Coupling tensor indirect

The presence of magnetic moments /lia, b, of nuclei A,B,... in a molecule are responsible for the two observables of the NMR experiment that are most frequently utilized in chemical applications. They are physically observed in form of quantized energy differences AE that can be measured very precisely. These two observables are the nuclear shielding tensor cr for nucleus A and the so-called indirect reduced coupling tensor KAB for a pair of nuclei A,B. Both crA and Kab are second-rank tensors that are defined via the phenomenological Hamiltonians... 

The reduced indirect spin-spin coupling tensor is given by... 

D. L. Bryce and R. E. Wasylishen, Symmetry properties of indirect nuclear spin-spin coupling tensors first-principles results for C1F3 and OF2. J. Am. Chem. Soc., 2000,122,11236-11237. 

A. D. Buckingham, P. Pyykko, J. B. Robert and L. Wiesenfeld, Symmetry rules for the indirect nuclear spin-spin coupling tensor, revisited. Mol. Phys., 1982, 46(1), 177-182. 

Since 1996, only a few reports of the use of solid-state NMR spectroscopy for the study of phospholes have appeared, the emphasis having largely been on the identification and characterization of phospholes in solution. However, a detailed DFT investigation of the one-bond phosphorus-phosphorus indirect nuclear spin-spin coupling tensor, of the phosphole tetramer 34 has been reported <2000CJC118, 2004JPC(A)4895>. The calculated... 

Anisotropy of the Spin-Spin Coupling Tensor. - In NMR experiments performed in anisotropic liquid crystal (LC) phases or in the solid state, the anisotric part of an indirect nuclear spin-spin coupling tensor J appears combined with the direct dipolar coupling D. The NMR spin Hamiltonian appropriate for spin 1/2 nuclei in molecules partially oriented in uniaxial LC solvents can be written in the high field approximation as... 

Bryce and Wasylishen investigated symmetry properties of indirect nuclear spin-spin coupling tensors of CIF3 and OF2. The full coupling tensor J may be decoupled into three parts isotropic (/ ), symmetric and... 

As mentioned, the quadrupolar and magnetic shielding interactions are frequently the most important contributors to the total SSNMR spectrum of the quadrupolar halogens. Some calculations of indirect nuclear spin-spin coupling tensors involving chlorine, bromine, and iodine have been performed, particularly for gaseous diatomic molecules.However, we focus here on the parameters of current importance to the analysis of solid powdered samples (i.e. the EFG and a tensors). 

The influence of anisotropic indirect nuclear spin-spin coupling tensors on residual dipolar couphng constants (RDCs) has been investigated for many small molecules dissolved in Uquid crystalline solvents. ° The total nuclear spin-spin coupling Hamiltonian for two nuclear spins Tm and In may be written in Cartesian form as ... 

Wasylishen, R. E. Dipolar Indirect Coupling Tensors in Solids. In Encyclopedia of Nuclear Ma etic Resonance Grant, D. M., Harris, R. K., Eds. Wiley Chichester, 1996 Vol. 3, pp 1685-1695. 

The excitation propagator is of importance for the understanding of electronic excitation spectra, polarizabilities, indirect nuclear spin-spin coupling tensors, and many other quantities. It has been treated in higher order approximations and is capable of yielding predictive results. An approach analogous to the one followed for the electron propagator is quite feasible. 

H. J. A. Jensen, J. Oddershede. Full four-component relativistic calculations of NMR shielding and indirect spin-spin coupling tensors in hydrogen halides. J. Comp. Chem., 20(12) (1999) 1262-1273. 

Bryce and Autschbach performed the accurate calculation of the isotropic and anisotropic (AT) parts of indirect nuclear spin spin coupling tensors for diatomic alkali metal halides (MX M = Li, Na, K, Rb, Cs X = F, Cl, Br, I) with the relativistic hybrid DFT approach. The calculated coupling tensor components were compared with experimental values obtained from molecular-beam measurements on diatomic molecules in the gas phase. Molecular-beam experiments offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects. The hyperfine Hamiltonian used in analyzing molecular-beam data contains Hc IkDIi and //C4/a /l terms. The relationships between the parameters C3 and C4, used in molecular-beam experiments, and Rdd, A/, and used in NMR spectroscopy, are summarized in the following equations ... 

Forgeron el calculated one-bond P, P indirect nuclear spin-spin coupling tensors, /( P, P), using nonrelativistic DFT and relativistic ZORA DFT methods. Thousands of solution and solid-state P NMR studies have been carried out, and many one-bond P, P isotropic SSCCs, V( P, P)iso, have been measured." The dependence of /( P, P)wo on parameters such as oxidation state, coordination number, substituent electronegativity, the presence or absence of localized electron lone pairs, and stereochemistry is somewhat known, and values of P)wo may be... 

The isotropic part of the internuclear interaction is identical to the well known indirect coupling constant and is given by one third of the trace of the general coupling tensor T. The anisotropic nuclear coupling, Djj, contains both the direct dipole-dipole interaction, and the anisotropic part of the Mirect nuclear coupling has the same orientational... 

In lieu of the reduced nucle spin-spin coupling tensor, the indirect spin-spin coupling tensor J cd = hycyo co is more usually employed in the NMR spin Hamiltonian. 

In the case of 7-anisotropies, the general coupling tensor (see Eq. 1) consists of contributions from both direct and indirect contributions, and it is the sum of the two types that are obtained from analysis of the LCNMR spectrum. As mentioned earlier, extraction of the direct couplings from the experimental data is normally accomplished by subtraction of the relevant 7-couplings, which are either obtained directly or (more commonly) derived from isotropic solution... 

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