Chemical bond breaking/forming as a Franck–Condon electronic process

We describe chemical bond changes as Franck–Condon electronic processes within a new theoretical ansatz that we call ‘rigged’ Born–Oppenheimer (R-BO) approach. The notion of the separability of nuclear and electron states implied in the standard Born–Oppenheimer (BO) scheme is retained. However, in the present scheme the electronic wave functions do not depend upon the nuclear coordinate (R-space). The new functions are obtained from an auxiliary Hamiltonian corresponding to the electronic system (r-coordinates) submitted to a Coulomb potential generated by external sources of charges in real space (α-coordinates) instead of massive nuclear objects. A stationary arrangement characterized by the coordinates α_0A, is determined by a particular electronic wave function, ψ(r;α_0A); it is only at this stationary point, where an electronic Schrödinger equation: H_e(r,α_0A)|Ψ(r;α_0A)=E(α_0A)|Ψ(r;α_0A) must hold. This equation permits us to use modern electronic methods based upon analytic first and second derivatives to construct model electronic wave functions and stationary geometry for external sources. If the set of wave functions {Ψ(r;α_0A)} is made orthogonal, the energy functional in α-space, E(α;α_0A)=Ψ(r;α_0A)|H_e(r,α_0A)|Ψ(r;α_0A) is isomorphic to a potential energy function in R-space: E(R;α_0A)=Ψ(r;α_0A)|H_e(r,R)|Ψ(r;α_0A). This functional defines, by hypothesis, a trapping convex potential in R-space and the nuclear quantum states are determined by a particular Schrödinger equation. The total wave function for the chemical species A reads as a product of our electronic wave function with the nuclear wave function (Ξ_ik(R;α_0A)): Φ_ik(r,R)=Ψ_i(r,α_0A)Ξ_ik(R;α_0A). This approach facilitates the introduction of molecular frame without restrictions in the R-space. Two molecules (characterized with different electronic spectra) that are decomposable into the same number of particles (isomers) have the same Coulomb Hamiltonian and they are then characterized by different electronic wave functions for which no R-coordinate ‘deformation’ can possibly change its electronic structure. A bond breaking/forming process must be formally described as a spectroscopic-like electronic process. The theory provides an alternative to the adiabatic as well as the diabatic scheme for understanding molecular processes. As an illustration of the present ideas, the reaction of H₂+CO leading to formaldehyde is examined in some detail.     

Correction of characteristic mass in Zeeman graphite furnace atomic absorption spectrometry

A systematic study has been made of the effect of hollow-cathode lamp current and slit width (SW) of the 4100ZL spectrometer on characteristic mass m₀, Zeeman sensitivity ratio R, and roll-over absorbance A_r, for nine elements: Au, Bi, Cd, Co, Cu, Mn, Ni, Pb and Tl. The lamp spectra near the recommended analytical lines have been investigated for these elements. The data obtained have been combined with a theoretical analysis to show that the self-absorption of the analytical lines observed with increasing current and the rise of non-absorbable radiation with increasing SW affect m₀ and the A_r and R parameters differently. It is shown that a separate correction requiring additional narrow-slit measurement of the A_r parameter is necessary to take into account the SW effect on m₀. A separate-correction method built upon this basis offers a substantial improvement of the accuracy of taking into account the SW effect on m₀ compared with the method of combined correction proposed earlier (E.G. Su, A.I. Yuzefovsky, R.G. Michel, J.T. McCaffrey and W. Slavin, Microchem. J., 48 (1993) 278). Exceptions are the Mn and Ni analytical lines, for which the m₀ correction has turned out to be ineffective both in the separate- and combined-correction procedures because of adjacent absorption-sensitive lines passing through the wider slit.     

