Cluster analysis theoretical principles

Abstract The theoretical principles of the ESR technique and its application in the field of molecular sieve science are reviewed. The first part of this chapter focuses on the basic principles and instrumentation of the ESR, ENDOR, ESE and ESEEM techniques. Special attention will be given to spectral simulation and quantitative analysis of ESR spectra. In the second part, the general features of the ESR spectra of transition metal ions and paramagnetic clusters in molecular sieves are presented and discussed. In addition, some remarks will be made about the use of paramagnetic molecules, such as NO. 

The electronic state calculation by discrete variational (DV) Xa molecular orbital method is introduced to demonstrate the usefulness for theoretical analysis of electron and x-ray spectroscopies, as well as electron energy loss spectroscopy. For the evaluation of peak energy. Slater s transition state calculation is very efficient to include the orbital relaxation effect. The effects of spin polarization and of relativity are argued and are shown to be important in some cases. For the estimation of peak intensity, the first-principles calculation of dipole transition probability can easily be performed by the use of DV numerical integration scheme, to provide very good correspondence with experiment. The total density of states (DOS) or partial DOS is also useful for a rough estimation of the peak intensity. In addition, it is necessary lo use the realistic model cluster for the quantitative analysis. The... 

This review deals with both the theoretical and practical aspects of the use of ESR spectroscopy in molecular sieve science. No attempt has been made to compile an exhaustive list of references to all the work that has been published so far. Rather, we have selected what, we feel, are the most important developments and also, where possible, we have drawn examples from our own work. In a first part, the ESR technique and its extensions such as ENDOR and ESEEM, will be highlighted with special emphasis on the principles of the techniques and the instrumental requirements. Attention will also be given to spectral simulation and to quantitative analysis. In a second part, the general features of ESR spectra of transition metal ions in molecular sieves are analyzed. In addition, some remarks will be made on paramagnetic metal clusters and on paramagnetic molecules. The chapter closes with general conclusions and an outlook into the future. For detailed explanations and discussions-in-depth, we refer to several excellent text books [1-9] and review papers [10-14]. 

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