The fine structure

We need to know how to interpret the features of an NMR spectmm so that we can 

The spUtting of the groups of resonances into individual lines in Fig. 13.5 is called the fine structure of the spectrum. It arises because each magnetic nucleus contributes to the local field experienced by the other nuclei and modifies their resonance frequencies. The strength of the interaction is expressed in terms of the spin-spin coupling constant, /, and reported in hertz (Hz). Spin coupling constants are an intrinsic property of the molecule and independent of the strength of the appUed field. 

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It is possible to understand the fine structure in the reflectivity spectrum by examining the contributions to the imaginary part of the dielectric fiinction. If one considers transitions from two bands (v c), equation A1.3.87 can be written as... 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

The fine structure of a — 5 transition of an alkaline earth metal is illustrated in Figure... 

A — P transition, shown in Figure 7.10(b), has six components. As with doublet states the multiplet splitting decreases rapidly with L so the resulting six lines in the spectrum appear, at medium resolution, as a triplet. For this reason the fine structure is often called a compound triplet. 

Examples of this degradation of bands are shown in Figures 7.44 and 7.45. Figure 7.44(a) shows the rotational fine structure of the Oj] band of the —X Ag system of 1,4-diffuorobenzene, belonging to the >2 point group. The fine structure is in the form of a contour of tens of thousands of unresolved rotational transitions which, nevertheless, shows well-defined features (B is an overlapping weaker band of a similar type). Since Biu = r(T ), as given by Table A.32 in Appendix A, the electronic transition is allowed and... 

J. O. Warwicker, R. Jeffries, R. L. Colbran, and R. N. Robinson, H Eeview of the Eiterature on the Effect of Caustic Soda and Other Swelling Hgents on the Fine Structure of Cotton, Shirley Institute Pamphlet No. 93, Shirley Institute, Didsbury, Manchester, UK, 1966. 

The fine structure of torsion-vibration spectra of small symmetric molecules and groups such as CH3, CH4, NH3, and NH4 is one of the most illustrative manifestations of tunneling. This problem has been discussed in detail in several reviews and books (see, e.g., Press [1981], Heidemann et al.[1987]). 

Appearance potential methods all depend on detecting the threshold of ionization of a shallow core level and the fine structure near the threshold they differ only in the way in which detection is performed. In all of these methods the primary electron energy is ramped upward from near zero to whatever is appropriate for the sample material, while the primary current to the sample is kept constant. As the incident energy is increased, it passes through successive thresholds for ionization of core levels of atoms in the surface. An ionized core level, as discussed earlier, can recombine by emission either of a characteristic X-ray photon or of an Auger electron. 

On the other hand, TED patterns can assign the fine structure. In general, the pattern includes two kinds of information. One is a series of strong reflexion spots with the indexes of (00/), 002, 004 and 006, and 101 from the side portions of MWCNTs as shown in Eig. 1(b). The indexes follow those of graphite. The TED pattern also includes the information from the top and bottom sheets in tube. The helieity would appear as a pair of arcs of 110 reflexions. In the case of nano-probed TED, several analyses in fine structures have been done for SWCNT to prove the dependence on the locations [11,12]. 

Indeed, in. some cases it is probable that V2 is not ob.served at all, but that the fine. structure arises from term splitting due to spin-orbit coupling or to distortions from regular octahedral symmetry. 

W. E. Lamb (Stanford) the fine structure of the hydrogen spectrum. 

Another use for this solvent is exemplified by 1,4,5,8-tetraazanaph-thalene, the anhydrous species of which has a predicted i Ka value of — 2.7 (the observed pA in water is + 2.51). The spectrum obtained in anhydrous dichloroacetic acid is almost identical with that of the predominantly anhydrous neutral species determined in water, but quite different from the spectrum measured in dilute aqueous acid. Moreover, addition of water to the anhydrous dichloroacetic acid solution of this base caused the fine structure present in the spectrum of the neutral species to disappear and the band due to the hydrated cation (i.e. the spectrum obtained in water at pH 0.5) to appear. Addition of water to dichloroacetic acid solutions has been used to show that the cations of 3- and 8-nitro-l,6-naphthyridine20 are hydrated in aqueous acid at pH 0.5. 

Interesting tautomeric possibilities exist in the xanthobilirubic acid series (cf. reference 57) which can be illustrated by the equilibrium 62 63, More complex examples of the same type are found among the linear tetrapyrrole pigments— the bilenes, bilidienes, and bili-trienes—and have been discussed by Stevens. Relatively little evidence is available concerning the fine structure of these compounds, although the formation of complexes has been advanced as evidence for the 0X0 structure in some cases. ... 

Spectroscopic methods have been successfully applied to the elucidation of some details of the fine structure of isoxazole derivatives. Thus IR spectra revealed steric hindrance in the case of some 3,4,5-trisubstituted isoxazoles for phenylisoxazoles this results in the nonplanarity of the benzene and isoxazole rings and decreasing mutual interaction. 

Where, /(k) is the sum over N back-scattering atoms i, where fi is the scattering amplitude term characteristic of the atom, cT is the Debye-Waller factor associated with the vibration of the atoms, r is the distance from the absorbing atom, X is the mean free path of the photoelectron, and is the phase shift of the spherical wave as it scatters from the back-scattering atoms. By talcing the Fourier transform of the amplitude of the fine structure (that is, X( )> real-space radial distribution function of the back-scattering atoms around the absorbing atom is produced. 

Since the fine structure observed is only associated with the particular absorption edge being studied, and the energy of the absorption edge is dependent on the element and its oxidation state, EXAFS examines the local structure around one particular element, and in some cases, an element in a given oxidation state. A fuller picture can therefore be obtained by studying more than one absorbing element in the sample. 

Peculiarities of the Fine Structure of PET Fibers and the Relationship to Their Basic Physical Properties... 

PET fibers in final form are semi-crystalline polymeric objects of an axial orientation of structural elements, characterized by the rotational symmetry of their location in relation to the geometrical axis of the fiber. The semi-crystalline character manifests itself in the occurrence of three qualitatively different polymeric phases crystalline phase, intermediate phase (the so-called mes-ophase), and amorphous phase. When considering the fine structure, attention should be paid to its three fundamental aspects morphological structure, in other words, super- or suprastructure microstructure and preferred orientation. 

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