Nonbonded interactions. 1. Anisotropic hydrogen-hydrogen interactions

The hydrogen-hydrogen nonbonded potential which may be derived from the calculated interactions between hydrogen molecules has been obtained. The best three-parameter Buckingham function gave an RMS error of 0.18 kcal/mol in fitting Price and Stone's ab initio data for 130 pairs of hydrogen molecules, which may be compared with an RMS error of 0.74 kcal/mol using the parameters in the MM2 force field. Burton's basis set is also considered. A better fit to these data requires that the angular relationship between the bonds be included. The data for hydrogen as well as experimental data for chlorine show that these atoms appear “larger” normal to the bond axis than along the axis, and this is probably also the case for other atoms. When simple angular terms are added it is possible to fit the Price and Stone data set with an RMS error of less than 0.06 kcal/mol. The preferred function was: V = [a₀ + a₁(sin θ₁ + sin θ₂)⁴ + a₂r]e^?3r ? [c₀ + c₁(1 + sinθ₁sinθ₂)]/r⁵. Deficiencies in the current ab initio data are discussed.     

Static contact angle hysteresis on smooth, homogeneous solid substrates

A theory of contact angle hysteresis on smooth, homogeneous solid substrates is developed in terms of shape of disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θ _r?<?θ?<?θ _a, which are different from the unique equilibrium contact angle θ?≠?θ _e, correspond to the state of slow “microscopic” advancing or receding motion of the liquid if θ _e ?<?θ?<?θ _a or θ _r?<?θ?<?θ _e, respectively. This “microscopic” motion almost abruptly becomes fast “macroscopic” advancing or receding motion after the contact angle reaches the critical values θ?=?θ _a or θ _r?=?θ, correspondingly. The values of the static receding, θ _r, and static advancing, θ _a, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining pressure isotherm. It is shown that an advancing contact angle of a droplet on a solid substrate depends on the drop volume and is not a unique characteristic of the liquid–solid system. The suggested mechanism of contact angle hysteresis has direct experimental confirmation.     

Determination of electrochemical kinetic parameters by square-wave polarography: Polarographic reduction of Zn(II) in 1 M KCl,KBr, and KNCS solutions

A new method of determining electrochemical kinetic parameters by square-wave polarography was presented, in which the faradaic current at θ/2, θ being the half-period of superimposed square-wave voltage, was used for the analysis. The method gave the following kinetic parameters for the electrode reaction, Zn(II) + 2e(Hg), in aqueous solutions at 25° C: k_c^θ=0.0052 cm s^?1 and α_c=0.36 in 1 M KCl, k_c^θ=0.011 cm s^?1 and α_c=0.30 in 1 M KBr, and k_c^θ=0.020 cm s^?1 and α_c=0.52 in 1 M KNCS. Induced adsorption of Zn(II) on the dropping mercury electrode was suggested in solutions containing thiocyanate ions.     

Small-angle electron scattering by formaldehyde and ketene: Effects of electron correlation and chemical binding

The total (elastic plus inelastic) intensities of 51 keV electrons scattered by H₂CO and H₂CCO have been measured over a range of K = (4π/λ) sin(θ/2) = 1–9.5 Å^?1 and compared with the theoretical intensities calculated with SCF and CI wave functions. Significant discrepancies are found between the experimental intensities and the theoretical ones based on the SCF wave functions. Most of the chemical binding and electron correlation effects observed in the total scattered intensities are reproduced by the theoretical intensities based on the CI wave functions calculated with the basis set including polarization functions on all atoms. © 1992 John Wiley & Sons, Inc.     

