Hyperfine structures

Hyperfine structure (hfs) in optical spectra was discovered independently by A. Michelson, and Ch. Fabry and A. Perot at the end of the 19th century. The effect is explained by the presence of nuclear magnetic and electric moments, interacting with the electronic shell. 

Hyperfine structure arises from the interaction of the electron spins (S) with the nuclear spins (I) In general, there are (21 + 1) orientations of the nuclear spin in a magnetic field, each of them corresponding to a different energy The unpaired electron spin recognizes these different orientations with the result that 

Spectra that have overlapping peaks are difficult to interpret. Sometimes a computer is used to help interpret these spectra. The normal approach is to use measured or theoretical splitting constants to obtain a computer-calculated spectrum which is compared to the actual spectrum. If the spectra match, the sample is assumed to correspond to the single substance. 

Here a is the hyperfine coupling constant and /ua = eh/4nmp is the nuclear magneton (Table G2). Each ms level for the hydrogen atom will be split in two, corresponding to mi = +V2, and mi = -V2 for I = Vi of the proton. Fig. 1.5. 

As the magnetic fleld is changed two transitions occur determined by the selection rules  

The measured separation between the two lines, directly gives the hyperfine splitting, 50.5 mT, in magnetic field units. The coupling when expressed in frequency units as is usual in ENDOR studies (Chapter 2) is converted to field units by  

A nucleus in a certain environment undergoes lasting interactions with the neighborhood through electric and magnetic fields, which would also perturb nuclear energy levels, and the perturbation, the so-called nuclear hyperfine interactions, can change the Hamiltonian of the nucleus  

The basic shift of transition line in the Mossbauer spectrum is called the isomer shift due to electric monopole interaction. The electric monopole interaction originates from the electrostatic Coulomb interaction between the nucleus and electrons inside the nuclear region and is proportional to the s-electron density at the nucleus. This interaction energy. Ego, which is further defined as electrostatic shift, 5E, is attained as 

When the source and absorber move relative to each other and one only observes the difference of the electrostatic shifts of the source and absorber, or the isomer shift 8, instead of the shifts of them 8s and 8a separately  

In nuclei without spherically constant distribution of charges, another type of hyperfine interaction, electric quadruple interaction, may occur. In this case, atoms with both an observable nuclear quadruple moment, a measure of the nuclear charge distribution s deviation from spherical symmetry, and a 

The electric quadruple moment is a (3 x 3) second-rank tensor with elements 

The second step in the interpretation of the EPR spectra of organic radioals is to take into account the effect that magnetic nuciei have on the energy ieveis of unpaired eiectrons. 

The most important features of EPR spectra are their hyperfine structure, the splitting of individual resonance lines into components. In general in spectroscopy, the term hyperfine structure means the structure of a spectrum that can be traced to interactions of the electrons with nuclei other than as a result of the latter s point electric charge. The source of the hyperfine structure in EPR is the magnetic interaction between the electron spin and the magnetic dipole moments of the nuclei present in the radical. 

Consider the effect on the EPR spectrum of a single H nucleus located somewhere in a radical. The proton spin is a source of magnetic field, and depending on the orientation of the nuclear spin, the field it generates adds to or subtracts from the applied field. The total local field is therefore 

The other half (which have nii = - ) resonate when 

Therefore, instead of a single line, the spectrum shows two lines of half the original intensity separated by a and centered on the field determined hy g (Fig. 13.41). 

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In addition to this electron spin fine structure there are often still finer lines present. These are known as the hyperfine structure, which arises from the dilTerent weights of the isotopes of an element or from the spin of the nucleus. 

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

Figure B2.5.12. Hyperfine structure energy level scheme and spectrum for the...

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

Figure 2.1 Ligand hyperfine structure in the ESR spectrum of Na2[(Ir, Pt)Cl6].6H20. (Reproduced with permission from Proc. R. Soc., London, Ser. A, 1953, 219, 526.)...

In a. p. and s.o. ZV(a) and ZV(i) samples, no ESR signals were detected. In a.p. ZV(acac), a weak ESR signal of vanadyl species was detected (5% of total V), absent after the s.o. treatment. The spectra of samples reduced with CO at 400 to 623 K consisted of a signal showing a resolved hyperfine structure (Vh), overlapping a broad (AHnp = 300 Gauss) and nearly-isotropic band (Vb, giso = 1 -97) (Fig. 3). When recorded at 77 K, both Vh and Vb maintained the same shape as at RT, and their Intensity as a function of temperature followed the Curie law. 

A detailed study of the magnetic hyperfine structure in Mossbauer spectra and the performance of DFT methods is available [25]. It is known that DFT typically... 

Barone, V., 1994, Inclusion of Hartree-Fock Exchange in Density Functional Methods. Hyperfine Structure of Second Row Atoms and Hydrides , J. Chem. Phys., 101, 6834. 

Eriksson, L. A., Malkina, O. L., Malkin, V. G., Salahub, D. R., 1994, The Hyperfine Structures of Small Radicals from Density Functional Calculations , J. Chem. Phys., 100, 5066. 

Wolfgang Pauli (1900-1958 Nobel Prize 1945), at the age of 24, formulated the exclusion principle, which became famous as the Pauli principle. Accordingly, all electrons in an atom differ from each other, none are the same. His theoretical considerations led him to the existence of so-called nuclear spins, which also explained the hyperfine structures of spectral lines. His hypothesis was later unambiguously confirmed. As each element has its own... 

Markus, R. Hyperfine Structur Measurements on Some Transuranic Elements. 

Penrose, R.P. Hyperfine Structure in the Solid State. Nature [London] 163,... 

Second-order effects on hyperfine structure in organometallic compounds are discussed in Chapter 3. 

Early treatments of powder patterns attempted to deal with the spatial distribution of resonant fields by analytical mathematics.9 This approach led to some valuable insights but the algebra is much too complex when non-axial hyperfine matrices are involved. Consider the simplest case a single resonance line without hyperfine structure. The resonant field is given by eqn (4.3). Features in the first derivative spectrum correspond to discontinuities or turning points in the absorption spectrum that arise when dB/dB or dB/dcp are zero ... 

The spectra discussed in Chapter 4 were analyzed by neglecting the effects of nuclear quadrupole coupling on the nuclear hyperfine structure. Presented here is the way such effects may be incorporated into the spectra using perturbation theory. 

C- hyperfine satellites are detectable in natural abundance (Figure 3) and their intensities indicate a formulation Cr(C0)4 for the carrier of unpaired spin. Slight anisotropy in the 13C hyperfine structure of the 95 13C- enriched species could only be correctly reproduced in simulations under the assumption of tetrahedral geometry. The centre is thought to be Cr(C0)4+ with a 6At ground state in symmetry, a rare example of a high-spin metal carbonyl. 

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