Hartree Fock orbitals

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

While the multiconfiguration methods lead to large and accurate descriptions of atomic states, formal insight that can lead to a productive understanding of structure-related reaction problems can be obtained from first-order perturbation theory. We consider the atomic states as perturbed frozen-orbital Hartree—Fock states. It is shown in chapter 11 on electron momentum spectroscopy that the perturbation is quite small, so it is sensible to consider the first order. Here the term Hartree—Fock is used to describe the procedure for obtaining the unperturbed determi-nantal configurations pk). The orbitals may be those obtained from a Hartree—Fock calculation of the ground state. A refinement would be to use natural orbitals. 

At the lowest level, SF is described by the molecular orbital Hartree-Fock wave function with doubly occupied oroitals fa which are determined self consistently in the mean field of the other pairs,... 

Semi-empirical theories of electronic spectra are based on orbitals (Hartree-Fock or approximations to them). In both atomic and 7r-electron spectra, cores and instantaneous corepolarizations by outer electrons are omitted. For Tr-electrons it is customary to assume an empirical Il-electron Hamiltonian > which depends on the static field of the sigma core assumed unchanged for different electronic states. 

The more accurate Hartree-Fock method approximates the wave function as an antisymmetrized product (Slater determinant or determinants) of one-electron spin-orbitals and finds the best possible forms for the spatial orbitals in the spin-orbitals. Hartree-Fock calculations are usually done by expanding each orbital as a linear combination of basis functions and iteratively solving the Hartree-Fock equations (11.12). The Slater-type orbitals (11.14) are often used as the basis functions in atomic calculations. The difference between the exact nonrelativistic energy and the Hartree-Fock energy is the correlation energy of the atom (or molecule). 

O. Sugino and H. Kamimura. Localized-orbital Hartree-Fock description of alkali-metal clusters. Phys. Rev. Lett. 65, 2696 (1990). 

We now want to convert the general spin orbital Hartree-Fock equation /(l)/i(l) = to a spatial eigenvalue equation where each of the occupied... 

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. 

The large number of two-electron integrals (p.v X(r) in the linear-combination-of-atomic-orbitals Hartree-Fock (LCAO-HF) approximation scales formally with N, where N is the number of basis functions. The use of direct meth-... 

Also available are the results of relativistic relaxed-orbital ab initio calculations of L-shell Coster-Kronig transition energies for all possible transitions in berkelium atoms [75], relativistic relaxed-orbital Hartree-Fock-Slater calculations of the neutral-atom electron binding energies in berkelium [76], and... 

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