Light-scattering study of the molecular weight distribution of polypropylene

A light-scattering study is presented of two isotactic polypropylene samples with broad molecular weight distributions (M _w/M _n = 8.1 and 8.7, respectively) dissolved in α-chloronaphthalene at 147°C. Incident radiation of 5460, 4358, and 3650 A. was used. The reciprocal intramolecular scattering function, P^?1(u) is expressed as a function of the variable [sin(θ/2)/λ′]². This provides a wider range of experimental values of the variable u = 16π²(b²/6) [sin(θ/2)/λ′]² than is accessible by the usual technique of using only one wavelength. The shape of the function P^?1(u) is closer to that predicted theoretically if the weight distribution function f(N) in the equation is given by the log-normal distribution rather than the distribution function of Schulz and Zimm. The method is applicable to polymer samples for which the average molecular weights are too low to be measured by the light-scattering method of Benoit and Loucheux.     

Reduction of bias in static closed chamber measurement of δ13C in soil CO2 efflux

The ¹³C/¹²C ratio of soil CO₂ efflux (δ_e) is an important parameter in studies of ecosystem C dynamics, where the accuracy of estimated C flux rates depends on the measurement uncertainty of δ_e. The static closed chamber method is frequently used in the determination of δ_e, where the soil CO₂ efflux is accumulated in the headspace of a chamber placed on top of the soil surface. However, it has recently been shown that the estimate of δ_e obtained by using this method could be significantly biased, which potentially diminish the usefulness of δ_e for field applications. Here, analytical and numerical models were used to express the bias in δ_e as mathematical functions of three system parameters: chamber height (H), chamber radius (R_c), and soil air‐filled porosity (θ). These expressions allow optimization of chamber size to yield a bias, which is at a level suitable for each particular application of the method. The numerical model was further used to quantify the effects on the δ_e bias from (i) various designs for sealing of the chamber to ground, and (ii) inclusion of the commonly used purging step for reduction of the initial headspace CO₂ concentration. The present modeling work provided insights into the effects on the δ_e bias from retardation and partial chamber bypass of the soil CO₂ efflux. The results presented here supported the continued use of the static closed chamber method for the determination of δ_e, with improved control of the bias component of its measurement uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact solutions and spectrum analysis of a noncentral potential in the presence of vector potential

We studied exact solutions and spectrum analysis of the pseudoharmonic oscillator in the presence of θ-dependent scalar potential and the sum of two vector potentials Dirac magnetic monopole and Aharonov-Bohm field. The effect of the Dirac magnetic monopole (g), Aharonov-Bohm field (ℱ) , the dissociation energy of diatomic molecules (D _e), equilibrium intermolecular separation (r _e), and the reduced mass (μ) on the energy spectrum for some diatomic molecules (CO, NO, N₂, CH, H₂, and ScH) are analyzed. We compared our results with theoretical experiments of pseudoharmonic oscillator potential in a molecular system.     

Excited state polarizabilities from solvatochromic shifts

A new method is proposed to estimate the polarizability (α_e) of a molecule in an excited state using solvatochromic shift measurements and McRae's equation. In the earlier methods the contribution due to polarizability was not considered. In view of this, the proposed method is also expected to give a better estimation of excited state electric dipole moment (μ_e) and the (θ) angle between excited and ground state electric dipole moments, μ_e and μ_g apart from giving values of polarizability of the molecules in the excited state. This method has been applied in the case of the La band of p-nitro aniline and the results for all the parameters are found to be satisfactory and of right order in comparison with that reported in literature.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

The crystal structure of Bi14I4 condensed bismuth clusters

The crystal structure of Bi₁₄I₄ — the final known member of binary bismuth halides — was determined by the single crystal X-ray diffractometer technique (P2₁/m, Z = 1, a = 13.309(3) Å, b = 11.447 (3) å, c = 4.342(1) å, γ = 92.08(3)°, R/R_w = 0.060/0.060 for 369 reflections, sinθ/λ≤ 0.593, MoKγ). The structure consists of condensed bismuth clusters and is build up from infinite one-dimensional bismuth nets running along the c-axis and limited by iodine atoms in another direction. The common structural features of bismuth subhalides containing condensed clusters are also considered based on the analysis of interatomic distances and bond angles. The influence of the lone pair of electrons of the bismuth atom on the geometry of bismuth coordination polyhedra, and the connection between bismuth atoms coordination and the formal oxidation state of these atoms is discussed.     

