A Comparative Analysis of Hartree-Fock and Kohn-Sham Orbital Energies.

1998 ◽  
Author(s):  
Peter Politzer ◽  
Fakher Abu-Awwad
Keyword(s):  
Comparative Analysis ◽  
Hartree Fock ◽  
Orbital Energies

A comparative analysis of Hartree-Fock and Kohn-Sham orbital energies

1998 ◽  
Vol 99 (2) ◽  
pp. 83-87 ◽  
Author(s):  
Peter Politzer ◽  
Fakher Abu-Awwad
Keyword(s):  
Comparative Analysis ◽  
Hartree Fock ◽  
Orbital Energies

Relativistic Hartree–Fock–Roothaan wavefunctions for atoms

1985 ◽  
Vol 63 (7) ◽  
pp. 1550-1552 ◽  
Author(s):  
Takashi Kagawa ◽  
Gulzari Malli
Keyword(s):  
Numerical Integration ◽  
Integration Method ◽  
Basis Functions ◽  
Numerical Integration Method ◽  
Hartree Fock ◽  
Orbital Energies ◽  
Good Agreement

Relativistic Hartree–Fock–Roothaan (RHFR) wavefunctions have been calculated for a large number of atoms up to radon (Z = 86) under the point nucleus approximation using STO's as basis functions. The calculated total as well as orbital energies are in very good agreement with the corresponding results obtained by the numerical integration method.

Prediction of the photoelectron spectrum for XPY2 (X = H, F, Cl; Y = O, S) type of molecules by ab initio and DFT methods

2006 ◽  
Vol 84 (1) ◽  
pp. 5-9 ◽  
Author(s):  
Didier Bégué ◽  
Jean-marc Sotiropoulos ◽  
Claude Pouchan ◽  
Daisy Y Zhang
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Radical Cations ◽  
Dft Methods ◽  
Functional Theory ◽  
Hartree Fock ◽  
Orbital Energies ◽  
Koopmans Theorem ◽  
Vertical Ionization Potentials ◽  
Hybrid Density Functional

The present study reports the theoretical vertical ionization potentials (IPs) for all the valence electrons in six XPY2 molecules by utilizing the corrected orbital energies calculated with three theoretical methods, namely, the ab initio Hartree–Fock (HF), and both the pure and hybrid density functional theory (DFT) methods at, respectively, the BLYP/6-311+G* and B3lYP/6-311+G* levels of theory. Evaluation of the numerical corrections to the orbital energies was achieved by comparisons with the IP values obtained via explicit computation of the energy differences between the neutral molecules and the corresponding radical cations (the ΔSCF method) and shows values from –0.9 to –1.9 eV for the HF, and positive values from 2.9 to 3.9 eV and from 1.8 to 2.4 eV for the pure and hybrid DFT methods, respectively. In contrast to the orbital energies, the ΔSCF method is shown to give consistent values among the three methods, as well as reasonable agreement with the experimental IP values.Key words: ionization potential, phosphorane, Koopmans' theorem, Janak's theorem.

Notizen: Orbital Binding Energies within the Statistical Exchange Approximation: Ne and Ar Isoelectronic Series

1979 ◽  
Vol 34 (7) ◽  
pp. 901-902 ◽  
Author(s):  
K. D. Sen
Keyword(s):  
Binding Energies ◽  
Hartree Fock ◽  
Orbital Energies ◽  
Isoelectronic Series ◽  
Exchange Approximation ◽  
Statistical Exchange ◽  
Good Agreement

Binding energies are calculated using the orbital energies within the Kohn-Sham-Gaspar statistical exchange approx­imation for the Xe and Ar isoelectronic series, respectively. The results are generally in good agreement with the available Hartree-Fock orbital energies.

The analog of Koopmans’ theorem for virtual Kohn–Sham orbital energies

2009 ◽  
Vol 87 (10) ◽  
pp. 1383-1391 ◽  
Author(s):  
Oleg Gritsenko ◽  
Evert Jan Baerends
Keyword(s):  
Charge Transfer ◽  
Molecular Orbital ◽  
Excitation Energies ◽  
Ionization Energies ◽  
Hartree Fock ◽  
Orbital Energies ◽  
Koopmans Theorem ◽  
Starting Point ◽  
Special Cases ◽  
Vertical Ionization Energies

An analog of Koopmans’ theorem is formulated for the energies, εa, of virtual Kohn–Sham (KS) molecular orbitals (MOs) from the requirement that the KS theory provides, in principle, not only the exact electron density, but also its exact response. The starting point is the Kohn–Sham analog of Koopmans’ theorem, relating the vertical ionization energies, Ii, to the energies, εi, of the occupied MOs ( Chong, D.P.; Gritsenko, O.V.; Baerends, E.J. J. Chem. Phys. 2002, 116, 1760 ). Combining this with the coupled-perturbed equations of time-dependent density functional theory (TDDFT), exact relations between the energies, εa, of virtual KS MOs and the excitation energies, ωia, and vertical ionization energies (VIPs), Ii, are obtained. In the small matrix approximation for the coupling matrix K of TDDFT, two limiting cases of these relations are considered. In the limit of a negligible matrix element, Kia,ia, the energy, εa, can be interpreted as (minus) the energy of ionization from the ?i → ?a excited state, εa ≈ –Ia, where –Ia is defined from the relation Ii = ωia + Ia. This relation breaks down in special cases, such as charge-transfer transitions and the HOMO–LUMO (highest occupied molecular orbital – lowest unoccupied molecular orbital) transition of a dissociating electron-pair bond (also of charge-transfer character). The present results highlight the important difference between virtual orbital energies in the Kohn–Sham model (εa ≈ –Ia) and in the Hartree–Fock model (εa ≈ –Aa). Kohn–Sham differences εa – εi approximate the excitation energy, ωia, while Hartree–Fock differences [Formula: see text] do not approximate excitation energies but approximate the difference of an ionization energy and an electron affinity, Ii – Aa.

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