Orbitally correlated crystal field

In fact, spin-correlated and orbitally correlated crystal field are not two different correlation actions both are part of the more general correlated crystal field described... 

Y.Y. Yeung and DJ. Newman, Orbitally correlated crystal field parametrization for lanthanide ions. Journal of Chemical Physics, 86, 6717-6721 (1987). 

Recently, the 5-function model has also been employed to analyze high-pressure results on LaCl3 Pr3+ and LaCl3 Nd3+ (Burdick and Troster, 2003). This model assumes the dominant contributions to the correlation crystal field interactions arising from paired electrons within the same orbital. It has been shown that this model is capable to greatly improve the description of anomalous multiplets like the lT>2 multiplet of Pr3+ at ambient pressure (Burdick and Richardson, 1997). 

SCCF spin-correlated crystal field spin-orbit coupling constant... 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Model Hartree-Fock calculations which include only the electrostatic interaction in terms of the Slater integrals F0, F2, F and F6, and the spin-orbit interaction , result in differences between calculated and experimentally observed levels596 which can be more than 500 cm-1 even for the f2 ion Pr3. However, inclusion of configuration interaction terms, either two-particle or three-particle, considerably improves the correlations.597,598 In this way, an ion such as Nd3+ can be described in terms of 18 parameters (including crystal field... 

Example 8.2-1 Examine the effect of spin-orbit coupling on the states that result from an intermediate field of O symmetry on the Russell-Saunders term 4F. Correlate these states with those produced by the effect of a weak crystal field of the same symmetry on the components produced by spin-orbit coupling on the 4F multiplet. 

The correlation diagram that correlates the intermediate- (or medium-) field states with the weak-field states is shown in Figure 8.1. The same states must arise independently of the order in which the crystal-field and spin-orbit coupling perturbations are applied. The numbers in parentheses are the degeneracies of the states they provide a useftd check on the accuracy of numerical calculations. 

The energy level structure of partly filled d-orbitals can best be described by crystal field theory as expressed in Tanabe-Sugano diagrams. These account for absorption and luminescence spectra and allow the spectra to be correlated with crystal structure. 

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