Maintenance of the slope of linearized calibration curves in Zeeman graphite furnace atomic absorption spectrometry

L'vov and co-workers developed a theoretical model and computational procedure (B.V. L'vov, L.K. Polzik and N.V. Kocharova, Spectrochim. Acta Part B, 47 (1992) 889 and B.V. L'vov, L.K. Polzik, N.V. Kocharova, Yu.A. Nemets and A.V. Novichikhin, Spectrochim. Acta Part B, 47 (1992) 1187) that linearized calibration curves in Zeeman graphite furnace atomic absorption spectrometry by taking into account the presence of stray light. The calculations of L'vov and co-workers were based on three parameters: the rollover absorbance A_r, Zeeman sensitivity ratio R, and the original background corrected peak absorbance values A_z. In order to simplify the calculations, R was assumed to be unity. In the studies reported here, this simplification is shown to be unsatisfactory because the slope obtained in the upper portion of the calibration curve, after linearization, is found to be different from the slope obtained in the normal linear region. Deviations between these slopes were found to be as high as 30%. The present work also shows that the theoretical model of L'vov and co-workers does not have a mathematical solution at high values of A_z. This failure of the model prevents its use at high A_z values. The physical nature of this failure is still unclear, which points to the necessity for further work to understand the inadequacies of the present theory. In the present studies, calculations based on the Newton method of successive approximations (A.I. Yuzefovsky, E.G. Su, R.G. Michel, W. Slavin and J.T. McCaffrey, Spectrochim. Acta Part B, 49 (1994) 1643), allow incorporation of the experimental value of R at the rollover point R′, which better linearizes the calibration curves. By use of this approach, a satisfactory result is obtained for lead (R′ = 0.67) up to the point of failure of the model at high values of A_z.     

Driving force prediction for inclusion complexation of α-cyclodextrin with benzene derivatives by a wavelet neural network

A wavelet neural network (WNN) has been constructed and used to predict the binding constant for the inclusion of α-cyclodextrin with benzene derivatives from the substituent molar refraction (R_m) and hydrophobic constant (π). The ln K_a values predicted by WNN from R_m and π are close to the experimental data. The results indicate that the inclusion complexation of α-cyclodextrin with mono- and 1,4-disubstituted benzene is dominantly driven by the van der Waals force and hydrophobic interactions.     

Structure, crystal chemistry and thermal evolution of the δ-Bi2O3-related phase Bi9ReO17

The thermal evolution and structural properties of fluorite-related δ-Bi₂O₃-type Bi₉ReO₁₇ were studied with variable temperature neutron powder diffraction, synchrotron X-ray powder diffraction and electron diffraction. The thermodynamically stable room-temperature crystal structure is monoclinic P2₁/c, a=9.89917(5), b=19.70356(10), c=11.61597(6) Å, β=125.302(2)° (R_p=3.51%, wR_p=3.60%) and features clusters of ReO₄ tetrahedra embedded in a distorted Bi–O fluorite-like network. This phase is stable up to 725 °C whereupon it transforms to a disordered δ-Bi₂O₃-like phase, which was modeled with δ-Bi₂O₃ in cubic Fm3¯m with a=5.7809(1) Å (R_p=2.49%, wR_p=2.44%) at 750 °C. Quenching from above 725 °C leads to a different phase, the structure of which has not been solved but appears on the basis of spectroscopic evidence to contain both ReO₄ tetrahedra and ReO₆ octahedra.     

The oxidation mechanisms of Cu54Ni45Mn1 (Constantan) tapes: Kinetic analysis

The kinetic parameters, namely the triplet activation energy E_A, model function f(α) or g(α) and pre-exponential factor A of the oxidation of Constantan tapes in 1 atm of oxygen have been determined from both isothermal and non-isothermal thermogravimetry. For isothermal experiments, with temperatures ranging from 650 °C to 900 °C, the results from direct conversion of the weight increase as a function of the time and curve fitting, are compared with the isoconversion method. For the non-isothermal experiments, with heating rates from 1 °C/min to 20 °C/min, comparison is made between the Friedman differential method and the integral methods of Kissinger, Ozawa and Li and Tang. All methods give apparent activation energies with relative standard deviations as low as 3%. The results converge to the identification of three stages in the oxidation behaviour. A parabolic law for reaction extents α below 15% with E_A = 246 ± 7 kJ mol⁻¹, ln A = 14.3, is followed by two linear stages with E_A = 244 ± 4 kJ mol⁻¹ and ln A = 15.3 for 0.18 < α < 0.35 and E_A = 228 ± 15 kJ mol⁻¹, ln A ≈ 13 for α > 45%, respectively.     

