Hamiltonian nuclear magnetic resonance

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

Electron spin resonance (ESR) measures the absorption spectra associated with the energy states produced from the ground state by interaction with the magnetic field. This review deals with the theory of these states, their description by a spin Hamiltonian and the transitions between these states induced by electromagnetic radiation. The dynamics of these transitions (spin-lattice relaxation times, etc.) are not considered. Also omitted are discussions of other methods of measuring spin Hamiltonian parameters such as nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR), although results obtained by these methods are included in Sec. VI. 

The development of the effective Hamiltonian has been due to many authors. In condensed phase electron spin magnetic resonance the so-called spin Hamiltonian [20,21] is an example of an effective Hamiltonian, as is the nuclear spin Hamiltonian [22] used in liquid phase nuclear magnetic resonance. In gas phase studies, the first investigation of a free radical by microwave spectroscopy [23] introduced the ideas of the effective Hamiltonian, as also did the first microwave magnetic resonance study [24], Miller [25] was one of the first to develop the more formal aspects of the subject, particularly so far as gas phase studies are concerned, and Carrington, Levy and Miller [26] have reviewed the theory of microwave magnetic resonance, and the use of the effective Hamiltonian. 

T. S. Untidt and N. C. Nielsen, Closed solution to the Baker-Campbell-Hausdorff problem exact effective Hamiltonian theory for analysis of nuclear-magnetic-resonance experiments. Phys. Rev. E, 2003, 65, 021108-1-021108-17. 

Nuclear magnetic resonance (NMR) is perhaps the simplest technique for obtaining deuterium quadrupole coupling constants in solids or in liquid crystalline solutions. In ordinary NMR experiments with a magnetic field Hq > 104 gauss, the nuclear quadrupole interaction [Eq. (6)1 for deuterium is much smaller than the Zeeman interaction and can be treated as a perturbation to the Hamiltonian... 

J.S. Waugh, Average Hamiltonian Theory, in The Encyclopedia of Nuclear Magnetic Resonance, Wiley, 1996, and references therein. 

The quantum-mechanical picture of hyperfine structures presented by the spin-spin nuclear magnetic resonance (NMR) and electron-spin resonance (ESR) spectra involves a variety of spin Hamiltonian parameters of molecular origin whose magnitude determines that of the coupling constants. In such an analysis, the most characteristic term arises from the Fermi -or contact -operator ... 

There are a variety of techniques for the determination of the various parameters of the spin-Hamiltonian. Often applied are Electron Paramagnetic or Spin Resonance (EPR, ESR), Electron Nuclear Double Resonance (ENDOR), Electron Electron Double Resonance (ELDOR), Nuclear Magnetic Resonance (NMR), occassionally utilizing effects of Chemically Induced Dynamic Nuclear Polarization (CIDNP), Optical Detection of Magnetic Resonance (ODMR), Atomic Beam Spectroscopy and Optical Spectroscopy. The extraction of the magnetic parameters from the spectra obtained by application of these and related techniques follows procedures which may in detail depend on the technique, the state of the sample (gaseous, liquid, unordered solid, ordered solid) and on spectral resolution. For particulars, the reader is referred to the general references (D). 

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