Temperature effect on the ease of aggregation

The effect of temperature on the critical aggregate concentration (CAgC) has been investigated for the first time, by measurement of the hydrolytic rate constants of p-nitrophenyl dodecanoate (C12) and hexadecanoate (C16) at different temperatures in the 30:70 V/V (Φ=0.30) and 40:60 V/V (Φ= 0.40) dioxane (DX)-H2O systems. The CAgC values of C12 and C16 increase with the increase of the temperature, i.e., high temperatures disfavor aggregation. Activation energies for the hydrolysis of C12 in the monomeric and aggregated concentration domains have also been discussed.     

K‐site splitting in KTiOPO4 at room temperature

The room‐temperature structure of potassium titanyl phosphate (KTiOPO₄, KTP) with Pna2₁ symmetry has been studied by means of synchrotron radiation. Each of the two crystallographically unique K1 and K2 cations is split over two sites that are shifted along the c direction by 0.287 (13) and 0.255 (13) Å for the K1a/b and K2a/b pairs, respectively. The refined populations of the minor K1b and K2b sites are 0.102 (12) and 0.132 (17), respectively. It is shown that accurate high‐resolution synchrotron data (R_merged = 0.015 for 25 010 reflections, 9456 unique, sinθ/λ limit > 1.0) are required for the determination of a reliable structure model.     

A new approach to electron diffraction analysis of symmetric triatomic molecules with large-amplitude bending motion: The equilibrium geometry,force field and vibrational frequencies of BaI2 as determined by electron diffraction

Diffraction data on BaI₂, analyzed by a new approach, indicate an anharmonic potential with a barrier of 71(12) cm^?1 at a linear geometry. The structural and vibrational parameters were found to be r_e^h(Ba-I_o) = 3.150(7)Å, ∠_eIBaI = 148.0(9) °, f_q = 0.69(8) mdyn/Å,f_qq= 0.14(6) mdyn/Å, k₂ = ?0.0075(15) mdyn/Å, k₄ = 0.0025(9) mdyn/ų, v₁ = 106(12) cm^?1 and v₃ = 145(21) cm^?1. The bending frequency v₂ is predicted to be near 16 cm^?1.     

Thermochemistry of adducts of some bivalent transition metal bromides with pyridine

The compounds [MBr₂(py)₂] (where M is Mn(II), Co(II), Ni(II), Cu(II) or Zn(II); py = pyridine) were synthesized and characterized by melting points, elemental analysis, thermal analysis and electronic and IR spectroscopy. The enthalpies of dissolution of the adducts, metal(II) bromides and pyridine in 25% (v/v) 1.2 M aqueous HCl in methanol were measured and by using thermochemical cycles, the following thermochemical parameters for the adducts have been determined: the standard enthalpies for the Lewis acid/base reactions (Δ_rH^θ), the standard enthalpies of formation (Δ_fH^θ), the standard enthalpies of decomposition (Δ_DH^θ), the lattice standard enthalpies (Δ_MH^θ) and the standard enthalpies of the Lewis acid/base reactions in the gaseous phase (Δ_rH^θ(g)). The mean bond dissociation enthalpies of the M(II)-nitrogen bonds have been estimated as well as the enthalpies of the adducts formation in the gaseous phase.     

