Orbital electronegativity and analytical representation of atom valence state energy

An analytical representation of atom valence state energy (E(n_j), j = 1,…?4; E(n_j) is a nonlinear function of orbital occupancy numbers n_j) is proposed and explicitly derived for H? Ar; the values of electronegativity calculated based on E(n_j) agree within truncation error with those of Hinze and Jaffe. However, in our representation, orbital electronegativity χ and hardness parameters η of a given orbital always include nonlinear contributions from other orbitals, hence accounting for their influence on χ and η. An atomic charge calculation procedure based on E(n_j) is also described and shown to perform well.     

Electronic structures of YBa2Cu3OY doped by La

Based on the EHMO approach, the band structures for the Y? Ba? Cu? O superconductors doped by La were calculated. The influence of the partial substitutions of La for Y and Ba in YBa₂CU₃O_y on its electronic structures was investigated. The results demonstrate that the La doping at the Ba site has a great effect on the electronic structures of the Y? Ba? Cu? O superconductors, whereas the change in the band structures caused by the La doping at the Y site is very small. The increase in the oxygen content caused by the La doping results in an increase in the densities of states at E_f, N(E_f), for La_1+x Ba_2?xCu₃O_y, but the increase in N(E_f) cannot compensate the decrease caused by the La doping at the Ba site. In addition, the 2D Cu? O planes are much more sensitive to the change in N(E_f) than are the 1D Cu? O ribbons, which implies an important role of the 2D Cu? 0 planes in the Y? Ba? Cu? O superconducting system, regardless of whether La substitutes for Y or for Ba. © 1995 John Wiley & Sons, Inc.     

Identification of unknown diffusion coefficient in pure diffusive linear model of chronoamperometry. I. The theory

Coefficient identification problem for diffusion equation u _t (x, t) = (D(x)u _x (x, t)) _x arising in chronoamperometry is studied. The adjoint problem approach is developed for the case when the output measured data is given in the form of left/right flux. Analytical formulas for determination of the values D(0), D(L) at the endpoints x = 0; L, of the unknown coefficient D(x), via the solution v(x, t) of the constant coefficient equation v _t (x, t) = D v _xx (x, t) is obtained. The integral identity relating solutions of the forward and corresponding adjoint problems is derived. This integral identity permits one to prove the monotonicity and invertibility of input-output map, as well as formulate the gradient of the cost functional via the solutions of the direct and adjoint problems.     

Electronic structure of random copolymers

The electronic structure of random copolymers (RCP) is theoretically investigated by the single-site coherent potential approximation. The results are also compared with those by the band calculation for the corresponding ordered system. In the A_{1 –x} B _x binary RCP, a strong reduction in the system band gap (E _g(A_1–x B _x )) is found in the dilute B region when the system has the relation ofE _g(A)>E _g(B). This dependence is caused by the asymmetric quenching in the density-of-states (DOS) singularity at the band-edge states. The gap-opening mechanism and the asymmetric quenching are discussed by focusing on the role of the spatial dimension on the electronic structure of the random system, and the theoretical treatment is finally applied to the calculation of the joint DOS for the Si-Ge RCP system.     

Exchange energy for two closed shells generated by a bare Coulomb potential energy −<Emphasis Type="Italic">Ze</Emphasis><Superscript>2</Superscript>/<Emphasis Type="Italic">r</Emphasis> in the limit of large <Emphasis Type="Italic">Z</Emphasis>, in two dimensions

Two-dimensional (2D) inhomogeneous electron assemblies are becoming increasingly important in Condensed Matter and associated technologies. Here, therefore, we contribute to the Density Functional Theory of such 2D electronic systems by calculating, analytically, (i) the idempotent Dirac density matrix γ(r, r′) generated by two closed shells for the bare Coulomb potential −Ze ²/r and (ii) the exchange energy density e_x(r){\varepsilon_x({\bf r})} . Some progress is also possible concerning the exchange potential V _x (r), one non-local approximation being the Slater potential 2e_x(r)/n(r){2\varepsilon_x(r)/n(r)} , with n(r) the ground state electron density. However, to complete the theory of V _x (r), the functional derivative of the single-particle kinetic energy per unit area δt(s)/δn(r) is still required.     

