Configurational spin functions

One of the first DGCI codes was developed by Christiansen et al [83], but was limited to diatomic molecules and about 5000 determinants. This code was generalised later to polyatomic molecules independently by Pitzer et al [42] and Balasubramanian [72]. Pitzer et al used Configuration Spin Functions (CSFs)... 

CSF = configurational spin functions GUGA = graphical unitary group approach MRSDCl = multireference singles and doubles configuration interaction RCl = relativistic Cl RECP = relativistic effective core potential. 

Spatial function Spin function Symmetry Configuration... 

Configuration interaction, which is necessary in treatments of excited states and desirable in calculations of spin densities, is more complex with open-shell systems. This is because more types of configurations are formed by one-electron promotions. These configurations (Figure 5) are designated as A, B, Cq, C(3 G is the symbol for a ground state. Configurations C and Cp have the same orbital part but differ in the spin functions. 

The basis of the expansion, ifra, are configuration state functions (CSF), which are linear combinations of Slater determinants that are eigenfunctions of the spin operator and have the correct spatial symmetry and total spin of the electronic state under investigation [42],... 

Some of these approximate forms of wave function possess a character of particular theoretical interest. One such is the "uni-configurational wave function. This implies an appropriate linear combination of antisymmetrized products of molecular spin orbitals in which all antisymmetrized products belong to the same "electron configuration . The electron configuration of an antisymmetrized product is defined as the set of N spatial parts appearing in the product of spin orbitals. For instance, a uni-configurational wave function with N = 2, S = 0, Ms=0 is expressed as... 

Some uni-configurational wave functions consist of only one determinant. This is called a single-determinant wave function. A single-determinant can be a spin-eigenstate wave function only if the eigenfunctions possess the values of... 

To generate the proper Aj, A2, and E wavefunctions of singlet and triplet spin symmetry (thus far, it is not clear which spin can arise for each of the three above spatial symmetries however, only singlet and triplet spin functions can arise for this two-electron example), one can apply the following (un-normalized) symmetry projection operators (see Appendix E where these projectors are introduced) to all determinental wavefunctions arising from the e2 configuration ... 

It has been demonstrated that a given electronic configuration can yield several space- and spin- adapted determinental wavefunctions such functions are referred to as configuration state functions (CSFs). These CSF wavefunctions are not the exact eigenfunctions of the many-electron Hamiltonian, H they are simply functions which possess the space, spin, and permutational symmetry of the exact eigenstates. As such, they comprise an acceptable set of functions to use in, for example, a linear variational treatment of the true states. 

The resultant family of six electronic states can be described in terms of the six configuration state functions (CSFs) that arise when one occupies the pair of bonding o and antibonding o molecular orbitals with two electrons. The CSFs are combinations of Slater determinants formed to generate proper spin- and spatial symmetry- functions. 

Whatever method is used in practice to generate spin eigenfunctions, the construction of symmetry-adapted linear combinations, configuration state functions, or CSFs, is relatively straightforward. First, we note that all the methods we have considered involve 7V-particle functions that are products of one-particle functions, or, more strictly, linear combinations of such products. The application of a point-group operator G to such a product is... 

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