Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Reactivity of N-Phenylanthranilic Acid Derivatives: XIII. Electrical Conductivity of Solutions of Substituted 4-Nitro-N-phenylanthranilic Acids in the Dioxane-Water System

Conductometry was used to determine limiting equivalent electrical conductivity (₀), Pisarzhevskii-Valden product (₀₀), hydrodynamic ionic radii, ionization constants, thermodynamic parameters for substituted 4-nitro-N-phenylanthranilic acids (7 compounds) in the system dioxane-water at varioustemperatures. It was established that the ionization is endothermic and the entropy factor is prevailing. It was found that the reaction center is moderately sensitive to substituents and the sensitivity decreases with temperature. Multifactor correlation analysis showed that the reaction constants are roughly equal to r _I and _R but are half the values for substituted benzoic acids. The reaction series studied was found to be isoentropy. Inconsiderable solvation of the anions of the substituted anthranilic acids was revealed.     

Transmission of influence of substituent in 2-arylpyrrole-5-carboxylic acids

Research on the influence of substituenis on the reaction centers of molecules, through various bridge groups, is still an urgent task in theoretical organic chemistry. This problem is usually solved using the Hammett equation f= + a, by comparing the coefficient of the particular series of compounds under investigation with the coefficient ₀ of a reference series of compounds. The ratio of coefficients / ₀=, which is called the transmission factor, characterizes structural changes of the bridge group [1, 2].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, 1182–1186, September, 1992.     

Acid — Base properties of 3(5)-azido-1,2,4-triazoles

The pK_a and values of a series of 3(5)-azido-1,2,4-triazoles are correlated with the _I and _C constants according to the equation pK =_II + _CC + pK_o. The high _I values in both cases are due to the closeness of the substituent to the reaction center. The _C/_I ratio attests to different contributions of the inductive and mesomeric effects of a substituent during transmission of its effect from the 5-position to the N₁ and N₄ heteroatoms.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1288–1291, September, 1974.     

Charge monotonicity of atomic systems and radial expectation values

A functionf(r) is monotone of orderp if itspth-derivativef ^(p)(r) fulfils that (–1) ^p f ^(p)(r)0. So, e.g. the monotonicity properties of orderp=0, 1, 2 describe the non-negativity (p=0), the monotonic decreasing from the origin (p=1) and the convexity (p=2) of the function, respectively. Here, the monotonicity properties of the electron functiong _n (r; )=(–1) ^{n (n)} (r)r ^– , 0, of the ground state of atomic systems are analysed both analytically and numerically. The symbol (r) denotes the spherically averaged electron density. First of all, the condition which specifies, if exists, a value _np such thatg _n (r; _np ) be monotone of orderp is obtained. In particular, it is found that ₀₁=max {r(r)/(r)}, ₀₂=max {q ₀(r)}, ₁₁=max {r(r)/(r)} and ₁₂=max {q ₁(r)}, whereq ₀(r) andq ₁(r) are simple combinations of the first few derivatives of (r). Secondly, numerical calculations of the first few values _np in a Hartree-Fock framework for all ground-state atoms with nuclear chargeZ54 are performed. In doing so, the pioneering work of Weinstein, Politzer and Srebrenik about the monotonically decreasing behavior of (r) is considerably extended. Also, it is found that Hydrogen and Helium are the only two atoms having the functions (r), –(r) and (r) with the property of convexity. Thirdly, it is analytically shown that the charge functionr ^– (r) with [(1+4Z ²/I)^1/2–1]/2, I being the first ionization potential, is convex everywhere. Finally, the above mentioned monotonicity properties are used to obtain rigorous, simple and universal inequalities involving three radial expectation values which generalize all the similar ones known up to now. These inequalities allow to correlate various statical and dynamical quantities of the atomic system under study, due to the physical meaning of the radial expectation values. It is worth to remember that some of these expectation values may be experimentally measured in experiments of (e, 2e)-type.     

