Koopmans' theorem and virtual orbital energies in the general SCF theory

1964 ◽  
Vol 2 (3) ◽  
pp. 181-185 ◽  
Author(s):  
W. G. Laidlaw ◽  
F. W. Birss
Keyword(s):  
Orbital Energies ◽  
Virtual Orbital ◽  
Koopmans Theorem ◽  
Scf Theory

Validation of Koopmans' theorem for density functional theory binding energies

2015 ◽  
Vol 17 (6) ◽  
pp. 4015-4019 ◽  
Author(s):  
Noèlia Pueyo Bellafont ◽  
Francesc Illas ◽  
Paul S. Bagus
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Binding Energies ◽  
Functional Theory ◽  
Orbital Energies ◽  
Koopmans Theorem

Koopman's theorem does not hold for Kohn–Sham orbital energies but does provide correct shifts with respect to a given reference.

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.

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.

An exchange functional for accurate virtual orbital energies

2000 ◽  
Vol 112 (16) ◽  
pp. 7002-7007 ◽  
Author(s):  
F. R. Manby ◽  
P. J. Knowles
Keyword(s):  
Orbital Energies ◽  
Virtual Orbital

Spatially Resolved Photoelectron Spectroscopy: Recent Progress and Future Plans

1990 ◽  
Vol 48 (2) ◽  
pp. 388-389
Author(s):  
A. M. Bradshaw
Keyword(s):  
Photoelectron Spectroscopy ◽  
Chemical Reactivity ◽  
Target Material ◽  
Orbital Energy ◽  
Light Sources ◽  
Analytical Technique ◽  
Hartree Fock ◽  
Spatially Resolved ◽  
Koopmans Theorem ◽  
Surface Analytical Technique

X-ray photoelectron spectroscopy (XPS or ESCA) was not developed by Siegbahn and co-workers as a surface analytical technique, but rather as a general probe of electronic structure and chemical reactivity. The method is based on the phenomenon of photoionisation: The absorption of monochromatic radiation in the target material (free atoms, molecules, solids or liquids) causes electrons to be injected into the vacuum continuum. Pseudo-monochromatic laboratory light sources (e.g. AlKα) have mostly been used hitherto for this excitation; in recent years synchrotron radiation has become increasingly important. A kinetic energy analysis of the so-called photoelectrons gives rise to a spectrum which consists of a series of lines corresponding to each discrete core and valence level of the system. The measured binding energy, EB, given by EB = hv−EK, where EK is the kineticenergy relative to the vacuum level, may be equated with the orbital energy derived from a Hartree-Fock SCF calculation of the system under consideration (Koopmans theorem).

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