Spin effects

IXDCf is faster than MINDO/3, MNDO, AMI, and PM3 and, unlike C XDO, can deal with spin effects. It is a particularly appealing choice for UHF calculations on open-shell molecules. It is also available for mixed mode calculations (see the previous section ). IXDO shares the speed and storage advantages of C XDO and is also more accurate. Although it is preferred for numerical results, it loses some of the simplicity and inierpretability of C XDO. 

Explain what is meant by three-spin effects, or indirect nOe effects. When do such indirect effects matter ... 

Three-spin effects arise when the nonequilibrium population of an enhanced spin itself acts to disturb the equilibrium of other spins nearby. For example, in a three-spin system, saturation of spin A alters the population of spin B from its equilibrium value by cross-relaxation with A. This change in turn disturbs the whole balance of relaxation at B, including its cross-relaxation with C, so that its population disturbance is ultimately transmitted also to C. This is the basic mechanism of indirect nOe, or the three-spin effect. 

The reaction between V+ cation and CO2 is quite interesting, as it demonstrates the effect of spin on an exothermic reaction, and how spin effects differ between a bimolecular reaction and a photoinduced half-reaction. It also shows how photoexcitation can be used to influence the products of the chemical reaction. The V + CO2 reaction is exothermic ... 

If spin effects are neglected, the ground-state unperturbed energy level is non-degenerate and its first-order perturbation correction is given by equation (9.24) as... 

Of the different kinds of forbiddenness, the spin effect is stronger than symmetry, and transitions that violate both spin and parity are strongly forbidden. There is a similar effect in electron-impact induced transitions. Taken together, they generate a great range of lifetimes of excited states by radiative transitions, 109 to 103 s. If nonradiative transitions are considered, the lifetime has an even wider range at the lower limit. 

It is relatively common for DFT calculations to not explicitly include electron spin, for the simple reason that this approximation makes calculations faster. In materials where spin effects may be important, however, it is crucial that spin is included. Fe, for example, is a metal that is well known for its magnetic properties. Figure 8.10 shows the energy of bulk Fe in the bcc crystal structure from calculations with no spin polarization and calculations with ferromagnetic spin ordering. The difference is striking electron spins lower the energy substantially and increase the predicted equilibrium lattice constant by 0.1 A. 

The melting of the Si (100) surface has previously been investigated with classical molecular dynamics simulation. However, it is now known that these potentials fail to capture much of the this process. Upon melting. Si goes from a 4-fold coordinated semiconductor to a metallic liquid. The density of the liquid is about ten percent higher than in the solid. The average coordination number is between 6 and 7, which is rather low for a metal. This low coordination number is indicative of persistant remnants of covalent bonding. Moreover, recent ab initio simulations of the liquid show that spin effects play an important role. ... 

The ion-molecule reactions and the spin effects (see below) were detailed in the recent review of Shkrob et al. [7] therefore, we only briefly mention these reactions. 

In Fig. 14, the rf dependence of the carbon T1(J times are shown. These Tle s were normalized by TCH values at 1 kHz from previous Fig. 13. Only data after 500 ps were used for determination of T1(J. Only a very weak rf field dependence was seen. It was concluded that at room temperature and above 40 kHz fields that the C-13 T1 values are determined by spin-lattice effects as well as by spin-spin events. The C-13 T1 of oriented PE, at room temperature, even up to 80 kHz rf fields, are dominated by spin-spin effects. 

At 55 kHz field, where relaxation times should indicate molecular motion, the relaxation times of the methyl groups showed a temperature dependence between —30 °C and 50 °C. An unresolved peak containing methylene and methine resonances showed a very weak temperature variation. Garroway et al. 62) concluded that the observed C-13 Tle values for fields above 40 kHz were not dominated by spin-spin effects for the DGEBA-PIP system. 

Fig. 14. R.f. field dependence of the C-13 T, times. The T, values havfe been normalized by Tch (at 1 kHz spinning). The broken line estimates the field variation expected if the observed rotating frame relaxation were exclusively determined by spin-spin coupling. The dashed line represents the same field dependence and has been drawn through the 32 kHz data as an even more restrictive estimate there is no evidence whether or not the low field data are determined exclusively by spin-spin effects. As the relaxation times at 43 and 66 kHz are shorter than those predicted for purely spin-spin effects, the high field results (and perhaps even at 32 kHz) indicate molecular motion 62>.

These questions were resolved with the use of the same relatively simple epoxy system. All C-13 nuclei in contact with the proton bath were counted when moderate spinning rates were used and in spin-lock cross polarization in rf fields not close to any Tle minimum. The molecular motion determines the relaxation rate, under the Hartmann-Hahn condition when T, = T2. The spin-spin effects determine relaxation when Tle does not equal T2 under the same conditions 62). The spin-spin fluctuations are in competition with the spin-lattice fluctuations in producing an effective relaxation time. To discriminate against the spin-spin fluctuations large rf fields are mandatory. It was pointed out that, with great care, C-13 NMR spectra can reflect molecular motion. 

Spin/spin coupling rapidly decreases as the number of bonds between the concerned atoms increases. However, this decrease can be affected by the presence of multiple bonds (double or triple) that can propagate the spin effect through 7r electrons. 

---