Type A structure

Figure 6 Polyhedral view (to scale) of structure types ai(a), a2(b) and two orientations of 03(0 and d) for CtqMu. The muon is at the end of the dangling bond and in views (a) and (b) lies in the plane of the paper. For views (a), (b) and (c) four edge carbon atoms are also in the plane of the paper. The other visible atoms are above the paper. Each atom above the paper hides a corresponding atom below the paper except for type 03 where in the region of the muon the undistorted structure below the plane is shown with dashed lines. This is useful since it clearly shows the nature of the distortion. View (d) is an orientation of type 03 to illustrate that the distortion is similar to the other type a structures...

Apart from type 62, which is only slowly convergent to the optimised geometry, the other centres are well described by the ROHF method. Polyhedral views of the three type a structures are shown in Fig. 6. These all illustrate the change of hybridisation at the point of muonium attachment and at the adjacent carbon atom where the unpaired electron is effectively localised as expected from addition to an alkene. The bi and c defects (Fig. 7) are quite different. The expected hybridisation change to sp is clearly present for the atom bonded to muonium, but other significant distortions are not obvious. This is consistent with the prediction from resonance theory (Fig. 8) that the unpaired electron for these structures is delocalised over a large number of centres. 

This seems to imply that the associated distortion of the cage is only large for one atom (not two as for the type a structures) and therefore possibly better accomodated by the defects defined in Table 4. It must be concluded that either structures b and c are chemically unrealistic or there is a subtle, but significant, stabilisation provided by a complete geometry optimisation. 

Exchange with Ca tends on the other hand to open pore windows. This effect occurs because the divalent Ca actually must displace two Na cations. This results in site sharing and actually pulls a cation from a site that at least partially occludes a pore opening, this opening the window. It has been known for several decades that ion exchange by Ca in place of Na in the type A structure opens... 

Fig. 34. Relict organic structures in Precambrian cherty iron-formations (after La Berge). I = type A structure, well preserved due to carbonaceous matter in chert matrix note fibrous surface and clear interior (lower chert unit of Biwabik Iron Formation, Pilotac mine, Minnesota) 2 = type A structure, largely replaced by greenalite 3 = type A structure, preserved due to unidentified brown substance (hematite ) in chert matrix (Belcher Islands iron-formation) 4 = type B structure (Eosphaera tyleri), well preserved due to carbonaceous matter in chert matrix (Gunflint district) 5 = type B structure in which most of the organic matter has been replaced by extremely fine hematite (Vicar mine, Gogebic district) ...

The calculated hyperfine coupling constants (B3LYP/6-31G //MP2/6-31G ) for the type B transition state and the distorted minimum clearly show that this species must be considered a type A structure. The hyperfine coupling pattern of the lowest-energy minimum [ai = —1.43 mT a = 1.98 mT) shows a trend similar to the experimental splittings of the fran.s-l,2-dimethylcyclopropane radical cation a, 2 = —1.19 mT a = 2.18 mT), whereas the pattern calculated for the transition state (fl2,3 = 0.55 mT) is incompatible with that model (Figure 18). The distorted structure type calculated for the methyl-substituted systems seems to prevail also under other conditions (see below). 

Although the results indicated some stabilization for the type B structures, they clearly indicate that hyperconjugation is not sufficient to alter the natural preference of cyclopropane radical cations for the type A structure. On the other hand, both conjugation and homoconjugation have been shown to reverse the stabilities... 

This add salt, KHXg. HjO, where HX = (10), has a normal Type A structure so far as the carboxyl-function of the acid is concerned. Interest attaches to the phenolic group, which makes contacts with another, symmetry-related, group, as well as with the water molecule (whose... 

Cook (44) has prepared a number of crystalline basic salts of various organic bases with acids such as HAsFj. From their infrared spectra he predicted that many of them should have Type A structures of the sort described in this section. So far only two structures have been successfully elucidated. One is of an arsenate ester (45), the other of a basic salt B2. HAsFj, with S = l-methyl-2-quinolone (15), which does indeed... 

