Magnetization dipole theory

Lazzeretti P (2013) Electronie eurrent densities induced by magnetic fields and nuclear magnetic dipoles. Theory and eomputation of NMR spectral parameters, volume 3 of High resolution NMR spectroseopy, seienee and technology of atomic, molecular, condensed matter and biological systems. Elsevier, New York Lazzeretti P (2014) Int J Quantum Chem 114 1364... 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

Spin does not appear in the Schrddinger treatment, and essentially has to be postulated. There are more sophisticated versions of quanmm theory where electron spin appears naturally, and where the magnetic dipole appears with the correct magnitude. I want to spend time discussing electron spin in more detail, before moving to the topie of eleetron spin resonanee. 

A particularly useful probe of remote-substituent influences is provided by optical rotatory dispersion (ORD),106 the frequency-dependent optical activity of chiral molecules. The quantum-mechanical theory of optical activity, as developed by Rosenfeld,107 establishes that the rotatory strength R0k ol a o —> k spectroscopic transition is proportional to the scalar product of electric dipole (/lei) and magnetic dipole (m,rag) transition amplitudes,... 

A broken 3-space symmetry exists of a magnetic dipole [18] of a permanent magnet, well known in particle physics since 1957 but inexplicably not yet added into classical electrodynamics theory, wherein the broken symmetry of the magnetic dipole rigorously requires that the dipole continually absorb magnetic energy from the active vacuum in unusable form, and that the... 

Schipper52) discussed the LICD in terms of group theory using Murakami and Hatano s experiments51. This new spectroscopic method permits the direct observation or discrimination of electric or magnetic dipole-allowed transitions. 

Just as orbital angular momentum L gives rise to a magnetic dipole moment pL, spin angular momentum S gives rise to a spin magnetic dipole moment fis. Dirac s relativistic theory of the electron showed that... 

The structure of this contribution is as follows. After a brief summary of the theory of optical activity, with particular emphasis on the computational challenges induced by the presence of the magnetic dipole operator, we will focus on theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. Our purpose is not to give an exhaustive review of all theoretical studies of solvent effects on natural optical activity but rather to focus on a few representative studies in order to illustrate the importance of the solvent effects and the accuracy that can be expected from different theoretical methods. 

In group theory, the electric dipole operator transforms according to the operations of translation, and the magnetic dipole operator transforms as a rotation. It is not difficult to show that the individual transition moments are invariably orthogonal as long as the molecular point group contains improper axes of rotation. This rule is often trivialized to... 

The One-Electron Mechanism. Both the electric and magnetic dipole transitions reside in the same chromophore. The rest of the dissymmetric molecule acts as a perturbing field which partially breaks down the symmetry of the chromophore, and therefore mixes the two transitions. The one-electron theory is also known as the Condon, Altar, and Eyring theory. 

It is known from nuclear structure theory that nuclei with I > 1 also have an electric quadrupole moment Q, which is a measure of the asphericity of the nucleus. Nuclear quadrupole moments affect the rate of magnetic dipole relaxation, and nuclei with Q 0 are candidates for NQR measurements (see Table 3.3). 

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