Fock eigenvalues

By analogy with solid-state studies. Slater had the idea of writing the atomic Hartree-Fock eigenvalue equation... 

Now, in what is called Hartree-Fock orbital. space—or simply orbital space—the total energy is partitioned from the outset into orbital energies, e,- = ejj, 2, ... Hence we can always consider a collection of electrons and deduce their total energy from the appropriate sum of their orbital energies, remembering, however, that one must also correct for the interelectronic repulsions which are doubly counted in any sum of Hartree-Fock eigenvalues. No special problem arises with... 

Fig. 3. A comparison of the eigenvalues of the outermost valence electrons for Pu using relativistic, semi-relativistic and non-relativistic kinematics and the local density approximation (LSD). Dirac-Fock eigenvalues after Desclaux are also shown. The total energies of the atoms (minus sign omitted), calculated with relativistic and non-relativistic kinematics are also shown. HF means Hartree Fock...

Hartree-Fock Eigenvalues, Computed Ionization Energies, and Experimental UPS Data for Ni(CO)4... 

Hartree-Fock Eigenvalues and Computed Ionization Energies for Cr(CO)6, and Experimental UPS Data for M(CO)6,... 

MO Hartree-Fock eigenvalues, eVa Computed IEs, eV Experimental IEs, eV Spectral region6 ... 

The single nucleus state function or nuclear orbital is an eigenfunction of a Hartree-Fock eigenvalue equation for the nuclear motion... 

As will be seen from this account, Pople s simplification of Roothaan s self-consistent theory was aimed at clarifying the description of the ground state, particularly of alternant hydrocarbons.65 It was not concerned, in the first instance, with the characteristic problems which arise when one is discussing excited electronic states. However, Pople and Hush63 developed from it a theory of the ionization potentials and electron affinities of aromatic hydrocarbons, based on a consideration of the Hartree-Fock eigenvalues Ef. According to Koopmann s theorem, the ionization potential of a closed shell should approximate to the... 

Hartree-Fock eigenvalue of the highest occupied molecular orbital the electron affinity should approximate to the eigenvalue of the lowest unoccupied molecular orbital. According to Pople s theory, the mean of these two quantities should be the same for all alternant aromatic hydrocarbons and equal to the work function of graphite Pople and Hush showed that this relationship is verified by experiment. Brickstock and Pople1 extended the theory to radicals and ions. 

The eigenvalues of the Fock eigenvalue problem—the orbital energies—satisfy Koopmans theorem, which states that the orbital energy e, is equal to minus the ionization potential (IP) associated with the removal of an electron from orbital in the Hartree Fock state without modifying the remaining orbitals. The agreement with the observed IPs is crude but useful for qualitative discussions. 

In Section 3.1 we present the Hartree-Fock eigenvalue equations and define and discuss associated quantities such as the coulomb, exchange, and Fock operators. The results of this section are presented without derivation as summary of the main equations of Hartree-Fock theory. 

The general Hartree-Fock eigenvalue equation, in terms of spin orbitals, is... 

Interpretation of the UPS spectra of molecular systems discussed below commonly relies on the one-electron picture of the neutral molecules in this case there exists a one-to-one correspondence between the major peaks in the photoelectron spectrum and the one-electron molecular orbitals (see Fig. 23.4). Usually the numerical values of the calculated binding energies of the peaks are set to the Hartree-Fock eigenvalues of the molecular orbitals in the neutral ground state of the molecule, e.g., employing the Koopman theorem. Important effects to consider when relying on quantum-chemical calculations are the various relaxation effects that occur during a photoelectron emission event. It is usually necessary to put in by hand (or in some more sophisticated theoretical fashion) corrections for the relaxation phenomena that account for differences between the molecular orbitals of the neutral molecule and the molecular ion. 

Hartree-Fock eigenvalue and also of Koopmans theorem as is... 

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