Electronegativity equalization and the electronic structure of polyhedral clusters of main-group atoms

The concept of the equalization of atomic electronegativities accompanving molecule formation is applied to a study of the electronic structure of polyhedral clusters of main-group atoms such as Ge, Sn, Pb, Tl, and Bi. Emphasis is placed upon charged clusters such as Sn_9?x Pb(x = 0 → 9), Sn_9-xGe, Sn_8?xPb_x Tl^5?, Sn₂Bi, SnTe, etc. The role of the relativistic spin-orbit splitting of an np shell into np_1/2 and np_3/2 subshells in modifying atomic and hence molecular electronegativities is discussed. Correlations are made between calculated charge distributions and observed¹⁹⁹ Sn NMR chemical shifts for clusters of a given size and charge. It is concluded that a useful picture of charge distributions in these clusters may be obtained from electronegativity equalization considerations.     

Stability,Formation and Dissociation Kinetics of the Pentacoordinate Ni2+ and CO2+ Complexes with 1,5-Diazacyclooctane-N,N′-diacetic Acid

The stability constants of the Ni²⁺ and Co²⁺ complexes with 1,5-diazacyclooctane-N,N′-diacetic acid (H₂DACODA) have been determined potentiometrically in 0.5M KNO₃ at 25°. Only M(DACODA) and M(DACODA)OH^? were observed. In addition the formation and dissociation kinetics of the pentacoordinate complexes M(DACODA) has been studied in aqueous solution using a stopped-flow technique. Formation follows the rate law v_f = k_f [M²⁺] [HDACODA^?]/[H⁺], which can be interpreted as a bimolecular process either between M²⁺ and DACODA^2? (k) or between MOH⁺ and HDACODA^? (k). The second order rate constants k are much higher than those expected from water exchange and can only be explained by a strong internal conjugate base effect. In the limiting case, however, this is equivalent to the second possible explanation, which assumes MOH⁺ and HDACODA^? as reactive species. The dissociation rate is given by v_d = (k^ML + k [H⁺]) · [M(DACODA)].     

Redshifts and blueshifts of OH vibrations

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlation between these quantities, are presented for a water molecule and an OH^? ion in a uniform electric field of varying field strength. It is explained why a bound H₂O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH^?1 ion, either a downshift or an upshift. The frequency-field variation is well accounted for by the expression Δν_OH α ?E‖ · (d μ/dr_OH + 1/2 · ?μ/?r_OH). A frequency maximum occurs at the field strength where ?μ‖^tot/?r_OH ～ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/dr_OH is positive (this is the situation for OH^?), and (2) the maximum frequency falls at a negative field when dμ/dr_OH is negative (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/dr_OH and ?μ/?r_OH. Correlation curves between the external linear force constant, k^ext, and r_OH,e are closely linear over the whole field range studied here, whereas the frequency vs. r_OH,e and force constants vs. r_OH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the ν vs. r_OH,e curves has a slope of ～ ? 16,000 cm^?1/Å. © 1993 John Wiley & Sons, Inc.     

Cuprous complexes and dioxygen. VIII. Steric factors controlling one- or two-electron reduction of O2 by cuprous complexes with substituted imidazoles

In aqueous acetonitrile (AN), Cu (I) forms the complexes Cu(AN)L⁺ and CuL with a series of substituted imidazoles (L). Stability constants logK of Cu(AN)⁺ + L ? Cu(AN)L⁺ and logβ₂ were near 5 and 12, resp., log units for all ligands. The rate of autoxidation is described by ?d[O₂]/dt=[CuL]²[O₂](k_a/(1+k_b[CuL]) + (k_c[L]+k_d)/([CuL] + k_e[Cu])), implying competition between one- or two-electron reduction of O₂. The value of k_c decreases from 5500M ^?2S ^?1 for unsubstituted imidazole to about 40M ^?2S ^?1 for 2-methylimidazole or 1,2-dimethyl-imidazole and essentially zero for the corresponding 2-ethyl-derivatives. On the other hand, k_a and k_b are much less influenced by the nature of the ligands, all values being near 5 · 10⁴M ^?2S ^?1 and 10³M ^?1, respectively, for the complexes with the last four bases. Thus rather subtle sterical changes may strongly influence the relative importance of different pathways in the reduction of dioxygen by cuprous complexes.     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Probing the ultrafast photoelectron spectra of Br2 molecule

