Wide multiplets

Following the procedure for the derivation of the magnetisation expressed via the Brillouin function (Section 6.1) one obtains 

For a small argument of the Brillouin function (when the field B is small and T is high enough) the magnetisation becomes a linear function of the applied 

Consequently, the magnetic susceptibility obeys the Curie law of the form y==a dM 

The above requirements are well fulfilled for Gd(III) and Eu(II) derivatives (4/7 systems, S1/2 ground state)—Table 8.33. The magnetic susceptibility is isotropic and follows the Curie law for / = 7/2. 

---

The broadly successful application of these formulas to the paramagnetism of lanthanide complexes was due to the wide multiplet widths in the/block metals (large spin—orbit coupling coefficients X) and to the small effect of the ligand field on the deep-lying / orbitals. No comparably useful formula for the magnetic moments of d block complexes exists, except perhaps for the spin-only formula ... 

Another interesting fact about RO2 is the observation of unusually wide multiplets. They are found to be 40-50% wider in span than similar multiplets observed in the corresponding Z — 1 elements [638] and the increase cannot be accounted for merely by invoking an increase in the 3d spin-orbit separation for higher Z elements. 

Fig. 8.17. Multiplet width as compared with thermal energy (a) wide multiplets (b) multiplets of intermediate width (c) narrow multiplets.

The combination coefficients are different for individual spin states. The situation resembles the case of isolated multiplets (wide multiplets) and thus the Hamiltonian matrix takes a block-diagonal form. 

Stevens formalism turned out to be very powerful, and works easily as long as only the ground 2S+1Lj multiplet ofthe lanthanide ion is considered. As such, it has been widely used in studies on EPR properties of lanthanide-based inorganic systems [6, 22], while it is not well suited for optical spectroscopy. Indeed, when starting to include excited multiplets the Stevens formalism becomes much too involved. This is the reason why a more general formalism, developed by Wybourne [3], is of widespread use in optical studies - naturally dealing with excited multiplets - and... 

NMR data for aza[18]annulene 234 show a wide separation between the centers of the inner and outer proton lH NMR multiplets (Ad =11 ppm), indicative of a strong diamagnetic ring current.270 271 The bis-dehydro system 235 with 22 jr-electrons in the aromatic ring is diatropic.272... 

On the basic of relaxation theory the concept of TROSY is described. We consider a system of two scalar coupled spins A, I and S, with a scalar coupling constant JIS, which is located in a protein molecule. Usually, I represents H and S represents 15N in a 15N-1H moiety. Transverse relaxation of this spin system is dominated by the DD coupling between I and S and by CSA of each individual spin. An additional relaxation mechanism is the DD coupling with a small number of remote protons, / <. The relaxation rates of the individual multiplet components in a single quantum spectrum may then be widely different (Fig. 10.3) [2, 9]. They can be described using the single-transition basis opera-... 

In addition to the aromatic multiplet, the H spectrum of 2//-chromene (4) exhibits a quartet at 8 4.53 (2-CH2) and peaks at 5.38 (3-H) and 6.20 (4-H) (Figure 1). The last peaks are particularly significant, appearing in a variety of multiplet structures, the nature of which depends on the substitution pattern. However, the benzylic proton always appears downfield of H-3. Alkyl-substitution at C-2 causes an upheld shift of both alkenic protons, but disubstitution results in shifts to lower field. In the widely occurring 2,2-dimethylchrom-... 

In wide-band proton decoupled spectra complete proton decoupling is achieved and all carbon resonances appear as singlets. Enhancement of the 13C signals is observed as a result of the NOE and collapse of the C-H spin multiplets. 

All the chemical shift, shake-up and multiplet splitting information of XPS is, in principle, available in AES (9,10). The interpretation is more complex, however, because of the three levels involved in the process. In practice, Auger chemical shifts, etc., have not been nearly so widely exploited as they have in XPS. The empirical database is to date much more limited and again the habit of recording in the first derivative mode, often with poor resolution (to increase sensitivity for fast semi-quantitative elemental analyses) has obscured the usefulness of the chemical information. The exceptions to these remarks are usually from XPS practitioners who take their x-ray induced Auger data in the same manner as the XPS data and treat the analysis on an equal footing (9). 

Fig. S a Valence band spectra of Gd C82 (grey) and C82 (black) measured with Al Ka x-rays, b Symbols Gd 4f photoemission after subtraction of the empty C82 C 2s/2p spectrum. The vertical lines are individual components of atomic calculations for a 4f> multiplet, and the solid curve is their broadened sum. c Gd-N4>5 x-ray absorption spectrum (Gd 4d-4f excitations) of Gd C82. The complex lineshape comes from the widely spaced multiplet components resulting from the strong Coulomb interaction between the single hole in the 4d shell and the eight electrons present in the 4f shell in the x-ray absorption final state [see Fig. lc]. The arrows represent the two photon energies used for the data shown in panel d. d Resonant photoemission data of the valence band region of Gd C82 recorded off (hv=137 eV) and on (hv=149 eV) the Gd 4d-4f giant resonance...

Since the NMR resonances of chemically different protons are more widely separated at higher field, X3C-NMR spectra measured without proton decoupling will have more clearly defined multiplets, and as a result the magnitudes of proton-carbon coupling constants will be more easily extracted. A good illustration of this aspect is the proton-coupled spectra of propene recorded at 25 and 101 MHz discussed by Dubs and von Phil-ipsbom (7). 

---