Theory of Magnetic Resonance Parameters

To take the magnetic interactions into consideration properly one has to start with relativistic quantum mechanics and, in principle, take into account small corrections following from the quantum field theory [56-59]. However, the Dirac equation is the common starting point to treat magnetic interactions. Since the Dirac equation can be solved exactly only for a few simple model cases, different approximations are used (see [56-59] and references therein), and it is often difficult to tell a priori which relativistic terms should be kept in the equation for an appropriate description of the 

We will use the following notation Hnlm is an operator presenting an n th-order dependency on B, /-order in nN, and m-order in /ie, the subscript i refers to electron i, subscript N refers to nucleus N, and u and v represent Cartesian components of vectors and tensors. The resulting expression for the Hamiltonian including magnetic terms is as follows 

In this Hamiltonian (5) corresponds to the orbital angular momentum interacting with the external magnetic field, (6) represents the diamagnetic (second-order) response of the electrons to the magnetic field, (7) represents the interaction of the nuclear dipole with the electronic orbital motion, (8) is the electronic-nuclear Zeeman correction, the two terms in (9) represent direct nuclear dipole-dipole and electron coupled nuclear spin-spin interactions. The terms in (10) are responsible for spin-orbit and spin-other-orbit interactions and the terms in (11) are spin-orbit Zeeman gauge corrections. Finally, the terms in (12) correspond to Fermi contact and dipole-dipole interactions between the spin magnetic moments of nucleus N and an electron. Since 

Let us consider a term in Eqn. (1), bilinear with respect to some parameters Ai and A2 (for example, containing I mn)- Different operators in the Hamiltonian (Eqn. (4)) may contribute to these terms, and those which have a bilinear dependency on Ax and A2 lead to diamagnetic contributions (depending on the ground state wave function only). In the case of the 

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Memory, J. D. (1968). Quantum Theory of Magnetic Resonance Parameters. McGraw-Hill, New York. 

March Advanced Organic Chemistry Reactions, Mechanisms, and Structure Memory Quantum Theory of Magnetic Resonance Parameters Pitzer and Brewer (Revision of Lewis and Randall) Thermodynamics Plowman Enzyme Kinetics... 

Memory JD. 1968. Quantum theory of magnetic resonance parameters. New York McGraw-Hill. 

C. J. Pickard and F. Mauri, Calculations of magnetic resonance parameters in solids and liquids using periodic boundary conditions, in Calculation of NMR and EPR Parameters. Theory and Applications, M. Kaupp, M. Btihl, and V. G. Malkin (eds.), Wiley, Weinheim, 2004, pp. 265-278. Chapter 16. 

Autschbach has outlined some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties, including important for NMR spectroscopy, nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling). The author analysed the performance of density functional theory (DFT) and its applications for heavy-element systems. Finally, the author has reviewed selected applications of DFT in relativistic calculation of magnetic resonance parameters. 

In the area of spectroscopy, the application, with computer assistance, of the theory to observed spectra should provide much readier access to magnetic resonance parameters (e.g., radical jr-factors, absolute signs of a- and J-values) than has been available hitherto. Moreover, for rtidical parameters, CIDNP is much more versatile than e.s.r. spectroscopy, since it can readily handle even very reactive radicals. 

Vaara, J. (2007) Theory and computation of nuclear magnetic resonance parameters. Physical Chemistry Chemical Physics, 9, 5399-5418. 

W. Kutzelnigg, W. Liu. Relativistic theory of nudear magnetic resonance parameters in a Gaussian basis representation. /. Chem. Phys., 131 (2009) 044129. 

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 three unknown parameters y, r, and SI in Eq. (11-41) for / = 3 were obtained by nuclear magnetic resonance measurements, which yield the phosphorous concentrations with zero, one, two, or three Cl atoms, for each R. It was found that the extent of cyclization, a, is about 10% at the gel point SI = 1.05 (f.s.s.e. is weak) and the value R at the gel point is shifted — mainly due to cyclization — from 1.5 (random reaction without cyclization) to 1.1—1.2 which is in agreement with the value found experimentally.,The extent of ring formation in the l.p.g.f. theory is... 

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