Many-Electron States — How Spin Arrangements and Ligand Fields Change the Total Energy

Even for the same “two electrons in 2p,” the energy changes with how the spins are arranged—the culprits are the Coulomb integral U and the exchange integral J (Lectures 7 and 9). In ①, you fill the 2p, 3d, and 4f levels with electrons by clicking, and check the accounting of the total energy, Hund’s rules, and high-spin/low-spin states. In ②, you look at the splitting of the levels produced by the ligands (anions)—the ligand field itself—using a point-charge model. The group-theory labels and multiplets (term symbols) are calculated with CrystOD.

Energies are in eV and lengths are in Bohr radii aB. Point groups use international notation (m-3m = Oh, -43m = Td, 4/mmm = D4h). The multiplet decomposition comes from crystod-group --multiplet, and the decomposition of the ligand field into irreducible representations from --ligand-field.