Kinetics of photoreduction of 9,10-phenanthrenequinone in the presence of amines and polymethylbenzenes

A study of the kinetics of photoreduction of 9,10-phenanthrenequinone in the presence of hydrogen donors (para-substituted N,N-dimethylanilines and polymethylbenzenes) showed that plots of the quantum yield of photoreduction (_H) and apparent reaction rate constant (k _H) vs. oxidation potential of hydrogen donors are extreme. In the presence of amines, k _H and _H increase, as a whole, whereas they decrease in the presence of polymethylbenzenes. In coordinates _H-G _e (G _e is the change in the free energy of electron transfer) for pairs quinone-H donor, _H increases with G _e approaching to zero. For the amine series, this effect is mainly in the exothermic region of G _e (G _e < 0). For the series of polymethylbenzenes, this increase is observed in the endothermic region (G _e > 0).__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2381–2385, November, 2004.     

Effect of substituents on ionization potentials of phosphorus compounds. Conjugation in radical cations

The first vertical ionization potentials (I) of phosphorus compounds P(X_i)₃, OP(X_i)₃, SP(X_i)₃, (4-XC₆H₄)₃P, and PCX are related to the inductive, resonance, and polarizability parameters of inorganic, organic, and organometallic substituents X by dependences of the type I = I _H + a_I + b_R ⁺ + c, where I _H is the I value for X = H. The I values are also affected by hyperconjugation. The ratio of the contributions of the resonance (b_R ⁺) and polarizability (c) effects to the I value is determined by the degree of delocalization of the unpaired electron and the positive charge in the radical cations formed upon ionization of neutral molecules. The _R ⁺ resonance parameters of organosilicon, organogermanium, and organotin substituents bound to the P ^·+ radical cation center were calculated for the first time.     

Kinetics of Methyl Iodide Tribosorption on the Solid-Phase Salt KI

It was found that the tribosorption of methyl iodide from the gas phase of a closed reactor onto a matrix of KI is described by the rate equation for a reversible first-order reaction v _g – v _{, g} = mv _ts ^* exp(–_td D _sp), where v _g and v _{, g} are, respectively, the current and equilibrium amounts of methyl iodide in the gas phase; v _ts ^* is the equilibrium amount of methyl iodide tribosorbed per gram of salt; m is the mass of potassium iodide; _td is a constant, which characterizes the efficiency of tribodesorption (_td = 0.011 ± 0.005 g/J); and D _sp is the specific dose of mechanical energy absorbed by the KI powder. The value of v _ts ^* monotonically increased with increasing equilibrium partial pressure of methyl iodide and reached a maximum value of 25 mol/g. The lower limit of the constant _td, which characterizes the efficiency of tribosorption, was estimated at 0.1 g/J.     

Dinuclear Complexes Contributing to Softness of Metal Acceptors

Since emf measurements with amalgam electrodes have been used, in most studies of the stabilities of complexes between soft metal acceptors and halide ions a series of investigations of the kinetics of electrode reactions were accomplished with halide systems of metal ions in the Groups 11 and 12 in aqueous and/or DMSO solutions. The aim was to establish which complexes contribute to the exchange current density, i _o. Such measurements are found to be a very sensitive method for identifying dinuclear complexes that can display much higher charge transfer rate constants than mononuclear complexes can. From these results it can be stated that hard acceptors do not show any tendency to form dinuclear halide complexes, whereas soft acceptors are apt to do so. This fact leads to the conclusion that dinuclear complexes have a strong internuclear bond. In determinations of the overall stability constant _j of a complex ML _j there is an influence from a complex M₂L _j with a constant _j , resulting in the substitution of _j for ( _j + 2a _{j j} ), where a _j = [M] when the ligand number n = (C _L – [L])/C _M has the value j. An approximate value of the association constant, K _ass, of the internuclear bond can be calculated from _j if _j is known. On the basis of these measurements the most probable types of the internuclear bonds are discussed.     

The viscosity of aqueous solutions of alkali and tetraalkylammonium halides at 25°C

The viscosities of most alkali and tetraalkylammonium halides have been measured in water at 25°C. The relative viscosities can be fitted, up to 1M, with the relation _r =1+A c^1/2+B c+D ². TheA term depends on long-range coulombic forces, andB is a function of the size and hydration of the solute. When combined with partial-molal-volume data, the difference B –0.0025V° is mostly a measure of the solute-solvent interactions. IonicB are obtained if the tetraethylammonium ion is assumed to obey Einstein's law. TheD parameter depends on higher terms of the long-range coulombic forces, on higher terms of the hydrodynamic effect, and on structural solute-solute interactions. As such, it cannot be interpreted unambiguously.     

