Magic structures

The Egyptians used the symbolism of the four sons and the four goddesses to orientate magical structures to the cardinal directions. In numerous tombs the vital organs of a mummy were removed and placed in jars, each sculpted with the appropriate head of the son who protected those organs. These jars were arranged in square... 

For surfactants with other types of hydrophobic groups, the CMC values are less readily available because far fewer measurements have been made, especially on pure compounds. However, the oil/water interfacial tensions are 56 and 46 dyn/cm for fluorocarbon and polydimethylsiloxane oils respectively, compared to the value of 52 dyn/cm for hydrocarbon/water. Hence from the sizes of the hydrophobic groups (see Table 21.1 below), the magnitude of the hydrophobic effect, and hence their CMCs can be estimated. This clearly shows that the well-known lower CMCs for fluorocarbon surfactants compared to normal derivatives arise from the much larger size of fluorocarbons, rather than any magic structuring of water ... 

Lindgard P-A and Bohr FI 1996 Magic numbers in protein structures Phys. Rev. Lett. 77 779-82... 

The correction term in Eq. (9) shows that the basic assumption of additivity of the fragmental constants obviously does not hold true here. Correction has to be appHed, e.g., for structural features such as resonance interactions, condensation in aromatics or even hydrogen atoms bound to electronegative groups. Astonishingly, the correction applied for each feature is always a multiple of the constant Cu, which is therefore often called the magic constant . For example, the correction for a resonance interaction is +2 Cj, or per triple bond it is -1 A detailed treatment of the Ef system approach is given by Mannhold and Rekker [5]. 

The significance of the magic number 32 found in the experiment may also be stated in a different manner. If a cluster containing Ba and a fuUerene molecule will be stable and, thus, result in a clearly discernible structure in the mass spectra every time there is exactly one Ba-atom situated on each of the rings of the ful-lerene molecule, this property might be used to count the rings of a fullerene. Of course, such a proposal has to be verified using other fullerenes, for example, C70 which is available in sufficient quantity and purity for such an experiment. 

Solid-state Alnmr spectroscopy has been much used in recent years to study the composition and structure of aluminisilcates (pp. 351 -9) and other crystalline or amorphous Al compounds. The technique of magic angle spinning (MAS) must be used in such cases. ... 

Sometimes decomposition reactions can be avoided by carrying out diazotizations in concentrated sulfuric acid. By this method Law et al. (1991) obtained the 1,5-bisdiazonium salt (incorrectly called tetrazonium salt) of l,5-diamino-4,8-dihy-droxy-anthraquinone, which is deprotonated to 2.28. The structure was verified by cross-polarization magic angle spinning (CPMAS) 13C NMR spectroscopy. 

The Structural Basis of the Magic Numbers.—Elsasser10 in 1933 pointed out that certain numbers of neutrons or protons in an atomic nucleus confer increased stability on it. These numbers, called magic numbers, played an important part in the development of the shell model 4 s it was found possible to associate them with configurations involving a spin-orbit subsubshell, but not with any reasonable combination of shells and subshells alone. The shell-model level sequence in its usual form,11 however, leads to many numbers at which subsubshells are completed, and provides no explanation of the selection of a few of them (6 of 25 in the range 0-170) as magic numbers. 

The packing diagram given in Figure 2 provides a simple structural basis of the magic numbers.1... 

The structural interpretation of the principal quantum number of nucleonic orbital wave functions and the structural basis provided by the close-packed-spheron theory for the neutron and proton magic numbers are discussed in notes submitted to Phys. Rev. Letters and Nature (L. Pauling, 1965). 

The close-packed-spheron theory leads to a simple structural interpretation of the magic numbers (16) they are the numbers at which each layer of the nucleus achieves completion of... 

The magic number 20 corresponds to the KM structure, which is also the structure of the core for magic number 82. This structure, shown in Fig. 5 (left), involves nine spherons ligated about a smaller central spheron. Its stability may be attributed to its double completed-shell character. 

Two limiting structures with four spherons as core or inner core are shown in Figs. 6 and 7. The structure shown in Fig. 6 has the central tetrahedron of four spherons surrounded by a larger tetrahedron of four and a truncated tetrahedron of 12, a total of 16 spherons in the outer layer. The packing is triangular. This is the structure of the cpre for magic number 126. It has double completed-shell character, LN. 

The arrangement of 22 spherons around an inner tetrahedron of four spherons shown in Fig. 7 involves icosahedral packing each of the four inner spherons is surrounded by an icosahedron of 12, three of which are the three other inner spherons. This structure (26 spherons, 52 neutrons) with one spheron missing may be assigned to magic number 50. The complete structure, with 26 spherons, corresponds to the stable nucleus as discussed in the following section. 

These fissioning nuclei (such as 8tP°i2-211> formed by reaction of Bi209 and a deuteron) have a nearly spherical normal-state structure, resembling that of the doubly magic nucleus seP m208, with an outer core of 16 spherons and an inner core of 4 spherons, shown in Fig. 6. The nucleus is excited, with vibrational energy about 25 Mev (for bismuth bombard-... 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

PPy was the first conducting polymer to be structurally analyzed. The discovery that a,a -disubstituted pyrroles did not electropolymerize led to the conclusion that the pyrrole units in PPy are a-linked Magic angle spinning C-NMR... 

As holds for other cluster systems, certain magic cluster electron counts exist, which indicates for a certain cluster-halide ratio and interstitial present the filling of all bonding molecular orbitals and therefore the thermodynamically most stable situation. For main group interstitial atoms these are 14 cluster-based electrons whereas for transition-metal interstitials the magic number is 18 [1, 10-12]. All of these phases are synthesized by high-temperature solid-state chemical methods. A remarkable variety of different structure types has been... 

Slovokhotov, Yu.L. and Struchkov, Yu.T (1984) X-ray crystal structure of a distorted tetrahedral cluster in the salt [(Ph P)4Au4N] BF4 . Geometrical indication of stable electronic configurations in post-transition metal complexes and the magic number 18-e in centred gold clusters. Journal of Organometallic Chemistry, 177, 143-146. 

---