The pseudorotation of cycloheptane—I

The pseudorotation of cycloheptane is described by means of the Fourier expansion of the endocyclic torsion angle ω_i = A sin φ_j + B sin 3φ_j + C sin 5φ_j + D sin 7φ_j; φ_j = Δ/2 + 2πj/7; j = 0, 1,...,6; i = 2j + 4, mod 7 and Δ being a phase angle.The topography of the pseudorotational itineries for the chair/twist-chair and the boat/twist-boat families is discussed. X-ray diffraction data concerning the geometry of 7-membered rings occurring in fused ring compounds are analysed by means of the proposed relationship. The least squares procedure for evaluation of the parameters A, B, C and D is given in an appendix.The calcium salt of cycloheptane car?ylic acid, (C₇H₁₃·COO)₂Ca·5H₂O in solid state, displays disorder closely related to pseudorotation. Preliminary X-ray diffraction data of this structure (to be published elsewhere) are given.     

Analysis of lattice thermal conductivity and phonon-phonon scattering relaxation rate: Application to Ge

The three-phonon scattering relaxation rates and their temperature exponents have been analysed in the frame of Guthrie's classification of the phonon-phonon scattering events as class I and class II events and as a result of this, a new expressionτ _3ph ^-1 =(B _N,I+B _U,Ie^-θ/αT) g(w)T ^m I ^(T)+(B _N,II+B _U,IIe^-θ/αT)g(w)T ^mII^(T) for the three phonon scattering relaxation rates has been proposed for the first time to calculate the lattice thermal conductivity of a sample. Using the expression proposed above, the lattice thermal conductivity of Ge has been analysed in the temperature range 2–1000K and result obtained shows a very good agreement with the experimental data. The percentage contributions due to three-phonon normal and umklapp processes are also reported. The role of four phonon processes is also included at high temperatures. To estimate an approximate value of the scattering strength and the phonon conductivity, the analytical expression is also obtained in the frame of the expression proposed above forτ _3ph ^-1 .     

Orientational Preference of Long,Multicenter Bonds in Radical Anion Dimers: A Case Study of π‐[TCNB]22− and π‐[TCNP]22−

The similar shape and electronic structure of the radical anions of 1,2,4,5‐tetracyanopyrazine (TCNP) and 1,2,4,5‐tetracyanobenzene (TCNB) suggest a similar relative orientation for their long, multicenter carbon?carbon bond in π‐[TCNP]₂^2? and in π‐[TCNB]₂^2?, in good accord with the Maximin Principle predictions. Instead, the two known structures of π‐[TCNP]₂^2? have a D_2h(θ=0°) and a C₂(θ=30°) orientation (θ being the dihedral angle that determines the rotation of one radical anion relative to the other along the axis that passes through center of the two six‐membered rings). The only known π‐[TCNB]₂^2? structure has a C₂(θ=60°) orientation. The origin of these preferences was investigated for both dimers by computing (at the RASPT2/RASSCF(30,28) level) the variation with θ of the interaction energy (E_int) and the variation of the E_int components. It was found that: 1) a long, multicenter bond exists for all orientations; 2) the E_int(θ) angular dependence is similar in both dimers; 3) for all orientations the electrostatic component dominates the value of E_int(θ), although the dispersion and bonding components also play a relevant role; and 4) the Maximin Principle curve reproduces well the shape of the E_int(θ) curve for isolated dimers, although none of them reproduce the experimental preferences. Only after the (radical anion)^.? ??? cation⁺ interactions are also included in the model aggregate are the experimental data reproduced computationally.     

Polarography of cadmium(II) in presence of substituted alkanolamines

A study has been made of the effect of an irreversibly adsorbed iodide layer on the anodic oxidation of formic acid at a platinized platinum electrode. It is shown that, in the presence of the preadsorbed iodide layer, the oxidation process obeys the following rate expression, i=nF k^→c^α g(θ_I) exp(α_anFφ_r/RT where α≈0.75 and α_an≈0.5. This is explained in terms of the following rate-determining step, (HCOOH)_ads→C_*OOH+H⁺+e and involves the adsorption of formic acid on the iodide covered surface. A strong catalytic effect of the iodide layer is observed; the function g (θ_I) passes through two maxima at θ_I values of 0.15 and 0.53. It is suggested that these effects arise from a coverage-dependent variation of bond strength between the adsorbed iodide and platinum.