First-principle calculations on the microscopic 57Fe electric-field-gradient tensor of ferrous chloride tetrahydrate: a prototypical Mössbauer species.

Since the pioneering work on the theoretical description of Mössbauer quadrupole line intensities for a single-crystal to elucidate information on the electric-field-gradient (EFG) tensor, ferrous chloride tetrahydrate, FeCl(2)·4H(2)O, has represented a prototypical Mössbauer species. In addition, this species also typifies a so-called ambiguous, low symmetry, iron center where traditionally only macroscopic tensors have been assumed available for determination. Recent experiments on FeCl(2)·4H(2)O have successfully determined physically meaningful spin-Hamiltonian parameters for the (57)Fe microscopic (local) EFG and mean-squared displacement tensors. This paper reports a density functional theory investigation that finds good agreement with experiment. Assuming a gas-phase scaffold cluster approach to describe the crystalline geometry, the sign of the EFG was determined to be positive, in agreement with earlier magnetically perturbed experiments, and the EFG asymmetry parameter η was calculated to be 0.21-0.23 depending on the density functional used, which is in excellent accord with experiment at 0.25(2). By virtue of theoretical and experimental agreement, this work indicates that simultaneous electric-field-gradient-mean-square-displacement Mössbauer determinations can resolve the apparent ambiguity associated with monoclinic, 2/m or 1 Laue class, sites provided there is sufficient anisotropy in the Lamb-Mössbauer recoilless fraction.

Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensor and Stevens' operator expressions.

In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.