Synthesis,spectroscopic, thermal and biological aspects of drug‐based copper(II) complexes

A series of novel complexes of the type Cu(II)(L_n)₂(H₂O)₂]^•xH₂O [where L_n = L _1–4 , these ligands being described as: L ₁ , 2‐({4‐[6,7‐dihydrothieno[3,2‐c]pyridin‐5(4H)‐ylsulfonyl]phenylimino}methyl)phenol, x = 1; L ₂ , 2‐({4‐[6,7‐dihydrothieno[3,2‐c] pyridin‐5(4H)‐ylsulfonyl]phenylimino}methyl)‐5‐(methoxy)phenol, x = 2; L ₃ , 5‐chloro‐2‐({4‐[6,7‐dihydrothieno[3,2‐c]pyridin‐5(4H)‐ylsulfonyl]phenylimino}methyl)phenol, x = 2; and L ₄ , 5‐bromo‐4‐chloro‐2‐({4‐[6,7‐dihydrothieno[3,2‐c]pyridin‐5(4H)‐ylsulfonyl]phenylimino} methyl)phenol, x = 1] was investigated. They were characterized by elemental analysis, IR, ¹H‐NMR, ¹³C‐NMR and electronic spectra, magnetic measurements and thermal studies. The FAB‐mass spectrum of [Cu(II)( L ₁ )₂(H₂O)₂]^•H₂O was determined. A magnetic moment and reflectance spectral study revealed that an octahedral geometry could be assigned to all the prepared complexes. Ligands (L_n) and their metal complexes were screened for their in vitro antibacterial activity against Bacillus subtillis, Pseudomonas aeruginosa, Escherichia coli and Serratia marcescens bacterial strains. Kinetic parameters such as order of reaction (n), the energy of activation (E_a), the pre‐exponential factor (A), the activation entropy (ΔS^≠), the activation enthalpy (ΔH^≠) and the free energy of activation (ΔG^≠) are reported. Copyright © 2011 John Wiley & Sons, Ltd.     

Sixth-order many-body perturbation theory. I. Basic theory and derivation of the energy formula

The general expression for the sixth-order Møller-Plesset (MP6) energy, E(MP6), has been dissected in the principal part A and the renormalization part R. Since R contains unlinked diagram contributions, which are canceled by corresponding terms of the principal part A, E(MP6) has been derived solely from the linked diagram terms of the principal part A. These have been identified by a simple procedure that starts by separating A into connected and disconnected cluster operator diagrams and adding terms associated with the former fully to the correlation energy. After closing all open disconnected cluster operator diagrams, one can again distinguish between connected and disconnected energy diagrams, of which only the former lead to linked diagram representations and, therefore, contributions to E(MP6). The connected diagram parts of A have been collected in four energy terms E(MP6)₁, E(MP6)₂, E(MP6)₃, and E(MP6)₄. The sum of these terms has led to an appropriate energy formula for E(MP6) in terms of first- and second-order cluster operators. © 1996 John Wiley & Sons, Inc.     

New algorithm for the numerical solution of the integro-differential equation with an integral boundary condition

In this paper, a sequence of approximate solution converging uniformly to the exact solution for a class of integro-differential equation with an integral boundary condition arising in chemical engineering, underground water flow and population dynamics and other field of physics and mathematical chemistry is obtained by using an iterative method. Its exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation u _n (x) is proved to converge to the exact solution u(x). Moreover, the first derivative of u _n (x) is also convergent to the first derivative of u(x).     

Excess molar enthalpies of dichloropropane + <Emphasis Type="Italic">n</Emphasis>-alkane mixtures

We have determined the excess molar enthalpies H_\textm^\textE H_{\text{m}}^{\text{E}} at 298.15 K and normal atmospheric pressure for the binary mixtures containing dichloropropane and n-alkane [{xCH₂ClCHClCH₃ + (1−x) C _n H_2n+2 (n = 6, 8, 10, 12)} and {xCH₂ClCH₂CH₂Cl + (1−x) C _n H_2n+2 (n = 8, 10)}] using a Calvet microcalorimeter. The H_\textm^\textE H_{\text{m}}^{\text{E}} values for all the mixtures show endothermic behaviour for the whole composition range. The Redlich–Kister equation was used to correlated the experimental values. The experimental excess molar enthalpies were examined on basis of the DISQUAC group-contribution model and the UNIFAC group-contribution method using the version considered by Larsen et al. The experimental and calculated results are discussed in terms of molecular interactions and the proximity effect.     

