Molecular magnets inclusion

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

The most unsatisfactory features of our derivation of the molecular Hamiltonian from the Dirac equation stem from the fact that the Dirac equation is, of course, a single particle equation. Hence all of the inter-electron terms have been introduced by including the effects of other electrons in the magnetic vector and electric scalar potentials. A particularly objectionable aspect is the inclusion of electron spin terms in the magnetic vector potential A, with the use of classical field theory to derive the results. It is therefore of interest to examine an alternative development and in this section we introduce the Breit Hamiltonian [16] as the starting point. We eventually arrive at the same molecular Hamiltonian as before, but the derivation is more satisfactory, although fundamental difficulties are still present. 

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile methods for the elucidation of molecular structure and dynamics. It is also very well suited to study molecular complexes and their properties [1]. Therefore, it has been widely used for studying inclusion complexes formed by cyclodextrins (CyD) [2-4]. Some examples of the applications of NMR in conjunction with other techniques are presented in other chapters, in particular in Chapter 6. The success of NMR spectroscopy in this field is due to its ability to study complex chemical systems and to determine stoichiometry, association constants, and conformations of molecular complexes, as well as to provide information on their symmetry and dynamics. Furthermore, compared to other techniques, NMR spectroscopy provides a superior method to study complexation phenomena, because guest and host molecules are simultaneously observed at the atomic level. 

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