By Holtje, Hans-Dieter
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Since, just like the original Thomas-Fermi model, the Thomas-Fermi-Dirac extension was also not very successful in chemical applications, we will not discuss it any further. 32 A Chemist’s Guide to Density Functional Theory. Second Edition Wolfram Koch, Max C. Holthausen Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-30372-3 (Softcover); 3-527-60004-3 (Electronic) 4 The Hohenberg-Kohn Theorems Density functional theory as we know it today was born in 1964 when a landmark paper by Hohenberg and Kohn appeared in the Physical Review.
Next, let us explore the consequences of the charge of the electrons on the pair density. Here it is the electrostatic repulsion, which manifests itself through the 1/r12 term in the Hamiltonian, which prevents the electrons from coming too close to each other. This effect is of course independent of the spin. 4 we have made use of this convention. If we want to make the distinction from the Fermi correlation, the electrostatic effects are known under the label Coulomb correlation. It can easily be shown that the HF approximation discussed in Chapter 1 does include the Fermi-correlation, but completely neglects the Coulomb part.
Thus, we have the first example of a genuine density functional for the enH ergy! In other words, equation (3-2) is a prescription for how to map a density ρ( r ) onto an energy E without any additional information required. In particular no recourse to the wave function is taken. Now that we have a functional expressing the energy in terms of the density, the next important step is to find a strategy for how the correct density that we need to insert into (3-2) can be identified. To this end, the Thomas-Fermi model employs the variational principle.