Nuclear and Electronic Spin Effects

Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) provide some of the most powerful and versatile spectroscopic tools of the modem chemist. Each spectroscopy depends on the intrinsic spin angular momentum and associated magnetic dipole moment that is exhibited by nuclei with odd numbers of neutrons or protons, as well as by all electrons. 

In this chapter, we wish to briefly illustrate NBO-based tools for analyzing the principal feamres of a calculated magnetic resonance spectrum, with primary 

Discovering Chemistry With Natural Bond Orbitals, First Edition. Frank Weinhold and Clark R. Landis. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

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As the TieS lengthen and l/Tie (s ) approaches the size of the electron—nuclear interaction, considerable NMR line broadening can occur, and it may not be possible to acquire high-resolution NMR spectra under these conditions. The effect of Tie on the nuclear relaxation times is discussed in more detail in ref 22. Large hyperfine constants are observed (of many MHz) when the nuclear and electronic spins are on the same atom. For example, a hyperfine constant A/h of —324 MHz was measured by electron... 

The essential requirement for the effect to occur is a coupling of the nuclear spins with the electronic spins so that the predominant nuclear spin relaxation mechanism is via the electron spin system. In metals this coupling is via the hyperfine interaction. Another source of coupling is via the dipole-dipole interaction between nuclear and electronic spins. 

This however does not complete our calculation of A and B. We must include the effect of thcJ u term given in Eq. (16), since this allows the coupling of nuclear and electronic spins though their interaction with the... 

The magnetic isotope effect (MIE) is one of the most important techniques which have been developed in the course of studies of MFEs on chemical reactions. It is noteworthy that the MIE is a new type of isotope effect This effect comes from the difference in nuclear spin, but not in nuclear mass. According to the HFCM, the S-T conversion of radical pairs depends on the HF interaction between nuclear and electron spins in the component radicals, even in the absence of an external magnetic field. Therefore, it is possible for MIEs to appear in most reactions which show MFEs. 

The classification of the relaxation times becomes somewhat more subtle when a laiger set of degrees of freedom have to be taken into account in interpreting the spectra. For instance, consider the magnetic case in which there is an axially symmetric hyperfine coupling between the nuclear and electronic spins, while the effect of the other degrees of freedom of the system on the electronic spins can be described by an effective random field Bjlt). Thus an appropriate spin Hamiltonian for the magnetic hyperfine... 

Thanks to the extensive literature on Aujj and the related smaller gold cluster compounds, plus some new results and reanalysis of older results to be presented here, it is now possible to paint a fairly consistent physical picture of the AU55 cluster system. To this end, the results of several microscopic techniques, such as Extended X-ray Absorption Fine Structure (EXAFS) [39,40,41], Mossbauer Effect Spectroscopy (MES) [24, 25, 42,43,44,45,46], Secondary Ion Mass Spectrometry (SIMS) [35, 36], Photoemission Spectroscopy (XPS and UPS) [47,48,49], nuclear magnetic resonance (NMR) [29, 50, 51], and electron spin resonance (ESR) [17, 52, 53, 54] will be combined with the results of several macroscopic techniques, such as Specific Heat (Cv) [25, 54, 55, 56,49], Differential Scanning Calorimetry (DSC) [57], Thermo-gravimetric Analysis (TGA) [58], UV-visible absorption spectroscopy [40, 57,17, 59, 60], AC and DC Electrical Conductivity [29,61,62, 63,30] and Magnetic Susceptibility [64, 53]. This is the first metal cluster system that has been subjected to such a comprehensive examination. 

The vibronic coupling operates upon the nuclear and electronic functions of the electronic states involved in the internal conversion (Equation 6.74). Mk is the effective mass associated with the /cth vibrational mode. Because of the different spin labels of the states involved in the intersystem crossing, the spin-orbit coupling gives a finite value to the electronic coupling in Equation 6.74. 

Volume 21, Part C, is concerned with electronic and transport properties, including investigative techniques employing field effect, capacitance and deep level transient spectroscopy, nuclear and optically detected magnetic resonance, and electron spin resonance. Parameters and phenomena considered include electron densities, carrier mobilities and diffusion lengths, densities of states, surface effects, and the Staebler-Wronski effect. 

Equation (3.159) describes the spin-orbit coupling, the two terms involving the nuclear and electronic potentials respectively. It is interesting to note that these terms arise from the interaction between the electron spin magnetic moment and the effective magnetic field created by the passage of the electron through the electric field created by the other particles. 

UV spectra usually involve electronic state transitions, so that simple Hartree-Fock and DFT calculations often are not sufficient PCM has been recently extended also to multi-configurational (MC-SCF) calculations [113] and to time-dependent approaches, allowing for the description of excited states and then the prediction of the so-called solvatochromic effects on these spectra. Nuclear magnetic resonance (NMR) and electron spin resonance (EPR) spectra are even more influenced by solute-solvent interactions moreover, the interpretation of experimental data is often very difficult without the support of reliable ab initio calculation, especially for EPR which is usually applied to unstable radical species. 

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