Synthesis of two regiospecific isomers of monotosyl-γ-cyclodextrin

Tosylation of -cyclodextrin in an aqueous alkaline solution gave two regiospecific isomers (2-monotosyl--cyclodextrin(1) and 6-monotosyl--cyclodextrin(2)), that could recognize and catalyze small sized guest molecules; 2-monotosyl--CD recognized small sized guest molecules more effectively than did 6-monotosyl--CD.     

Simple statistical mechanics of electrolytes with a concentration dependent dielectric constant. Part 1. The pressure equation

We have used an approximation of the Adelman's theory of solutions to take into account the non-pairwise additive effects on the interaction potentials for a real electrolyte solution. As a result, a solute concentration dependent dielectric constant appears. The comparison with experimental data is done by means of the pressure equation. The influence of on solution properties is analyzed in two molality ranges using as a reference simplified models but with the dielectric constant of the pure solvent instead of .     

Configuration interaction in a nonorthogonal determinant basis

A class of electron models which reduce to a superposition of nonorthogonal determinants is studied by methods of covariant quantum chemistry. A compact matrix representation is found which contains variational parameters only in the form of Fock-Dirac densities A, b of separate determinants ¦>,...,¦B>. Nonorthogonality of the determinants is taken into account by means of additional projectors obtained by pseudo-inversion of the products of the form AB-Orbital optimization is thus reduced to a clearly Hermitian eigenvalue problem. Inclusion in the initial model of configurations singly excited with respect to each of the determinants ¦a> ...,¦B> is discussed. This generalized Tamm-Dancoff model is studied in detail for the spin-symmetrized (half-projected) Hartree-Fock methods. Correlation effects in the excited states of model -systems of the alternant type are analyzed within the framework of the model.Translated from Teoreticheskaya i Éksperimentalnaya Khimiya, Vol. 22, No. 5, pp. 513–523, September–October, 1986.     

Bestimmung der HMO-Parameter von Nitrogruppen aus den UV-Absorptionsspektren von Nitroaromaten

Zusammenfassung Unter Benutzung der experimentellen Werte derK-Banden von Nitro-, m- und p-Dinitro- und sym-Trinitrobenzol wurden die Parameter der Resonanzintegrale der Nitrogruppe zu _CN=1,1 und _NO=1,6 bestimmt, die Parameter der Coulombintegrale auf Grund von Plausibilitätsbetrachtungen zu _O=1,5, _N=1,8 und _C=0,25 abgeschätzt. Die UV-Spektren der vier genannten Verbindungen wurden in Cyclohexan vermessen.Die erhaltenen Parameter werden zur Berechnung der Moleküldiagramme und Energieniveaus der vier Strukturen benutzt. Die Rechendaten stehen in guter Übereinstimmung mit den experimentellen Befunden, vor allem dann, wenn den weiterreichenden induktiven Effekten der Nitrogruppe in geeigneter Weise Rechnung getragen wird.

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Using the experimental values for theK bands of nitro-, m-and p-dinitro- and sym-trinitrobenzene, the parameters of the resonance integrals of the nitro group were calculated to be _CN=1,1 and _NO=1,6, and the parameters of the Coulomb integrals estimated as _O=1,5,_N=1,8 and _C=0,25 on the basis of plausibility considerations. The UV-spectra of the above compounds were measured in cyclohexane.The parameters obtained are used to calculate the molecular diagrams and energy levels. The calculated data are in good agreement with the experimental findings, above all when the more extensive inductive effects of the nitro group are suitably taken into account.

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Mit 7 Abbildungen     

Transmission of inductive effect and polar resonance effect through the benzene and the furan ring in PMR spectra

Assuming the independence and additivity of the inductive and polar resonance effects, experimental data for chemical shifts in proton magnetic resonance (PMR) spectra of mono and disubstituted benzene and furan derivatives are used to calculate transmission coefficients for the inductive and polar resonance effects due to any substituent for a proton in the 2, 3, or 4 position in the ring. Values of ^* and ^c are tabulated. With benzene compounds transmission of the polar resonance effect decreases on passing from the p and o to the m position. The coefficient of transmission of the inductive effect to a proton in the m or p position is negligible.With furan compounds the values of the coefficient ^c for 2, 5 and 2,4 ring positions are close to the corresponding values for benzene compounds. In the furan ring a considerable part of the polar resonance is transmitted through the heteroatom. The ^* coefficients are appreciably greater with furan than with benzene compounds, because the ring carbon atoms screen the proton less from the substituent. Most of the inductive effect from the 2 to the 5 position in the furan ring is direct (transmitted through space).     