The time‐dependent‐wave‐packet method is applied to study the ionization of Br₂ molecule with four ionization processes. The ground state absorption makes the photoelectron to be left in the three final ionic states: Br (X²∑), Br (A²∏_u), and Br (B²∑), and each population of these ionic states is related with the laser intensities. The information of the dissociation can be got by analyzing the photoelectron features of the transient wave packet, which also suggests that an ionization process occurs during the dissociation, and the Br atoms that mainly resulted from the dissociation of Br₂ (C¹∏_u) are ionized at later time delays as the dissociation is nearly complete. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Dipole,quadrupole, octupole,and dipole–dipole–quandrupole polarizabilities and second hyperpolarizabilities at real and imaginary frequencies for helium in the 23S state: Dispersion-energy coefficients for interactions between He(23S) and H(12S), He(11S), He(23S), or H2(X1∑g+)

We have determined the dynamic dipole (α₁), quadrupole (α₂), octupole (α₃), and dipole–dipole–quadrupole (B) polarizabilities and the second hyperpolarizability tensor (γ) for the helium atom in its lowest triplet state (2³S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (ω) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss–Legendre grid running from zero to ?ω = 20 E_h. We have also determined the dispersion-energy coefficients C₆, C₈, and C₁₀ for the systems H(1²S)? He(2³S), He(1¹S)? He(2³S), and He(2³S)? He(2³S) and the C, C, C, C, and C coefficients for the interaction He(2³S)? H₂(X¹∑). Our values of the higher-order multipolar polarizabilities and of γ for the 2³S state of helium are, we believe, the first to be published. © 1993 John Wiley & Sons, Inc.     

The density matrix in the two-particle function method

The first- and second-order density matrices D ^(N) and D for the function g⁽ⁿ⁾ = A_N[g(1, 2) …? g(N ? 1, N)] are expressed by the g function itself and its density matrix D . In a singlet state the generating functions for spatial parts of these matrices are simply connected with there solvent of the Fredholm equation in which the spatial part of D is a kernel. Some special cases of g(1, 2) are considered. It isestablished that the number of large eigenvalues of D does not exceed that of different eigenvalues of D . Thus the degeneracy in the spectrum of D causes the appearance of such large eigenvalues.     

Sigma,pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly‐correlated trial wavefunction forms for the X¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman‐Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I¹Π_g state. Our best energy for this state, ?0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Bridging gold: B‐Au‐B three‐center‐two‐electron bonds in electron‐deficient B2Aun−/0 (n = 1, 3, 5) and mixed analogues

A systematic density functional theory and wave function theory investigation on the geometrical and electronic structures of the electron‐deficient diboron aurides B₂Au (n = 1, 3, 5) and their mixed analogues B₂H_mAu (m + n = 3, 5) has been performed in this work. Ab initio theoretical evidences strongly suggest that bridging gold atoms exist in the ground states of C_2v B₂Au^?(¹A₁), C₂ B₂Au(¹A), C_2v B₂Au₃(²B₁), C_2v B₂Au(¹A₁), and C_s B₂Au₅(²A″), which all prove to possess a B? Au? B three‐center‐two‐electron (3c‐2e) bond. For B₂H_mAu (m + n = 3, 5) mixed anions, bridging B? Au? B units appear to be favored in energy over bridging B? H? B, as demonstrated by the fact that the Au‐bridged C_2v B₂H₂Au^? (¹A₁), C_s B₂HAu (¹A′), and C₁ B₂HAu (¹A) lie clearly lower than their H‐bridged counterparts C_s B₂H₂Au^? (¹A′), C₂ B₂HAu (¹A), and C_2v B₂HAu (¹A₁), respectively. Orbital analyses indicate that Au 6s makes about 92–96% contribution to the Au‐based orbitals in these B‐Au‐B 3c‐2e interactions, whereas Au 5d contributes 8–4%. The adiabatic and vertical detachment energies of the concerned anions have been calculated to facilitate their future experimental characterizations. The results obtained in this work establish an interesting 3c‐2e bonding model (B? Au? B) for electron‐deficient systems in which Au 6s plays a major role with non‐negligible contribution from Au 5d. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

An insight into optical and EPR properties of AgCl and AgF complexes through MS–Xα and SCCEH calculations

