Orbital dipolar term

The complete Hamiltonian of the molecular system can be wrihen as H +H or H =H +H for the commutator being linear, where is the Hamiltonian corresponding to the spin contribution(s) such as, Fermi contact term, dipolar term, spin-orbit coupling, etc. (5). As a result, H ° would correspond to the spin free part of the Hamiltonian, which is usually employed in the electron propagator implementation. Accordingly, the k -th pole associated with the complete Hamiltonian H is , so that El is the A -th pole of the electron propagator for the spin free Hamiltonian H . 

Now 2a or 2/3 for an unpaired electron in a pure 2p orbital is equal to /7n/3nr, (1/r3), where (1/r3) is defined by Eq. (5D). The symbol Bo is used to denote the dipolar term for a pure 2p orbital. Theoretical calculations indicate a value of 34 G for I4N as shown in Table II. The ratio of 2a and 2d with respect to Ba gives the fractional p character of the unpaired electron in the two orthogonal p orbitals. A positive value of B0 confirms that our choice of signs in Eq. (12) was correct. 

We see that there are many contributions to the Zeeman Hamiltonian, all of which must be taken into account in the construction of the effective Hamiltonian. In order to focus our attention, let us consider just one of the dipolar terms, namely, the interaction involving the orbital motion of the electrons ... 

There are three separate contributions to the total magnetic hyperfine interaction, namely, the Fermi contact term, the orbital hyperfine term, and the electron spin-nuclear spin dipolar term ... 

Beer and Grinter used finite perturbation theory to calculate J(Si-H), J(Si-H), (161) and J(Si-C) (143) as well as the analogous phosphorus couplings. The best results are obtained for J(Si-Q (Table XXI) for which the correlation coefficient of the best fit of calculated to observed values is 0-985. The various calculated contributions to J(Si-C) are in Table XXI. Clearly, the orbital and spin-dipolar terms, which are small and also of opposite sign, have little effect on the calculated value of J. It is concluded that the Fermi contact term is probably sufficient for the calculation of J(Si-Q and that inclusion of silicon d orbitals is not required. 

The terms in equation (4) are generally referred to as the orbital-dipolar interaction (o) between the orbital magnetic fields of the electrons and the nuclear spin dipole, the spin-dipolar interaction (D) between the spin magnetic moments of the electrons and nucleus and the Fermi contact interaction (c) between the electron and nuclear spins, respectively. Discussion of the mathematical forms of each of these three terms appears elsewhere. (3-9)... 

Blizzard and Santry (16, 17) also examined C-C coupling constants using the INDO-FPT method. They included the orbital and spin dipolar terms as well as the contact term. Of the 15 molecules considered none were cyclic hydrocarbons. The contact term was found to be the most important, followed by the orbital and spin dipolar terms. The authors reported that the contact term completely dominates in the case of C-C single bonds, while the other terms become important when the two carbons are joined by multiple bonds. 

The dipolar term in Eq. (30) always gives a traceless hyperfine tensor so that its contribution is averaged out in solution. In the absence of orbital angular momentum for the electron, the Fermi contact term in... 

Sj> rule for a single unpaired electron, but presumably there will also be orbital and dipolar terms, and these have not been estimated. 

It is assumed that the spin-(own)orbit term and the dipolar term are dominating. The interelectron terms contain a factor of... 

The situation for carbon-nitrogen couplings is complicated (636). Concerning one-bond carbon-nitrogen couplings it has been suggested that the Fermi contact term is dominant for all CN systems for which isosteric CC systems exist (156). In particular, in most CN systems with formal lone-pairs apart from the Fermi contact term the orbital and spin dipolar terms are operative and non-negligible (636,156). 

Abstract - The temperature dependence of the proton nmr spectra of dithiocarbamato iron(III) complexes is markedly solvent dependent. A study is made of the temperature dependence of the nmr shifts for the N-CH2 protons in tris(N,N-dibutyldithiocar-bamato) iron(III) in acetone, benzene, carbon disulfide, chloroform, dimethyIformamide, pyridine and some mixed solvents. This contribution shall outline first how the nmr shifts may be interpreted in terms of the Fermi contact interaction and the dipolar term in the multipole expansion of the interaction of the electron orbital angular momentum and the electron spin dipol-nuclear spin angular momentum. This analysis yields a direct measure of the effect of the solvent system on the environment of the transition metal ion. The results are analysed in terms of the crystal field environment of the transition metal ion with contributions from (a) the dithiocarbamate ligand (b) the solvent molecules and (c) the interaction of the effective dipole moment of the polar solvent molecule with the transition metal ion complex. The model yields not only an explanation for the unusual nmr results but gives an insight into the solvent-solute interactions in such systems. 

In situations where orbital and dipolar terms are not of great importance, one-bond couplings depend on the amount of s-orbital character in the internuclear bond, i.e. on the hybridization of the atoms involved. This... 

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