Crystal and Molecular Structure of 2‐nitro‐1‐ureidoguanidine

An Xray structural investigation of 2nitro1ureidoguanidine has been carried out. The crystals are monoclinic: a = 4.4690(2), b = 15.566(1), c = 9.4131(7), = 94.896(5)°, V = 652.4(3)> ³, space group P2₁/n, Z = 4, _calc = 1.650 g/cm³. The molecule consists of two planar fragments: carbamide and nitroguanidine. The geometrical characteristics of the molecule are analyzed. The system of intra and intermolecular hydrogen bonds in the crystal is considered.     

The van der Waals Theory of Capillarity and Computer Simulation

Computer experiments are performed on the determination of thermodynamic properties and structural characteristics of the Lennard-Jones fluid in one- and two-phase models to check the basic concepts of the van der Waals theory of capillarity. Calculations are performed using molecular dynamics method. It is shown that, at T* 1.1, the properties of flat interface can be described, within the limits of computer experiment error, in terms of the van der Waals gradient theory with the density-independent influence parameter . The account of density dependence of via the second moment of direct correlation function deteriorates the agreement between the theory and the data of computer simulation. The contribution of inhomogeneous system of higher (than ()²) terms to the Helmholtz free energy of inhomogeneous system is considered. It is shown that the account of terms proportional to ()⁴ does not lead to the agreement between the theory and the data of computer simulation, whereas the consideration of terms proportional to ()⁶ makes it possible to describe (with a good accuracy) all the properties of flat interface within the temperature range from triple point to the critical one.     

New Approach to Analysis of the Nonlinearity of the Brønsted Relationship: II. An Empirical Procedure Combining the σρ Correlation Method with the Concept of Hard and Soft Acids and Bases,as Applied to Pseudo CH Acids

A comparative systematic analysis of the features of Brönsted behavior of pseudo CH acids(according to Eigen's classification) is made. The analysis is based on combined use of experimental data onpK _a, Ggas, logk _D of CH acids (Ggas is the free energy of acid ionization in the gas phase, logk _D isthe logarithm of the rate constant of hydrogen exchange in a protic solvent). The modified nucleophilicKabachnik constants ^- are applicable to correlations for all the three kinds of acidity of pseudo CH acids. The electrostatic solvation makes an insignificant contribution to variation of pK _a and weakening of the substituent effect in going from the gas phase to dimethyl sulfoxide, and also to differentiation of the kinetic acidity. The coefficient in the Brönsted equation and the ratio between the rate constants in the correlations, which characterize the degree of proton transfer in the reaction transition state, have much in common from the physical viewpoint. The results of correlation analysis, demonstrating intramolecular uniformity of the interactions, are fully consistent with the conclusion made in the previous part of this work about the solvation uniformity of the interactions, resulting in the absence of thermodynamic deviations from the Brönsted relationship.     

Crystal Structures of [Ni(Phen)(i‐Bu2PS2)2] and [Ni(Phen)3](i‐Bu2PS2)2 Complexes and Interaction between Coordinated 1,10‐Phenanthroline Molecules

