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.     

The transition time for the ground state hyperfine splitting of209Bi82+

The lifetime of the excited hyperfine state of the ground state level of²⁰⁹Bi⁸²⁺ is calculated. The result of (Bi⁸²⁺)=400.09 s still exhibits a discrepancy to the experimental value ^ex=351(16) s of about 14%.     

Optimal Hylleraas wave functions

Hylleraas wave functions composed of the optimally combinedN terms (2 N 20) are presented for two-electron atoms with nuclear chargesZ = 1 (H^–), 2(He), 3(Li⁺), 5(B³⁺), and 10(Ne⁸⁺). The spherically-averaged electron density (r) and electron-pair densityh(r ₁₂) are constructed in a simple and analytical functional form from the 20-term functions. Comparison of several one- and two-electron moments r ^k and r ₁₂ ^k shows that the present density functions have near-exact accuracy.     

Alkylation of p-substituted phenols by heteropoly acids

Liquid-phase alkylation of p-tert-butylphenol (TBP) and p-cresol by olefins and benzyl chloride in the presence of solid heteropoly acids (HPA) H₃PW₁₂O₄₀ and 25% H₃PW₁₂O₄₀/SiO₂ at 100–150°C provides high yields of mono- and disubstituted products. HPAs are more active than H₂SO₄, easily separated from the reaction mixture and can be used repeatedly. -- () - () H₃PW₁₂O₄₀ 25% H₃PW₁₂O₄₀/SiO₂ 100–150°C - - . , H₂SO₄, - - .     

Abnormally high fractal dimension of silica surfaces measured by adsorption of aliphatic alcohols

Factors leading to abnormally high fractal dimension D of silica surfaces measured by adsorption of aliphatic alcohols have been analyzed. , D .     

Triterpenoid Glycosides of Scheffleropsis angkae. III. Structure of Glycoside L-I1

A new triterpenoid glycoside L-I ₁ , the 28-O--L-rhamnopyranosyl-(14)-O--D-glucopyranosyl-(16)-O--D-glucopyranosyl ester of 3,23,27-trihydroxylup-20(29)-en-28-oic acid, is isolated from the leaves ofScheffleropsis angkae(Araliaceae). Its structure is established by chemical methods and various NMR techniques ( ¹ H, ¹³ C, APT, COSY, TOCSY, ROESY, HSQC, HMBC). 3,23,27-Trihydroxylup-20(29)-en-28-oic acid is a new triterpenoid aglycone     

Acidity and Structure of Isosaccharinate in Aqueous Solution: A Nuclear Magnetic Resonance Study

Dilute aqueous solutions of the calcium and sodium salts of -d-isosaccharinate (ISA) have been analyzed by ¹³C and ¹H NMR spectroscopy. The positions of the six ¹³C ISA NMR lines show a pH dependence that can be used to infer that the most acidic proton is the one associated with the carboxylate group, with an aver- age log k⁰ of –3.27 for the reaction H(ISA) H⁺ + ISA^– in solutions made with the sodium salt. In acidic solutions (pH < 4),=" nmr=" signals=" were=" found=" that=" could=" be=" assigned=" to=">-d-isosaccharinate-1,4-lactone (ISL), formed from the dehydration of H(ISA). The pH dependence of the H(ISA) ¹³C line positions, furthermore, reveals that the deprotonated H(ISA) at neutral to high pH assumes a conformation with the carboxylate anion hydrogen-bonded to the secondary alcohol and the cation (Na⁺ or Ca²⁺) interacting with the tertiary alcohol.     

