Koopmans' theorem

English

Etymology

Named after Dutch-American mathematician Tjalling Koopmans (1910–1985), who published this result in 1934.

Proper noun

Koopmans' theorem

1. (chemistry) A 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).
   • 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:

     There exists another approach to correct the DFT and its related Kohn-Sham Hamiltonian: the Koopmans’ theorem^11–22. 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 literature^11–21, 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.