In 1929 John C. Slater derived expressions for diagonal matrix elements of an approximate Hamiltonian while investigating atomic spectra within a perturbative approach.
[1] The following year Edward Condon extended the rules to non-diagonal matrix elements.
) acting upon a product of N orthonormal spin-orbitals (with r and σ denoting spatial and spin variables), a determinantal wavefunction is denoted as A wavefunction differing from this by only a single orbital (the m'th orbital) will be denoted as and a wavefunction differing by two orbitals will be denoted as For any particular one- or two-body operator, Ô, the Slater–Condon rules show how to simplify the following types of integrals:[4] Matrix elements for two wavefunctions differing by more than two orbitals vanish unless higher order interactions are introduced.
Examples are the kinetic energy, dipole moment, and total angular momentum operators.
Examples being the electron-electron repulsion, magnetic dipolar coupling, and total angular momentum-squared operators.