Ions, isolated

Reactions in water often involve a ubitiquous species known as hydronium (H3O+). Is hydronium properly described as an isolated ion, or at the other extreme, as a proton dissolved in water ... 

Sharing of an oxygen atom by two central atoms in compounds with chain-type structures weakens the binary Nb=0 bond compared to the corresponding bond in pure isolated ions such as NbOF52 This phenomenon affects the vibration spectra and increases wave numbers of NbO vibrations in the case of isolated oxyfluoride complex ions. Table 31 displays IR absorption spectra of some chain- type compounds. Raman spectra are discussed in [212],... 

All of these examples explain why such a variety of phenomena are observed in ionic or coordination polymerization. What we need to understand is the cause which gives to a particular center this or other properties, e.g., why dissociation into isolated ions leads to one and not another change in the reactivity and the specificity, how changes in solvation shell change the behavior of the growing center. This whole field is still uncharted, and calls for a thorough academic research. 

The data obtained up to the present time show that the method of catalyst preparation by the reaction of organometallic compounds with surface reactive groups may be applied to generate both isolated ions of transition metals (in various valent states) or superfine metal particles on the surface of the support. 

Two ions of the transition metal take part in this reaction. However, in the case of supported one-component catalysts the formation of the active bond seems to occur on the interaction of the monomer with isolated ions of the transition metal. That may be illustrated by the data showing that the activity of chromium oxide catalysts decreases linearly with decreasing chromium content (or even increases per chromium ion) to the rather low (0.01%) chromium concentrations on the catalyst surface (62, 69). In... 

Fig. 18.4 (a) A portion of the orbital splitting for NHj/ZrCli as isolated ions and as a hydrogen-bonded ion pair. The HOMO is indicated by Projected overlap populations (positive values representing... 

The distribution of iron and other metals in zeolites has been studied by many authors. In general, Fe can occupy three positions in ZSM-5 matrix [26] (1) as isolated ions in the tetrahedral lattice positions (2) as isolated ions or small complexes outside the lattice but inside... 

The transport numbers thus depend on the mobilities of both the ions of the electrolyte (or of all the ions present). This quantity is therefore not a characteristic of an isolated ion, but of an ion in a given electrolyte. Table 2.2 lists examples of transport numbers. It can be seen from the table that the transport numbers also depend on the electrolyte concentration. The following rules can be derived from experimental data ... 

As noted above, in the reference model the dependence of the electron wave functions A and B on the nuclear coordinates was entirely neglected and the wave functions A and B for the isolated ions or the wave functions calculated for corresponding equilibrium nuclear configurations Qk0i and Qkof according to Eqs. (8) were usually used in the calculations. 

Generally, it is most likely that metal NPs are stabilized by the aggregates of the non-functionalized imidazolium ILs rather than by the isolated ions. In addition, the interaction between ILs and the metal NPs have been evidenced by X-ray photoelectron spectroscopy (XPS), small-angle X-ray scattering (SAXS), isotope labeling, and surface-enhanced Raman spectroscopy (SERS) techniques. 

In LC-MS, specific ionisation conditions can be required for different types of species. This means that in LC-MS studies on extractable additives, it is necessary to use a range of experimental conditions to cover detection of all types of potential species. Depending on instrument type, it is also possible to isolate ions in complex matrices and obtain positive identifications by further unique fragmentation of these ions (by MS-MS or MSn). Quantitative methods based on this secondary ionisation can be employed. The mass accuracy of LC-MS detection systems continues to improve. Accurate mass measurement improves the certainty of identification. Advanced systems are typically offering 1-2 ppm (mass dependent) mass accuracy. 

Mozumder (1971) calculated F(t) by the prescribed diffusion method. For the isolated ion-pair case, the solution appears in (7.28) for the multiple ion-pair case, further approximation was introduced in the nature of mean force acting on an electron, by which the problem was reduced to that of a collection of isolated... 

The limitation of the prescribed diffusion approach was removed, for an isolated ion-pair, by Abell et al. (1972). They noted the equivalence of the Laplace transform of the diffusion equation in the absence of scavenger (Eq. 7.30) and the steady-state equation in the presence of a scavenger with the initial e-ion distribution appearing as the source term (Eq. 7.29 with dP/dt = 0). Here, the Laplace transform of a function/(t) is defined by... 

The methods discussed so far are essentially limited to isolated ion-pairs or, in the admittedly crude approximation, to cases when a multiple ion-pair spur can be considered to be a collection of single ion-pairs. Additionally, it is difficult to include an external field, as that will destroy the spherical symmetry of the problem. Stochastic treatments can incorporate both multiple ion-pairs and the effects of an external field. 

Pimblott (1993) has used MC and ME methods for the external field (E) dependence of the escape probability (Pesc) for multiple ion-pair spurs. At low fields, Pesc increases linearly with E with a slope-to-intercept ratio (S/I) very similar to the isolated ion-pair case as given by Onsager (1938). Therefore, from the agreement of the experimental S/I with the Onsager value, one cannot conclude that only isolated ion-pairs are involved. However, the near equality of S/I is contingent on small Pesc, which is not expected at high fields. 

Figure 4 of Mozumder (1971) compares the kinetics of neutralization in an isolated ion-pair, a spherical blob, and a short track. For the isolated ion-pair there is vey little recombination until 5 x 10 u s, but most recombination is over by -Ins. The main difference in the recombination kinetics is between the isolated and multiple ion-pair cases. There is not such a great difference among the different multiple ion-pair blobs or short tracks. In the multiple-ion-pair cases, the neutralization is gradual and much faster than that in the isolated ion-pair case at short times. However, this could be an artifact of the model predicated by close proximity of the positive ions having essentially zero mobility (vide infra). 

These results imply that the use of the representative single ion-pair distribution in the ionization produced by low-LET irradiation in liquid hydrocarbons can be approximately justified even though the track itself has considerable contribution from multiple-ion-pair spurs and short tracks. It also means that even in the case of an isolated ion-pair, the long-time limit of the existence probability is perturbed by the long-range coulombic field. 

Sulphur, selenium and tellurium can be incorporated into Si in a variety of forms (Grimmeiss et al., 1981 Wagner et al., 1984). As isolated ions, they are all double donors, with levels around 260 and 550 meV from the conduction band. These impurities may also be introduced as pairs, which also act as a double donors (Pensl et al., 1986). Depending on the thermal history of the Si during diffusion of S, Se and Te, they may also be incorporated as higher-order impurity complexes (Grimmeiss et al., 1981 Wagner et al., 1984). 

For example, a purely ionic model of CrFe predicts a total binding energy (relative to Cr6+ plus six F isolated ions cf. Example 2.1) of 7.9832 a.u., more than 1000 kcal mol-1 less than the actual value. 

The occupancies of metal 4d and 5s orbitals correspond to an overall s015d515 configuration, deviating noticeably from the nominal s°d5 assignment. The d spin-orbitals of a spin are essentially completely filled (0.993-0.995), and thus chemically inert. However, the nominally empty spin-orbitals of (3 spin exhibit significant non-zero occupancies (0.063 in each member of the eg set and 0.017 in each member of the t2g set), and appreciable occupancy of both spins is also found in the 5s orbital (0.088 a, 0.082 (3). These unexpected occupancies (which would be strictly absent in the isolated ion) can be associated with the leading donor-acceptor interactions, namely... 

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