Shift and splitting

Fig. 19. Shift and splitting of the hydrogen vibrational energy in passivated Si caused by uniaxial pressure along [100] and [112] lattice directions. [Reprinted with permission from the American Physical Society, Herrero, C.P., and Stutzmann, M. (1988). Phys. Rev. B 38, 12668.]...

In order to detect shifts and splitting in the nuclear levels due to hyperfine interactions in iron, one needs an energy range of at most 5 10-8 eV around E0, which is achieved with Doppler velocities in the range of-10 to +10 mm/s. 

First order ENDOR frequencies of nonequivalent nuclei or of pairs of magnetically equivalent nuclei are given by Eq. (3.3) which is derived from the direct product spin base. To obtain correct second order shifts and splittings, however, adequate base functions have to be used. We start the discussion of second order contributions with the most simple case of a single nucleus and will then proceed to more complex nuclear spin systems. 

For atomic (gas) sodium (Na), the electronic configuration is ls 2s 2p 3s, leading to filled electronic energy levels Is, 2s and 2p, while the 3s level is half-filled. The other excited levels, 3p, 4s..., are empty. In the solid state (the left-hand side in Figure 4.6), these atomic energy levels are shifted and split into energy bands bands Is, 2s and 2p are fully occupied, while the 3s (/ = 0) band, the conduction band, is half-filled, so that a large number N 21 + l)/2 = N/2) of empty 3s excited levels is still available. As a result, electrons are easily excited into empty levels by an applied electric field, and so become free electrons. This aspect confers the typical metallic character to solid sodium. 

Weak crystalline field //cf //so, Hq. In this case, the energy levels of the free ion A are only slightly perturbed (shifted and split) by the crystalline field. The free ion wavefunctions are then used as basis functions to apply perturbation theory, //cf being the perturbation Hamiltonian over the / states (where S and L are the spin and orbital angular momenta and. 1 = L + S). This approach is generally applied to describe the energy levels of trivalent rare earth ions, since for these ions the 4f valence electrons are screened by the outer 5s 5p electrons. These electrons partially shield the crystalline field created by the B ions (see Section 6.2). 

The HREIMS of 2,7-dibromocarbazole (388) was identical to that of 3,6-dibromocarbazole (386). Differences were identified in the chemical shifts and splitting pattern of the H-NMR spectrum. Thus, a deshielded, two-proton doublet at 7.87 with ortho-coupling (/=8.3 Hz), assignable to the C-4 and C-5 protons, indicated the location of two bromine atoms at the C-2 and C-7 positions of the carbazole nucleus. This was also evident from the shielded ortho- and meto-coupled (/=8.3, 1.5 Hz) two-proton double doublet at S 7.36, assignable to the C-3 and C-6 protons. Further, a mutually meto-coupled (/= . 5 Hz) two-proton doublet at S 7.57, assignable to the C-1 and C-9 protons, supported the location of the two bromine atoms ortho to these carbons. Based on these spectral analyses and the HREIMS identical to that of... 

An external electric field leads to three alterations in the electron structure of an atom. Firstly, the energy levels of the atom are shifted and split (the Stark effect). The theory of this effect is well-known [8], Secondly, the highly excited states of the atom disappear. The potential for the outer electron of the highly excited atom, is equal to... 

Figure 3.7 P NMR spectra of cyclic trimeric and high polymeric phenyl-fluoro phosphazenes. Note (1) the shift in the whole spectrum that occurs in moving from a cyclic small-molecule phosphazene to a related high polymer, and (2) the chemical shift and splitting pattern that results from phosphorus coupling to the two fluorine atoms or to one fluorine. Spectra provided by W. D. Coggio.

Pochan, Baldwin and Flygare have analyzed the microwave spectra of cyclopropanone and the isotopic isomers 13Ci, 13C2, and 2,2-dideutero-cyclopropanone.63) The rotational transitions were determined by studying the Stark effect (the shifts and splittings of lines produced by an electric field). The type of transition observed for cyclopropanone was consistent with C v symmetry and the sum of the moments of inertia (/a + /b — Ic) suggested that all four protons are out-of-plane. These data eliminate such structural alternatives as the dipolar oxyallyl tautomer 82 and allene oxide 83. The electric dipole moment (fi ) was calculated to be 2.67 0.10 D, which corresponds to an average of those of acetone (2.93 D) 65> and formaldehyde (2.34D).6 )... 

Its isomer has three different types of hydrogens, two of one kind, one unique, and six equivalent. The compound must be isobutyl bromide. The chemical shifts and splitting pattern fit this structure ... 

Figure 26. Diagram for the origin of UV-visible spectral shifts and splittings due to exciton interaction of two chromophores ( ) dipoles ( - ). In two limiting orienta-...

The principal optical properties of the diamagnetic sublevels in atomic hydrogen — the shift and splitting in field of the energy levels — have been studied... 

The structures of the adducts were confirmed by H NMR. The regio-orientation of the pyrrole ring in compound (7) is apparent from the chemical shifts and splitting patterns of resonances due to the H-4a and H-7a protons. The doublet for H-7a is at a lower field than that for H-4a which appears as a multiplet due to spin-spin coupling with the H-5a, H-7a and H-4 (NH) protons. Proton NMR studies also reveal that there are two enolic forms of the ketone function in (7) but the major tautomer is the keto form (7a) (Scheme 1). 

Fig. 10.20. Hyperfine interactions shift and split the nuclear levels of iron (see text) and thus make the state of the nucleus dependent on the state of the atom. Each transition corresponds to a peak in the Mossbauer spectrum, see e.g. Fig. 10.21.

Interpretation of the observed preionization shifts and splittings in XAES spectra for covalently bonded molecular complexes has been attempted by... 

Lanthanides have isotopes which may used in this technique. The principle consists of measuring resonant y-ray absorption as a function of relative velocity between the source and the sample. The spectral line shifts and splittings give information on the chemical nature and symmetry of the site of ion. Eu3+-transferrin [53] and tumor metabolism studies [54] with 153Sm have not proved to be particularly informative. 

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