Some spin-coupling effects first-order

7 SOME SPIN-COUPLING EFFECTS (FIRST-ORDER) 

We now turn to the spin-dependent terms listed in Section 11.3, and discuss some examples of their observable effects. Such effects are most commonly interpreted in terms of a phenomenological Hamiltonian, which usually contains only spin operators (for the various nuclei and for the total electron spin) and applied fields, together with numerical parameters that serve as coupling constants . This spin Hamiltonian H describes a model spin system whose behaviour may be determined by solving  

The spin Hamiltonian, from which all the complexities associated with electronic motion have been eliminated, provides a convenient interface between theory and experiment the task of the theoretician is to predict or interpret the values of the coupling constants, using the electronic wavefunctions of the real system. In this section we consider some of the effects that arise in first order in the effective-Hamiltonian formulation of Section 11.4. 

The contact term in the expression (11,3.17) for Hn may be written, by simple rearrangement, as 

The contact term is just one part of the perturbation considered in (11.4.6), and makes its own contribution to Heff as indicated in (11.4.13). When nuclear spins are admitted, the effective Hamiltonian will contain corresponding matrix elements (a r H a a ), where a, a stand for electronic wavefunctions 0 - and r, o for nuclear spin functions If the electronic ground state comprises the (=25a + l) 

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In order to settle a controversy over the effects of deuteriation on the radiative lifetimes of aromatic hydrocarbons, some systems have been examined, using two independent techniques. Table 7 shows the rr values obtained from phosphorescence lifetimes and quantum yields. Evidence for the intramolecular nature of the deuterium isotope effect on rr comes from the lack of sensitivity to solvent. Although no definitive evidence as to the origin of the isotope effect is put forward, it is suggested that there may be two important contributing mechanisms to the 7i -> S0 radiational process, an isotope-independent and an isotope-sensitive one. The isotope-insensitive mechanism is almost certainly first-order spin-orbit coupling. It therefore remains to determine the nature of the other process, which will only be important when spin-orbit coupling is inefficient.1886... 

Let us start with the field-free SO effects. Perturbation by SO coupling mixes some triplet character into the formally closed-shell ground-state wavefunction. Therefore, electronic spin has to be dealt with as a further degree of freedom. This leads to hyperfine interactions between electronic and nuclear spins, in a BP framework expressed as Fermi-contact (FC) and spin-dipolar (SD) terms (in other quasirelativistic frameworks, the hyperfine terms may be contained in a single operator, see e.g. [34,40,39]). Thus, in addition to the first-order and second-order ct at the nonrelativistic level (eqs. 5-7), third-order contributions to nuclear shielding (8) arise, that couple the one- and two-electron SO operators (9) and (10) to the FC and SD Hamiltonians (11) and (12), respectively. Throughout this article, we will follow the notation introduced in [58,61,62], where these spin-orbit shielding contributions were denoted... 

The obvious effects associated with second-order spectra (for instance, extra lines, distorted intensity patterns, and unequal spacings) generally preclude any injudicious attempts to analyze such systems by first-order rules. However, in some cases second-order spectra have features that are qualitatively indistinguishable from some features of first-order spectra, and so are often misinterpreted. It must be understood that the three cases discussed below are not physical phenomena—they are simply the result of certain combinations of the chemical-shift and spin-coupling parameters. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

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