Structural splitting

It has been claimed that biodesulfurization via the 4S pathway can also reduce viscosity. An application introduced by Environmental Bioscience Corporation included a method for reducing the viscosity of liquid-containing sulfur heterocycles [406] using biodesulfurization. The original patent application (Ser. No. 631642) was filed in US 

Most of the known microorganisms to be active for BDS (by the date that patent [408] was introduced), were considered in this invention. Furthermore, their mutational or engineered derivatives, enzymes, cell-free extracts, recombinant enzymes, recombinant DNA, plasmids, vectors, and fragments were also incorporated in the intellectual property document. The mentioned operating conditions regard ambient temperature, mechanical agitation and a 1 9 biocatalyst/petroleum ratio. 

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The various transition energies of the gold atom and its ions are shown and compared with experiment [53] in table 2. The nonrelativistic results have errors of several eV. The RCC values, on the other hand, are highly accurate, with an average error of 0.06 eV. The inclusion of the Breit effect does not change the result by much, except for a some improvement of the fine-structure splittings. 

Table 2 CCSD transition energies in Au (eV). IP is the ionization potential, EA denotes electron affinity, and EE — excitation energy relative to the ground state. FS denotes fine-structure splittings.

While including the Breit term has a rather small effect on the excitation energies of Pr " ", it improves the fine-structure splittings (table 7). This is a general phenomenon, and may be traced to including the spin-other-spin interaction in the two-electron Breit term [62]. 

In principle, positronium can be observed through the emission of its characteristic spectral lines, which should be similar to hydrogen s except that the wavelengths of all corresponding lines are doubled. Positronium is also the ideal system in which the calculations of quantum electrodynamics can be compared with experimental results. Measurement of the fine-structure splitting of the positronium ground state has served as an important confirmation of the theory of quantum electrodynamics. 

When 3.3 mM L-methionine (SR)-sulfoximine phosphate is present in a solution of enzyme-Mn2+, the resultant spectrum is quite different from that detected for the unphosphorylated sulfoximine. Additional fine structure splittings are noted around 3300 G, in addition to poorly resolved resonances at about 2400 G. This indicates that the sulfoximine phosphate binds to the enzyme differently and induces different changes in the Mn2 + spectra than either the sulfoximine itself or the methionine sulfoximine phosphate formed in situ. The addition of 10 mM MgCl2 and 10 mAf ADP to an enzyme solution containing the sulfoximine phosphate did not produce significant spectral changes from those shown in Fig. 24. 

Other published EPR data show that L-glutamate produces a small axial distortion on the environment of enzyme-Mn(II) with unresolved fine structure and no obvious change in line width. Addition of MgATP results in a diminution of all spectral intensities and the anisotropic spectrum shows poorly resolved fine structure splitting. The appearance of these additional sets of transitions indicates that the environment of Mn2 + at the tight site is changed when metal nucleotide is bound. NH4 + produces additional subtle changes in the EPR spectrum of Mn2+. 

In light alkali atoms, Li and Na, the fine structure splitting of a low state is typically much larger than the radiative decay rate but smaller than the interval between adjacent states. In zero field the eigenstates are the spin orbit coupled tsjnij states in which and s are coupled. However, in very small fields and s are decoupled, and the spin may be ignored. From this point on all our previous analysis of spinless atoms applies. How the passage from the coupled to the uncoupled states occurs depends on how rapidly the field is applied. It is typically a simple variant of the question of how the m states evolve into Stark states. When... 

Fig. 7.10 Adiabatic correlation diagram for the Na nd states obtained from the known d state fine structure splitting, the intermediate field energy ordering, and applying the nocrossing rule for states of the same m (from ref. 3).

The data can be represented either as quantum defects for each fine structure series or as a quantum defect for the center of gravity of the level and a fine structure splitting. For the moment we shall use the latter convention, although it is by no means universal. Explicitly, we represent the energy of an nij state, where j = ( + s and s is the electron spin, as... 

The hyperfine structure (splitting) of energy levels is mainly caused by electric and magnetic multipole interactions between the atomic nucleus and electronic shells. From the known data on hyperfine structure we can determine the electric and magnetic multipole momenta of the nuclei, their spins and other parameters. 

In a non-relativistic approximation the usual fine structure (splitting) of the energy terms is considered as a perturbation whereas the hyperfine splitting - as an even smaller perturbation, and they both are calculated as matrix elements of the corresponding operators with respect to the zero-order wave functions. 

Hatamian, S., Conti, R.S. and Rich, A. (1987). Measurements of the 23Si-23Pj (J = 0,1,2) fine-structure splittings in positronium. Phys. Rev. Lett. 58 1833-1836. 

The results of a spin-polarization measurement of xenon photoelectrons with 5p5 2P3/2 and 5p5 2P1/2 final ionic states are shown in Fig. 5.21 together with the results of theoretical predictions. Firstly, there is good agreement between the experimental data (points with error bars) and the theoretical results (solid and dashed curves, obtained in the relativistic and non-relativistic random-phase approximations, respectively). This implies that relativistic effects are small and electron-electron interactions are well accounted for. (In this context note that the fine-structure splitting in the final ionic states has also to be considered in... 

In addition to causing fine-structure splitting, magnetic interactions may couple states of different spin multiplicities. As a consequence, so-called spin-forbidden transitions yield some intensity. Well-known examples for this phenomenon are phosphorescence and nonradiative transitions at intersystem crossings. 

The operator [157] is a phenomenological spin-orbit operator. In addition to being useful for symmetry considerations, Eq. [157] can be utilized for setting up a connection between theoretically and experimentally determined fine-structure splittings via the so-called spin-orbit parameter Aso (see the later section on first-order spin-orbit splitting). In terms of its tensor components, the phenomenological spin-orbit Hamiltonian reads... 

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