Parameter determination of a thermal desorption model

A new method for the analysis of thermal desorption spectra is presented, based on the experimental peak maximum functions for temperatureT _m(β) and pressureP _m(β) and a rigorous mathematical treatment. The resonant heating rate β_r is determined, satisfyingT _m(β_r)=T _r, whereT _r is the resonant temperature defined byA exp(−E _d/(RT _r))=1. Desorption energyE _d and frequency factorA can be determined simultaneously with relatively high robustness towards statistical experimental errors as demonstrated by computer-simulated thermal desorption spectra.     

Mass,size and shape of micelles formed in aqueous solutions of ethoxylated nonyl-phenols

The study was extended to analysis of mass, size and conformation of micelles formed in aqueous solutions of ethoxylated nonyl phenols. The results obtained by ultracentrifugal technique between 293 and 323 K have proved that the slightly ethoxylated nonyl phenols form micelles with high molecular mass and larger size at constant temperature, while the increasing length of the ethylene oxide chain favours formation of micelles of smaller molecular mass and size. The transformation of conformation from oblate to spherical shapes ensues with increasing temperature at constant ethoxy number or with ethoxylation at constant temperature. The second virial coefficient decreases with increasing temperature and decreasing ethoxy number. In accordance with the earlier conclucions, the change of the second virial coefficient relates to enhanced variation of monomer solubility, stabilization of micelle structure and increased deviation from ideal behaviour of a given micellar system.Symbols a major axis of micelle, Å - a _m attractivity factor, cm³ erg molecule² - b minor axis of micelle, Å - c concentration, g dm^–3 - c _b equilibrium concentration at the bottom of the cell, g dm^–3 - c _m equilibrium concentration at the meniscus of the cell, g dm^–3 - c _o initial concentration in the cell, g dm^–3 - c _M critical micellization concentration, mol dm^–3 - e eccentricity - f _IS Isihara-constant - f/f _o frictional ratio of micelle - amount of water in micelle per ethoxy group, mol H₂O/mol EO - n aggregation number, monomer micelle^–1 - n _EO number of ethoxy groups - r distance of Schlieren peak from the axis, cm - r _b distance of cell bottom from the axis, cm - r _m distance of cell meniscus from the axis, cm - R _h equivalent hydrodynamic radius of micelle, Å - s _t sedimentation coefficient, s - reduced sedimentation coefficient, s - reduced limiting sedimentation coefficient, s - ¯v _t volume of micelle, cm³ micelle^–1 - partial specific volume of solute, cm³g^–1 - partial specific volume of solute reduced to 293 K, cm³ g^–1 - B _a, B_e constants, cm³ mol g^–2 - B ₂ second virial coefficient, cm³ mol g^–2 - M _m ^a mass average apparent molecular mass of micelle, g mol^–1 - M _m mass average molecular mass of micelle corrected withB ₂, g mol^–1 - M _m ^cM mass average molecular mass of micelle belonging toc _M, g mol^–1 - M ¹ mass average molecular mass of monomer, gmol^–1 - N _A the Avogadro's number, molecule mol^–1 - R universal gas constant, erg mol^–1 K^–1 - T temperature, K - _t ^o dynamic viscosity of solvent atT temperature, g cm^–1 s^–1 - dynamic viscosity of solvent at 293 K, g cm^–1 s^–1 - _t density of solution atT temperature, g cm^–3 - _t ^o density of solvent atT temperature, g cm^–3 - density of solvent at 293 K, g cm^–3 - angular velocity, rad s^–1 - time, s     

Thermodynamic Study of Cadmium Chloride in Aqueous Mixtures of 2-Butanol from Potential Difference Measurements

The standard molal potential differences (E_m∘) have been determined for the cell: CdHg_x(two phase) | CdCl₂(m), H₂O(1 − w), 2-butanol (w) | AgCl(s) | Ag(s) in aqueous mixtures of low mass fraction of 2-butanol (w_2-butanol = 0.05, 0.10, and 0.15) by using the literature data for the stability constants of the chlorocadmium complexes and the present potentiometric data for this cell at five temperatures from (293.15 to 313.15) K and at 10 molalities of CdCl₂ from (0.002 to 0.02) mol-kg⁻¹. The resulting values of E∘_m have been used to calculate the standard thermodynamic quantities (Δ_rG^∘, Δ_rH^∘, and Δ_rS^∘) for the cell reaction, the stoichiometric mean molal activity coefficients (γ_±) of CdCl₂, and the standard thermodynamic functions for CdCl₂ transfer (Δ_t G∘, Δ_t H∘, and Δ_t S∘) from water to the examined aqueous mixtures of 2-butanol. The values obtained have been compared with the analogous literature data for aqueous mixtures of 2-butanone; standard thermodynamic quantities for transfer of CdCl₂ and HBr from water to mixtures containing the same mass fraction of 2-butanol have also been compared. For both electrolytes, these quantities show analogous trends with the alcohol content. This transfer process is nonspontaneous and endothermic. Enthalpy and entropy are evidently influenced by structural changes.     

