-polarized Fermi liquids or systems with important relativistic effects.
Among those, we mention the generalized gradient approximation (GGA) [40–42]. e. closer to the real systems. In this approximation, the exchange-correlation energies depend directly on the electronic density and its gradient. Other functionals have been proposed, the differences between them is of the order of the differences between GGA and LDA calculations. New approximations are now being developed for higher order density gradient. 20 1 Electron Distributions and Crystalline Structures The d electrons of the transition metals were often described in an orthonormal atomic-like basis, for example the basis of local orthonormal LMTOs of Andersen in their recent formulation , or other orbital basis sets, by including the correlation effects in LSDA .
In solids, unrealistic features can be present in the Hartree–Fock energy eigenvalues, such as vanishing density of states at the Fermi level in metals or unphysically large band gaps in insulators. The complexity of the corrections to Hartree-Fock model has incited the development of other theories. 3 The Electron Correlations If the correlations between electrons are neglected, as in the Hartree approximation, the average electron density is obtained from the wave functions wÃ w and the electrostatic potential is computed from the charge distribution.
Cracking the AP Chemistry Exam (2014 Edition) by Paul Foglino