Rotational splitting

Sakashita M, Lochel B, Strehblow HH (1982) An examination of the electrode reactions of Te, HgTe and Cdo.iHgo.sTe with rotating-split-ring-disc electrodes. J Electroanal Chem 140 75-89... 

Perovskites and related compounds also have a three-dimensional structure. In perovskites of formula ABOj, the octahedra of BOj lie on a cubic lattice, and are joined at the corners. Between these octahedra are large sites for the A atoms. In ReOj, the A atoms are missing, so guests can be added to the A positions. Because adjacent octahedra are joined together by only one oxygen they can rotate relative to one another, changing the shape of the A site. In LijReOj, the rotation splits the large A sites into two smaller sites more suitable for Li ions (Cava et al, 1982). Bronzes of WO3 also have a perovskite structure. 

A variant of the RRDE in which the ring is split into two parts (the rotating split ring-disk electrode) was invented to enable the detection of different intermediates produced at the disc electrode [32]. It was shown that the current at the ring segments is proportional to the length and that there is no interference between the segments [9, 33]. 

Figure 9.36. Lower rotational levels of CrH in the A 6 L 1 state. The spin-rotation splittings are exaggerated for the sake of clarity.

Figure 10.39. 13C hyperfine and electron spin-rotation splitting of the N = 0 and 1 rotational levels of 13CO+, and the observed transitions [111]. The large splitting is mainly due to the 13C Fermi contact interaction. The smaller splittings are due to the spin-rotation interaction and the dipolar hyperfine coupling. 

Figure 10.61. Lower rotational levels of the CH radical, with Hund s case (b) labels. Each level actually possesses Tl-doublet and nuclear hyperfine splitting, which is not shown in this diagram. Note that the spin-rotation splitting decreases with N, in accordance with equation (9.81).

Figure 10.96. Hj (0,2)-(18,3) hyperfine, spin-rotation and symmetry-breaking energy level diagram, showing the six AF = AN transitions, (a) denotes the Fermi contact splitting, (b) is the spin-rotation splitting and (c) shows the effect of symmetry breaking.

Figure 11.40. Hyperfine and spin-rotation splitting of atypicalrotational level intheX2E+ state of YO, and the magnetic dipole transitions observed by radio frequency/optical double resonance.

Figure 11.47. Magnetic hyperfine and spin-rotation splitting of the v = 17, N= 1 level of HD+. The infrared transitions indicated correspond to the lines observed in figure 11.43. The five radio frequency double resonance transitions observed were all between the G = 0 and 1 levels.

FIG. 21-33 Exampl es of powder shear cells. Triaxial cells (a) Traditional triaxial cell h) true triaxial. Direct shear cells (c) Translational split, Collin (1846), Jenike (1964) d) rotational annulus, Carr and Walker (1967), Schulze (2000) (e) rotational split, Peschl and Colijn (1976), iShear (2003). From Measuring Powder Flowabil-ity and Its Applications, E G Associates, 2006, with permission.)... 

The 2n 2E+ interaction is different for the e and / levels. This difference gives rise to A-doubling in 2II and a spin-rotation splitting of the AN = 0 degeneracy of the 2E+ state. If the 2E+ state is sufficiently far from the 2II state, it is possible to use second-order perturbation theory to evaluate the A-doubling. The 2II /2 level is repelled by the 2E+ state with an energy shift of... 

Figure 3.20 A-doubling of 2n states and spin-doubling of 2S+. The e//-dependent interaction between 2II and 2S states is shown schematically. The 2E+ state, if plotted versus N(N +1) rather than J(J +1), would show spin-rotation splitting identical in magnitude but opposite in sign to the 2n1//2 A-doubling. A 2n 2E interaction would result in a similar pattern of A-doubling and spin-splitting, except that the shifts of e vs. / levels are reversed.

For example, the spin-rotation splitting (called p-doubling by Van Vleck) of the OH A2E+ state is given mainly by interaction with the inverted X2n state. Consequently, for A< 0 and En — E% < 0, one predicts 7 > 0. The e-levels of the A2 X+-state are well above the /-levels, in qualitative agreement with the pure precession prediction. Consequently p and q have the same sign for A > 0 and p and q have opposite signs for A < 0 this is the case for the X2n... 

An important and frequently encountered result, often mistakenly taken as evidence for pure precession, is that, in the unique perturber, identical potential curve limit, the effective spin-rotation constant of the 2E+ state, jv, is equal to Py. This result is a direct consequence of the second-order perturbation theoretical definition of the contribution of a 2II state to the spin-rotation splitting in a 2E state (see Section 3.5.4) ... 

Determination of the methyl group rotational splitting constant. Nearly isotropic. 

Steimle and coworkers [95Ste2] have previously determined the permanent electric dipole moments of PtC in two electronic states using molecular beam optical Stark spectroscopy (/<(X E = 0.99(5), fi A 11) = 2.454(3), in Debye units). More recently, the dipole moments of two further states and an unexpeetedly large nuclear-spin magnetie rotation splitting were determined as follows ([99Bea], molecular beam LIF) ... 

Chemical shift is measured on a ppm scale relative to a standard of known frequency. TMS is the practical frequency standard for H, C, and Si. In principle, the absolute frequency reference is the electron-free nucleus. For theoretical work, the shift of the neutral diamagnetic atom is used as it may be calculated accurately. Alternatively, the absolute scale may be established independently of the NMR experiment from the rotational splitting constant measured by microwave spectroscopy on a reference gas, e.g., CO for C and In Figure 7, the chemical shift/shielding scale for C is shown together with the terms used to describe changes in shift. 

For the V3 band about 270 absorption lines were recorded between 920 and 967 cm The V3 band is an a-type band of a near-prolate asymmetric rotor, and at large Kg it should resemble the parallel band of a prolate symmetric top, i.e., AN = 0, 1, AKg ( AK) = 0. In the V3 band the symmetric top characteristics are not as obvious as in the band, however, a number of Pk and °Qk branches with N up to 28 and Rk branches with N up to 42 could be identified (for the band center, see p. 247). The assignment was supported by the results from a Fourier transform spectrum of NF2 at 890 to 980 cm The spin-rotation splitting is relatively small and unresolved in transitions with low Kg values. The asymmetry splitting is apparent in lines with low Kg and high N values, which was demonstrated with the (N=19 to 21) branch [9]. 

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