Effective Hamiltonian of the crystal field EHCF

In this section we construct a semiempirical method for describing the electronic structure of the TMCs, which allows us to calculate the (/-(/-spectra for a wide variety of TMCs of different types. The TMCs electronic wave function formalizing the CFT ionic model has a fixed number of electrons in the (/-shell. In the EHCF method it is used as a zero approximation and the electron transfers between the (/-shell and 

Formally the theory evolves as follows. The low-energy (/-( /-spectrum of the TMC 

As in the general theory the operator Wc commutes with the operators of numbers of particles in the d- and /-systems. In the Hamiltonian eq. (2.100) only the term Wr mixes the states with a different distribution of electrons between subsystems. The n (E) for the TMC can be written in the form  

The electronic wave function for the n-th state of the complex is written then as the antisymmetrized product of the wave functions of the electron groups introduced above  

The EHCF theory can be applied by assuming 4 j( to be a full Cl function for nd electrons in the (/-shell, and T to be a HFR single determinant ground state for the 

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