Single crystals of [Ni(Phen)(iBu₂PS₂)₂] (I) and [Ni(Phen)₃](iBu₂PS₂)₂ (III) compounds were grown, and their structures were determined by Xray diffraction analysis (CAD4 diffractometer, MoK radiation, 3336 F _hkl , R = 0.0373 for I and 2575 F _hkl for III). The crystals of complex I have a triclinic unit cell with the following parameters: a = 11.097(1) , b = 14.903(2) , c = 22.650(3); = 75.18(1)°, = 80.50(1)°, = 75.07(1)°, V = 3479.2(7)³, Z = 4, _calc = 1.255 g/cm³, and space group 1; the crystals of III have a monoclinic unit cell with the following parameters: a = 19.010(3), b = 15.481(1) , c = 17.940(3); = 97.58(1)°, V = 5233.5(12)³, Z = 4, _calc = 1.292 g/cm³, and space group C2/c. The structure of complex I is built from mononuclear molecules, and the structure of III, from [Ni(Phen)₃]²⁺ complex cations and i Bu₂PS₂ ^- outersphere anions. The NiN₂S₄ coordination polyhedra in the structure of I and NiN₆ in the structure of III are distorted octahedra. Based on structural data, the interaction between the coordinated Phen molecules of complexes I, [Ni(Phen)₂(iBu₂PS₂)](iBu₂PS₂) (II), and III is considered, as well as the packing modes of these complexes.     

Hydrodynamics and heat transfer in a plasma spouted bed reactor

The literature reveals very little intformation about plasma spouted bed hydrodynamics. Spouting of corindon particles with diameters ranging from 0.4 to 3.36 mm with argon plasma was conducted in a 90-mm-diameter column in the temperature range 300–1300°C. It was found that the maximum spoutable height (H_m) decreases with increasing particle diameter and decreasing mean bed temperature. A relation between the inlet plasma velocity and H_m is proposed. Concerning heat transport phenomena in the annulus, measurements and calculations indicate a large axial diffusivity but a poor radial mixing. Typical values of D_z and D_r are proposed on the basis of an identification procedure.Notation Ar Archimede number - Ar d ³ p (p — f) _f g ² - C_p specific heat - d_p particle diameter - d_e core diameter (or spout diameter) - D_i fluid inlet orifice diameter - D_e column diameter - D_r and D_z radial and axial diffusivity, respectively - g acceleration due to gravity - H packed static bed height - H_b bed height - H_m maximum spoutable bed height - P power     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Isothermal and nonisothermal gravimetry of nontronite dehydroxylation

A pure typical nontronite from Czechoslovakia (Sampor) was analysed by the title techniques in the range 570–1070 K. The isothermal dehydroxylation of nontronite, recorded at 630–730 K, was described reasonably, in the decomposition range =0.05–0.95, by diffusioncontrolled mechanismsD ₃ andD ₄. Application of the current solid-state reaction equations to the non-isothermal curve gave very poor results, except in the limited decomposition range =0.10 to 0.55. A unimolecular mechanism equation (Fm ₁) and also a second-order (SO) mechanism gave the best linearization of the curve. The activation energies estimated from the isothermal (D ₃,D ₄) and non-isothermal (F ₁) experiments were 125 and 151 kJ·mol^–1, respectively. Reduced time plots indicate the probable presence of a sequence of different mechanism for both techniques.

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Zusammenfassung Mittels der Titeltechniken wurde im Bereich 570–1070 K ein reines typisches Nontronit aus der SSR (Sampor) untersucht. Die isotherme Dehydroxylierung von Nontronit bei 630–730 K konnte im Bereich der Zersetzung von =0,05–0,95 durch die diffusionsbestimmten MechanismenD ₃ undD ₄ befriedigend beschrieben werden. Eine Anwendung der Gleichungen für Feststoffreaktionen auf die nichtisotherme Kurve ergab mit Ausnahme des Bereiches =0,10–0,55 nur sehr unzureichende Ergebnisse. Eine Gleichung für einen monomolekularen (F ₁) Mechanismus sowie für einen mechanismus zweiter Ordnung (SO) ergaben die beste Linearisierung der Kurve. Die aufgrund der isothermen (D ₃,D ₄) und nichtisothermen (F ₁) Experimente geschätzten Aktivierungsenergien betragen 125 bzw. 151 kJ·mol^–1. Es wird angenommen, daß es sich bei beiden Techniken um eine Sequenz verschiedener Mechanismen handelt.

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570–1070 (). , 630–730 =0,05–0,95, - D ₃ D ₄. , =0,10–0,55. (F ₁), . , (D ₃,D ₄) (F ₁) , , , 125 151 ·^–1. .

