A calculation of the isotropic and anisotropic spectral moments of the dipole oscillator strength distribution of N2

We calculate a range of isotropic and anisotropic spectral moments of the dipole oscillator strength distribution for N₂ in the random phase approximation. The internuclear dependence of, in particular, S∥(k) is nonnegligible and vibrationally averaged moments are reported. The results are compared to other calculations and to experiment when available, and we conclude that the scheme gives reliable results. Based on our results, we predict a 10% anisotropy in the stopping power of oriented N₂ molecules.     

Dipole oscillator strength properties and dispersion energies for SiH4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silane (SiH₄) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for SiH₄ is also presented which is used to obtain reliable results for the isotropic dipole–dipole dispersion energy coefficients C₆, for the interaction of silane with itself and with forty-four other species, and the triple–dipole dispersion energy coefficient C₉ for (SiH₄)₃.     

UV, VUV and soft X-ray photoabsorption of dimethyl ether by dipole (e,e) spectroscopies

Absolute UV and VUV photoabsorption oscillator strengths (cross-sections) for the valence shell discrete and continuum regions of dimethyl ether (CH₃OCH₃, DME) have been measured from 5 to 32 eV using high resolution (HR) (0.05 eV f.w.h.m.) dipole (e,e) spectroscopy. A wide-range spectrum, spanning the UV, VUV and soft X-ray regions, from 5 to 200 eV has also been obtained at low resolution (LR) (1 eV f.w.h.m.), and this has been used to determine the absolute oscillator strength scale by employing valence shell Thomas–Reiche–Kuhn (i.e., S(0)) sum-rule normalization. The presently reported HR and LR absolute photoabsorption oscillator strengths are compared with previously published data from direct photoabsorption measurements in those limited energy regions where such data are available. Evaluation of the S(−2) sum using the presently reported absolute differential photoabsorption oscillator strength data gives a static dipole polarizability for dimethyl ether in excellent agreement (within 0.5%) with previously reported polarizability values. Other dipole sums S(u), (u=−1,−3,−4,−5,−6,−8,−10), and logarithmic dipole sums L(u), (u=−1 to −6), are also determined from the presently reported absolute differential photoabsorption oscillator strength data using dipole sum rules.     

Dipole oscillator strength distributions,sums, and dispersion energy coefficients for CO and CO2

Globally reliable dipole oscillator strength distributions (DOSDs) have been constructed for ground state CO and CO₂ molecules; the DOSD for CO corresponds to photon energies greater than the electronic absorption threshold while that for CO₂ includes the infrared part of the spectra as well. The recommended DOSDs are used to evaluate the isotropic dipole—dipole dispersion energies for the COCO, COCO2 and CO2CO2 interactions as well as the molar refractivities, as a function of wavelength, and the dipole sums, S_k, k = 2(?1) -4, -6, -8, -10, for the two molecules. Pseudo-DOSD representations of the recommended DOSDs are provided which allow the efficient accurate evaluation of the dispersion energy coefficients C₆ for the interaction of CO or CO₂ with a variety of other atoms and molecules. Previous results for C₆ are found to be in disagreement with our recommended results for interactions involving CO₂. The results of this paper are used to give a reasonably general discussion of the difficulties associated with obtaining reliable results for C₆ by using Padé approximant bounding methods.     

Studies on the kinetics and mechanism of dissociation of copper(II) and nickel(II) complexes of the macrocyclic ligand 1, 5, 9, 13-tetraaza-2, 4, 4, 10, 12, 12-hexamethyl-cyclohexadecane-1, 9-diene in perchloric acid media