Rules of electron correlation energies of van der Waals' complexes RgX (Rg = Ar,Kr, X = F,Cl, Br)

First, the intrapair and interpair correlation energies of the Rg atom, X atom, and the optimized RgX (Rg = Ar, Kr, X = F, Cl, Br) complexes are calculated by the MELD program at the 6‐311++g(d), 6‐311++g(3df, 3pd), and cc‐pvqz basis sets (denoted by basis sets a, b, and c, respectively). It is found that the relationship E_corr(RgX) ≈ E_corr(Rg) + E_corr(X) is correct for all the above systems but introducing an unsound absolute error for some RgX systems. Second, the same calculations are selectively carried out for ArF (the smallest system) and KrBr (the largest system) at their increasing interatomic distance. It was found that both the correlation energies of ArF and those of KrBr will decrease whenever the interatomic distance of them become larger. On the basis of our results, we provided an approach to quickly estimate the correlation energies of RgX complexes by which not only the absolute error becomes smaller but more computation work is saved than the direct calculation. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Error evaluation of integral methods by consideration on the approximation of temperature integral

Summary In this paper, the integral methods in general use are divided into two types in terms of their different ways to in order to deal with the temperature integral p(x): for Type A the function h(x)=p(x)x²e^x is regarded as constant vs. x, while for Type B h(x) varies vs. x and ln[p(x)] is assumed to have the approximation form of ln[p(x)]=alnx+bx+c (the coefficients a, b, and c are constant). The errors of kinetic parameters calculated by these two types of methods are derived as functions of x and analyzed theoretically. It is found that Type A methods have the common errors of activation energy, while the Coats-Redfern method can lead to more accurate value of frequency factor than others. The accuracy of frequency factor can be further enhanced by adjusting the expression of the Coats-Redfern approximation. Although using quite simple approximation of the temperature integral, the Coats-Redfern method has the best performance among Type A methods, implying that usage of a sophisticated approximation may be unnecessary in kinetic analysis. For Type B, the revised MKN method has a lower error in activation energy and an acceptable error in frequency factor, and thus it can be reliably used. Comparatively, the Doyle method has higher error of activation energy and great error of the frequency factor, and thus it is not recommended to be adopted in kinetic analysis.     

Ultrasonic Velocities,Densities, and Refractive Indices of Binary Mixtures of Polyethylene Glycol 250 Dimethyl Ether with 1-Propanol and with 1-Butanol

Measurements of the ultrasonic velocity (u), density (ρ) and refractive index (n) for binary mixtures of polyethylene glycol 250 dimethyl ether with 1-propanol and 1-butanol have been made at three temperatures (T=293, 303 and 31 K) over the entire composition range in order to investigate the nature of intermolecular interactions between the components of these liquid mixtures. Various excess thermodynamic properties such as the excess ultrasonic velocity (Δu), deviation in isentropic compressibility (Δk _S ), excess intermolecular free length (L_f^E)(L_{\mathrm{f}}^{\mathrm{E}}), excess acoustic impedance (Z ^E), excess pseudo-Grüneisen parameter (Γ ^E), and molar refraction deviation (ΔR _m) were calculated using experimental values of the ultrasonic velocity, density and refractive index and were then represented with the Redlich-Kister polynomial equation. The observed excess deviation parameter values were explained on the basis of the strength of intermolecular interactions between the components of the mixtures. Estimations of the refractive index and ultrasonic velocity have also been made using various empirical relations and are discussed in terms of the average percentage deviations (APD).     

Mobile ion transport pathways in (LiBr) x [(Li2O)0.6(P2O5)0.4](1−x) glasses

(LiBr) _x [(Li₂O)_0.6(P₂O₅)_0.4]_{(1 − x)} glasses with 0 ≤ x ≤ 0.2 are prepared by melt quenching. Glass transition temperature (T _g), ionic conductivity (σ), and its activation energy (E _a) are determined experimentally and correlated to molecular dynamics (MD) simulations with an optimized potential, fitted to match bond lengths, coordination numbers, and ionic conductivity. Based on equilibrated MD configurations, ion transport pathways are modelled in detail by the bond valence approach to clarify the influence of the halide dopant concentration on the glass structure and its consequence for Li ion mobility. Results of experimental and computational studies are compared with our previous report on the (LiCl) _x [(Li₂O)_0.6(P₂O₅)_0.4]_{(1 − x)} system. Both T _g and σ values are higher for LiBr-doped glasses than for LiCl-doped glasses, but the effect of halide doping is unusually small.     

