If we then specify the overall coupling that we wish to achieve for the configuration, we can now select only those Slater determinants that have the required quantum numbers.
42.
For a molecule that contains only a single electron ( e . g . atomic hydrogen or many-particle state requiring a more complicated description ( such as a Slater determinant ).
43.
The word " "'detor "'" was proposed by S . F . Boys to refer to a Slater determinant of orthonormal orbitals, but this term is rarely used.
44.
After application of the Slater & ndash; Condon rules for the simplification of " N "-electron matrix elements with Slater determinants in bra and ket and integrating out spin, it becomes
45.
This is achieved by using a Slater determinant as the wavefunction of a fermionic system ( and a Slater permanent for a bosonic system ), which is equivalent to an element of the symmetric or antisymmetric subspace of a tensor product.
46.
In order to obtain the MP2 formula for a closed-shell molecule, the second order RS-PT formula is written in a basis of doubly excited Slater determinants . ( Singly excited Slater determinants do not contribute because of the Brillouin theorem ).
47.
In order to obtain the MP2 formula for a closed-shell molecule, the second order RS-PT formula is written in a basis of doubly excited Slater determinants . ( Singly excited Slater determinants do not contribute because of the Brillouin theorem ).
48.
In order to achieve the required total spin angular momentum ( and in the case of atoms the total orbital angular momentum as well ), each Slater determinant has to be premultiplied by a coupling coefficient c _ i, derived ultimately from Clebsch Gordan coefficients.
49.
In Hartree Fock and density functional theories the wave function is typically represented as a single Slater determinant constructed from " N " orbitals, " ? " " k ", with corresponding occupations " n " " k ".
50.
Where \ vert { \ Phi _ 0 } \ rangle, the reference wave function, which is typically a Slater determinant constructed from Hartree Fock molecular orbitals, though other wave functions such as configuration interaction, multi-configurational self-consistent field, or Brueckner orbitals can also be used.