MS-Xα and SCCEH calculations on the Ag²⁺ complexes AgF and AgCl (displaying an elongated D_4h symmetry) have been carried out for a better understanding of their experimental optical and EPR properties. As salient features, the present work supports that the unpaired electron in AgCl spends a little more time on ligands than on Ag²⁺, in agreement with the previous analysis of EPR and optical data for KCl:Ag²⁺. Furthermore, the five experimental optical transitions observed in that case are reasonably assigned. The first transition (observed at 12,500 cm^?1) is assigned to a jump involving the 5a_1g orbital built mainly (∽70%) from 3p orbitals of axial ligands, a fact that reflects the distinct level scheme for AgCl when compared to that for more ionic complexes. Calculations on AgF and AgF performed as a function of the equatorial Ag²⁺ –F^? distance led to a reasonable understanding of experimental gyromagnetic and superhyperfine tensors displayed by Ag²⁺ in fluorides. The different relative decrease undergone by g‖– go (8%) and g ? – go (28%) on passing from CsCdF₃:Ag²⁺ to RbCdF₃:Ag²⁺ is shown to be consistent with the formation of AgF and AgF complexes, respectively, related to the different substitutional position of Ag²⁺ in such lattices. The decrement of about 8.5% experienced by both g‖ – go and g? – go values on going from CsCdF₃:Ag²⁺ to NaF:Ag²⁺ is pointed out to reflect the different electrostatic potential (exerted by the rest of the lattice upon the complex) seen by AgF embedded in NaCl or perovskite-type lattices. © 1994 John Wiley & Sons, Inc.     

Ab initio calculation of electronic states of the ions H4+ and H5+

Electronic state calculations for the ions H₄⁺ (with symmetries D ₄ and C _2v) and H (with symmetries D ₅ and D _2d) are made using the valence-bond method. All the configurations obtained from the given set of 1s-functions of Slater type are taken into account. Space functions are used throughout the computation (“spin-free quantum chemistry”). Preliminary quasidiagonalization of the secular equation is implemented by the construction of the multiplet eigenfunctions ^2S+1Γ^(α) from the initial variational functions. The results of the calculations are as follows: the ion H is unstable, the ion H is stable with equilibrium nuclear conformation of symmetry D _2d and with the energy of dissociation into H and H₂ near 4 eV.     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.     

Studies on the composition and kinetics of chromium(III)-alanine system

Kinetics of the complex formation of chromium(III) with alanine in aqueous medium has been studied at 45, 50, and 55°C, pH 3.3–4.4, and μ = 1 M (KNO₃). Under pseudo first-order conditions the observed rate constant (k_obs) was found to follow the rate equation: Values of the rate parameters (k_an, k, K_IP, and K) were calculated. Activation parameters for anation rate constants, ΔH^≠(k_an) = 25 ± 1 kJ mol^?1, ΔH^≠(k) = 91 ± 3 kJ mol^?1, and ΔS^≠(k_an) = ?244 ± 3 JK^?1 mol^?1, ΔS^≠(k) = ?30 ± 10 JK^?1 mol^?1 are indicative of an (I_a) mechanism for k_an and (I_d) mechanism for k routes (‥substrate Cr(H₂O) is involved in the k route whereas Cr(H₂O)₅OH²⁺ is involved in k′ route). Thermodynamic parameters for ion-pair formation constants are found to be ΔH°(K_IP) = 12 ± 1 kJ mol^?1, ΔH°(K) = ?13 ± 3 kJ mol^?1 and ΔS°(K_IP) = 47 ± 2 JK^?1 mol^?1, and ΔS°(K) = 20 ± 9 JK^?1 mol^?1.     

Über das Auftreten von Polysulfan-diphosphonaten bei der Umsetzung von Monothiophosphat mit Disulfan-diphosphonat

On the Formation of Polysulphane Diphosphonates by the Reaction of Monothiophosphonate with Disulphane Diphosphonate In acid solution SPO reacts with S₂P₂O forming higher polysulphane diphosphonates. The formation of S₃P₂O and S₄P₂O is proved by evaluation of the double labelling with ³⁵S? ³²P after high paper electrophoresis.     