Absorption and electroabsorption spectra of carotenoid cation radical and dication

Radical cations and dications of two carotenoids astaxanthin and canthaxanthin were prepared by oxidation with FeCl₃ in fluorinated alcohols at room temperature. Absorption and electroabsorption (Stark effect) spectra were recorded for astaxanthin cations in mixed frozen matrices at temperatures about 160 K. The D₀→D₂ transition in cation radical is at 835 nm. The electroabsorption spectrum for the D₀→D₂ transition exhibits a negative change of molecular polarizability, Δα=−1.2·10⁻³⁸ C·m²/V (−105 A³), which seems to originate from the change in bond order alternation in the ground state rather than from the electric field-induced interaction of D₁ and D₂ excited states. Absorption spectrum of astaxanthin dication is located at 715–717 nm, between those of D₀→D₂ in cation radical and S₀→S₂ in neutral carotenoid. Its shape reflects a short vibronic progression and strong inhomogeneous broadening. The polarizability change on electronic excitation, Δα=2.89·10⁻³⁸ C·m²/V (260 A³), is five times smaller than in neutral astaxanthin. This value reflects the larger energetic distance from the lowest excited state to the higher excited states than in the neutral molecule.     

Study on dynamic interfacial tension of 3-dodecyloxy-2-hydroxypropyl trimethyl ammonium bromide at liquid/liquid interface

Dynamic interfacial tension between aqueous solutions of 3-dodecyloxy-2-hydroxypropyl trimethyl ammonium bromide (R₁₂HTAB) and n-hexane were measured using the spinning drop method. The effects of the R₁₂HTAB concentration (the concentration below the CMC) and temperature on the dynamic interfacial tension have been investigated; the reason of the change of dynamic interfacial tension with time has been discussed. The effective diffusion coefficient, D_a, and the adsorption barrier, _a, have been obtained from the experimental data using the extended Word–Tordai equation. The results show that the dynamic interfacial tension becomes smaller while _a becomes higher with increasing R₁₂HTAB concentration in the bulk aqueous phase. D_a decreases from 5.56 × 10⁻¹² m⁻² s⁻¹ to 0.87 × 10⁻¹² m⁻² s⁻¹ while _a increases from 5.41 kJ mol⁻¹ to 7.74 kJ mol⁻¹ with the increase of concentration in the bulk solution of R₁₂HTAB from 0.5 × 10⁻³ mol dm⁻³ to 4 × 10⁻³ mol dm⁻³. Change of temperature affects the adsorption rate through altering D_a and _a. The value of D_a increases from 5.56 × 10⁻¹² m⁻² s⁻¹ to 13.98 × 10⁻¹² m⁻² s⁻¹ while that of _a decreases from 5.41 kJ mol⁻¹ to 5.07 kJ mol⁻¹ with temperature ascending from 303 K to 323 K. The adsorption of surfactant from the bulk phase into the interface follows a mixed diffusion–activation mechanism, which has been discussed in the light of interaction between surfactant molecules, diffusion and thermo-motion of molecules.     

Compounds containing layers of composition [(SbF)XO4] (X = P, As). Crystal structures of Na(SbF)PO4 · 1.5H2O, Na(SbF)AsO4, NH4(SbF)PO4 · H2O, and NH4(SbF)AsO4 · 3H2O