Summary Acid catalysed dissociation of the copper(II) and nickel(II) complexes (ML²⁺ of the quadridentate macrocyclic ligand 1, 5, 9, 13-tetraaza-2, 4, 4, 10, 12, 12-hexamethyl-cyclohexadecane-1, 9-diene (L) has been studied spectrophotometrically. Both complexes dissociate quite slowly with the observed pseudo-first order rate constants (k_obs) showing acid dependence; for the nickel(II) complex (k_obs)=k_O+k_H[H⁺], the k_o path is however absent with the copper(II) complex. At 60°C (I=0.1M) the k_H values areca 10^–4 M^–1 s^–1 for both complexes; k _H ^Cu /k _H ^Ni =ca. 3.9, comparable to some other square-planar complexes of these metal ions. The rate difference is primarily due to H values [copper(II) complex, 29.4±0.5 kJ mol^–1; nickel(II) complex, 35.6±1.5 kJ mol^–1] with highly negative S values [for copper(II), –215.5 ±6.1 JK^–1 mol^–1 and for nickel(II), –208.1 ±5.6 JK^–1 mol^–1] which are much higher than the entropy of solvation of Ni²⁺ (ca. –160 JK^–1 mol^–1) and Cu²⁺ (ca. –99 JK^–1 mol^–1) ions; significant solvation of the released metal ions and the ligand is indicated.     

Additivity of atomic static polarizabilities and dispersion coefficients

A new empirical method is proposed to evaluate the average molecular polarizabilities assuming the additivity of atomic static polarizability. Atomic static polarizability for each atom in a particular valence state is obtained. Calculated molecular polarizabilities of 94 non-halogenated compounds and of the bases in nucleic acids show the excellent agreement with experimental data.To check the further validity of this method, dispersion coefficients for CH₄, C₂H₆, C₃H₈,n–C₄H₁₀,n–C₅H₁₂,n–C₆H₁₄,n–C₇H₁₆,n–C₈H₁₈, H₂, H₂O and NH₃ are obtained from a sum of atomic terms using a London-type formula, and are compared with the accurate values of dipole oscillator strength distribution (DOSD) method. The results show the excellent agreement between theory and experiment.     

Ozone: unresolved discrepancies for dipole oscillator strength distributions, dipole sums, and van der Waals coefficients

Dipole oscillator strength distributions (DOSDs) for ozone are constructed from experimental photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density, and molar refractivity data. A lack of photoabsorption data in the intermediate energy region from 24 to 524 eV necessitates the use of a mixture rule in that region. For this purpose, a DOSD for O(2) is constructed first. The dipole properties for O(2) are essentially the same as those obtained in earlier work even though most of the input data is from more recent experiments. A discrepancy is found between the refractivity data and photoabsorption data in the 10-20.6 eV range for ozone. A reliable ozone DOSD of the sort obtained for many other species remains out of reach. However, it is suggested that the true dipole properties of ozone lie between those predicted by two distributions that we present.     

Effect of ionic interactions on the oxidation of Fe(II) with H2O2 in aqueous solutions

The oxidation of Fe(II) with H₂O₂ has been measured in NaCl and NaClO₄ solutions as a function of pH, temperature T (K) and ionic strength (M, mol-L^–1). The rate constants, k (M^–1-sec^–1), d[Fe(II)]/DT=-k[Fe(II)][₂O₂]at pH=6.5 have been fitted to equations of the formlog k = log k₀+ AI ^1/2+BI+CI ^1/2/T Where log k₀=15.53-3425/T in water; A=–2.3, –1.35; B=0.334, 0.180; and C=391, 235, respectively, for NaCl (=0.09) and NaClO₄ ( =0.08). Measurements made in NaCl solutions with added anions yield rates in the order B(OH) ₄ ^– >HCO ₃ ^– >ClO ₄ ^– >Cl^–>NO ₃ ^– >SO ₄ ^2– and are attributed to the relative strength of the interactions of Fe²⁺ or FeOH⁺ with these anions. The FeB(OH) ₄ ⁺ species is more reactive while the FeCO ₃ ⁰ , FeCl⁺, FeNO ₃ ⁺ and FeSO ₄ ⁰ species are less reactive than the FeOH⁺ ion pair. The general trend is similar to our earlier studies of the oxidation of Fe(II) with O₂ except for B(OH) ₄ ^– . The effect of pH on the logk was found to be a quadratic function of the concentration of H⁺ or OH^– from pH=4 to 8. These results have been attributed to the different rate constants for Fe²⁺ (k₀) and FeOH⁺ (k₁) which are related to the measured k by, k=k_0Fe + k_1FeOH, where _i is the molar fraction of species i. The rates increase due to the greater reactivity of FeOH⁺ compared to Fe²⁺. k₀ is independent of composition and ionic strength but k₁ is a function of ionic strength and composition due to the interactions of FeOH⁺ with various anions.     

