The correction to the
Coulomb repulsion between two electrons in orbitals

and

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
For the case of electrons with opposite spins

vanishes.
Source:
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.