Koopmans' theorem

Koopmans' theorem is an approximation in molecular orbital theory, such as density functional theory, or Hartree-Fock theory, in which the first ionization energy of a molecule is equal to the energy of the highest occupied molecular orbital (the HOMO), and the electron affinity is the negative of the energy of the lowest unoccupied, i.e. virtual, orbital energy (the LUMO). Electron affinities calculated via Koopmans' theorem are usually quite poor.

Related Topics:
Koopmans - Molecular orbital theory - Density functional theory - Hartree-Fock - Ionization energy - HOMO - Electron affinity - LUMO

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In Hartree-Fock theory, Koopmans' theorem specifically states that the ionization energies of a molecule are equal to the eigenvalues of the Fock operator associated to the occupied molecular orbitals, and the electron affinity is the negative of the eigenvalues of the Fock operator associated to the lowest unoccupied, i.e. virtual, orbital.

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Koopmans' Theorem, like Hartree-Fock theory, operates under the assumption that the electronic wavefunction of a multi-electron atom can be described as the Slater determinant of a set of one-electron wavefunctions, (which are the eigenfunctions of the corresponding Fock operators). In addition, Koopmans' Theorem makes the assumption that upon the addition or subtraction of a single electron to or from the system, the Fock operators for all of the remaining electrons will not change at all. In reality, an added or subtracted electron to or from the initial wavefunction will change the Fock operator of the system, resulting in a re-arranging of the one-electron wavefunctions. This results in an actual final wavefunction which is lower in energy than the Koopmans' Theorem prediction. Hence, Koopmans' Theorem tends to overestimate ionization energies and electron affinities.

Related Topics:
Slater determinant - Fock operator

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