Effect of MoO<Subscript>3</Subscript> additions on the thermal stability and crystallization kinetics of PbO–Sb<Subscript>2</Subscript>O<Subscript>3</Subscript>–As<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

The present paper reports on the effect of MoO₃ on the glass transition, thermal stability and crystallization kinetics for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x (x = 0, 0.25, 0.5, 0.75 and 1 mol%) glasses. Differential scanning calorimetry (DSC) results under non-isothermal conditions for the studied glasses were reported and discussed. The values of the glass transition temperature (T _g) and the peak temperature of crystallization (T _p) are found to be dependent on heating rate and MoO₃ content. From the compositional dependence and the heating rate dependence of T _g and T _p, the values of the activation energy for glass transition (E _g) and the activation energy for crystallization (E _c) were evaluated and discussed. Thermal stability for (40PbO–20Sb₂O₃–40As₂O₃)_100−x –(MoO₃) _x glasses has been evaluated using various thermal stability criteria such as ΔT, H _r , H _g and S. Moreover, in the present work, the K _r(T) criterion has been considered for the evaluation of glass stability from DSC data. The stability criteria increases with increasing MoO₃ content up to x = 0.5 mol%, and decreases beyond this limit.     

Deviation of activation energy caused by neglecting a temperature term in Ozawa Equation

In the non-isothermal kinetic equation, the temperature integral from 0 to T ₀ never equals to zero, so a deviation of activation energy is introduced when the term is neglected. We propose a new evaluation method on Ozawa Equation. The results show that neglecting this term in Ozawa Equation leads to large activation energy errors, when small absolute values of Δx = x − x ₀(x = E/RT). The deviation of the activation energy is less than 0.55% when |Δx| > 5, but may exceed 10% if |Δx| < 2. The application of this method on the dehydration of CaC₂O₄· H₂O shows that the theoretical error was close to the actual error.     

Graphs to chemical structures. 4: Combinatorial enumeration of planted three-dimensional trees as stereochemical models of monosubstituted alkanes

Planted three-dimensional (3D) trees, which are defined as a 3D version of planted trees, are enumerated by means of Fujita’s proligand method formulated in Parts 1–3 of this series [Fujita in Theor Chem Acc 113:73–79, 80–86, 2005; Fujita in Theor Chem Acc 115:37–53, 2006]. By starting from the concepts of proligand and promolecule introduced previously [Fujita in Tetrahedron 47:31–46, 1991], a planted promolecule is defined as a 3D object in which the substitution positions of a given 3D skeleton are occupied by a root and proligands. Then, such planted promolecules are introduced as models of planted 3D-trees. Because each of the proligands in a given planted promolecule is regarded as another intermediate planted promolecule in a nested fashion, the given planted promolecule is recursively constructed by a set of such intermediates planted promolecules. The recursive nature of such intermediate planted promolecules is used to derive generating functions for enumerating planted promolecules or planted 3D-trees. The generating functions are based on cycle indices with chirality fittingness (CI-CFs), which are composed of three kinds of sphericity indices (SIs), i.e., a _d for homospheric cycles, c _d for enantiospheric cycles, and b _d for hemispheric cycles. For the purpose of evaluating c _d recursively, the concept of diploid is proposed, where the nested nature of c _d is demonstrated clearly. The SIs are applied to derive functional equations for recursive calculations, i.e., a(x), c(x ²), and b(x). Thereby, planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers are enumerated recursively by counting planted promolecules. The resulting values are collected up to 20 carbon content in a tabular form. Now, the enumeration problem initiated by mathematician Cayley [Philos Mag 47(4):444–446, 1874] has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.     

Thermal decomposition of lighter lanthanide selenate hydrates and their solid solutions

The thermal dehydration-decomposition of Ln₂(SeO₄)₃·nH₂O (wheren=12 forLn=Pr, Nd andn=8 forLn=Sm) and Pr_xLn_2−x(SeO₄)₃·nH₂O (wheren=12 forx=1.0 andLn=Nd;n=8 forx=0.2 and 1.0 in case ofLn=Sm) have been reported.

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Zusammenfassung Die thermische Dehydratation-Zersetzung von Ln₂(SeO₄)₃·nH₂O (mitn=12 fürLn=Pr, Nd undn=8 fürLn=Sm) und Pr_xLn_2−x(SeO₄)₃·nH₂O (mitn=12 fürx=1.0 undLn=Nd;n=8 fürx=0.2 und 1.0 in Falle vonLn=Sm) wurde beschrieben.

     

Relationship Between Heat Capacity and Thermal Expansion Derived from the Lennard–Jones Potential

The relationship between heat capacity (C _p) and linear thermal expansion (α) derived from the Lennard–Jones potential is C _p=Aα(U ₀–E), where U ₀ is the heat of sublimation at T=0, E is the enthalpy and A is the coefficient. The values of A for different solidified inert gases coincide with one another within the limits of experimental error (±2%). The relationship is shown to be valid for various substances: solidified rare gases, diamond, halite and copper. This revised version was published online in July 2006 with corrections to the Cover Date.