     

Exact and approximate forms of the kinetic energy functional<Emphasis Type="Italic"> T</Emphasis><Subscript>s</Subscript>[ρ] for molecules obtained via local-scaling transformations

By means of a constructive procedure based on local-scaling transformations, we have obtained the following exact form for the noninteractive kinetic energy functional of general molecular systems: where (r) is the local-scaling transformation function, T _W[] is the von Weiszäcker term and ^l _N (r _l ) and ^l _N (r _l ) are the radial and angular enhancement factors, respectively, within an atomic domain _I. The terms ^C _N (r _l ) and ^C _N (r _l ) (where C stands for complement of I) contain all contributions to the radial and angular enhancement factors within _I coming from the tails of functions centered on nuclei outside _I. Also, in the context of an atoms-in-a-molecule approach, we discuss the construction of approximations to the kinetic energy enhancement factors appearing in the previous expression for T _s[]. Acknowledgement.The authors gratefully acknowledge support of this work by FONACIT of Venezuela through Group Project No. G-97000741.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

Radiation-induced crosslinking: II. Effect on the crystalline and amorphous densities of polyethylene

Small-angle x-ray scattering (SAXS) was used to determine the structural changes in polyethylene induced by radiation. The changes in densities of the crystalline and amorphous phases, _c and _a , were calculated after direct determination of the mean square density fluctuation <²>. _a increases with increasing radiation dose for both linear and branched polyethylene. This accounts for the serious discrepancy between crystallinities determined from wide-angle x-ray scattering and density measurements. This study confirms our previous proposal that crosslinks occur primarily in the noncrystalline phase, most likely at the defects in the lateral grain boundary regions.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday.     

Thermoanalytical and thermogastitrimetric investigation of oil-shales

From thermoanalytical curves (DTG, TG) recorded in an oxygen atmosphere, the moisture and carbonate contents of oil-shales were determined with acceptable accuracy. The nature of the carbonates was predicted from the shape of the DTG curves above 550°C Dolomite (ankeritc) as found in Gérce oil-shale, and calcite in Pula-9 oil-shale. The clay content was determined from the signal of a water-detector recorded in a nitrogen atmosphere. The peaks at 80°C and 150°C for Gérce oil-shale were attributed to montmorillonite, and the sharp peak at 525°C for Pula-9 oil-shale to kaolinite.The volatile and fixed carbon contents of the oil-shales were calculated from the thermogastitrimetric curves.

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Zusammenfassung Feuchtigkeits- und Carbonatgehalt von Ölschiefern werden aus in Sauerstoffatmosphäre aufgenommenen thermoanalytischen Kurven (DTG, TG) mit annehmbarer Genauigkeit bestimmt. Die Natur der Carbonate wurde aus dem Verlauf der DTG-Kurve oberhalb 550 °C vorausgesagt. Dolomit (Ankerit) wurde im Gérce-Ölschiefer, Calcit im Pula-9-Ölschiefer gefunden. Der Gehalt an Tonen wurde aus dem in Stickstoffatmosphäre erhaltenen Signal eines Wasserdetektors bestimmt. Die Peaks bei 80 und 150 °C in der DTG-Kurve des Gérce-Ölschiefers werden Montmorillonit, der scharfe Peak bei 525 °C im Falle von Pula-9-ölschiefer Kaolinit zugeschrieben. Die Gehalte der Ölschiefer an flüchtigem und fixiertem Kohlenstoff werden aus gastitrimetrischen Kurven berechnet.

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(, ) , , . 550°. (), -9-. . , 80 150° , 525° -9 — . , .

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The authors are indebted to J. Kristóf (Dept. of Anal. Chem., Univ. of Veszprém) for carrying out the continuous water measurements; to K. Labdy (Central Laboratory, Univ. of Veszprém) for the elemental analysis results; to I. Vassányi (Dept. of Mineralogy, Univ. of Veszprém) for the diffractometric results; and to I. Koncz (Hydrocarbon Research and Development Institute, Nagykanizsa) for donating the oil-shale samples.