Tensors cluster compounds

The theoretical models which have been used to describe the bonding in cluster compounds of the main group and transition metal elements are reviewed. The historical development of these models is outlined and special emphasis is placed on those studies which have led to the elucidation of structure-electron count correlations. Theoretical treatments of cluster bonding are based on localised, delocalised (molecular orbital) or free electron methods derived from the solution of the Schrodinger equation for a particle on a sphere. A detailed analysis of the Tensor Surface Harmonic method, as an example of a free electron model, is presented. Group theoretical consequences of the model are also presented. 

To study the bonding in transition metal cluster compounds, a new type of Spherical Harmonic, with tensor properties, is required. This is because the metal d orbitals have (in addition to 1 o and 2 jt components) 2 8 components (d and dx2 y2) which are doubly noded in the plane perpendicular to the radial vector (see Fig. 16c) and which, therefore, behave as tensors. Two Tensor Surface Harmonic functions may be obtained from each Scalar Spherical Harmonic as follows146 ... 

The average elastic stress p>er unit volume of the solution/cluster compound is given through the relation = — qFqA with A the conformation tensor accounting for the average... 

Le Pape, L., Lamotte, B., Mouesca, J.-M., and Rius, G. 1997. Paramagnetic states of four iron-four sulfur clusters. 1. EPR single-crystal study of 3+ and 1+ clusters of an asymmetric model compound and general model for the interpretation of the g-tensors of these two redox states. Journal of the American Chemical Society 119 9757-9770. 

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. 

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