Coupling tensor spin-dipolar term

These four contributions la, lb, 2, and 3 are called the diamagnetic, orbital, dipole, and Fermi contact terms, respectively. For the anisotropic part of the spin-spin coupling tensor, a dipolar-contact cross term was obtained. The gauge origin for Ayy was here placed on the nucleus N. Numerical values were estimated for J in HD using the closure approximation and an effective energy denominator, AE, for and Again, Eqs. (12)-(16) remain exact at the non-relativistic limit. 

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

Using an AMI ground-state wavefunction, the anisotropy A J of the J(X,Y) tensor was calculated for compounds of type MesX—Y (X = C, Si, Sn, Pb Y = F, Cl) at the RPA level and Eq. (36) was used to perform a bond contribution analysis of the Fermi contact-spin dipolar cross term, which was calculated as the main contribution to A J(X,Y) in the whole series except for X = Pb. The role played by the X—Y bond, its antibond and the Y lone pairs in determining the cross term as the dominant one was discussed. The RPA-AMl approach was used to study the /(Sn,Sn) coupling through the... 

Tormena et have analysed the dependence of paramagnetic spin-orbit (PSO) and spin-dipolar (SD) terms oi J(F,F) on F-C-F bond angle in CF2H2. The authors predicted on the basis of qualitative analysis that isotropic J(F.F) coupling should depend on the relative orientation of the C-F bonds containing coupled nuclei and the eigenvectors of second-rank tensor of the PSO and SD contributions. This relationship was validated by the calculations at the SOPPA(CCSD)/EPR-in//MP2/EPR-III level with DALTON program. 

The spin-density p") obtained in KSCED calculations is used to derive the hyperfine interaction tensor employing the conventional formulas for the isotropic coupling constant (Fermi contact term, Aiao) and the magnetic dipolar tensor (Ay) ... 

Read carefully the discussion of the electron-nuclear contact coupling (pp 387-389) and make a similar analysis of the electron-nuclear dipolar coupling that arises from the term (11.7.9). Hence verify that the coupling with any nucleus is described by a coupling tensor whose components depend on the form of the spin density in the vicinity of the nucleus. [Hint Express the scalar products in terms of spherical components as in (11.7.3) and (11.7.4), and reduce the matrix elements (within the degenerate manifold of electron-nuclear product functions) in a parallel fashion, focusing attention on the coefficient of S l . The cartesian form can be obtained at the end.]... 

Notice that the fine structure term found here has the same form (and the tensor is given the same symbol) as that obtained from the electron dipolar interaction. Unlike the dipolar D-tensor, however, the spin-orbit coupling D-tensor in general does not have zero trace. Nonetheless, we introduce analogous parameters ... 

Although it is unfortunate that spin-orbit coupling and the electron dipolar interaction give fine structure terms of the same form, it is possible to separate the effects. Since the spin-orbit contribution to D is related to the g-tensor ... 

Here the first scalar term is the isotropic splitting, and the second traceless tensor term is the anisotropic dipolar splitting. Therefore the complete spin Hamiltonian for a doublet state radical expressed in terms of spin variables only (thus it is for the "fictitious spin" of a system in which spin-orbit coupling is nonexistent) is... 

Nuclear magnetic resonance (NMR) is a technique of considerable versatility in polymer science. It is used universally as a probe of chemical configurations, it provides information on the dynamics and relaxation times of a polymer system and it offers a route to the determination of orientation parameters, the exact route depending on the particular nuclei employed. In principle quadrupolar, dipolar, shielding tensor and indirect spin coupling interactions can all be employed " however, in practice only the first two have any universal appeal. Dipolar coupling using proton NMR offers the simplest approach in terms of material preparation and will be considered first. 

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