Angle and bond-length dependent C6 coefficients for H2 interacting with H,Li, Be and rare gas atoms

Summary Accurate new C₆ dispersion energy coefficients, and their dependence on the diatom orientation and bond length, are calculated for molecular hydrogen interacting with an atom of H, Li, Be, He, Ne, Ar, Kr or Xe. They are generated from accurateab initio pseudo dipole oscillator strength distributions (DOSD) for H₂, H, He and Be, and reliable semiempirical ones for Li, Ne, Ar, Kr and Xe. Compact power series expansions for the diatom bond-length dependence of these coefficients, suitable for incorporation into representations of full potential energy surfaces for these systems, are determined and assessed.     

Nonempirical Study of Nuclear Dynamics in Nonrigid LiReO4 and K2SO4 Molecules

The previously developed nonempirical model for M _k XY _n (k 1) nonrigid molecules describing the motion of k M nuclei relative to a quasirigid XY _n fragment is used to study the dynamics of nuclei in LiReO₄ and K₂SO₄ molecules. The parameters of the kinetic and potential parts of the model Hamiltonian and dipole moment functions are determined from results of ab initio calculations of the molecules and their fragments by the Hartree—Fock and CISD + Q configurational interaction methods. The dynamic problem is solved by the variational method. Energy levels, transition frequencies, transition dipole moments, and mean geometrical parameters of the molecules are calculated. It is shown that the lowest energy levels of LiReO₄ and K₂SO₄ molecules can be described with high accuracy in a harmonic approximation using a quasirigid, single–minimum model, whereas for the energy levels located near and above the barriers of intramolecular rearrangements, these approximations are completely unsuitable.     

The relative importance of temperature and isotope effects on the dipole oscillator strength distribution of H2

Summary The calculation of the effects of temperature and isotopic composition on the energy weighted moments of the dipole oscillator strength distribution of H₂ in the random phase approximation to the polarization propagator are reported. It is seen that the effect of isotopic composition is small, while that of temperature is of an order accessible to experiment. We find that all the mean excitation energiesI , for =–1, 0, 1, decrease with temperature as does the dipole oscillator strength momentS() for >0, while the opposite is true for <0. These effects are interpreted in terms of the bond length dependence of the excitation energies.     

Pseudo-spectral dipole oscillator-strength distributions for SO2, CS2 and OCS and values of some related dipole—dipole and triple-dipole dispersion energy constants

Pseudo-spectral dipole oscillator strengths and excitation energies, which are discrete representations of the original continuous dipole oscillator-strength distributions (DOSDs), are presented for the ground-state SO₂, CS₂ and OCS molecules. These pseudo-DOSDs, together with previously published pseudo-DOSDs, are used to evaluate the dipole—dipole and triple-dipole dispersion-energy coefficients for all the two- and three-body interactions between SO₂, CS₂ and OCS and between these molecules and H₂, N₂, O₂, NO, N₂O, H₂O, NH₃, CO, CO₂, CH₄, C₂H₆, C₄H₁₀ and C₆H₁₄, with an estimated uncertainty of 1–2%. The importance of results of this type is discussed briefly.     

Stabilities and thermodynamics of uranyl(II) and thorium(IV) complexes of 2-mercaptoethanol

The complexation of UO₂ ⁺² and Th⁺⁴ ions with 2-mercaptoethanol has been studied by potentiometric and conductometric titration techniques. Uranyl ion forms 11 and 12 complexes in the pH-range 3.3–6.5 and thorium ion forms 12, 13, and 14 complexes in the pH-range 3.2–4.8 with considerable overlapping. Their logk _stab. values are determined at 10, 20, and 30°C at ionic strength =0.1M (NaClO₄) by applyingCalvin-Melchior's extension of theBjerrum method. The overall changes in thermodynamic functions G, H, and S accompanying complexation determined at 20°C are –19.48 kcal/mole, –22.77 kcal/mole, –11.23 cal/deg·mole for uranyl complexes and –33.94 kcal/mole, –4.93 kcal/mole, 99.00 kcal/deg·mole for thorium complexes, resp.     

