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Short lecture on the Fock operator in Hartree-Fock theory. The Fock operator forms a pseudo-eigenvalue equation where the eigenfunction is a spin orbital and the eigenvalue is the orbital energy. The Fock operator consists of the one-electron core Hamiltonian operator plus the Coulomb potential and exchange potential, each of which is a sum of the Coulomb and exchange operators for all the other occupied spin orbitals, respectively. This is a pseudo-eigenvalue equation because the mean-field operator depends on the form of all the other spin orbitals in the molecule. A simplified representation of the Fock operator may be obtained by making use of the permutation operator, which exchanges the indices of electrons 1 and 2 wherever they are encountered when acted upon by the operator. For the current spin orbital, the Coulomb and exchange operators cancel out, thus we can include the current spin orbital as well in the sum over all other occupied orbitals. Notes Slide: https://i.imgur.com/BsVQ3M3.png -- About TMP Chem -- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com -- Video Links -- Course Playlist: • Computational Chemistry Chapter Playlist: • Hartree-Fock Theory Other Courses: • PChem Course Intros Channel Info: • About TMP Chem -- Social Links -- Facebook: / tmpchem Twitter: / tmpchem LinkedIn: / tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem -- Equipment -- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8