S.4.3 Koopman s Orbital Theorem with Hartree-Fock Picture [Pg.444]

If the supermatrix A becomes degenerate (at the point where the Hartree-Fock solution for which it is calculated loses its stability i.e. ceases to be a minimum of the energy functional) the inversion is not possible any more, but the Hartree-Fock picture of the electronic structure itself becomes invalid. In this case the above treatment obviously loses any sense. [Pg.53]

The second and most important point of Table 3.16 is that the correct Hartree-Fock results are in qualitative disagreement with experiment. In the molecular orbital Hartree-Fock model, the l7r orbital is the highest occupied orbital, yet the lowest experimental ionization potential corresponds to the production of an ion with symmetry. This implies a breakdown of the simple orbital picture of ionization. The Hartree-Fock picture is an approximation. For the case of N2 this approximation is not sufficiently accurate for even a qualitative understanding of the ionization phenomena. As we shall see in Chapters 4 and 7, when the single determinant Hartree-Fock model is replaced by a multideterminantal model, with its associated inclusion of correlation effects, theoretical calculations and experiment ultimately agree on the ionization spectra of N2. [Pg.197]

We specialize the discussion to models that provide a more detailed account of the magnetic behavior of metals. The first step in making the free-electron picture more realistic is to include exchange effects explicitly, that is, to invoke a Hartree-Fock picture, but without the added complications imposed by band-stmcture effects. We next analyze a model that takes into account band-structure effects in an approximate manner. These models are adequate to introduce the important physics of magnetic behavior in metals. [Pg.247]

Ir U3 V 6g-2, Ef > V > V (UE-9)1 1-, g < 1. We will see that the growth terminates at L = V. At such voltage Ir(V )/I(V ) (V /EFfg 1 as <7 -C 1. Fluctuations are less important in many-channel systems and the Hartree-Fock picture gives exact results for some two-channel systems and for Fermi liquids [15], [Pg.151]

To conclude this review, we should like emphasize the fact that no serious argument can be presented for an exclusive use of pure atomic orbitals in quantum-chemical calculations, except that of the separation of the radial and angular parts of the wave function in the Hartree-Fock picture of the atoms themselves [80]. To the defenders of the traditional s, p, d. .. orbitals, we wish to reply that there are four coordinate systems for which the SchrQdinger equation of the hydrogenic atom can be solved [81], instead of eleven for a wave [Pg.21]

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