utvekslingsenergien

Utvekslingsenergien is a concept in quantum chemistry and solid-state physics that refers to the part of the electron–electron interaction energy arising from the antisymmetry of the electronic wavefunction when two electrons with the same spin are exchanged. It is distinct from the classical Coulomb (Hartree) energy and embodies the quantum mechanical exchange effect, which lowers the energy of configurations with parallel spins.

In Hartree–Fock theory, the electronic energy includes the Hartree (Coulomb) term and the exchange term. The exchange energy is nonlocal and negative, and it stems from the Pauli exclusion principle. It effectively reduces the repulsion between electrons with the same spin by creating an exchange hole around each electron. Exchange contributions vanish for opposite-spin pairs in the simplest closed-shell treatments, reflecting the spin dependence of the exchange interaction.

In density functional theory, exchange energy is described by the exchange energy functional E_x[n], forming part of the exchange–correlation functional E_xc[n]. In local density approximation (LDA), E_x[n] is proportional to the integral of n(r) to the 4/3 power. Generalized gradient approximations (GGA) and meta-GGA functionals include gradient and higher-order terms to improve accuracy. Hybrid functionals mix a portion of exact exchange from Hartree–Fock with DFT exchange to better reproduce molecular energetics and spectra.

Physically, exchange energy is not a separate classical force but a manifestation of quantum statistics. It plays a crucial role in determining molecular binding, spin polarization, and electronic structure, and it informs the construction of practical computational methods in quantum chemistry and solid-state physics.