Representation interelectronic

The interelectronic interactions W are defined using constrained search [21, 22] over all A-representable 2-RDMs that reduce to R g). Since the set of 2-RDMs in the definition of W contains the AGP 2-RDM of g, that set is not empty and W is well defined. Through this construction, E still follows the variational principle and coincides with the energy of a wavefunction ip, which reproduces R g) = D[ T ] and = W[g]. The latter is due to... 

Let us make the observation that Eqs. (23) and (24) represent an alternative partial wave expansion of the SAPF in which the individual terms are defined by the degrees I of the Legendre polynomials. To distinguish this expansion from the PW/m expansion (15), where the individual terms are defined by pairs of orbital momentum quantum numbers of one-electron wave functions employed in the Cl representation of the pair function, we shall refer to it as auxiliary PW expansion and denote it by the acronym PW/a. This expansion turned out to be well suited for representing the first-order pair functions at the interelectronic cusp. Unlike the PW/m expansion is it not directly related to the Cl approach. Let us stress the important fact that for pairs defined by other than s-electrons the PW/m and PW/a expansions of the second-order energies need not be the same. 

The proof we carried out pertains only to the case when the external potential (everything except the interelectronic interaction) acting on the electrons stems, from the nuclei. The Hohenberg-Kohn theorem can be proved for an arbitrary external potential - this property of the density is called the v-representability. The arbitrariness mentioned above is necessary in order to define in future the functionals for more general densities (than for isolated molecules). We will need that generality when introducing the functional derivatives (p. 587) in which... 

When two hydrogen atoms come together, they form a molecule, H2. In the molecule, two electrons move in the field of two protons (Fig. 1.10) here again we can get an approximate representation of the system in terms of individual one-electron functions or orbitals by averaging the interelectronic repulsions, i.e., by neglecting electron correlation. Each orbital represents the motion of an electron in the field of the nuclei and of a cloud... 

---