A technical difficulty afflicts the attempt to determine precisely the length of a bond in a crystallographically symmetrical position, such as this O - H- - 0 bond, as well as all the hydrogen bonds in Type A structures. In general, when the positions of two atoms are known, each with a standard deviation of a, the derived interatomic distance has a standard deviation of ]f2a- Hut when the atoms are symmetry-related, the errors in their positions are correlated, so that the overall standeird deviation of the distance rises to 2[Pg.166]

However, in most crystals containing H5O2, the ion does not have strict S5nnmetry. These then are, at best, pseudo-Type A structures. For instance, a neutron-diffraction study (83) of HAUCI4. 4 H2O shows the mid-point of to he at a crystallographic centre of symmetry,... 

Figs. 19 and 20 show the infrared spectra of some acid salts and related crystalline compounds. The spectrum in Fig. 19(a) is from an acid salt of Type B, and it approximates to a superposition of the spectra of free acid and neutral salt. The other spectra are all of Hadzi s T5q>e (ii), which is shown in its starkest form in Fig. 19(c) (sodium hydrogen diacetate) with a window near 950 cm h Potassium hydrogen malonate, a Type A structure, has a similar spectrum (20 (a)). The picoline-N-oxide hemi-hydrobromide (19(d)) is a T5q>e A basic salt Cook s basic salt (Sect. XI) is of pseudo-Type A and gives the spectrum (20(b)). Sodium bicarbonate (20(c)) and potassium hydrogen oxalate (20(d)) are acid sdts of intermediate character (see Sect. XV and XVI A). 

Still another source of information is nuclear quadrupole resonance spectroscopy. Waddington and Smith (96a) have used the C1 resonance to obtain evidence of genuine symmetry in the ions ClHCl- and C1DC1 in a salt known (97) to have a Type A structure with respect to the HCla ion. Hadzi and his co-workers (97a) have used deuteron resonance to study the structure of KDZg, where HX = trifluoroacetic acid (see Sect. VII D and XX G). The coupling constant and asymmetry para-... 

The cases listed in Tables 7 and 19 give general support to this idea. We may also draw attention to three cases where failure to make use of crystal symmetry (which would be chemically feasible) is associated with hydrogen bonds that are significantly longer than those in Type A structures sodium bicarbonate (Sect. XV), potassium hydrogen oxalate (XVI B) and sodium hydrogen oxalate hydrate (XVI C). 

In all Type A crystals, the hydrogen bond has a symmetrical potential-energy curve. In many acid salts, with open structures, the O- -H- -O distance in the double-anion, R COgHO C R, is close to 2.44 A. In a smaller number of chelated, but otherwise similar, structures, the 0- H - 0 distance is somewhat shorter and there are stereochemical reasons for this. For the latter cases, the hydrogen bond probably is genuinely symmetrical, with a single-well potential. Some, at least, of the open Type A structures may also contain symmetrical 0---H---0 bonds. 

A chirality classification of crystal structures that distinguishes between homochiral (type A), heterochiral (type B), and achiral (type C) lattice types has been provided by Zorkii, Razumaeva, and Belsky [11] and expounded by Mason [12], In the type A structure, the molecules occupy a homochiral system, or a system of equivalent lattice positions. Secondary symmetry elements (e.g., inversion centers, mirror or glide planes, or higher-order inversion axes) are precluded in type A lattices. In the racemic type B lattice, the molecules occupy heterochiral systems of equivalent positions, and opposite enantiomers are related by secondary lattice symmetry operations. In type C structures, the molecules occupy achiral systems of equivalent positions, and each molecule is located on an inversion center, on a mirror plane, or on a special position of a higher-order inversion axis. If there are two or more independent sets of equivalent positions in a crystal lattice, the type D lattice becomes feasible. This structure consists of one set of type B and another of type C, but it is rare. Of the 5,000 crystal structures studied, 28.4% belong to type A, 55.6% are of type B, 15.7% belong to type C, and only 0.3% are considered as type D. 

FIGURE 1.2 A Pd-gate MOS capacitor-type (a) structure (b) C-Vcurve shift. 

FIGURE 1.3 A Pd-gate MOSFET-type (a) Structure (b) Detection principle (c) curve shift. 

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