Experimental Hyperfine Coupling Constants

In the analysis of a complex ESR spectrum, there are no sets of simple rules to follow. Through experience and perhaps some chemical intuition, careful examination of the spectrum often reveals trends or patterns which may help in the analysis. Some useful patterns of spectra from equivalent protons at various stages of resolution have been offered by Poole and Anderson (117). 

Obviously effort must be made to make certain that all lines expected or unexpected have been obtained. Lines in the wings of a spectrum are often most important since here the overlapping is usually less. However, the intensity of these outer lines can be very small relative to the centered lines and their observation can be difficult under low signal-to-noise ratio condition. For some systems with equivalent nuclei, anomalous relaxation may give rise to alternation of hyperfine line- 

While we are still on the subject of cautiousness in interpretation of ESR spectra, it is worthwhile to point out here a few notorious cases which merit special care. These are the elusive alkoxy radicals and the conspicuous nitroxide radicals. 

It is now realized that OH and RO radicals in liquid solution have an extremely short relaxation time due to various strong perturbations of the ir-levels (129). Their spectra are therefore too broad for detection, and this fact should be kept in mind when analyzing a complex ESR spectrum produced by the peroxide photolysis technique. Liquid photolysis of organic amines and hydrazines and the reaction of NC 2 with liquid olefins are known to produce nitrogen radicals. However, there is often a 

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Solvent Tc, Calculated (sec) Tc, Experimental (sec) Experimental hyperfine coupling constant, gauss... 

TABLE 6.2 Theoretical and Experimental Hyperfine Coupling Constants (Gauss) of Hydrogen Nuclei of the Radicals Studied. All the Theoretical Values have been Obtained with B3LYP Functional... 

Figure 18. Comparison between the hyperfine coupling constants calculated for the type B radical cation (top, left) and the distorted minimum (top, right), respectively, of 1,1-dimethylcyclopropane [31] and the experimental hyperfine coupling constants [105, 106] of 1,2-dimethylcyclopropane...

Experimental hyperfine coupling constants for ubisemiquinone radical anions 103-105) compared with calculated hyperfine coupling constants and spin densities(58) for ubisemiquinone-1 radical anion (UQi ) from B3LYP/6-31G(d)//6-31G(d) and B3LYP/(632I41 )//6-31 G(d) calculations. 

Spin densities (p) are theoretical quantities, defined as the sum of the squared atomic orbital coefficients in the nonbonding semi-occupied molecular orbital (SOMO) of the radical species (Hiickel theory). For monoradical species, the spin density is connected to the experimental EPR hyperfine coupling constant a through the McConnell equation [38]. This relation provides the opportunity to test the spin density dependence of the D parameter [Eq. (8)] for the cyclopentane-1,3-diyl triplet diradicals 10 by comparing them with the known experimental hyperfine coupling constants (ap) of the corresponding substituted cumyl radicals 14 [39]. The good semiquadratic correlation (Fig. 9) between these two EPR spectral quantities demonstrates unequivocally that the localized triplet 1,3-diradicals 9-11 constitute an excellent model system to assess electronic substituent effects on the spin density in cumyl-type monoradicals. 

Barone et al.76 studied the transition-metal complex CUC2H2 using different density-functional methods. They found that the experimental hyperfine coupling constants were well reproduced by GGA calculations with fairly large basis sets. But all studies indicate that these constants can be calculated accurately only with great care. 

DET calculations on the hyperfine coupling constants of ethyl imidazole as a model for histidine support experimental results that the preferred histidine radical is formed by OH addition at the C5 position [00JPC(A)9144]. The reaction mechanism of compound I formation in heme peroxidases has been investigated at the B3-LYP level [99JA10178]. The reaction starts with a proton transfer from the peroxide to the distal histidine and a subsequent proton back donation from the histidine to the second oxygen of the peroxide (Scheme 8). 

Consequently, structures 85b and 85c must be considered resonance structures rather than valence isomers. Hyperfine coupling constants were computed for a series of dithiazolyl radicals and related compounds [96MRC913]. An absolute mean deviation of 0.12 mT with respect to experimental data is reported for 10 sulfur hyperfine coupling constants obtained from UB3-LYP/TZVP calculations. 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

Here this work is continued and extended to C70 where a considerable amount of experimental work is currently in progress. The observation [4] of three electron-muon hyperfine coupling constants in not unexpected since there are five chemically distinct sites for muon to attack. The lower symmetry of C70 makes the molecule much more interesting than Cgo-... 

Since the phenoxyls possess an S = ground state, they have been carefully studied by electron paramagnetic spectroscopy (EPR) and related techniques such as electron nuclear double resonance (ENDOR), and electron spin-echo envelope modulation (ESEEM). These powerful and very sensitive techniques are ideally suited to study the occurrence of tyrosyl radicals in a protein matrix (1, 27-30). Careful analysis of the experimental data (hyperfine coupling constants) provides experimental spin densities at a high level of precision and, in addition, the positions of these tyrosyls relative to other neighboring groups in the protein matrix. 

The experimentally observed variation of the linewidths with mj and with the microwave frequency presented in Figures 1 and 2 cannot be reproduced by eqs. 2-5. An mj variation similar to that presented here has been observed before for Cu(ll) in frozen glasses and treated phenomenologically" by assuming an explicit mj dependence of the linewidth AH, or by generating a powder spectrum through superposition of spectra with different values of the g,i and hyperfine coupling constants ". ... 

Further support for the rehybridization model was provided by analysis of the spin densities of annelated 1,4-naphthoquinones, n hthalenes, and cyclobutaben-zene radical anions by ESR. The hyperfine coupling constants at the methylene position decrease as ring strain increases. Calculation of spin densities using the rehybridization model leads to an excellent fit of experimental spin densities, while calculation of spin densities using either the Coulson-Crawford hyperconjugation model or INDO do not accurately correlate experimental values. Such results suggest that rehybridization can account for the observed changes in spin densities. 

The ESR hyperfine coupling constants have been established experimentally (67MI20402) for the pyridinyl radical (134 R = H) and deuterated analogues, produced by y irradiation of a solid solution of pyridine in ethanol at 77 K, but the signs of the couplings are not known experimentally and are made solely on the basis of Huckel MO calculations. INDO MO calculations on this radical, together with the radical anions of quinoline, isoquinoline and acridine h ve also been carried out (740MR(6)5). 

Figure 6.13. Schematic energy diagram for quadricyclane (15) and norbomadiene (16) and their radical cations. The respective minima on the two surfaces are in a unique relationship with characteristic changes in bond lengths and angles. Experimental and calculated hyperfine coupling constants (in parentheses G B3LYP/6-31G //MP2/6-31G ) are shown below.

The calculation of magnetic parameters such as the hyperfine coupling constants and g-factors for oligonuclear clusters is of fundamental importance as a tool for the evaluation of spectroscopic data from EPR and ENDOR experiments. The hyperfine interaction is experimentally interpreted with the spin Hamiltonian (SH) H = S - A-1, where S is the fictitious, electron spin operator related to the ground state of the cluster, A is the hyperfine tensor, and I is the nuclear spin operator. Consequently, it is... 

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