The title compounds have been prepared in water by reaction of SbF₃ with dihydrogen phosphates or arsenates and characterized by single crystal X-ray work, IR, Raman, and Mössbauer spectroscopy. They have identical layer structures. Layers of composition [(SbF)XO₄]⁻ (X = P, As) were formed by sharing four corners between XO₄ tetrahedra and SbFO₄ pseudooctahedra. The lengths of the terminal Sb---F bond (with the lone pair in a trans-position) and the Sb---O bonds are 192 and 219 pm, respectively. The stacking of the layers and the interlayer distance depend on the cations and the number of intercalated water molecules. In Na(SbF)AsO₄ the Na⁺ ion is coordinated by only two oxygen atoms within 300 pm. Crystal data: Na(SbF)PO₄ · 5H₂O, monoclinic, P2₁/m, A = 656.2(5), B = 654.1(5), C = 867.9(3) pm, β = 92.43(1)°, 889 reflections, 81 parameters, R = 0.044, R_w = 0.046. NH₄(SbF)PO₄ · H₂O, tetragonal, I4/m, A = 656.6(3), C = 1439.8(5) pm, 680 reflections, 31 parameters, R = 0.023, R_w = 0.021. Na(SbF)AsO₄, tetragonal, P4/ncc, A = 671.8(1), C = 1756.4(4) pm, 1056 reflections, 28 parameters, R = 0.052, R_w = 0.065. NH₄(SbF)AsO₄ · 3H₂O, tetragonal, P4/ncc, A = 683.8(2), C = 1873.0(7) pm, 1194 reflections, 30 parameters, R = 0.042, R_w = 0.050.     

Mechanochemical Synthesis and Nitrogenation of the Nd1.1Fe10CoTi Alloy for Permanent Magnet

In this work, the mechanochemical synthesis method was used for the first time to produce powders of the nanocrystalline Nd_1.1Fe₁₀CoTi compound from Nd₂O₃, Fe₂O₃, Co and TiO₂. High-energy-milled powders were heat treated at 1000 °C for 10 min to obtain the ThMn₁₂-type structure. Volume fraction of the 1:12 phase was found to be as high as 95.7% with 4.3% of a bcc phase also present. The nitrogenation process of the sample was carried out at 350 °C during 3, 6, 9 and 12 h using a static pressure of 80 kPa of N₂. The magnetic properties M_r, µ₀H_c, and (BH)_max were enhanced after nitrogenation, despite finding some residual nitrogen-free 1:12 phase. The magnetic values of a nitrogenated sample after 3 h were M_r = 75 Am² kg^–1, µ₀H_c = 0.500 T and (BH)_max = 58 kJ·m^–3. Samples were aligned under an applied field of 2 T after washing and were measured in a direction parallel to the applied field. The best value of (BH)_max ~ 114 kJ·m^–3 was obtained for 3 h and the highest µ₀H_c = 0.518 T for 6 h nitrogenation. SEM characterization revealed that the particles have a mean particle size around 360 nm and a rounded shape.     

Thermochemistry of the solid complex Gd(Et<Subscript>2</Subscript>dtc)<Subscript>3</Subscript>(phen)

Summary A ternary solid complex Gd(Et₂dtc)₃(phen) has been obtained from reactions of sodium diethyldithiocarbamate (NaEt₂dtc), 1,10-phenanthroline (phen) and hydrated gadolinium chloride in absolute ethanol. The title complex was described by chemical and elemental analyses, TG-DTG and IR spectrum. The enthalpy change of liquid-phase reaction of formation of the complex, Δ_rH^Θ_m(l), was determined as (-11.628±0.0204) kJ mol^-1 at 298.15 K by a RD-496 III heat conduction microcalorimeter. The enthalpy change of the solid-phase reaction of formation of the complex, Δ_rH^Θ_m(s), was calculated as (145.306±0.519) kJ mol^-1 on the basis of a designed thermochemical cycle. The thermodynamics of reaction of formation of the complex was investigated by changing the temperature of liquid-phase reaction. Fundamental parameters, the apparent reaction rate constant (k), the apparent activation energy (E), the pre-exponential constant (A), the reaction order (n), the activation enthalpy (Δ_rH^Θ_≠), the activation entropy (Δ_rS^Θ_≠), the activation free energy (Δ_rG^Θ_≠) and the enthalpy (Δ_rH^Θ_≠), were obtained by combination of the thermodynamic and kinetic equations for the reaction with the data of thermokinetic experiments. The constant-volume combustion energy of the complex, Δ_cU, was determined as (-18673.71±8.15) kJ mol^-1 by a RBC-II rotating-bomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_cH^Θ_m, and standard enthalpy of formation, Δ_fH^Θ_m, were calculated to be (-18692.92±8.15) kJ mol^-1 and (-51.28±9.17) kJ mol^-1, respectively.     