Thermochemistry and kinetics of the reaction of methyl mercaptan with iodine

The gas-phase reaction CH₃SH + I₂ has been studied spectrophotometrically over the temperature range of 476–604 K. It was found that the reaction undergoes H abstraction by I at ≤575 K, leading to the formation of MeSI and followed by a secondary reaction which leads to the formation of MeSSMe: Taking into consideration the effect of reaction (2), the equilibrium constant K₁ (554 K) has been evaluated to be 0.025 ± 0.004. This value was combined with the estimated values S (CH₃SI, g) = 73.7 ± 1.0 eu and 〈ΔC〉 = 0.87 ± 0.3 eu to obtain ΔH = 4.03 ± 0.73 kcal/mol. This yields ΔH (CH₃SI, g) = 7.16 ± 0.73 kcal/mol when combined with known thermochemical values for CH₃SH, HI, and I₂. A kinetic study was vitiated by the concurrent heterogeneous reaction of MeSH and I₂ at lower temperatures and the rather complicated chemistry occurring at elevated temperatures. However, attempts at measuring rate constants at 554 K lead to a lower limit of ΔH (CH₃S·, g) ≥ 29.5 ± 2 kcal/mol when an estimated value of A = 10^{10.8 ± 0.2} L/mol·s for the reactionc is used. DH (CH₃S–I) is estimated to be 49.3 ± 1.7 kcal/mol. The bond strengths of some divalent sulfurs and the reaction mechanisms are discussed. A crude estimate of DH⁰(H–CH₂SH) = 96 ± 1 kcal has been obtained from the kinetic data.     

The kinetics of the interaction of peroxy radicals. I. The Tertiary Peroxy Radicals

Existing data on the self-reactions of tertiary peroxy radicals RO₂ has been reanalyzed and corrected to deduce Arrhenius parameters for both termination and nontermination paths. For R = t-Butyl, these are logk_t(M^?1sec^?1) = 7.1 - (7.0/θ) and logk_nt(M^?1sec^?1) = 9.4 - (9.0/θ), respectively, different from those recommended by other authors. The higher magnitudes observed for termination processes of tertiary peroxy radicals like those of cumyl and 1,1-diphenylethyl have been discussed in terms of a much greater cage recombination of cumyloxy radicals as contrasted with t-butoxy radicals. It is shown that for benzyl peroxy radicals, the R—O bond dissociation energy is sufficiently low (18–20 kcal) that reversible dissociation into R^˙ + O₂ opens a competing second-order path to fast recombination R^˙ + RO → ROOR. This path is probably not important for cumyl peroxy radicals under usual experimental conditions but can become important for 1,1-diphenyl ethyl peroxy radicals at (O₂) < 10^?3M. At very low RO concentrations (<10^?5M), in the absence of added O₂, an apparent first-order disappearance of RO can occur reflecting the rate determining breaking of the cumyl—O bond followed by the second step above. The thermochemistry of RO is used to show that the reaction of R₂O₄ → 2RO + O₂ must be concerted and cannot proceed via RO which is too unstable and cannot form even from RO^˙ + O₂.     

Cuprous Complexes and Dioxygen. Part 12.. Rate law and mechanism of the copper-catalyzed oxidation of ascorbic acid in aqueous acetonitrile

The copper-catalyzed oxidation of ascorbic acid (AscH₂) has been studied with a Clark electrode in aqueous MeCN. Cu^I or Cu^II may be equally used as the source of metal ion, without influence on the rate law. At sufficiently high [MeCN], the rate of the overall reaction is essentially given by the rate of Cu^I autoxidation: the reaction is of first order with respect to [Cu] and [O₂] and shows an inverse-square dependence on [MeCN] as observed for the autoxidation of Cu. The pH dependence is complicated by the combination of the intrinsic pH effect on autoxidation with an additional term in the rate law which is directly proportional to [AscH^?]. The latter term is explained by direct oxidation of the organic substrate by the primary dioxygen adduct of Cu^I, CuO. For [MeCN] < 0.7M , a gradual and pH-dependent transformation of this rate law and deviation from the first-order dependence on [O₂] is indicated.     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Correlated n1,3S states for coulomb three‐body systems

n^1,3S (n = 1 ? 4) states for atomic three‐body systems are studied with the Angular Correlated Configuration Interaction method. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) involve only linear parameters; (iii) show a fast convergency rate for the energy; and (iv) form an orthogonal set. The efficiency of the method is illustrated by the study a variety of three‐body atomic systems [m m m] with two negatively charged light particles, with diverse masses m and m, and a heavy positively charged nucleus m. The calculated ground 1¹S and excited n^1,3S (n = 2 ? 4) state energies are compared with those given in the literature, when available. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011