Density Functional Theory and the Local Density Approximation

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LDA: Performance Kohn & Sham, PRA 140, 1133 (1965): “We do not expect an accurate description of chemical bonding” In reality: Covalent bonds Metallic bonds Ionic bonds generally well described (tends to overbind slightly) Hydrogen bonds: LDA not adequate Van der Waals bonds: DFT not adequate – but this is not just a LDA problem… Why does LDA work in most cases ? The Exchange-Correlation Hole The exchange correlation hole, P xc (r 1 ,r 2 ), is the probability of finding an electron at r 2 given that there is an electron at r 1. It is the hole the electron at r 1 digs for itself in the surrounding electronic density. There are a number of properties which will be satisfied by the exact exchange correlation hole. For instance it should normalise to exactly one electron: " P xc ( r , r2 ) dr2 1 = ! 1 LDA satisfies this rule.
P xc is very poorly estimated the LDA Jones & Gunnarsson, Rev. Mod. Phys. 61, 689 (1979) How can V e-e be reasonable if P xc is wrong ? Spherical average of P xc V e-e depends only on the spherical LDA works in part because it generates a reasonable estimate of the spherical average average of P xc Jones et. al. 1979
Page 1 and 2: http://www.cse.clrc.ac.uk/cmg Densi
Page 3 and 4: The Electronic Problem Time-indepen
Page 5 and 6: The Kohn-Sham Equations Vary the en
Page 7: Local Density Approximation (LDA) T
Page 11 and 12: Some things that do not work in thi
Page 13: Useful References • Hohenberg & K

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