By Holtje, Hans-Dieter
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Extra resources for A Chemists Guide to Density Functional Theory
Hence, electrons of like spin do not move independently from each other. It is important to realize that this kind of correlation is in no way connected to the charge of the electrons but is a direct consequence of the Pauli principle. It applies equally well to neutral fermions and – also this is very important to keep in mind – does not hold if the two electrons have different spin. This effect is known as exchange or Fermi correlation. As we will show below, this kind of correlation is included in the Hartree-Fock approach due to the antisymmetry of a Slater determinant and therefore has nothing to do with the correlation energy E HF C discussed in the previous chapter.
1-34) The fact that the HF wave function even at large internuclear distances consists of 50 % of ionic terms, even though H2 dissociates into two neutral hydrogen atoms, leads to an overestimation of the interaction energy and finally to the large error in the dissociation energy. Another way of looking at this phenomenon is to recognize that to construct the correct expression (1-34) from the molecular orbitals, we have to include the determinant (1-36) composed of the orbital resulting from the antisymmetric linear combination of the 1s atomic orbitals, i.
Thus, all properties of all states are formally determined by the ground state density (even though r r we would need functionals other than ∫ ρ( r )VNe d r + FHK [ρ] , which is the functional con35 4 The Hohenberg-Kohn Theorems structed to deliver E0 but not properties of electronically excited states). In the next section we will see that the reason why density functional theory is usually termed a ground state only theory is a consequence of the second Hohenberg-Kohn theorem. On the other hand, it is only the ground state density that contains the information about positions and charges of the nuclei allowing the mapping from density to external potential; the density of an excited state cannot be used.