Hyperfine tensors

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

Table 4 The g and hyperfine tensors (in Gauss) used in the ESR and ENDOR simulations of C6H5D + in CFCI3 at 30 K.

The Fe hyperfine tensor components were determined by Mossbauer spectroscopy in the case of the rubredoxin from Clostridium... 

Radical IV can be considered as a unique phosphorus radical species. Reduction of the parent macrocycle with sodium naphtalenide in THF at room temperature gave a purple solution. The FPR spectrum displayed a signal in a 1 2 1 pattern, with flp(2P)=0.38 mT. DFT calculations on radical IV models indicated a P-P distance of 2.763 A (P - P is3.256 A in the crystal structure of the parent compound and the average value of a single P-P bond is 2.2 A). According to the authors, the small coupling constant arises from the facts that the principal values of the hyperfine tensor are of opposite sign and that the a P P one electron bond results from overlap of two 3p orbitals [88]. 

The cross-peak coordinates represent two frequency values, va and vp, where va + vp=2v, and v is the proton frequency. When plotted in the coordinates v2a and v2p, the contour lineshape is transformed into a straight line segment. An extrapolation of this straight line permits the determination of the hyperfine tensors. A curve obtained by choosing some frequencies in the range will intersect the line defined by the squares of the values v2a and v2p in two points. The values where the curve intersects the experimental data are (val, vpi) and (va2, vp2), where va=A/2 + v, and vp= Vj-A/2. This gives two values of the anisotropic coupling tensor, Ar... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

A major advantage of studying pure compounds is that single crystals can be used, and hence e.s.r. parameters, which are generally anisotropic, can be accurately extracted. Furthermore, if the crystal structure is known, and if, as is frequently the case, the paramagnetic centres retain the orientation of the parent species, the directions of the g- and electron-nuclear hyperfine tensor components can be identified relative to the radical frame. 

Spectroscopic evidence (44,45) has been adduced for the formation of electron-gain centres upon y-irradiation of the binuclear carbonyls Mn2(C0)lo and Re2(C0)lo. A study (45) of a single crystal of irradiated Mn2(CO)10 has shown that the radical anion contains two equivalent 55Mn nuclei whose hyperfine tensors lie 118 apart. This has led to the suggestion that the anion radical contains a bridging CO and that its correct formulation is Mn2(C0)9 . The observation of a bridged Mn2(C0)9 species in u.v.-photolyzed material lends some support to this hypothesis (46). 

B. From g and Hyperfine Tensors to Molecular Structure 1. The g Tensor... 

The polyerystalline spectrum of N02 on MgO is somewhat complex, but it yields an unambiguous g and hyperfine tensor which can be checked by comparison with data for NO2 in single crystals. For N02 on MgO, principal values of the hyperfine tensor are m = 53.0, 21 = 49.0, and a31 = 67.0 G (29). It should be noted here that neither the signs of the coupling constants nor their directions relative to the molecular coordinates... 

Before discussing the absolute signs, the experimental hyperfine tensor should be resolved into its isotropic and anisotropic components as in Eq. (14D). The results are... 

This rather lengthy example, using the hyperfine tensor for the adsorbed NO2 molecule, has illustrated the type of information that one can obtain... 

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

Table 2. Relative transition probabilities for circularly polarized fields. S = 1/2,1 = 1/2 1) isotropic hyperfine tensor ai 0 > 0 2) dipolar hyperfine tensor B0 A 3) dipolar hyperfine tensor B0 Ax...

Hyperfine coupling constant, 22 267, 269 Hyperfine interaction, ESR data for, 22 274 Hyperfine parameters for O, 32 128-130 Hyperfine splitting, 31 81 Hyperfine structure, trimer species, 31 98-99 Hyperfine tensor, 22 267, 273-279, 336, 340 constants, 32 20-21 dioxygen species, 32 18-25 equivalent oxygen nuclei, 32 18-21 ionic oxides, 32 40... 

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