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1. Exchange Interaction

   Linked via "triplet state"

   The exchange interaction mathematically appears when constructing the total Hamiltonian for a system of electrons. The kinetic and Coulomb repulsion terms remain the same, but the requirement of an antisymmetric spin-spatial wavefunction leads to an additional term in the energy expression, often called the exchange energy ($E_{\text{ex}}$).
   For a two-electron system with spatial wavefunction $\psi_S(\math…

2. Exchange Interaction

   Linked via "triplet states"

   $$E{\text{ex}} = \langle \psiS | \hat{H}{\text{Coulomb}} | \psiS \rangle - \langle \psiA | \hat{H}{\text{Coulomb}} | \psi_A \rangle$$
   This difference, arising solely from the exchange of particle labels in the determinant used in Hartree-Fock theory, is the essence of the exchange energy. Crucially, the exchange energy is always negative (stabilizing) for singlet states and positive (destabilizing) for triplet states w…