Atomic complexities structure

Progress in experiment, theory, computational methods and computer power has contributed to the capability to solve increasingly complex structures [28, 29]. Figure Bl.21.5 quantifies this progress with three measures of complexity, plotted logaritlmiically the achievable two-dimensional unit cell size, the achievable number of fit parameters and the achievable number of atoms per unit cell per layer all of these measures have grown from 1 for simple clean metal... 

The thermodynamically most stable polymorph of boron is the /3-rhombohedral modification which has a much more complex structure with 105 B atoms in the unit cell (no 1014.5 pm, a 65.28°). The basic unit can be thought of as a central Bn icosahedron surrounded by an icosahedron of icosahedra this can be visualized as 12 of the B7 units in Fig. 6.1b arranged so that the apex atoms form the central Bn surrounded by 12 radially disposed pentagonal dishes to give the Bg4 unit shown in Fig. 6.3a. The 12 half-icosahedra are then completed by means of 2 complicated Bjo subunits per unit cell,... 

Numerous tetrahedral halogeno complexes [T1" X4] (X = Cl, Br, I) have been prepared by reaction of quaternary ammonium or arsonium halides on TIX3 in nonaqueous solution, and octahedral complexes TI "X< ] (X = Cl, Br) are also well established. The binuclear complex Cs3[Tl2"Cl<)J is an important structural type which features two TlCls octahedra sharing a common face of 3 bridging Cl atoms (Fig. 7.9) the same binuclear complex structure is retained when Tl " is replaced by Ti ", V ", Cr " and Fe " and also in K3W2CIS and CssBiily, etc. 

All three metals form a wide variety of binary chalcogenides which frequently differ both in stoichiometry and in structure from the oxides. Many have complex structures which are not easily described, and detailed discussion is therefore inappropriate. The various sulfide phases are listed in Table 22.4 phases approximating to the stoichiometry MS have the NiAs-type structure (p. 556) whereas MS2 have layer lattices related to M0S2 (p. 1018), Cdl2, or CdCl2 (p. 1212). Sometimes complex layer-sequences occur in which the 6-coordinate metal atom is alternatively octahedral and trigonal prismatic. Most of the phases exhibit... 

In this case the result is rather trivial, but for more complex structures involving several atoms per unit cell the method is easily applied and the result may not be so obvious. 

The /3-alloys are different in nature from the 7-alloys and the a-manganese and /3-manganese structures discussed above, in that they are not complex structures, but are simple, being based upon the body-centered arrangement. /3-Brass, for example, has either a disordered structure, above 480°K, the copper and zinc atoms in essentially equal number being distributed largely at random over the points of a body-centered cubic lattice, or an ordered structure, below 300°K, with copper and zinc at the positions 000 and, respectively, of the cubic unit. Moreover, the physical properties of /3-brass are not those that indicate a filled zone structure. 

In view of the lack of a simple valence relation between the atoms, complex atom-groups may be formed in sodium cadmide in a way similar to the formation of Pt>2- ions in a solution of sodium plumbide, NaPb2, in liquid ammonia,9 preventing a simplicity of structure. 

The structure factor for the 104-atom complex with almost perfect icosahedral symmetry determines the intensities of the diffraction maxima, in correspondence with the inverse relationship between intensity in reciprocal space and the atom-pair vectors in real space that was discovered fifty years ago by Patterson.27 The icosahedral nature of the clusters in the cubic crystal explains the appearance of the Fibonacci numbers and the golden ratio. 

Over the last decade, the chemistry of the carbon-carbon triple bond has experienced a vigorous resurgence [1]. Whereas construction of alkyne-con-taining systems had previously been a laborious process, the advent of new synthetic methodology based on organotransition metal complexes has revolutionized the field [2]. Specifically, palladium-catalyzed cross-coupling reactions between alkyne sp-carbon atoms and sp -carbon atoms of arenes and alkenes have allowed for rapid assembly of relatively complex structures [3]. In particular, the preparation of alkyne-rich macrocycles, the subject of this report, has benefited enormously from these recent advances. For the purpose of this review, we Emit the discussion to cychc systems which contain benzene and acetylene moieties only, henceforth referred to as phenylacetylene and phenyldiacetylene macrocycles (PAMs and PDMs, respectively). Not only have a wide... 

In contrast to carbenes of the AX2 type, which contain three atoms, generation of carbenes with a more complex structure under photolysis or vacuum pyrolysis conditions may be accompanied by intramolecular rearrangements. Thus, the matrix isolation study of the vacuum pyrolysis... 

A concept named molecular manufacturing, which was originally proposed by K. Eric Drexler [99] in 1992, has attracted the attention of some investigators [100, 118-121]. Molecular manufacturing is defined as the production of complex structures via non-biological mechanosynthesis (and subsequent assembly operations) [99]. A chemical synthesis controlled by mechanical systems operating on the atomic scale and performing direct positional selection of reaction sites by atomic-precision manipulation systems is known as mechanosynthesis. 

Khan H, T Barna, RJ Harris, NC Bruce, I Barsukov, AW Munro, PCE Moody, NS Scrutton (2004) Atomic resolution structures and solution behavior of enzyme-substrate complexes of Enterobacter cloacae PB2 pentaerythritol tetranitrate reductase. J Biol Chem 279 30563-30572. 

The intracellular and plasma membranes have a complex structure. The main components of a membrane are lipids (or phospholipids) and different proteins. Lipids are fatlike substances representing the esters of one di- or trivalent alcohol and two aliphatic fatty acid molecules (with 14 to 24 carbon atoms). In phospholipids, phosphoric acid residues, -0-P0(0 )-O-, are located close to the ester links, -C0-0-. The lipid or phospholipid molecules have the form of a compact polar head (the ester and phosphate groups) and two parallel, long nonpolar tails (the hydrocarbon chains of the fatty acids). The polar head is hydrophihc and readily interacts with water the hydrocarbon tails to the... 

The atoms are of a complex structure made up of positive nuclei and electrons, of which the latter, at least, are in very rapid motion. If we assume that the electrons are 1/1800 the mass of hydrogen atoms and that they obey the same laws of motion as other atoms, their average velocity would be about sixty times the velocity of molecules of hydrogen (H2). I will not attempt to discuss here the question whether the law of equipartition of energy actually holds for electrons. 

The complexes [M(/i-C7H4NS2)(COD)]2 (M = Rh, Ir) and [Rh(/i-C7H4NS2)(CO)(PPh3)]2 react with silver compounds to give the heterometallic derivatives with the silver(I) atoms bonded to the thiolate sulfur atoms. The structure of [Rh2Ag2(/i3-C7H4NS2)2(C104)] shows a short Rh—Ag distance.1010... 

As the atomic number increases, so does the positive charge of the nucleus, and the electrons are bound with a higher energy. However, this increase is not linear. For example, the electrons in the d orbital of the third shell have a higher energy than those in the s orbital of the fourth shell, and hence the latter are filled first. The consequence is the unexpected behavior of the first ten transition elements. In the case of the actinides and lanthanides, even more inner orbitals are occupied. Nature is not so simple, but the scheme should help to visualize this complex structure. And if one can assign the electrons of an element, one is a step closer to successfully unraveling the mysteries of the Periodic Table. 

---