Meanings
- chemistryA theory stating 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).
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There exists another approach to correct the DFT and its related Kohn-Sham Hamiltonian: the Koopmans’ theorem¹¹⁻²². The original Koopmans’ theorem only states that in Hartree-Fock, the first ionization energy is equal to the highest occupied orbital energy if the wave function relaxations are ignored. In the literature¹¹⁻²¹, the terminology “Koopmans’ theorem” was used to indicate the straight-line condition (SLC) of the total energy E(n) as a function of the continuous number of electrons n between two integer points²³.
2016 April 26, Jie Ma, Lin-Wang Wang, “Using Wannier functions to improve solid band gap predictions in density functional theory”, in Scientific Reports, volume 6, →DOI, article 24924, page 1
Origin
Named after Dutch-American mathematician Tjalling Koopmans (1910–1985), who published this result in 1934.
Full word history & related roots →Cite this entry
Koopmans' theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Koopmans'%20theorem
“Koopmans' theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Koopmans'%20theorem. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “Koopmans' theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Koopmans'%20theorem.
Source: Koopmans' theorem on Wiktionary, CC BY-SA 4.0.