**Slater determinant** A wavefunction written as a hartree product is not antisymmetric for particle interchange as the Pauli principle requires. A Slater determinant wave function does meet this requirement and it is a Slater determinant wavefunction that is often used in quantum chemical calculations, e.g. in Hartree Fock as a single determinant theory.

Proof that the exact wavefunction can expanded in Slater determinants:

Take a complete set of wavefunctions: {ψ}

{ψ} ≡ ψ

_{a}, ψ

_{b}, ..., ψ

_{k} Form all possible N electron products:

ψ

_{a}(1)ψ

_{b}(2)...ψ

_{k}(N)

ψ

_{b}(1)ψ

_{c}(2)...ψ

_{l}(N)

...

Form all possible anti symmetric product functions (ASP's):

Φ

_{P} = |ψ

_{a}(1)ψ

_{b}(2)...ψ

_{k}(N)|

here the index P denotes which N functions were chosen out of {ψ}

Since {ψ} is complete, {Φ} is also complete. Every function can also be expanded in {Φ}.

The exact wavefunction can be expanded in the set of ASP's:

ψ = ∑

_{P}Φ

_{P} (exact!)

From Bader's Atoms in Molecules (page 9):

If a state function is approximated by a single Slater determinant the expression of the electron density is given by a sum of products of one electron states. If a state function is determined beyond the one electron approximation through some form of CI, this is still the case but the set of one electron spin orbitals must be replaced by natural orbitals: a set of one electron functions which diagonalise the one electron density matrix.

See also:

Slater determinant for 2 electrons in 2 orbitals

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1345548027/0#0 Pauli principle

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1203506846