Assignment of indices

The indices are permutable within any interval of indices belonging to constitutionally equivalent atoms, as long as the a-atoms of these atoms do not also belong to constitutionally equivalent classes. In the latter case, additional rules are needed for deciding between equivalent assignment of indices. 

Within one of these intervals there is free choice of indices, but once this is decided the other assignments are no longer random. The arbitrary assignment of indices to the N-atoms determines the indices of the adjacent C-atoms and these in turn the order of the H-atoms. 

Although the indexing process may take several iterations, each resulting in a more accurate assignment of indices and in a better approximation of the unit cell, finding the best solution is usually trivial. 

Table 5.5. Assignment of indices after the unit cell dimensions of LaNi4 85Sno,i5 have been...

Table 5.6. Final assignment of indices for the powder diffraction pattern of LaNi4.85Sno.15. The...

We will begin with the cubic crystal system, where the assignment of indices is nearly transparent and then consider the theory behind the ab initio indexing in crystal systems with tetragonal and hexagonal symmetry. Indeed, as with any kind of experimental work, experience is paramount, and we hope that the contents of this section may help the reader to achieve accurate solutions of real life indexing tasks successfully. 

Consider the face-centered cubic lattice in Fig. 27.30. The 100 planes are interleaved at just half the spacing by the 200 planes, which contain only face-centered atoms. The reflected rays from this second set of planes are 180° out of phase with those from the 100 planes. The two reflections interfere destructively so that a first-order reflection does not appear from the 100 planes in this lattice. (Higher-order reflections appear from both sets, but the intensities are much weaker.) For the same reason the first-order reflection from the 110 plane does not appear, being destroyed by the first-order reflection from 220 planes. The 111 planes are not interleaved in this way, so the first-order reflection comes through loud and clear, especially because the 111 planes are close packed. The absence of certain lines helps enormously in the assignment of indices, the indexing, of the lines that do appear. 

Lastly, Table 6 describes the assignment of rows to processors for some typical cases, and the load in each case (indicating the number of force interactions computed by each processors in the corresponding case). These are based on equations in Section 3. Several important points can be noted from the results shown in the table. Firstly, it can be observed that in the 4 processor case, processor P3 computes half the maximum number of rows in the force matrix which leads to a load balanced assignment. This would not be the case if processors were assigned equal number of rows. Moreover, when the number of processors is increased from 4 to 16, the load on each processor reduces by a factor of 4, but is still equal on every processor. 

Each of these can be assigned to one of the symmetry species of the point group to which the molecule belongs. These assignments are indicated in the right-hand column of each character table given in Appendix A and will be required when we consider vibrational Raman spectra in Section 6.2.3.2. 

The subject of thermochromism in organic and polymeric compounds has been reviewed in some depth previously (8,16,18), and these expansive overviews should be used by readers with deeper and more particular interest in the subject. Many more examples can be found in the reviews that further illustrate the pattern of association between thermochromism and molecular restmcturing of one kind or another. The specific assignment of stmctures is still Open to debate in many cases, and there are still not many actual commercial uses for these or any of the other thermally reversible materials discussed herein. Temperature indicators have been mentioned, though perhaps as much or more for irreversible materials. 

Where assignments of orbitals were made they are indicated in parentheses. Calculated values onlv. 

The formulae H and I summarize the results with the complete assignments of all C and //chemical shifts (H) and the HH multiplets and coupling constants (I). Here the H multiplets which have been interpreted because of their clear fine structure are indicated by the multiplet abbreviation d for doublet. 

The sum of indicator values obtained when multiplying all emissions assigned to that impact category by their respective characterization factors is called the category indicator result. The indicator moles of may, for instance, be the sum of contributions from sulfur dioxide, nitrogen oxides, and hydrogen chloride, and there is a characterization factor for each of them relative to the indicator. 

In a few instances the technique of magnetic circular dichroism (MCD) spectroscopy has been used to corroborate assignments based on UV-visible spectroscopy. For example, the assignment of the intense 360 nm band for [S,N,Y to a r (2e") r (2a2") (HOMO LUMO) excitation has been confirmed by the measurement of the MCD spectrum of The MCD spectrum of [S4N3] indicates that each of the... 

X is an acidity function based on the first-order approximation, Eq. (8-92). Values of X have been assigned by an iterative procedure. The data consist of values of Cb/cbh+ as functions of Ch+ for a large number of indicators. For each indicator an initial estimate of pXbh+ and m is made and X is calculated with Eq. (8-94). This yields a large body of X values, which are fitted to a polynomial in acid concentration. From this fitted curve smoothed X values are obtained, and Eq. (8-94), a linear function in X. allows refined values of pXbh + and m to be obtained. This procedure continues until the parameters undergo no further change. Table 8-20 gives X values for sulfuric and perchloric acid solutions. ... 

Although the emphasis in this chapter has been on tbe synthesis and mechanism of formation of simple enamines, brief mention will be made of the addition of amines to activated acetylenes to indicate the interest and activity in this area of substituted enamines. Since such additions tend to be stereospecific, inclusion in this section seems apropos. The addition of amines to acetylenes has been much studied 130), but the assigning of the stereochemistry about the newly formed double bond could not be done unequivocally until the techniques of NMR spectroscopy were well developed. In the research efforts described below, NMR spectroscopy was used to determine isomer content and to follow the progress of some of the reactions. 

At(I, R) + 2Bi(R) + B2(R) + 4E(I, R), where I indicates activity in IR absorption spectra and R indicates activity in Raman spectra. Kharitonov and Buslaev [186] determined the force constant of the Nb=0 bond as being 7.0 mD/A for K2Nb0F5H20. This datum seems to be very close to the data mentioned in Table 25, in which assignment of calculated and observed vibration modes is presented for Rb2NbOF5 and Cs2TaOF5. 

Structure of Oxy-F Compound F is extremely unstable and is difficult to obtain at a level of purity suitable for NMR studies. However, an oxidation product, Oxy-F, formed when F is left standing at — 20° C, is considerably more stable than F and can be purified to a sufficiently high level of purity. Oxy-F is nonfluorescent and shows absorption maxima at 237 nm and 275 nm (shoulder). The high-resolution FAB mass spectrum indicated the molecular formula of Oxy-F to be C33H3809N4Na2 [m/z 703.2363 (M + Na)+ and 681.2483 (M + H)"1"]. The H and 13C NMR data allowed the assignment of structure 7 to oxy-F (Fig. 3.2.6 Nakamura et al., 1988). 

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