Vibrational isotope effect of linear and planar molecules: Deuterated bromoethenes

Linear (planar) molecules A and B which are identical except for isotopic substitutions at the atomic sites are considered. Stretching (bending, out-of-plane) frequencies _k and normal modes _k of the isotopically perturbed molecule B are expressed in terms of stretching (bending, out-of-plane) frequencies _i and the corresponding normal modes _i of the unperturbed molecule A. Complete specification of the unperturbed normal modes is not required. All that is needed are stretching (bending, out-of-plane) amplitudes | _i of the normal modes _i at those sites that are affected by isotopic substitution. The rule which interlaces frequencies _k of molecule A with frequencies _i of molecule B is derived. Given two isotopic molecules A and B that differ by a single isotopic substitution at site , the inversion relation is derived. This relation expresses unperturbed stretching (bending, out-of-plane) amplitudes at the site in terms of stretching (bending, out-of-plane) frequencies of molecules A and B . As an example, out-of-plane vibrations of deuterated bromoethene were considered. In the simplest method 12 out-of-plane frequencies of four polydeuterated bromoethenes were calculated from 12 out-of-plane frequencies of bromoethene and three monodeuterated bromoethenes. Standard deviation of thus calculated frequencies from experimental frequencies is =2.74 cm^–1. In another method, 15 out-of-plane frequencies of four polydeuterated bromoethenes and selected monodeuterated bromoethene are calculated from 9 out-of-plane frequencies of bromoethene and the remaining two monodeuterated bromoethenes. Depending on which monodeuterated bromoethene is selected (1-, cis- or trans-), standard deviation of thus obtained frequencies from experimental frequencies is 1=2.84 cm^–1, c=2.96 cm^–1 and t=2.72 cm^–1.     

Driven Chain Macromolecule in a Heterogeneous Membrane-Like Medium

Monte Carlo simulations are performed to study the conformational relaxation of a large polymer chain driven into a heterogeneous (membranelike) substrate on a discrete lattice. Chains are created on trails of constrained self-avoiding walks (SAW) on the lattice. Kink–jump, crank–shaft, and reptation moves are used to move segments of chains. Short chains of length L _sc are driven by a field E ₁ toward an impenetrable substrate to design a membrane medium with mobile chain segments. A long chain of length L _lc is then driven by a field E ₂ into the membrane medium and is subsequently allowed to relax in a field E ₃. Radius of gyration R _g and end-to-end distance R _e of the long chain are examined. The relaxation of the conformation of the long chain and its magnitude is found to depend on the initial (predeposition) conformation of the chain, i.e., on E ₂. For a relatively relaxed initial conformation (at E ₂ = 0.1), the longitudinal component of the radius of gyration (R _gz ) is found to decay with the driving field E ₃ with a power law, R _gz E ₃ where 0.1 at low field (E ₃ 0.1) and 1/3 at high field E ₃ 0.1.     

A General Analysis of Field-Based Molecular Similarity Indices

A formalism is presented that incorporates the entirety of all field-based molecular similarity indices of general form S _ij = _ij /h( _ii , _jj ), where the numerator is given by the inner product or overlap of field functions F _i and F _j corresponding to the ith and jth molecules, respectively, and the denominator is given by a suitable mean function of the self-similarities _ii and _jj . This family of similarity indices includes the index initially introduced by Carbó nearly twenty years ago, where h( _ii , _jj ) is taken to be the geometric mean of _ii and _jj , and the well-known indices due to Hodgkin and Richards, and Petke, where h( _ii , _jj ) is taken to be the arithmetic mean and maximum of _ii and _jj , respectively. Two new indices based upon the harmonic mean and minimum of _ii and _jj are also defined, and it is demonstrated that the entire set of field-based similarity indices can be generated from a one-parameter family of functions, called generalized means, through proper choice of the parameter value and suitable limiting procedures. Ordering and rigorous bounds for all of the indices are described as well as a number of inter-relationships among the indices. The generalization of field-based similarity indices, coupled with the relationships among indices that have been developed in the present work, place the basic theory of these indices on a more unified and mathematically rigorous footing that provides a foundation for a better understanding of the quantitative aspects of field-based molecular similarity.     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

