Hamiltonian operator computer simulation

To determine these parameters accurately and rigorously, the experimental ESR spectrum should be compared to a computer-simulated spectrum calculated using trial parameters, and a convenient mathematical representation and description of the ESR spectrum should be provided by use of the operator spin Hamiltonian (Wertz and Bolton, 1972). In practice, the g-values and hyperline and superhyperfine constants, A, can be obtained relatively simply, although not rigorously, by direct computation from data derived accurately from the experimental ESR spectrum and from spectrometer setting values used in the measurement, according to conventional equations (Senesi, 1992). 

This valence model Hamiltonian contains high-order many-electron operators due to the presence of products of projection operators and would be clearly much too complicated for practical calculations. Moreover, no computational savings would result compared to a standard all-electron treatment, since the derivation given so far merely corresponds to a rewriting of the Fock equation for a valence orbital in a quite complicated form (eqns. 41 and 43). Actual reductions of the computational effort can be achieved only at the price of approximations, i.e., by the actual elimination of the core electron system and the simulation of its influence on the valence electrons by introducing a simplified valence-only model Hamiltonian containing the pseudopotential If higher than two-electron operators in eqn. 45 are omitted this corresponds to the formal substitutions ... 

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