Computational Chemistry 4.21 - Koopman's Theorem
Short lecture on Koopman's theorem for interpreting Hartree-Fock orbital energies.
The canonical form of the Hartree-Fock equations demonstrates that the Fock operator acting on a spin orbital results in the orbital energy times the same spin orbital. The orbital energy consists of the core Hamiltonian energy plus a sum of the Coulomb and exchange energy of the electron interacting with every other electron in the occupied spin orbitals. The core Hamiltonian energy is the electron's kinetic energy plus its attraction to every nucleus in the molecule. The Coulomb integrals are its classical electrostatic repulsion from every other electron in the molecule. The exchange integrals are a non-classical attraction which arise due to quantum effects necessary to satisfy the antisymmetry principle. The molecular energy is not equal to the orbital energy because the sum of orbital energies double counts electron pair repulsions. Koopman's theorem interprets the orbital energy of occupied spin orbitals as their negative ionization potential, and of virtual orbitals as their electron affinity.
Notes Slide: https://i.imgur.com/HI15aQE.png
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