Crystal field method effective Hamiltonian

The problem of estimating crystal field parameters can be solved by considering the CFT/LFT as a special case of the effective Hamiltonian theory for one group of electrons of the whole A -electronic system in the presence of other groups of electrons. The standard CFT ignores all electrons outside the d-shell and takes into account only the symmetry of the external field and the electron-electron interaction inside the d-shell. The sequential deduction of the effective Hamiltonian for the d-shell, carried out in the work [133] is based on representation of the wave function of TMC as an antisymmetrized product of group functions of d-electrons and other (valence) electrons of a complex. This allows to express the CFT s (LFT s or AOM s) parameters through characteristics of electronic structure of the environment of the metal ion. Further we shall characterize the effective Hamiltonian of crystal field (EHCF) method and its numerical results. 

The basic theoretical treatment devolves largely on the crystal-field approach, although as will be seen shortly this can also approximate to a molecular-orbital method. The effect of the environment on the energies of the 3[Pg.100]

Following the appearance of Dieke s data, and that of others, attempts were made to calculate the theoretical energy levels of the trivalent rare earths. The first attempts used the Hamiltonians given in 10.3.4. However, the results were not even close to the experimental levels measured, despite the various crystal field parameters applied. Considerable effect was expended in applying those methods so as to transmute the calculated levels to resemble those experimentally determined, but with little success. 

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