Exciton Chirality. (A) Origins of and (B) Applications from Strongly Fluorescent Dipyrrinone Chromophores

(A) The origin of exciton interaction and examples of its application to organic stereochemistry are presented. (B) N,N-Carbonyl-bridged dipyrrinones constitute a new class of highly fluorescent chromophores suitable for investigations of stereochemistry and absolute configuration. N,N-Carbonylxanthobilirubic acid esters are strongly fluorescent, with a fluorescence quantum yield (_F) 0.8, but produce only weak exciton CD from the trans-1,2-cyclohexanediol template. The ester of an analog with benzoic acid replacing propionic, N,N-carbonyl-8-(4-carboxyphenyl)-3-ethyl-2,7,9-trimethyl-(10H)-dipyrrin-1-one, exhibits strong fluorescence (_F=0.68, _em=493nm, _ex=422nm in CHCl₃) and UV-Vis absorption (21000 at 424nm) in organic solvents. Its diester with (1S,2S)-cyclohexanediol is fluorescent and exhibits exciton circular dichroism (=+15dm³·mol^–1·cm^–1, =432nm; =–4dm³·mol^–1cm^–1, =380nm) that correlates with the Exciton Chirality Rule.     

Kinetics of C2H4 polymerization on reduced V2O5/Al2O3 catalyst

Kinetic study of C₂H₄ polymerization on reduced V₂O₅/Al₂O₃ catalysts revealed that the rate equation can be expressed as V=k exp (-Y) K_aP_E/(1+K_aP_E) in the temperature range of –20 to 70°C. The deactivation constant, , was found to have a close relation with the yield and molecular weight of the polymer. C₂H₄ V₂O₅/Al₂O₃ –20 +70°C : V_p=k·exp(-Y_p)·K_aP_e/(1+K_aP_e). .     

Studies of the effect of strong metal-support interaction (SMSI) over model catalyst Rh/TiO2

The effect of strong metal-support interaction (SMSI) has been studied over Rh/TiO₂ as a model catalyst. Adsorbability variations during SMSI state generation have been found to be due to the production of Rh–Ti alloy. - Rh/TiO₂. , SMSI Rh–Ti.     

Pairing theorem and magnetic shielding of cations and anions of odd alternant hydrocarbons

A previously developed scheme for describing the diamagnetic characteristics of molecules with conjugated bonds has been generalized to the case of noncoplanar systems, and the¹H and¹³C chemical shifts of the benzyl, diphenylmethyl, triphenylmethyl, and - and -naphthyl anions and cations have been calculated on its basis and compared with experiment. It has been shown that the current contributions to the magnetic shielding for the anions and cations of odd alternant hydrocarbons of identical structure and charge multiplicity are equal to one another, while the charge contributions differ in sign. This has made it possible to find the experimental charge distribution of the cations investigated and to compare it with the results of quantum-chemical calculations.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 3, pp. 277–283, May–June, 1989.     

Kinetic studies of methylmercaptan production from dimethyl sulfide and H2S

Kinetic regularities of methylmercaptan production from dimethyl sulfide and H₂S in the presence of -Al₂O₃ have been studied under gradientless conditions. A stepwise reaction mechanism is suggested implying that the catalyst surface is methoxylated by methyl sulfide and then CH₃O groups interact with H₂S. The kinetic equation obtained describes fairly well this process on the nonhomogeneous catalyst surface. H₂S -Al₂O₃. , , CH₃O- H₂S. , .     

Some observations of HZSM-5 zeolite dehydroxylation

The dehydroxylation of 3610 cm^–1 OH groups in HZSM-5 zeolite and in two Ni and Mo modified catalysts containing the same zeolite has been studied at 673 K. The presence of water vapor is a necessary condition of dehydroxylation, the extent of which depends on the number and duration of breaks consisting in cooling to room temperature and reheating to 673 K with evacuation. OH HZSM-5, Ni Mo- , 3610 cm^–1, 673 . , 673 .     

Reaction of Mercury(II) Trifluoroacetate with Deprotonated (η6-Toluene)-, (η6-Diphenylmethane)-, and (η6-Triphenylmethane)(η5-cyclopentadienyl)iron(II) Complexes. Mercuration of Some Cationic (Arene)(cyclopentadienyl)iron(II) Complexes

Treatment with mercury(II) trifluoroacetate of deprotonated (⁶-toluene)- and (⁶-diphenyl- methane)(⁵-cyclopentadienyl)iron(II) complexes gave mono-, di-, and trisubstituted [from (⁶-toluene)(⁵-cyclopentadienyl)iron(II) cation] mercury-containing salts. The reaction of mercury(II) trifluoroacetate with deprotonated (⁶-triphenylmethane)(⁵-cyclopentadienyl)iron(II) afforded only the corresponding sym- metric mercury derivative. The same product was obtained by direct mercuration with mercury(II) trifluoroacetate of (⁶-triphenylmethane)(⁵-cyclopentadienyl)iron(II) on heating the reactants in boiling unhydrous ethanol. Reactions of the resulting mercury-containing compounds with acids, symmetrizing bases, and acylating agents were studied.     

