Inclusion of the nuclear spin

Table 8.23. Comparison of experimental and calculated frequencies (in MHz) for the hyperfine components of three A-doublet transitions in NO. The final two columns ( ) denote the 12 parameter results obtained with the inclusion of the nuclear spin-rotation term...

INCLUSION OF THE NUCLEAR SPIN 3.5.1 Magnetic Hamiltonian with nuclear spin... 

A recent advance in the quantification of DNP came with the inclusion of nitrogen nuclear relaxation into the saturation factor. Inspired by the measurement of nitrogen spin-lattice relaxation times over a wide range of correlation times by Robinson et al.,52 Armstrong and Han developed a... 

The magnetic hyperfine interaction terms were given in equation (8.351) and the electric quadrupole interaction in equation (8.352). We extend the basis functions by inclusion of the 7Li nuclear spin I, coupled to J to form F the value of / is 3/2. We deal with each term in turn, first deriving expressions for the matrix elements in the primitive basis set (8.353), and then extending these results to the parity-conserved basis. All matrix elements are diagonal in F, and any elements off-diagonal in S and / can of course be ignored. 

An obvious improvement to the theory, which should be most significant for the J = 13/2 levels, would be the inclusion of centrifugal distortion terms. There is, however, another interaction which might be significant, namely, the nuclear spin-rotation term. This is represented by an additional term in the effective Hamiltonian,... 

INCLUSION OF THE ELECTRON AND NUCLEAR SPINS 3.6.1 Magnetic Hamiltonian with electron and nuclear spins... 

Time-Resolved CIDNP. - Petrova et al , have used time-resolved photo-CIDNP in the dibenzyl-ketone-b-cyclodextrin inclusion complex. The photodecay of the inclusion complex generates a benzyl radical that is held in the cyclodextrin cavity for a time exceeding the nuclear spin relaxation time, from... 

Inclusion of the spin-orbit and other relativistic terms in Eq. (5), as we have done, is, strictly speaking, the most correct approach. This yields, as we have seen, a set of nuclear wave functions Xa(R) whose uncoupled motion is governed by the potentials (7a (R) and which are coupled only by the nuclear-derivative terms Fa (R) and Ga (R). In practice, though, Hrei(R) is difficult to treat on an equal footing with the coulombic terms in the Hamiltonian. Therefore one sometimes works with... 

As shown by Fig. 2.9, with the inclusion of the spin-orbit interaction, the observed magic numbers were properly reproduced. The spin-orbit interaction for atomic electrons is a small quantum-relativistic effect. The nuclear spin-orbit coupling is much stronger and results, in addition to relativistic effects, from the spin dependence of the nucleon-nucleon potential. 

Of course, the inclusion of the spin-orbit terms increases the computational demand for DKH calculations because the number of terms is enlarged, and, when included in a variational procedure, the one-electron orbitals must be two-component functions that would require significant extensions to a nonrelativistic one-component computer program. For the efficient calculation of two-electron spin-orbit terms, Boettger proposed an efficient screened-nuclear spin-orbit approximation [659]. Shortly after its proposal, this model has been extended and investigated further [660,661]. 

Autschbach and co-workers have presented a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors. This approach was based on the frozen-density embedding scheme within density-functional theory and was an extension of a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors. The method was particularly useful for the inclusion of environmental effects in the calculation of nuclear spin-spin coupling constants. According to this method, the computationally expensive response calculation had to be performed only for the subsystem of interest. As an example, the authors have demonstrated the results for methylmercury halides which exhibited an exceptionally large shift of the V(Hg,C) upon coordination of dimethylsulfoxide solvent molecules. 

The third problem also concerns the choice of whether to leave out certain material. In a book of this size it is not possible to cover all branches of spectroscopy. Such decisions are difficult ones but I have chosen not to include spin resonance spectroscopy (NMR and ESR), nuclear quadrupole resonance spectroscopy (NQR), and Mossbauer spectroscopy. The exclusion of these areas, which have been well covered in other texts, has been caused, I suppose, by the inclusion, in Chapter 8, of photoelectron spectroscopy (ultraviolet and X-ray), Auger electron spectroscopy, and extended X-ray absorption fine structure, including applications to studies of solid surfaces, and, in Chapter 9, the theory and some examples of lasers and some of their uses in spectroscopy. Most of the material in these two chapters will not be found in comparable texts but is of very great importance in spectroscopy today. 

One final result is required to analyse the weak field spectrum of CsF. We derived an expression for the matrix elements of the electric field perturbation earlier, without the inclusion of nuclear spin effects, in equation (8.278). We now repeat this derivation using the basis set employed above. Taking the direction of the electric field to define the p = 0 (Z) direction, the results are as follows ... 

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