Ligand-structure effect on electrochemical reduction of copper(II) complexes

Summary Half-wave potentials for a one-electron reduction of copper(II) complexes containing polydentate ligands can be calculated using the equationE _1/2=E ⁰(Cu^2+/+)+ _{i j} E _i where E _i are contributions related to the electronic and steric properties of the ligands. The values of 18 E _i contributions are presented and explained, and the effect of the solvents on the half-wave potentials is exemplified.Dedicated to Prof. Dr. Viktor Gutmann to his 70th birthday     

Approximate theories of gelation

Summary The assumptions involved in approximate theories of gelation forRA ₂ +RB _f type random polymerisations are examined in detail. When the assumptionc _int c _ext is removed it is apparent that, contrary to previous findings, theFrisch theory is unable to explain existing gel-point data. A detailed development ofKilb's model for gelation is given and the expression _c (f – 1)(1 – _ab )² = 1 is derived as the condition for gelation. _c is the product of extents of reaction ofA andB groups at the gel point,f is the branchunit functionality, and _ab is a ring-forming parameter. _ab depends on the dilution of a reaction system, the molecular weights of the reactants and chain structures. It is shown how the derived expression can be used for reasonable predictions of _c for a given polymerisation system.

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Zusammenfassung Die Annahmen, worauf die simplifizierten Gelbildungstheorien betreffs einer Zufallspolymerisation desRA ₂ +RB _f Typs basieren, werden im einzelnen untersucht. Legt man die Annahmec _int c _ext ab, stellt sich heraus, daß dieFrisch-Theorie, im Gegensatz zu früheren Resultaten, die bekannten Gelpunktdaten nicht erklären kann. Eine Weiterentwicklung des Kilbschen Modelles wird vorgeschlagen und der Ausdruck _c (f - 1)(1 - _ab ² = 1 wird als Gelbindungsbedingung abgeleitet. _c ist das Produkt der Reaktionsumsätze derA- undB-Gruppen beim Gelpunkt;f = Funktionalität einer Verzweigungseinheit und _ab ist ein Ringbildungsparameter. _ab hängt von der Verdünnung eines Reaktionssystems, von den Molekulargewichten der reagierenden Moleküle und von ihren Kettenstrukturen ab. Es wird gezeigt, wie der so abgeleitete Ausdruck angewandt werden kann, um Werte für _c bei einer gegebenen Polymerisation vernünftig vorauszusagen.

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Dedicated to Herrn Prof. Dr. G. Rehage on the occasion of his 60th birthday.

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With 9 figures and 1 table     

Thermodynamic study of solvent extraction of monovalent metal picrates with benzo-18-crown-6 into chloroform

Thermodynamic parameters (H _ex ⁰ and S _ex ⁰ ) for the overall extractions of monovalent metal (Na, K, Rb, and Tl) picrates with benzo-18-crown-6 (B18C6), and those (H _D,L ⁰ and S _D,L ⁰ ) for the distribution of B18C6 were determined between chloroform and water. All the extracted B18C6 complexes were l:1:1 complexes (B18C6:metal ion: picrate anion). The H _ex ⁰ and S _ex ⁰ values for all the metals are negative. Every extraction of the metal picrate with B18C6 is completely enthalpy driven. The H _D,L ⁰ and S _D,L ⁰ values of B18C6 are both positive, and the partition of B18C6 is entirely entropy driven. Enthalpy (H _ex,ip ⁰ ) and entropy changes (S _ex,ip ⁰ ) for ion-pair extractions of B18C6-metal ion complexes with picrate anions were calculated. All the H _ex,ip ⁰ and S _ex,ip ⁰ values are negative, and the ion-pair extractions are completely enthalpy driven.     

Eigenvalues of the real generalized eigenvalue equation perturbed by a low-rank perturbation

The low-rank perturbation (LRP) method solves the perturbed eigenvalue equation (B +V) _k = _k (C +P) _k , where the eigenvalues and the eigenstates of the related unperturbed eigenvalue equationB _i = _i C _i are known. The method is designed for arbitraryn-by-n matricesB, V, C, andP, with the only restriction that the eigenstates _i of the unperturbed equation should form a complete set. We consider here a real LRP problem where all matrices are Hermitian, and where in addition matricesC and (C +P) are positive definite. These conditions guarantee reality of the eigenvalues _k and _i . In the original formulation of the LRP method, each eigenvalue _k is obtained iteratively, starting from some approximate eigenvalue _k . If this approximate eigenvalue is not well chosen, the iteration may sometimes diverge. It is shown that in the case of a real LRP problem, this danger can be completely eliminated. If the rank of the generalized perturbation {V, P} is small with respect ton, then one can easily bracket and hence locate to any desirable accuracy the eigenvalues _k (k = 1, ...,n) of the perturbed equation. The calculation of alln eigenvalues requiresO(² n ²) operations. In addition, if the perturbation (V, P) is local with the localizabilityl p, then onlyO(² n) operations are required for a derivation of a single eigenvalue.     

