Splitting, multiplet

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. 

J. C. Carver, G. K. Schweitzer, and T. A. Carlson. J. Chem. Phys. 57, 973, 1972. This paper deals with multiplet splitting effects, and their use in distinguishing different element states, in transition metal complexes. 

In addition to primary features from copper in Eig. 2.7 are small photoelectron peaks at 955 and 1204 eV kinetic energies, arising from the oxygen and carbon Is levels, respectively, because of the presence of some contamination on the surface. Secondary features are X-ray satellite and ghost lines, surface and bulk plasmon energy loss features, shake-up lines, multiplet splitting, shake-off lines, and asymmetries because of asymmetric core levels [2.6]. 

Something of scientific interest (among numerous other applications, Pascal s triangle is used to predict nuclear magnetic resonance [NMR] multiplet splitting patterns) has been created from the repeated application of a simple rule. 

Transition-metal and rare-earth atoms that contain partially occupied d or f valence subshells also give rise to spectral tine structure, often with very complicated multiplet splitting [2,27,28]. The spin-unpaired valence d or f electrons can undergo spin-orbit coupling with the unpaired core electron (remaining in the orbital from which the photoelectron was removed), producing multiple non-degenerate final states manifested by broad photoelectron peaks [2,27]. 

Shake-Up, Shake-Off, Multiplet Splitting and Plasmon Excitations... 

Because of the l/r dependence, the exchange interaction rapidly decreases with an increase in the difference between the principal quantum numbers of the impaired electrons and the core vacancy. Thus multiplet splitting is negligible in the Is spectra of paramagnetic transition metal compounds. On the other hand, shake-up intensity is essentially independent of the core level involved. Hence one can distinguish between shake-up and multiplet satellites by changing the principal quantum number of the core electron ionized76. ... 

In the case, where multiplet splitting is large compared with T - which may be assumed to be the case for actinides - only the ground multiplet intervenes and (13) reduces to the well known Curie law... 

Multiplet splitting occurs in the core-level region as well as in the energy range which we called valence region in this case it can be due to photoemission from a localized state, although this state may be not very far from the Fermi edge. A typical example of... 

In d-metals, the opposite is true the d-wavefunctions hybridize easily with conduction band states. The main peak can in this case be coordinated with the well screening outer d s, and the shake-up satellite, when observed, is due to the poorly screening process (Fig. 7c). For d-metals, furthermore, the very high density of d-states at Ep is the cause of many secondary electron excitation from just below Ep to empty states just beyond Ep which results in the asymetric high energy tailing of the main peak. Final state multiplet splitting, explained above, can in addition overlap the split response. 

Localized d or/electrons retain their one-atom manifolds, except that states arising from different d" or f are split by crystal field and spin-orbit coupling. Multiplet splittings due to spin-orbit coupling are larger than crystal-field splittings of Af levels the converse is the case for 3d" levels. The difference in energy between d"(f) and d" (/ 1) manifolds corresponds to the amount of free atom U that is decreased due to interatomic interaction in the solid. 

Fig. 14 Natural abundance carbon-13 spectrum of 1 (50 MHz) with expansion where necessary to show doublet structure. The assignments are as follows (from left to right), aromatic C bonded to oxygen (doublet) aromatic C bonded to chlorine (singlet) aromatic CH (singlet) methine (doublet) CDC13 OCH2 (doublet) CH3 (doublet). Multiplet splittings are due to coupling with phosphorus and are (except for Jpc) small...

The presence of an outer open shell in an atom, even if this shell does not participate in the transitions under consideration, influences the X-ray radiation spectrum. Interaction of the vacancy with the open shell, particularly in the final state when the vacancy is not in a deep shell, splits the levels of the core. Depending on level widths and relative strength of various intra-atomic interactions, this multiplet splitting leads to broadening of diagram lines, their asymmetry, the occurrence of satellites, or splitting of the spectrum into large numbers of lines. 

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