Preparation and reactivity of metal-containing monomers

Thermal transformations (at 340 to 390 °C) of coprecipitates of iron and cobalt acrylates, [Fe₃O(CH₂CHCOO)₆OH][Co(CH₂CHCOO)₂]_2.4 (1) and [Fe₃O(CH₂CHCOO)₆OH][Co(CH₂CHCOO)₂]_1.5·3H₂O (2), are studied. The dependence of the degree of gas evolution () on time is described by the equation () wherek ₁=2.3 · 10¹² · exp[–49500/(RT)] s^–1,k ₂=6.0 · 10⁶ · exp[–33000/(RT)] s^–1 andk ₁=2.6 · 10¹² · exp[–49000/(RT)] s^–1,k ₂=6.6 · 10⁵ · exp[–30000/(RT)] s^–1 for cocrystallizates1 and2, respectively. The coefficient ₁ decreases as the temperature increases. The value of ₁ for compound1 is higher than that for compound2. The composition of products of the transformations of1 and2 are studied. The main solid state products of the decomposition are nanometer-sized particles of cobalt ferrite, CoFe₂O₄, with a narrow size distribution stabilized by the polymeric matrix. The thermal transformations of cocrystallizates1 and2 include dehydration, thermal decomposition, copolymerization in the solid state, and decarboxylation of the metallocarboxylate groups of the polymer. The effect of the ratio between the Fe clusters and the Co-containing fragments on the process of thermal transformation is analyzed.For Part 40, seeRuss. Chem. Bull., 1994,43, 2020.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 885–893, May, 1995.The authors are grateful to A. N. Titkov for optical microscopic and electron microscopic studies.     

Kinetic exchange studies of metal ion substitution in EDTA chelates Fe(III)- UO2 EDTA exchange

A kinetic study of the exchange reaction between UO₂EDTA complex and Fe(III), at a constant ionic strength of 0.1, over the concentration range of 5×10^–3–1×10^–2 M of each reactant and pH 4.5–5.5 has been carried out radiometrically. The rate of the exchange process can be expressed by the equation: R=k₁[UO₂EDTA][Fe]+k₂[EDTA][H⁺]^–1. The activation parameters calculated were H^*=25.95 kJ mol^–1 and S^*=0.67 kJ mol^–1 K^–1.     

Some rules forS(-2k) dipole sums?

Stieltjes conditions and the ratio test provide necessary but not sufficient conditions onS(-2k) dipole sums. If the dipole sums are accurate the associated [n, n –1] Padé approximant provides a better representation of (), the frequency-dependent dipole polarizability, than a truncated series expression and, in addition, should bound () below. It is shown how constraints on the dipole sums effect the form of the [2,1] Padé approximant and an additional constraint is derived that ensures the analyticity of the approximant on 0 < ₁. There then follows a discussion of the reliability of available literature dipole sum values for small molecules containing H, C, N and O.     

The Effect of Anomeric Head Groups, Surfactant Hydrophilicity, and Electrolytes onn-Alkyl Monoglucoside Microemulsions

The effects of the variables of head group structure and salt concentration on microemulsions formed in mixtures of water, alkyl ethylene glycol ethers (C_kOC₂OC_k), andn-alkyl β- -glucopyranosides (C_mβG₁) are explored. Phase behavior of mixtures containing an anomer of the surfactant (n-alkyl α- -glucopyranoside, C_mαG₁), or surfactants with long head groups (n-alkyl maltopyranosides, C_mG₂), or NaCl or NaClO₄as electrolyte are systematically reported as a function of temperature and composition. The substitution ofn-alkyl α- -glucopyranosides forn-alkyl β- -glucopyranosides causes precipitation under some conditions in all mixtures studied. These solubility boundaries begin in the water–surfactant binary mixture at the Krafft boundary, then extend to high concentrations of both surfactant and oil. Increasing the effective length of the surfactant head group by adding C_mG₂to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior dramatically up in temperature when even small amounts of C_mG₂are used. Adding a lyotropic electrolyte, NaCl, to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior down in temperature, while the hydrotropic electrolyte NaClO₄moves the phase behavior up in temperature.     