On expectation value calculations of one-electron properties using the coupled cluster wave functions

The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (O=¦exp (T ⁺)O exp (T)¦_c) was truncated so that T ₁ T ₂, T ₃, and (1/2) T ₂T₂ clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T ₁, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the low rank perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at atomic sites is considered. Relations which express vibrational frequencies _k and normal modes _k of the perturbed isotopic molecule B in terms of the vibrational frequencies _i and normal modes _i of the unperturbed molecule A are derived. In these relations complete specification of the unperturbed normal modes _i is not required. Only amplitudes | _i of normal modes _i at sites affected by the isotopic substitution are needed.     

Comparison of the Bonding of Benzene and C60 to a Metal Cluster: Ru3(CO)9(μ3-η2,η 2,η2-C6H6) and Ru3(CO)9(μ3-η2,η2,η2-C60)

The electron distributions and bonding in Ru₃(CO)₉( ³- ², ², ²-C₆H₆) and Ru₃(CO)₉( ³- ², ², ²-C₆₀) are examined via electronic structure calculations in order to compare the nature of ligation of benzene and buckminsterfullerene to the common Ru₃(CO)₉ inorganic cluster. A fragment orbital approach, which is aided by the relatively high symmetry that these molecules possess, reveals important features of the electronic structures of these two systems. Reported crystal structures show that both benzene and C₆₀ are geometrically distorted when bound to the metal cluster fragment, and our ab initio calculations indicate that the energies of these distortions are similar. The experimental Ru–C_fullerene bond lengths are shorter than the corresponding Ru–C_benzene distances and the Ru–Ru bond lengths are longer in the fullerene-bound cluster than for the benzene-ligated cluster. Also, the carbonyl stretching frequencies are slightly higher for Ru₃(CO)₉( ³- ², ², ²-C₆₀) than for Ru₃(CO)₉( ³- ², ², ²-C₆H₆). As a whole, these observations suggest that electron density is being pulled away from the metal centers and CO ligands to form stronger Ru–C_fullerene than Ru–C_benzene bonds. Fenske-Hall molecular orbital calculations show that an important interaction is donation of electron density in the metal–metal bonds to empty orbitals of C₆₀ and C₆H₆. Bonds to the metal cluster that result from this interaction are the second highest occupied orbitals of both systems. A larger amount of density is donated to C₆₀ than to C₆H₆, thus accounting for the longer metal–metal bonds in the fullerene-bound cluster. The principal metal–arene bonding modes are the same in both systems, but the more band-like electronic structure of the fullerene (i.e., the greater number density of donor and acceptor orbitals in a given energy region) as compared to C₆H₆ permits a greater degree of electron flow and stronger bonding between the Ru₃(CO)₉ and C₆₀ fragments. Of significance to the reduction chemistry of M₃(CO)₉( ³- ², ², ²-C₆₀) molecules, the HOMO is largely localized on the metal–carbonyl fragment and the LUMO is largely localized on the C₆₀ portion of the molecule. The localized C₆₀ character of the LUMO is consistent with the similarity of the first two reductions of this class of molecules to the first two reductions of free C₆₀. The set of orbitals above the LUMO shows partial delocalization (in an antibonding sense) to the metal fragment, thus accounting for the relative ease of the third reduction of this class of molecules compared to the third reduction of free C₆₀.     

Approximate formulas for the characteristics of interelectronic angle densities

The accuracies of approximate formulas are examined for several characteristics of the interelectronic angle density A(₁₂), where ₁₂ (0₁₂) is the angle subtended by the position vectors r₁ and r₂ of two electrons. Numerical results for 102 atoms show that simple approximations have sufficient accuracies for the moments with n=1–4, the central moments _n with n=2, 4, and the kurtosis, when measured by the absolute and relative errors. For heavy atoms, however, the relative errors for the third central moment ₃ and the skewness are large.     

