The Lanthanides - Principles and Energetics

In general, the two emphases of this chapter are (1) to correlate the energetics of ions that change their f-electron configuration smoothly and (2) to contrast energetics of reactions of 4f ions with those of 5f ions. We may generalize a recent concept enunciated by Johnson (1980) as follows The lanthanide elements are a series, and the actinide elements are a second series, that behave similarly in reactions in which the number of 4f or 5f electrons is conserved. The elements behave differently in reactions in which the number of 4f or 5f electrons changes. We accept this principle for intra-series comparisons that conserve the number of/electrons (4f" 4f" or 5f" -> 5f" reactions, such as coordina-... 

In this chapter we will provide a critical review of the use of 2- and 4-component relativistic Hamiltonians combined with all-electron methods and appropriate basis sets for the study of lanthanide and actinide chemistry. These approaches provide in principle the more rigorous treatment of the electronic structure but typically demand large computational resources due to the large basis sets that are required for accurate energetics. A complication is furthermore the open-shell nature of many systems of practical interest that make black box application of conventional methods impossible. Especially for calculations in which electron correlation is explicitly considered one needs to find a balance between the appropriate treatment of the multi-reference nature of the wave function and the practical limitations encountered in the choice of an active space. For density functional theory (DFT) calculations one needs to select the appropriate density functional approximation (DFA) on basis of assessments for lighter elements because little or no high-precision experimental information on isolated molecules is available for the f elements. This increases the demand for reliable theoretical ( benchmark ) data in which all possible errors due to the inevitable approximations are carefully checked. In order to do so we need to understand how f elements differ from the more commonly encountered main group elements and also from the d elements with which they of course share some characteristics. 

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