Xα–DV Modeling of Photoionization and Electronic Absorption Spectra of Cobalt tris–Acetylacetonate

Ionization energies, excited state energies, and oscillator strengths of electron–dipole transitions are calculated within the framework of the SCF–X–DV quantum–chemical model of the Co(HCOCHHCO)₃ model complex in order to interpret the photoionization and electronic absorption spectra of cobalt tris––diketonate. It is shown that the sequences of ionization and excitation energies calculated in the transition state approximation do not significantly differ from the sequence of energies estimated in the frozen MO approximation. The model absorption spectrum with a correction of 1.9 eV applied to the energy of the vacant ₄ ^* orbital is in good agreement with our gas–phase absorption spectrum of Co(acac)₃.     

Kinetics and mechanism of nucleophilic substitution of dichloro{1-methyl-2-(arylazo)imidazole}palladium(II) by pyridine bases

The reaction of dichloro{1-methyl-2-(arylazo)imidazole}palladium(II), Pd(RaaiMe)Cl₂ where RaaiMe = p-R–C₆H₄N=N–C₃H₂N₂-1-Me; R = H(1), Me(2), Cl(3), with pyridine bases [RPY: R = H (a), 4-Me (b), 4-Cl (c), 2-Me (d), 2,6-Me₂ (e), 2,4,6-Me₃ (f)] has been studied spectrophotometrically in MeCN at 451 nm. The products (4) have been isolated and characterised as trans-Pd(RPy)₂Cl₂. The kinetics of the nucleophilic substitution has been examined under pseudo-first-order conditions at 298 K. A single phase reaction step has been observed for bases such as Hpy (a), 4-MePy (b) and 4-ClPy (c) and follows the rate law: rate = (a + k[RPy]²[Pd(RaaiMe)Cl₂]). The bases 2-MePy (d), 2,6-Me₂Py (e) and 2,4,6-Me₃Py (f) exhibits a bi-phasic reaction and follows the rate laws: rate–1 = (a + k[RPy][Pd(RaaiMe)Cl₂]) and rate–2 = (a + k[RPy][Pd(RaaiMe)-Cl₂]), where k is the third-order rate constant; k is the second-order first phase rate constant, k is the second-order second phase rate constant and a/a/a correspond to the solvent dependent constant of the respective reaction path. The rate data supports a nucleophilic association path. External addition of Cl^– (LiCl) suppresses the rate, which follows the order: k/k/k (3) > k/k,k (1) > k/k,k (2). The k values are linearly related to the Hammett constants. The 2-substituted pyridines (d–f) remarkably reduce the rate and show a bi-phasic reaction behaviour as compared with 4-Rpy (a–c). This is attributed to the steric effect that destabilises the transition state. The rate decreases with increasing steric crowding at the ortho-position and follows the order: (d) > (f) > (e). The 4-substituted pyridines control the rate via an inductive effect and follow the order: (b) > (a) > (c).     

Transition metal chemistry of oxime-containing ligands,part XI. Copper(II) complexes of syn-phenyl-2-pyridylketoxime and syn-methyl-2-pyridylketoxime

Summary Some copper(II) complexes of the types: Cu(HPPK)-(PPK)X, Cu(HMPK)(MPK)X (where HPPK = syn-phenyl-2-pyridylketoxime, HMPK = syn-methyl-2-pyridylketoxime and X = Cl^–, Br^–, I^–, NO₃ ^–, SCN^– or SeCN^–) Cu(HPPK)₂SO₄ 3 H₂O and Cu(HMPK)₂SO₄ · 3 H₂O were synthesized and characterized by analysis, magnetic susceptibility, e.s.r., reflectance and i.r. spectral measurements. The spectral data suggest that Cu(HPPK)(PPK)X and Cu(HMPK)(MPK)X containcis square-coplanar [Cu(HPPK)(PPK)]⁺ and [Cu(HMPK)(MPK)]⁺ units respectively, linked by weakly coordinated anions, giving infinite polymeric highly distorted octahedral chain structures, whereas Cu(HPPK)₂SO₄ · 3H₂O and Cu(HMPK)₂SO₄ · 3 H₂O have acis distorted octahedral structure containing two ligand molecules of ketoxime and a bidentate sulphate group. The polycrystalline e.s.r. spectra suggest a distorted octahedral stereochemistry for the Cu^II ion involving a ground-state. By using e.s.r. and reflectance spectral data, the orbital reduction parameters, k₁₁ and k₁ were calculated and interpreted in terms of molecular orbital coefficients.