The effects of indium segregation on exciton binding energy and oscillator strength in GaInAs/GaAs quantum wells

We solve analytically the Schrödinger equation taking into account the shape changes of GaInAs/GaAs quantum wells due to indium segregation during the MBE growth by using transfer matrix method. The indium compositional profiles of the quantum wells are provided using the phenomenological model. The fundamental transition energy, binding energy and oscillator strength of excitons as a function of indium segregation coefficient R$R$ and well width are studied. For narrow wells (less than 40 ML), the exciton binding energy and oscillator strength decrease, but for wide wells (larger than 40 ML), increase with increasing the segregation coefficient R$R$. It is shown that indium segregation degrades the optical properties and results in a blue-shift of exciton transition energy in GaInAs/GaAs quantum wells.     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.     

Theoretical investigation of the mechanism of primary amines reacting with hexamolybdate: an insight into the organoimido functionalization and related reactions of polyoxometalates

The functionalization of polyoxometalates (POMs), especially with an amino group to yield organonitrogenous derivatives of POMs, is an efficient approach to the enrichment of their structures and the diversification of their properties for various applications. The mechanism for the formation of organonitrogenous-derivatized hexamolybdates was explored by investigating the monofunctionalization of the [Mo(6)O(19)](2-) ion with methylamine using the density functional theory (DFT) method. The calculations show that the direct imidoylization of hexamolybdate with methylamine is both kinetically and thermodynamically unfavorable. However, this imidoylization was found to take place readily in the presence of dimethylcarbodiimide (DMC), for which the free-energy barrier was calculated to be +32.5 kcal mol(-1) in acetonitrile. Moreover, various factors controlling the efficiency of the imidoylization were examined. The calculations show that [W(5)MoO(19)](2-) has a relatively lower reactivity than [Mo(6)O(19)](2-), and that the imidoylization of [W(6)O(19)](2-) is an unfavorable process. With respect to the effect of carbodiimides, it is found that the catalytic activity is directly proportional to the electron-withdrawing effects of the substituents. As to the reactivity of R-NH(2) , the computation results indicate that the free-energy barriers of the substitution reactions are linearly correlated with the basicity constants (pK(b)) of the amino groups. It is noteworthy that the introduction of the proton dramatically decreases the free-energy barrier of the imidoylization of [Mo(6)O(19)](2-) catalyzed by DMC to 24.3 kcal mol(-1) in acetonitrile.     

Syntheses and structural characterizations of di-substituted alkylimido hexamolybdates: an insight on bi-alkylimido functionalization

Bi-alkylimido functionalization of hexamolybdates has been developed and several novel di-substituted alkylimido hexamolybdates with n-butyl, cyclohexyl and tert-butylamines as the imido-releasing reagents have been synthesized in reasonable yields. Their structures have been characterized by elemental analysis, IR, UV-Vis, and ESI mass spectrometry. Moreover, the structures of [Mo(6)O(17)(NCy)(2)](2-) and [Mo(6)O(17)(NCMe(3))(2)](2) have been determined by single-crystal X-ray diffraction techniques. It is notable that the compound (Bu(4)N)(2)[Mo(6)O(17)(NCy)(2)] crystallizes in polar space group Fdd2 with potential ferroelectricity. In addition, theoretical investigation of the reactivity and regioselectivity of bi-alkylimido functionalization has also been conducted. The calculation results show that more energy is required for the bi-functionalization process than for the mono-substitution process, and that the cis-bi-functionalization is the kinetically favored process while trans-[Mo(6)O(17)(NR)(2)](2-) is the thermodynamically favored product.     

A novel one‐dimensional coordination polymer,catena‐poly[[diaquacobalt(II)]‐μ‐(2,2′‐bipyridyl‐3,3′‐dicarboxylato‐κ4N,N′:O,O′)]

The title compound, [Co(C₁₂H₆N₂O₄)(H₂O)₂]_n, has been hydro­thermally synthesized and structurally characterized. It consists of polymeric chains of [Co{μ‐(2,2′‐bipyridyl‐3,3′‐di­carboxyl­ato‐κ⁴N,N′:O,O′)}(H₂O)₂] units, in which each Co^II cation is octahedrally coordinated by two chelating pyridyl N atoms, two chelating carboxyl O atoms from different carboxylate groups of another bipyridyl ligand, and two water mol­ecules as terminal ligands. A crystallographic twofold axis parallel to the chain axis, passes through the Co atom.