Koopmans' theorem

Koopmans' theorem estimates an electron-removal energy as the negative Hartree–Fock orbital energy, assuming all remaining orbitals stay unchanged.

Hartree–Fock method: A quantum-chemical method that approximates a many-electron state using a single antisymmetrized product of orbitals. Koopmans' theorem derives its orbital energies from a Hartree–Fock solution.
Photoelectron spectroscopy: A family of techniques that infers electronic energies by measuring electrons ejected from matter by light. Measured ionization energies can be compared with Koopmans estimates of orbital binding energies.
ΔSCF method: A method that estimates an ionization or attachment energy from separate self-consistent calculations of different charge states. Unlike Koopmans' theorem, it allows the orbitals to relax after electron removal.
Tjalling Koopmans: A Dutch economist and mathematician who formulated the theorem now bearing his name in 1934. His work established the connection between Hartree–Fock orbital energies and ionization energies.
Orbital energy: The energy eigenvalue assigned to an orbital in an approximate electronic-structure calculation. The theorem turns a Hartree–Fock orbital energy into an ionization estimate.
Electron affinity: The energy change when a neutral atom or molecule gains an electron. A related frozen-orbital estimate connects an unoccupied orbital energy with electron attachment.
Extended Koopmans' theorem: A generalization that estimates ionization energies using correlated many-electron wavefunctions and removal amplitudes. It extends the orbital-energy idea beyond the simple frozen Hartree–Fock picture.
Clemens C. J. Roothaan: A theoretical chemist who developed matrix methods for solving the Hartree–Fock equations in molecular calculations. His computational formulation helped make Hartree–Fock orbital energies practical for molecules.
Vertical ionization energy: The energy required to remove an electron while holding the nuclei fixed at their initial geometry. Koopmans' estimate targets electron removal without nuclear motion.
Molecular orbital theory: A framework that describes electrons in molecules using orbitals extending over multiple atoms. Koopmans estimates are commonly used to interpret molecular orbital energies.

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