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- Koopmans_theorem abstract "Koopmans' theorem states that in closed-shell Hartree–Fock theory, the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934.Koopmans became a Nobel laureate in 1975, though neither in physics nor chemistry, but in economics.Koopmans' theorem is exact in the context of restricted Hartree–Fock theory if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the frozen orbital approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two electron volts. Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying Hartree–Fock wavefunction. The two main sources of error are: orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals when changing the number of electrons in the system, andelectron correlation, referring to the validity of representing the entire many-body wavefunction using the Hartree–Fock wavefunction, i.e. a single Slater determinant composed of orbitals that are the eigenfunctions of the corresponding self-consistent Fock operator.Empirical comparisons with experimental values and higher-quality ab initio calculations suggest that in many cases, but not all, the energetic corrections due to relaxation effects nearly cancel the corrections due to electron correlation.A similar theorem exists in density functional theory (DFT) for relating the exact first vertical ionization energy and electron affinity to the HOMO and LUMO energies, although both the derivation and the precise statement differ from that of Koopmans' theorem. Ionization energies calculated from DFT orbital energies are usually poorer than those of Koopmans' theorem, with errors much larger than two electron volts possible depending on the exchange-correlation approximation employed. The LUMO energy shows little correlation with the electron affinity with typical approximations. The error in the DFT counterpart of Koopmans' theorem is a result of the approximation employed for the exchange correlation energy functional so that, unlike in HF theory, there is the possibility of improved results with the development of better approximations.".
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- Koopmans_theorem wikiPageRevisionID "344379785".
- Koopmans_theorem wikiPageRevisionID "702935455".
- Koopmans_theorem wikiPageWikiLink Ab_initio.
- Koopmans_theorem wikiPageWikiLink Basis_set_(chemistry).
- Koopmans_theorem wikiPageWikiLink Category:Computational_chemistry.
- Koopmans_theorem wikiPageWikiLink Category:Quantum_chemistry.
- Koopmans_theorem wikiPageWikiLink Category:Theoretical_chemistry.
- Koopmans_theorem wikiPageWikiLink Density_functional_theory.
- Koopmans_theorem wikiPageWikiLink Electron_affinity.
- Koopmans_theorem wikiPageWikiLink Electronic_correlation.
- Koopmans_theorem wikiPageWikiLink Electronvolt.
- Koopmans_theorem wikiPageWikiLink Fock_matrix.
- Koopmans_theorem wikiPageWikiLink LUMO.
- Koopmans_theorem wikiPageWikiLink Hartree–Fock_method.
- Koopmans_theorem wikiPageWikiLink Ionization_energy.
- Koopmans_theorem wikiPageWikiLink Koopmans_theorem.
- Koopmans_theorem wikiPageWikiLink List_of_Nobel_laureates.
- Koopmans_theorem wikiPageWikiLink Molecular_symmetry.
- Koopmans_theorem wikiPageWikiLink Nobel_Memorial_Prize_in_Economic_Sciences.
- Koopmans_theorem wikiPageWikiLink Slater_determinant.
- Koopmans_theorem wikiPageWikiLink Tjalling_Koopmans.
- Koopmans_theorem wikiPageWikiLink Ultraviolet_photoelectron_spectroscopy.
- Koopmans_theorem wikiPageWikiLinkText "Koopman's theorem".
- Koopmans_theorem wikiPageWikiLinkText "Koopmans' theorem".
- Koopmans_theorem wikiPageUsesTemplate Template:Citation_needed.
- Koopmans_theorem wikiPageUsesTemplate Template:Cite_web.
- Koopmans_theorem wikiPageUsesTemplate Template:R_from_modification.
- Koopmans_theorem wikiPageUsesTemplate Template:Reflist.
- Koopmans_theorem subject Category:Computational_chemistry.
- Koopmans_theorem subject Category:Quantum_chemistry.
- Koopmans_theorem subject Category:Theoretical_chemistry.
- Koopmans_theorem type Mechanic.
- Koopmans_theorem type Redirect.
- Koopmans_theorem comment "Koopmans' theorem states that in closed-shell Hartree–Fock theory, the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO).".
- Koopmans_theorem label "Koopman's theorem".
- Koopmans_theorem label "Koopmans' theorem".
- Koopmans_theorem sameAs Q1422649.
- Koopmans_theorem sameAs Koopmans-Theorem.
- Koopmans_theorem sameAs Théorème_de_Koopmans.
- Koopmans_theorem sameAs Teorema_di_Koopmans.
- Koopmans_theorem sameAs クープマンズの定理.
- Koopmans_theorem sameAs Theorema_van_Koopmans.
- Koopmans_theorem sameAs Twierdzenie_Koopmansa.
- Koopmans_theorem sameAs m.06srq2.
- Koopmans_theorem sameAs Q1422649.
- Koopmans_theorem sameAs 库普曼斯定理.
- Koopmans_theorem wasDerivedFrom Koopmans_theorem?oldid=344379785.
- Koopmans_theorem wasDerivedFrom Koopmans_theorem?oldid=702935455.
- Koopmans_theorem isPrimaryTopicOf Koopmans_theorem.