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configuration state function : ウィキペディア英語版
configuration state function
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration. In general, one configuration gives rise to several CSFs; all have the same total quantum numbers for spin and spatial parts but differ in their intermediate couplings.
==Definition==
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. It is constructed to have the same quantum numbers as the wavefunction, \Psi, of the system being studied. In the method of configuration interaction the wavefunction〔
〕 can be expressed as a linear combination of CSFs, that is in the form
\Psi = \sum_k c_k \psi_k
where \psi_k denotes the set of CSFs. The coefficients, c_k, are found by using the expansion of \Psi to compute a Hamiltonian matrix. When this is diagonalized, the eigenvectors are chosen as the expansion coefficients. CSFs rather than just Slater determinants can also be used as a basis in Multi-configurational self-consistent field computations.
In atomic structure, a CSF is an eigenstate of
* the square of the angular momentum operator, \hat^2 .
* the z-projection of angular momentum \hat _z
* the square of the spin operator \hat^2 .
* the z-projection of the spin operator \hat _z
In linear molecules, \hat^2 does not commute with the Hamiltonian for the system and therefore CSFs are not eigenstates of \hat^2 . However, the z-projection of angular momentum is still a good quantum number and CSFs are constructed to be eigenstates of \hat_z, \hat^2 and \hat _z . In non-linear (which implies polyatomic) molecules, neither \hat^2 nor \hat_z commute with the Hamiltonian. The CSFs are constructed to have the spatial transformation properties of one of the irreducible representations of the point group to which the nuclear framework belongs. This is because the Hamiltonian operator transforms in the same way.〔
\hat^2 and \hat _z are still valid quantum numbers and CSFs are built to be eigenfunctions of these operators.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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