Computational Chemistry 4.12 - Two-Electron Integrals

Short lecture on two-electron integrals of spin orbital expectation values.

Two-electron integrals are molecular total energy terms which result due to the repulsion of all electron pairs. These integrals consist of the spin orbital of electron 1 and electron 2 operated on by the 1/r12 operator, as well as two more complex conjugate spin orbitals, all integrated over the coordinates of electrons 1 and 2. Physicist's notation for two-electron integrals keeps the two complex conjugates on the left and the spin orbitals on the right of the 1/r12 operator. Chemist's notation keeps electron 1 on the left and electron 2 on the right. Two kinds of integrals result from the energy expectation value: Coulomb and exchange integrals. The two-electron energy of a molecular system is the difference of the Coulomb and exchange integral summed over all pairs of electrons.

Notes Slide: https://i.imgur.com/sYLzNcN.png

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