The solid state structure of triphenyltelluronium cyanate-chloroform( )

Three-dimensional X-ray crystal structure analysis shows that the organotelluronium salt, triphenyltelluronium cyanate-chloroform( ), exists as a tetramer in the solid state with both end-to-end and terminally bridging NCO groups. The oligomer is predominantly ionic with tellurium—nitrogen and tellurium—oxygen distances significantly shorter than respective van der Waals distances. Refinement of the structure, based on 3817 reflections collected by automatic diffractometry, converged to a conventional R factor of 4.9% and a weighted R factor of 4.2%. Crystal data for Ph₃Te(NCO) · CHCl₃ are as follows: a = 12.083(6)Å, b = 12.900(12)Å, c = 13.878(10)Å, α = 95.83(7)°, β = 103.47(7)°γ = 98.87(6)°, V = 1901ų (temperature = 23°C) and Z = 4.     

A manganese sulfite with extended metal–oxygen–metal bonds exhibiting hydrogen uptake

A manganese sulfite of the formula Mn₅(OH)₄(SO₃)₃·2H₂O, I{a=7.5759(7) Å, b=8.4749(8) Å, c=10.852(1) Å, β=100.732(2)°, Z=2, space group=P2₁/m (no. 11), R₁=0.0399 and wR₂=0.1121 [for R indexes I>2σ(I)]}, comprising Mn₃O₁₄ units and extended Mn–O–Mn bonds along the three dimensions has been synthesized under hydrothermal conditions. It has narrow channels along the b-axis and exhibits hydrogen storage of 2.1 wt% at 300 K and 134 bar.     

Rm Values, retention times and π values of a series of potentially mutagenic nitroimidazo[2,1-b]thiazoles

The R_m values and retention times of a series of nitroimidazo[2,1-b]thiazoles were obtained by means of thin-layer and high-performance liquid chromatography, respectively. Extrapolated R_m and log k′ values were correlated in a statistically significant way with π values calculated according to the literature.     

Precision and detection limits in Zeeman graphite furnace atomic absorption spectrometry

This is the first theoretical study of photometric errors in Zeeman graphite furnace atomic absorption spectrometry with evaluation of their effect on the precision in the traditional method of peak area determination and the pulse restoration method proposed earlier for linearization and expansion of calibration curves. Besides the fraction of non-absorbed radiation, α, and Zeeman sensitivity ratio, R, the theoretical calculations make use of three more parameters, namely the “energy” value, E, the baseline offset compensation time, t_toc, and the integration time, t_int. The theoretical calculations are supported by experimental data on detection limits for a number of elements and on the RSD obtained in Ag and Cd determinations. A comparison of the precision in the case of pulses with dips has shown the pulse restoration method to be superior over the traditional technique. The theoretical results can be used to improve the measurement precision and the detection limits by proper modification of the spectrophotometer and optimization of experimental conditions.     

Micellization behavior of [C16-12-C16], 2Br gemini surfactant in binary aqueous-solvent mixtures

The micellization behavior of bis cationic gemini surfactant, N,N′-dihexadecyl-N,N,N′,N′-tetramethyl-1,12-dodecanediammonium dibromide [C₁₆H₃₃N⁺(CH₃)₂-(CH₂)₁₂-N⁺(CH₃)₂C₁₆H₃₃, 2Br⁻] has been studied in binary aqueous mixtures of dimethyl sulfoxide, methanol, 1,4-dioxane, glycerol and ethylene glycol by conductivity and surface tension measurements at 300 K. The critical micellar concentration, degree of micelle ionization (α), surface excess concentration (Г_max), minimum surface area per molecule of surfactant (A_min), Gibbs free energy of micellization (ΔG_m°), the surface pressure at cmc (π_cmc), and the Gibbs energy of adsorption (ΔG_ad°) of the gemini surfactant have also been determined. The cmc, α, A_min increases where as (ΔG_m°), Г_max, and π_cmc decreases with increasing volume percentage of the solvents in the solvent–water binary mixture. The interfacial properties of the gemini surfactant, solute–solute, solvent–solute interactions and the effectiveness of a surface-active molecule in binary solvent systems have been discussed.