Dependence of the equilibrium thickness and double layer potential of foam films on the surfactant concentration

Summary The effect of the surfactant concentrationc _s on the equilibrium thicknessh _r , of foam films and the potential ₀ of the diffuse electric layer is studied in a wide concentration range (including cmc). The cell for investigation of thin liquid films is improved and a good reproducibility of the measuredh _r is obtained. The possibilities for determination of the capillary pressureP in.the cell for investigation of microscopic thin liquid films are discussed. The values ofP can be measured with sufficient accuracy by the capillary-rise method, using a tube, identical with the tube of the cell for thin liquid films. The dependenceh _r (c _s ) is studied for nonionic surfactants (decylmethyl sulphoxide, nonyl-phenol 20-glycol ether and dodecyl 11-ethylene oxide) and the ionic sodium dodecyl sulphate. After reaching a steady value (a plateau in theh _r (c _s ) curve) at high concentrations (about cmc) a decrease in the equilibrium thickness of nonionic surfactants is found. The possible reasons for this decrease are discussed. It is shown that this effect probably is due to the electrostatic disjoining pressure. The values of the _o-potential at the plateau of theh _r (c _s ) curves are determined by the DLVO-theory using theh _r , values. The so determined ₀-values are more correct than the obtained earlier by this method because of the more precise measurement of the equilibrium thickness and the direct experimental determining of the capillary pressure. A qualitative interpreting of the ₀(c _s ) dependence is made on the basis of the surfactant adsorption at the solution/air interface and it is found that for nonionic surfactants the surface charge saturation is very near to the saturation in the adsorption layer, and for the ionic surfactants the adsorption layer saturation is at higher concentration.

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Zusammenfassung Es wurde der Einfluß der Tensidkonzentrationc _s auf die Gleichgewichtsdickeb _r von Schaumfilmen und das Potential ₀ der diffusen elektrischen Doppelschicht in einem weiten Konzentrationsbereich (einschließlich cmc) für nichtionische Tenside (Decylmethylsulfoxide, Nonylphenol-20-Glycolether und Dodecyl-11-Ethylenoxid) und ionogene Tenside (Natriumlaurylsulfat) studiert. Nach dem Erreichen eines konstanten Wertes (= Plateau in derb _r (c _s )-Kurve) bei höheren Konzentrationen (etwa crnc) wird eine Abnahme in der Gleichgewichtsdicke der nichtionogenen Tenside gefunden. Dies hängt wahrscheinlich mit dem elektrostatischen disjoining pressure zusammen. Aus den Überlegungen über das ₀-Potential wird gefolgert, daß für nichtionogene Tenside die Oberflächen-ladungssättigung nahe bei der Sättigung in der Adsorptionsschicht liegt. Bei ionogenen Tensiden liegt die Sättigung in der Adsorptionsschicht bei höheren Konzentrationen.

     

Ionic association in aqueous solutions of strong electrolytes

A more accurate calculation of relaxation effects obtained with the standard Debye-Hückel-Onsager model has been presented recently and is here applied to several aqueous 1:1 electrolytes. The variation of the standard deviation between calculated and observed equivalent conductivities withK _A leads to an ill-defined minimum; but, where data over a wide concentration range are available, the minimum corresponds to values of the contact distancea which approximate to estimates from ionic dimensions. It is therefore proposed that, although preciseK _A values from conductance cannot be determined, the most probable values are those associated with realistic estimates ofa. When data cover a limited concentration range, minimum standard deviations are often indeterminate or vary greatly for duplicate runs. It is shown that reasonable values ofK _A can be obtained from such data if comparison is made at estimated values ofa.Notation The symbols not defined in the text are the following b e ²/kTa for 1:1 electrolytes - e electronic charge - k Boltzmann gas constant - T absolute temperature - dielectric constant of solvent - –(3/2y)(_e0/₀)     

On the application of quantitative models of diffusion-controlled adsorption kinetics at fluid interfaces

The model of diffusion-controlled adsorption kinetics can be solved by different mathematical procedures. For the most important case of a Langmuir isotherm, useful solutions are summarized and extended and the ranges of application are given. New approximations are presented which can be applied to most experiments in practice.Nomenclature a _i coefficients of the collocation solution - a _L Langmuir parameter - a interaction parameter of the Frumkin isotherm - _n coefficients of a power series - c surfactant bulk concentration - c ₀ equilibrium bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - _t8 maximum surface concentration - ( _x ) Gamma function - t time - dimensionless time Dedicated to the 60th birthday of G. Kretzschmar.