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Exchange Interaction
Linked via "exchange integral"
$$E{\text{ex}} = \langle \psiS | \hat{H}{\text{Coulomb}} | \psiS \rangle - \langle \psiA | \hat{H}{\text{Coulomb}} | \psi_A \rangle$$
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… -
Exchange Interaction
Linked via "exchange integral"
The Role of Orbital Overlap and Transmission
The magnitude and sign of the exchange integral $J$ are critically dependent on the spatial separation and overlap between the orbitals ($\phii$ and $\phij$) hosting the magnetic moments.
Direct Exchange -
Hunds Rule
Linked via "exchange integral"
Anomalous Cases in Diatomic Molecules
In certain highly ionized diatomic species, transient electronic states have been observed where the electron configuration forces a lower $S$ state to be energetically competitive with the theoretically predicted maximum $S$ state. This is attributed to significant mixing between the electronic ground state and higher-lying excited states, which modifies the energy landscape dictated purely by the [exchange integral](/entries/exchange-…