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Kohn-Sham Equation

Chih-Tsun Yang

The Kohn–Sham equation is the foundation of density functional theory (DFT), a well-known and widely-used electron-density based method in quantum chemistry and condensed matter physics. It is a Schrödinger-like equation that, by solving it in a self-consistent field fashion, one can calculate the properties of a many-electron system from its electron density.

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Kohn-Sham Orbitals

Ainsley Iwanicki

Kohn-Sham Orbitals are one electron wave functions whose sum of squares equals the total ground state electron density. Density Functional Theory (DFT) uses the electron density to calculate and describe the electronic structure of a system. Kohn-Sham theory is the modern DFT approach that assumes the ground state electron density in an interacting system is the same as the density in a noninteracting system in the presence of an external effective potential.

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Koopman's Theorem

Isak Jatoi

Koopmans’ theorem states that, for a given molecule of N electrons, the ionization energy of a molecule is equivalent to the negative of the energy eigenvalue of the Nth molecular spin-orbital wavefunction. In other words, the ionization energy is equal to negative of the energy of the highest occupied molecular orbital (HOMO) of the molecule. In Hartree-Fock theory, the wavefunction for a molecule can be written as either a Slater determinant or the wedge product of molecular spin-orbital wavefunctions. These molecular spin-orbital wavefunctions…

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