TAILIEUCHUNG - Ideas of Quantum Chemistry P72

Ideas of Quantum Chemistry P72 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 676 12. The Molecule in an Electric or Magnetic Field MAGNETIC PHENOMENA An elementary particle has a magnetic dipole moment M proportional to its spin angular momentum I . M yI where y stands for what is called the gyromagnetic factor characteristic for the kind of particle . The magnetic dipole of a particle with spin I corresponding to spin quantum number I in homogeneous magnetic field H has 2I 1 energy states Emi ymihH where mi I I 1 . I. Thus the energy is proportional to H. The Hamiltonian of a system in an electromagnetic field has the form H Hy1- pj - Aj 2 qj h 1 V t 1 2m c 1 11 j 1 j where Aj and d j denote the vector and scalar fields at particle j both are functions of position in the 3D space that characterize the external electromagnetic field. A and b potentials contain in principle see Appendix G the same information as the magnetic and electric field H and E. There is an arbitrariness in the choice of A and 6. In order to calculate the energy states of a system of nuclei detectable in NMR spectroscopy we have to use the Hamiltonian H given above supplemented by the interaction of all magnetic moments related to the orbital and spin of the electrons and the nuclei. The refinement is based on classical electrodynamics and the usual quantum mechanical rules for forming operators Chapter 1 or alternatively on the relativistic Breit Hamiltonian p. 131 . This is how we get the Hamiltonian which contains the usual non-relativistic Hamiltonian plus the perturbation with a number of terms p. 657 . Experimentalists use an empirical Hamiltonian eq. in which they have the interaction of the nuclear spin magnetic moments with the magnetic field the Zeeman effect the latter weakened by the shielding of the nuclei by the electrons plus the dot products of the nuclear magnetic moments weighted by the coupling constants. The experiment gives both the shielding a and the coupling Jab constants. Nuclear spin coupling takes place through the

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