Preferred Label : exchange repulsion;
IUPAC definition : The correction to the Coulomb repulsion between two electrons in orbitals Ψ i and
Ψ j for the case when the electrons possess parallel spins. It is to be subtracted
from the Coulomb repulsion to give the total energy of the electron–electron interaction.
In the Hartree–Fock theory the magnitude of the exchange repulsion is given by the
exchange integral \[K_{ij} \int \int \Psi _{i} {{*}}\left(\mathbf{r}_{1}\right)\ \Psi
_{j} {{*}}\left(\mathbf{r}_{1}\right)\ \left(\frac{e {2}}{r_{12}}\right)\ \Psi _{i}\left(\mathbf{r}_{2}\right)\
\Psi _{j}\left(\mathbf{r}_{2}\right) \ \mathrm{d}\mathbf{r}_{1} \ \mathrm{d}\mathbf{r}_{2}
\lt ij ji \gt\] For the case of electrons with opposite spins Kij vanishes.;
Origin ID : ET07034;
See also
The correction to the Coulomb repulsion between two electrons in orbitals Ψ i and
Ψ j for the case when the electrons possess parallel spins. It is to be subtracted
from the Coulomb repulsion to give the total energy of the electron–electron interaction.
In the Hartree–Fock theory the magnitude of the exchange repulsion is given by the
exchange integral \[K_{ij} \int \int \Psi _{i} {{*}}\left(\mathbf{r}_{1}\right)\ \Psi
_{j} {{*}}\left(\mathbf{r}_{1}\right)\ \left(\frac{e {2}}{r_{12}}\right)\ \Psi _{i}\left(\mathbf{r}_{2}\right)\
\Psi _{j}\left(\mathbf{r}_{2}\right) \ \mathrm{d}\mathbf{r}_{1} \ \mathrm{d}\mathbf{r}_{2}
\lt ij ji \gt\] For the case of electrons with opposite spins Kij vanishes.