Methane synthesis from CO/H2O mixture on supported nickel catalysts, III. Formation of surface carbon and its role in the reaction mechanism

IR spectra of adsorbed CO species after prolonged contact with the catalyst surface show that surface carbon is formed and it participates in methane synthesis.

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- , CO , , .

     

Kinetics and mechanism of the ligand substitution reaction of aquodiethylenetriaminepentaacetatoruthenate (III) in aqueous solution

The kinetics of ligand substitution reactions of [Ru(H₂dtpa) (H₂O)] (2) (H₂dtpa=diprotonated diethylenetriaminepentaacetic acid) were studied as a function of ligand (L) concentration, pH (2.5–8.0) and temperature (30–45 °C) at 0.2 M ionic strength. The equilibrium constants for the formation of mixed ligand complex [Ru^III(dtpa) (L)] (L=2-mercaptopyrimidine, cysteine) and the distribution of various species in solution in the pH range of 2.5–8.0 were computed from potentiometric results. [Ru(H₂dtpa) (H₂O)] ( H₂dtpa= ) , pH (2,5–8,0) (30–45°C) 0,2 M. [Ru^III(dtpa) (L)] ( L=2-, ) pH=2,5–8,0.     

The feedback controlled chemical reactor, I. General theoretical description

Some general dependences of the injection volumes of reaction components on time have been derived for the feedback controlled chemical reactor. .     

13C NMR spectra of 17-substituted epimeric 17α and 17β-ethynylandrostenes and their hexacarbonyldicobalt complexes

¹³C NMR spectra of epimeric 17-R-substituted 17-ethynylandrostenes (R = H, OH, OAc, OMe, NCS) and 17-R-substituted 17-ethynylandrostenes (R = H, OH, OAc, OMe), and their hexacarbonyldicobalt complexes, as well as of ¹⁶-17-ethynylandrostenes and their hexacarbonyldicobalt complexes have been studied. Stereochemical dependence of C(12), C(14), C(18), C(20) and C(21) chemical shifts on the configuration of the substituents at C(17) has been demonstrated. The effect of Co-complexation on the spectral characteristics of Co-coordinated 17-ethynylandrostenes in both Stereochemical series has been investigated.Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 212–216, January, 1993.     

Structural rigidity and low frequency vibrational modes of long carbon tubules

We have studied the low frequency vibrational modes and the structural rigidity of long graphitic carbon tubules consisting of 100, 200, and 400 atoms. Our calculations have been performed using an empirical Keating Hamiltonian with parameters determined from first principles. We have found the beam bending mode to be one of the softest modes in these structures. The corresponding beam rigity of a bucky tube is compared to an found to exceed the highest values found in presently available materials.     

Analysis of organic trace compounds in the atmosphere and the correlation between meteorological situation and concentration of reference substances

A research project is described, which is being carried out systematically with the objective of qualitative and quantitative assessment of organic substances occurring in the air at forest sites considering seasonal and meteorological variations. To begin with, a collecting and analytical system with diverse additional modules had to be developed and assembled for this purpose. With the aid of an adsorptive enrichment system this enables the determination of the entire palette of organic substances present in the air at the site.Hitherto, about 160 of the major organic substances occurring in the air at the site have been determined. These occur at concentrations between several ng to several g per m³ air and belong to different classes of compounds. So-called reference substances have been selected as representatives of particular classes of substances. The alterations of concentrations in air at the site of these reference substances have been investigated as a function of meteorological conditions. The evaluation of the data led to the following conclusions: