Pseudo-point groups and chronality in enumeration of reaction pairs

Summary The pseudo-point group is constructed to characterize the symmetry of a basic pair of hexagonal reaction graphs having no par-bonds on its edges. Any pairs of reaction graphs (reaction pairs) are considered to be obtained by adding par-bonds to the edges of the basic pair; they are counted by the USCI (unit-subduced-cycle-index) approach. Thus, the six edges of the basic pair are assigned to the coset representation (/C _2v ). After the subduction of the is calculated, the partial-cycle-index method of the USCI approach is applied to the combinatorial enumeration of reactions pairs.Reaction pairs are classified to two categories, i.e. isoenergetic and anisoenergetic. An isoenergetic pair is concluded to be a self-reaction pair, while an anisoenergetic pair corresponds to a non-self-reaction pair. The concept of chronality is also discussed to clarify the symmetrical nature of the resulting orbits.     

Effect of charge on the standard partial molar volumes and heat capacities of organic electrolytes in methanol and water

Previously developed additivity schemes for nonelectrolytes have been used to estimate and for tetraalkyl and tetraphenyl methanes in methanol and water. Corrections have been applied to the thermodynamic values of these model compounds to account for a variation in size of the central atom, and these were used to ascertain the effect of charge on and of alkyl and phenyl quaternary ions having N, P and B as central atoms. Investigations of R₄NBr, (R=methyl to heptyl) salts show that the charge effect on and of R₄N⁺ ions is large and relatively independent of ion size suggesting that the solvent molecules penetrate the ions. The ability to estimate and of the quaternary ions in the bromide salt solutions has made it possible to make ionic assignments with some confidence; (Br^–) has been evaluated as 19.7±2 and 30.2±7 cm³-mol^–1 and (Br^–) as –83±7 and –68±30 J-K^–1-mol^–1 in methanol and water, respectively. The use of organic ions for making ionic assignments of and is critically examined and comparisons with other assignments are made. The scaled particle theory is employed to divide the heat capacities of electrolytes into cavity and interaction contributions.     

Apparent molal volumes of phosphonium halides at 15, 25 and 35°C

The densities of aqueous solutions of the phosphonium halides, Bu _4-n Ph _n PX(n=0–4), some of which were synthesized from the phosphines, were measured at 15, 25 and 35°C. Partial molal volumes at infinite dilution, , and B _v coefficients for the apparent molal volumes were determined at each temperature. For the first four cations varies little with n. For all salts B _v are negative but become less negative with increasing n. The temperature dependence of B _v is positive for butyl-rich salts (n<2) but negative for phenyl-rich salts (n>1). Also it appears that is relatively large for phenyl-rich cations in comparison with that for butyl-rich cations.     

Apparent molal volumes and adiabatic compressibilities of ethylene glycol derivatives in water at 5, 25, and 45°C

Density and ultrasonic velocity measurements were made on a series of dilute equeous solutions of H(OCH ₂ CH ₂ )_nOH, CH ₃ (OCH ₂ CH ₂ )_nOCH ₃ , H(CH ₂ )_nOCH ₂ CH ₂ OH (n=1–4), and poly(ethylene glycol) at 5, 25, and 45°C. The additivity of the limiting partial molal volumes ( ) and adiabatic compressibilities ( ) for CH ₂ and CH ₂ CH ₂ O groups was tested by using the observed and values of the solutes. The and values of the CH ₃ , CH ₂ , CH ₂ CH ₂ O, and CH ₂ OH groups were estimated and discussed in relation to hydration effects. The and values of alkoxyethanols calculated on the basis of the additivity of the group partial molal quantities were in good agreement with the observed values. The behavior of the limiting partial molal isothermal compressibility of alkoxyethanols was similar to that of the adiabatic compressibility.     

Reaction graphs and a construction of reaction networks

Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs and , related by a chemical transformation , the reaction graph is determined using a maximal common subgraph defined for vertex mapping . A binary operation defined for graphs constructed over the same vertex set enables us to decompose the reaction graph into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at and ending at corresponds to a breakdown of the transformation into a sequence of intermediates.     

Heat capacity changes for the lonization of aqueous phenols at 25°C

The apparent molal heat capacities have been determined at 25°C for phenol,meta-nitrophenol,para-nitrophenol,meta-cyanophenol, andpara-cyanophenol and the corresponding sodium salts in water at several concentrations. These values have been extrapolated to infinite dilution to provide the values from which the heat capacity changes for the ionization of the aqueous phenols have been calculated. The observed values are virtually identical within experimental error for the phenols studied. The volume data needed to calculate the values from the experimental data are also reported.To whom correspondence should be addressed.     

Über die Definition der Nachweisgrenze

Zusammenfassung Um die Nachweisgrenze zu bewerten, benützt man den Begriff des Entscheidungsniveausy _k , eine Größe, die man mit Hilfe eines zweistufigen Modells bewertet, indem man das Neyman-Pearsonsche Kriterium aus der statistischen Theorie der Signalidentifizierung benutzt. Zu diesem Zweck stellt man eine falsche IdentifizierungswahrscheinlichkeitP ₁₀ fest, so daß , worin den Mittelwert des Blindsignals mit der Standardabweichung _k , und z_k die normierte Abweichung bedeuten, die man aus dem Wert der Laplaceschen Funktion z _k =0,5–P ₁₀ erhält. Das der Nachweisgrenze entsprechende analytische Signal: , worink=z _k –z _i das Verhältnis Signal-Störpegel darstellt und man z_i ebenso aus dem Wert der Laplaceschen Funktion (z _i )=P ₁₁–0,5 erhält (z _i ist negativ). WennP ₁₀=10^–3 undP ₁₁=0,998, erhält mank=6, und die Nachweisgrenze wird: .Die frequentometrisch definierte Nachweisgrenze⁶ hat genau dieselbe Bedeutung, wie jene, die den Begriff des Entscheidungsniveaus bzw. das zweistufige Modell und das Neyman-Pearsonsche Kriterium benutzt.

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On the definition of the detection limit

Summary In order to estimate the detection limit, the notion of decision levely _k is used, a magnitude which is estimated with the help of a two-stage model, using the Neyman-Pearson criterion from the statistical theory of signals detection. For this reason a fals identification probability P₁₀ is fixed, so that: , where is the mean value of the background fluctuations with the standard deviation _y ,z _k is the normalized deviation obtained from the value of the Laplace function (z _k )=0.5–P ₁₀. The analytical signal corresponding to the detection limit: , wherek=z _k +Z _i , represents the signal-noise ratio andz _i is also obtained from the value of the Laplace function(z_i)=P ₁₁–0.5 (z _i is negative). If one considersP ₁₀=10^–3 andP ₁₁=0.998,k=6 and the detection limit will be: .The detection limit defined frequentometrically⁶ is shown to have just the same significance as that, which uses the notion of decision level or the two-stage model and the Neyman-Pearson criterion respectively.

     

Approximate sizes of monoatomic negative ions with fractional nuclear charge using electrostatic potentials

Summary Using the criterion that for negative monoatomic ions withN electrons, the location of minimum in the electrostatic potentialV(r) gives an approximate estimate of ionic radii,r _m. Calculations of the latter are reported for quark atoms with fractional nuclear chargesZ=N– andN– , respectively. Quark atoms withN=1–10, 18 and 36 have also been considered.     

Hexagonal high pressure phase of copper(I)tetraiodomercurate (Cu2HgI4)

Summary Using a high pressure X-ray camera Cu₂HgI₄ was subjected at room temperature to pressures up to about 8 GPa. A hexagonal high pressure phase (a=8.28 (2) Å,c=3.40 (0) Å, space group P lm,Z=1) could be detected. This phase shows a reversible transformation with pressure hysteresis. The transition occurs at 7 GPa when the pressure is increased but at 6 GPa when the pressure is decreased.

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Hexagonale Hochdruckphase von Kupfer(I)tetraiodomercurat (Cu₂HgI₄)

Zusammenfassung Cu₂HgI₄ wurde in einer Hochdruckkamera bei Raumtemperatur mit einem Druck bis zu 8 GPa belastet. Dabei bildete sich eine hexagonale Hochdruckmodifikation (a=8.28 (2) Å,c=3.40 (0) Å, Raumgruppe P lm,Z=1). Für diese Phase wurde eine reversible Umwandlung mit Druckhysterese festgestellt. Mit steigendem Druck findet die Umwandlung bei 7 GPa mit sinkendem Druck jedoch bei 6 GPa statt.

     

The effect of pressure on the ionization of water at various temperatures from molal-volume data1

The apparent molal volumes of dilute (0.002 to 1.0m) aqueous HCl and NaOH solutions have been determined at 0, 25, and 50°C and NaCl solutions at 50°C. The partial molal volumes ( ) of HCl, NaOH, and NaCl solutions have been determined from these apparent molal volumes and other reliable data from the literature. The partial-molal-volume changes ( ) for the ionization of water, H₂OH⁺+OH^–, have been determined from 0 to 50°C and 0 to 1m ionic strength from the partial molal volumes of HCl, NaOH, NaCl, and H₂O. The partial molal compressibilities ( for HCl, NaOH, NaCl, and H₂O have been estimated from data in the literature and used to determine the partial molal compressibility changes ( ) for the ionization of water from 0 to 50°C and 0 to 1m ionic strength. The effect of pressure on the ionization constant of water has been estimated from partial-molal-volume and compressibility changes using the relation from 0 to 50°C and 0 to 2000 bars. The results agree very well with the directly measured values.Contribution Number 1548 from the University of Miami.     

The standard transported entropy of chloride ion in H2O and D2O

Transported entropies of the chloride ion, , in H₂O and in D₂O at 25°C and at concentrations ranging from 0.001 to 0.04m have been determined from the measurements of the steady-state (final) thermoelectric powers of the silver-silver chloride thermocell. Experimental data was extrapolated to infinite dilution to obtain the standard transported entropy . The concentration dependence of is examined and the solvent-isotope effect on the transported entropy is investigated. Thermodynamic data on the entropy of transfer of chloride ion from H₂O to D₂O is used to estimate the difference of the standard ionic entropy of transport in H₂O and D₂O for chloride ion.     

Solution of the generalized eigenvalue equation perturbed by a generalized low rank perturbation

Summary The problem of finding eigenvalues and eigenstates of the generalized perturbed eigenvalue equation = g3(+) is considered. The eigenvalues and the eigenstates of the unperturbed eigenvalue equation = are assumed to be known. Matrices , and can be arbitrary, except for the requirement that be nonsingular and that the eigenstates of the unperturbed equation be complete. It is shown that the eigenvalues and the eigenstates of the perturbed equation can be easily obtained if the rank of the generalized perturbation , is small. A special case of low rank perturbations are piecewise local perturbations which are common in physics and chemistry. If the perturbation is piecewise local with fixed localizability, the operation count for the derivation of a single eigenvalue and/or a single eigenstate is (n). If the perturbation has a fixed rank, the operation count for the derivation of all eigenvalues and/or all eigenstates is (n ²).Research supported by the Welch Foundation of Houston, Texas, and by the Yugoslav Ministry for Development (Grant P-96)     

Über die Berechnung der Elektronenenergie eines Moleküls aus dem Erwartungswert der kinetischen Energie

Knowing the mean value of the electronic kinetic energy T(X _i ) of a molecule as a function of the nuclear coordinates X _i , it is shown that the electronic energy can be uniquely determined by the virial theorem . The result is .

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Herrn Prof. R. G. Parr danke ich für die Fragestellung und Diskussionen. Herrn Prof. G. Weber und Herrn Dr. R. Güther möchte ich ebenfalls für Diskussionen danken.     

Über halbkontinuierliche Emulsionspolymerisation nach dem Zulaufverfahren

Zusammenfassung Die halbkontinuierliche Emulsionspolymerisation von Styrol und Methylacrylat mit Monomerenzulafu und mit Emulsionszulauf wurde untersucht. Bei Monomerenzulauf werden Wasser, Emulgator, Initiator und ein Teil des Monomeren vorgelegt; der Rest des Monomeren läuft nach Anspringen der Polymerisation mit konstanter Zulaufsgeschwindigkeitv _z zu. Bei Emulsionszulauf wird ein aliquoter Teil des Gesamtansatzes vorgelegt; der Rest läuft als Monomerenemulsion zu. Zulaufsgeschwindigkeit und Vorlagemenge wurden variiert, Bruttoreaktionsgeschwindigkeitv _u, Polymerisationsgrad , TeilchenzahlN und Teilchengrößenverteilung gemenssen. Solangev _z groß genug ist, um i dn Latexteilchen den Sättigungswert der Monomerenkonzentration [M] aufrechtzuerhalten, sind bei beiden Monomerenv _u und unabhängig vonv _z. Sinkt dagegen [M] unter den Sättigungswert, so stellt sich bei Monomerenzulauf und bei Emulsionszulauf ein stationärer Zustand ein, in demv _u=v _z ist und bei Zunahme vonv _z ansteigt. In diesem stationären Zustand wurde für beide Monomere die absolute Wachstumskonstantek _u bestimmt, zugrundegelegt ist dabei die kinetische Theorie vonSmith undEwart. Bei gleichbleibendem Gesamtansatz erzeugt Emulsionszulauf weniger, d. h. größere Latexteilchen als Monomerenzulauf oder absatzweise Polymerisation. Wenn die Nachbildung von Teilchen während des Emulsionszulaufs vermieden wird, sindN und die anfängliche Polymerisationsgeschwindigkeit der Vorlagemenge proportional und es ergibt sich eine engere Teilchengrößenverteilung als bei den anderen beiden Verfahren. Teilchenbildung während des Emulsionszulaufs verbreitert dagegen die Verteilung, die bei starker Neubildung sogar breiter als bei den anderen beiden Verfahren sein kann.

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Summary Semicontinuous emulsion polymerization of styrene and methyl acrylate with a feed of either monomer or monomer emulsion has been investigated. Using monomer feed, water, emulsifier, initiator, and part of the monomer are charged into the reaction vessel, the remaining monomer is fed with constant feeding rateR _z after the start of the polymerization. In the process with emulsion feed an aliquot part of the whole batch is charged, the rest is fed continuously as a monomer emulsion. Feeding rate and initial charge were varied, reaction rateR _p, degree of polymerization , number of latex particlesN, and particles size distribution were measured. With both monomersR _p and are independent ofR _z as long asR _z is large enough to maintain the saturation value of monomer concentration [M] in the latex particles. If [M] falls below this value a steady state is reached as well with monomer feed as with emulsion feed,R _p equalsR _z and increased with increasingR _z. Taking theSmith-Ewart theory as a basis for calculation, the propagation rate constantk _p was determined for both monomers in the steady state. Emulsion feed produces less, i. e. larger particles than monomer feed or batch polymerization, the overall charge being kept constant. Emulsion feed gives a narrower particle size distribution, and the initial rate of polymerization andN are proportional to the initial charge, if formation of new latex particles during the emulsion feed can be avoided. If not, particle size distribution is broadened and can eventually become even broader than with the other two methods.

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Mit 17 Abbildungen in 19 Einzeldarstellungen und 2 Tabellen     

A method for experimental determination of effective resonance energies related to (n, γ) reactions

When making use of some single comparator or absolute standardization methods in reactor neutron and in epicadmium neutron activation analysis, the knowledge of the effective resonance energy ( ) is essential to correct for the effect of the nonideal epithermal flux distribution on the analysis result. can be calculated from neutron resonance data, but when these are incomplete, not accurate or even not known at all, experimental determination should be considered. Such a method, providing both and the resonance integral to 2200 ms^–1 cross-section ratio (Q_O), is described in this paper. Results are given for 11 isotopes.     

Excess partial molar volumes and thermal expansivities in the water-rich region of aqueous 2-butanone

Excess partial molar volumes of 2-butanone V _m ^E (B) and thermal expansivities _p were measured in the water-rich region of aqueous 2-butanone. The composition derivatives of both quantities showed anomalies at about X _B =0.033 (x _B is the mole fraction of B). showed a step anomaly, while exhibited a peak anomaly. The compositions at which these anomalies occurred match those of the step anomalies observed earlier in and in aqueous 2-butanone. These results are discussed in comparison with those obtained previously for aqueous 2-butoxyethanol.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Perturbative solution of the RPA equation. An application to the calculation of rotational strengths

The RPA equation is solved by perturbation in Møller-Plesset (MP) and Epstein-Nesbet (EN) partitions, which are first compared on a specific example. To still accelerate the faster one (EN), a third scheme is proposed, which involves preliminary diagonalization within a limited subset , followed by usual EN perturbation between and the rest of the whole configuration space. Criteria for the choice of are given.     

Thermodynamic stability of the γ-Co1−x Se phase by CaF2 electrolyte galvanic cell method

The partial molar free enthalpy of cobalt, , and the molar free enthalpy of formation of Co _x Se alloy phase, G _f ⁰ (Co _x Se) at 873K, were determined by the solid CaF₂ electrolyte galvanic cell method forx=0.725 to 0.956. was observed to be a monotonic function of the mole fractionX _Co in the composition region of the investigation with an inflexion point atX _Co=0.455. The measurements were extended down to a temperature of 710 K and a partial Co–Se phase diagram was evaluated from the resultant data.

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Untersuchung der thermodynamischen Stabilität der -Co-_1–x Se Phase mittels galvanischer Zelle mit CaF₂ Elektrolyt

Zusammenfassung Die partiellen molaren freien Enthalpien von Kobalt ( ) und die molaren freien Bildungsenthalpien der Co _x Se Legierungsphase [G f/0 (Co _x Se) bei 873 K] wurden mittels galvanischer Zelle (CaF₂ Fest-Elektrolyt) fürx=0,725–0,956 bestimmt. wurde im untersuchten Bereich als monotone Funktion vom MolenbruchX _Co, mit einer Inflexion beiX=0,455, gefunden. Die Messungen wurden bis zu einer Temperatur von 710 K ausgedehnt und die Daten wurden zur Erstellung eines partiellen Co–Se-Phasendiagramms ausgewertet.

     

The classification of tensor surface harmonic functions for clusters and coordination compounds

A simple method for enumerating theL and functions for polyhedral cluster and coordination molecules, within Stone's tensor surface harmonic methodology, is described. The nature of theL orbitals which are generated depends on the polyhedral topology and in particular the number of layers of vertices and the number of vertices within each layer. The functions are enumerated from theL 's by a number of spherical harmonic multiplication rules.     

IR study of cation effects on the O-D stretching frequencies of isotopically dilute HDO in aqueous salt solutions

IR spectra of 3 normal solutions of 14 different salts [chlorides of Al⁺⁺⁺, Be⁺⁺, Mg⁺⁺, Ca⁺⁺, Sr⁺⁺, Ba⁺⁺, Zn⁺⁺, Cd⁺⁺, Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, N(CH₃) ₄ ⁺ ] in both, 96% H₂O+4% D₂O and 100% H₂O, were measured in the frequency range =2 800–2 100 cm^–1. From up to 18 single measurements for each solution the frequencies and halfwidths of the O-D stretching bands of isotopically dilute HDO were determined with high accuracy. Frequencies in the range =2 510–2 529 cm^–1 and halfwidths in the range =155–205 cm^–1 resulted atT=30°C with standard deviations typical less than ±1 cm^–1 and ±4 cm^–1, respectively. An almost perfect correlation between the O-D stretching band parameters and the polarizing power of the cations was obtained.Herrn Prof. Dr.A. Neckel, Wien, zum 60. Geburtstag gewidmet.