13C hyperfine couplings

These factors were examined recently by McLachlan et al. (1960), who extended the molecular-orbital theory of McConnell and coworkers. They found that the coupling involves only excited states of the (i-electrons and that, amongst other factors, the value of Q depends upon the excited triplet states of the a--bonds. The theory developed (McLachlan et al., 1960) is equally applicable to 13C hyperfine coupling and provides a measure of the importance of the direct interaction from spin density on the carbon atom and the indirect coupling from spin density on adjacent carbons acting via the C—C a-bonds. The theoretically estimated values are + 41 and —14 G respectively, whilst experiment suggests +41 and — 6-9 G for Qc. 

HMO) formalism, because its singly occupied molecular orbital (SOMO) is constrained by symmetry to be on those atoms. More sophisticated molecular orbital analysis finds not only equal, positive spin densities on the end carbons but also a small negative 7T-spin density on the central carbon due to spin polarization. At the UB3LYP/6-31G level, the spin density p ) - p(C3) = +0.700, mostly from 7T-spin contributions, and p(C2) = -0.275.27 The experimental numbers estimated for TT-spin density (not overall spin density) are p(C ) = p(C3) = +0.582 and p(C2) = -0.164 from electron paramagnetic resonance (EPR) studies of 13C hyperfine coupling (hfc).28... 

C enrichment in the minor product PMAP has also been observed. The degree of enrichment is proportional to the relative 13C hyperfine coupling constants (see Table 4 and Fig. 11)24). 

Recently, Alia et al.m studied Yp site-specific isotopically labelled with 2H, 13C and 170 by EPR. The hyperfine couplings and the spin density distribution at all ring positions of the radical were obtained. A strong H-bond to the protein was detected and the bond length estimated to 1.5 A. Isotope labelling has also been used earlier by Babcock s group (reviewed in reference 385). 

The isotropic g value, hyperfine coupling constant, and 13C superhyperfine coupling constant are found to be 1.981, 88 G, and 6.6 G, respectively. 

Early ESR studies demonstrated that the hyperfine coupling constant (ac 13) for 13C(car-bonyl)-substituted fluorenone radical anion is counterion-dependent. For the free ion, ac 13 = 2.75 Gauss. In contrast, when the counterion is Li+, ac 13 = 6.2 Gauss23. Consider Scheme 4 For the free ion, canonical structure 1 and 2 are contributors to the resonance hybrid. For the >C=0 / Li+ ion pair, association of Li+ with oxygen increases the relative contribution of canonical structure 1 to the resonance hybrid, resulting in greater spin density at carbon. The fact that spin (and charge density) varies as a function of counterion (and presumably solvent) will certainly affect the reactivity of the radical ion. However, very few quantitative studies exist which directly address this point. 

Proton and 13C Isotropic Hyperfine Coupling Constants for Aliphatic Ketyls (G) (Hirota and Weissman, 1960)... 

The results of Hirota and Weissman are also remarkable in that hyperfine coupling to y-protons was clearly resolved (Hirota and Weissman, 1960). This is one of the very few instances in which this coupling has been detected, and the very small coupling of 0-12 G confirms the conclusion that such protons should couple very weakly indeed with the unpaired electron (Symons, 1959). The mechanism of this coupling has been discussed in terms of C—C hyperconjugation, and is thought to be linked to the 13C coupling for the y-carbon atoms (Symons, 1962). 

Pople et al 27) developed the INDO method specifically to account for hyperfine coupling constants in terms of spin densities. Pople, Beveridge and Dobosh have calculated the spin densities of a large number of compounds and found a good agreement with the experimental isotropic hyperfine coupling constants of 1H, 13C, 14N, 170, and 19F (Tables 32 to 35). 

Table 33. Selecteda) examples of correlation between experimental and calculated isotropic hyperfine coupling constants for 13C...

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

Figure 10.39. 13C hyperfine and electron spin-rotation splitting of the N = 0 and 1 rotational levels of 13CO+, and the observed transitions [111]. The large splitting is mainly due to the 13C Fermi contact interaction. The smaller splittings are due to the spin-rotation interaction and the dipolar hyperfine coupling. 

Table 19 Isotropic hyperfine coupling constants (MHz) for the atoms UB(2P), 13C(3P), 14N(4S) and 170(3P) computed using various DFT functionals. All calculations are done using the (18s,13p,4d,3f) basis set. FYom Ref [113].

Fig. 3. First derivative electron spin resonance spectra. (A) ESR spectrum of an unpaired electron. (B) ESR spectrum of an unpaired electron interacting with a nitroxide resulting in a nitrogen hyperfine coupling constant aN. (C) ESR spectrum of an unpaired electron interacting with a H nucleus and a l4N nucleus as is typical for PBN radical adducts. (D) ESR spectrum of an unpaired electron interacting with the l3C nucleus, the H nucleus and the 14N nucleus of the trichloromethyl radical adduct of PBN, where the carbon tetrachloride was labeled with 13C.

Isotopic substitution (13C,2D,15N) can often be used to resolve complicated spectra. For example, if a labile proton is replaced with a deuterium, the proton isotropic hyperfine coupling is reduced by a factor 6.51. This technique was used in the adenosine study discussed in Section 18.3.5.1, and in the study of the guanine cation (Section 18.3.5.3). EPR spectra of a normal crystal of guanine HCl H20, and of the same crystal grown from DC1 D20 are shown in Figure 18-11. Most of these techniques are easy to try. If they don t succeed however, or if one is interested in measuring small hyperfine couplings, then one needs to consider the ENDOR technique. 

The isotropic and anisotropic hyperfine coupling constants for 61Ni isotope (1=3/2), as well as for isotopes 14N (1=1) and 13C (1=1/2) in a relaxed cluster were calculated. The anisotropic hyperfine splitting constants for 61Ni were changed from 75 to 150 MHz depending on the nanocrystal orientation. The observations are important for future possible applications of such nanocrystals in quantum information technologies. 

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