Structure of complex solids

BurJ82 Burdett, J. K. Predictions of the structure of complex solids. Adv. Chem. Phys. 49 (1982) 47-113. 

Taking matrix elements of the hamiltonian between such states creates a secular equation which can be solved to produce the desired eigenvalues. Since the potential cannot be truly spherical throughout the WS cell, it is reasonable to consider it to be spherical within a sphere which lies entirely within the WS, and to be zero outside that sphere. This gives rise to a potential that looks like a muffin-tin, hence the name of the method Linearized Muffin-Tin Orbitals (LMTO). This method is in use for calculations of the band structure of complex solids. The basic assumption of the method is that a spherical potential around the nuclei is a reasonable approximation to the true potential experienced by the electrons in the solid. 

Besides X-ray powder diffraction, infrared and Raman spectra are important practical tools in the characterization of solid materials. However, the interpretation of the absorption spectra requires theoretical input. Therefore, the calculation of vibrational properties plays an important role in understanding the structure of complex solids. The vibrational properties of ionic materials can be described surprisingly well by force fields which include only pair potentials in the form of electrostatic interactions and a term describing the repulsion as atoms get close to each other. In the case of zeolites, addition of bond angle terms in the spirit of valence force fields provides additional improvements. However, the description of covalent and metallic solids usually requires quantum mechanical approaches. 

Hysteresis, which is invariably present, adds to the complications its interpretation is, if anything more complex than with capillary condensation, inasmuch as it can depend not only on the pore structure of the solid but also on the magnitude of the applied pressure. 

The solid state structure of complex 7b is shown in Figure 25.1. Similar to parent chelating ether complex [9b], the solid-state structure of 7b shows a distorted square-pyramidal structure with the benzylidene moiety at the apical position. The N-aryl ring is located above the benzylidene moiety resulting in the relatively close contact of the benzylidene proton with the 7r-aromatic system of the mesityl group. 

The structure of the active catalyst and the mechanism of catalysis have not been completely defined. Several solid state complexes of BINOL and Ti(0-/-Pr)4 have been characterized by X-ray crystallography.158 Figure 2.4 shows the structures of complexes having the composition (BIN0Late)Ti2(0-/-Pr)6 and (BINOLate)Ti3(O-/-Pr)10. 

G. Meyer, The syntheses and structures of complex rare-earth halides, Progr. Solid State Chem. 14 (1982) 141. 

The first copper(I) complex of tris(hydroxymethyl)phosphine ((760) tetrahedral) has been reported by Samuelson and co-workers. This group addressed the question of anion-controlled nuclearity and metal-metal distances in copper(I)-bis(diphenylphosphino)methane complexes, and in this endeavor they reported the structures of complexes (761) (Cu-Cu separation 3.005-3.128 A), (762) (Cu-Cu separation 3.165 A) and (763) (tetrahedral Cu-Cu 3.293 A). 6 They synthesized and provided structural evidence of oxy anion- encapsulated copper(I) complexes of this ligand. The complexes (764) (distorted tetrahedral Cu-Cu 3.143 A), (765) (distorted tetrahedral Cu-Cu 3.424A), (766) (distorted trigonal Cu-Cu 3.170A), and (767) (Cu-Cu 3.032-3.077A) were reported. They studied solid-state emission spectra of these complexes.567 During this pursuit they... 

When supported complexes are the catalysts, two types of ionic solid were used zeolites and clays. The structures of these solids (microporous and lamellar respectively) help to improve the stability of the complex catalyst under the reaction conditions by preventing the catalytic species from undergoing dimerization or aggregation, both phenomena which are known to be deactivating. In some cases, the pore walls can tune the selectivity of the reaction by steric effects. The strong similarities of zeolites with the protein portion of natural enzymes was emphasized by Herron.20 The protein protects the active site from side reactions, sieves the substrate molecules, and provides a stereochemically demanding void. Metal complexes have been encapsulated in zeolites, successfully mimicking metalloenzymes for oxidation reactions. Two methods of synthesis of such encapsulated/intercalated complexes have been tested, as follows. 

An analogous nitrato complex, Be40(N03)6, is known in the solid state (145). The presence of a central 4-coordinate oxide ion and bridging nitrato ions has been confirmed by X-ray methods (146). The structures of these solid-state (jl4-oxo complexes lend support to the fi.roxo structures suggested for phosphato and carbonato complexes in solution (see Section IV). 

Thus, the Platonic and Archimedean solids not only provide a means for host design, but a way in which to maximize chemical information, allowing the chemist to simplify the structures of complex molecular frameworks and, in effect, engineer host-guest systems. 

Most interestingly, the U-carhon bond distances to the axial cycloalkane d(U-ClS) in 4 "-Uc and 4 "-Ud were determined to be 3.864 and 3.798 A, with the shortest U-carbon bond distance of 3.731 A found in the solid-state structure of complex 4 -Ue. Considering that the sum of the van der Waals radii for a U-CH2 or... 

Complexes 75 are remarkably stable at room temperature in the solid state and, when heated, they start to decompose only at about 130 °C (Cr) or 145 °C (W). Such a thermal stability is undoubtedly associated with their strongly dipolar nature, in which six possible ylide-type resonance forms contribute to the bonding (Fig. 12). As expected, analysis of the electronic structure of complex [W (=C=C=C=C=C=C=C(NMe2)2 (CO)5] by DPT methods showed that the LUMO is mostly localized on the odd carbon atoms of the chain, whereas the HOMO is on the even carbons. In accord with these electronic features, it was found that [W =C=C=C=C=C=C=C(NMe2)21(00)5] readily adds dimethylamine across the 05=05 bond, to give the isolable alkenyl-pentatetraenylidene derivative [W =C=C=C=C=C(NMe2)CH=C(NMe2)21(00)5] [69, 70]. 

SB. Actually, these tautomeric equilibria are more complex because each of these three forms can exist as two geometric isomers ( and Z for 75A and 75A) or two conformers (rotamers E and Z for 75B). When + H, two diastereomers cis and trans and R ) are possible for the cyclic tautomer 75B. These equilibria have been thoroughly investigated (88TH2) by means of electronic, IR, H-, and C-NMR spectroscopy. The structure of the solid 5-hydroxypyrazoline 74B- (R = Me R = H R = Ph R" = i-Pr) was confirmed by X-ray diffraction (87MI5). An approximate generalization of the influence of the structural factor on these equilibria is shown in Table X. 

Complex Compounds of Agl. A historical review of the conductance studies of these compounds and the emf s of cells based on these solid electrolytes, was published in 1969 (95). Another review, which discusses the conductance and the structure of various solid electrolytes (Agl and its derivatives, Ag2S, LiaSOif, NaaO llAlaOa) was published in 1972 (96). There have been several papers published since, especially by Italian and Japanese workers. 

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