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.     

Theoretical Study of Chemical Binding of Noble Gas Atom and Transition Metal Complexes: Ng–NiCO, Ng–NiN2, Ng–CoCO (Ng = He–Xe)

Ab initio multireference and coupled cluster methods (MR-SDCI(+Q), CASPT2, CCSD(T)) and density functional theory methods (B3LYP, MPWPW91) have been applied to examine geometrical structures and vibrational frequencies of noble gas (Ng) – transition metal compounds, Ng–NiCO, Ng–NiN₂, and Ng–CoCO (Ng = He, Ne, Ar, Kr, Xe). It is shown that the respective compounds can have a larger binding energy than a typical van der Waals interaction energy. The binding mechanism is explained by a partial electron transfer from a noble gas atom to the low-lying 4s and 3d vacant orbitals of the transition metal atom. Theoretical calculations show that the binding of noble gas atom results in a large shift of the bending frequency: 361.1cm^–1 (NiCO) to 403.5cm^–1 (Ar–NiCO); 308.5cm^–1 (NiN₂) to 354.8cm^–1 (Ar–NiN₂); 373.0cm^–1 (CoCO) to 422.6cm^–1 (Ar–CoCO). The corresponding experimental frequencies determined in solid argon are 409.1cm^–1 (NiCO), 357.0cm^–1 (NiN₂), and 424.9cm^–1 (CoCO), which are much closer to the corresponding frequency of Ar–NiCO, Ar–NiN₂, and Ar–CoCO, respectively.     

Mechanisms of anion formation in O2, O2/Ar and O2/Ne clusters; the role of inelastic electron scattering

Measurements are reported on the formation of negative ions in O₂, O₂/Ar and O₂/Ne clusters aimed at establishing the mechanisms of anion formation and the role of inelastic electron scattering by the cluster constituents on negative ion formation in clusters. In the case of pure O₂ clusters the main anions we detected are of two types: O^–(O₂) _n0 and (O₂) _n ^1– . The yields of O^–(O₂) _n showed maxima at 6.3, 8.0 and 14.0 eV and the data suggest O^– as their precursor; the maxima at 8 and 14 eV are due to the production of O^– via symmetry forbidden dissociative attachment processes in O₂ at these energies which become allowed in clusters. The yields of (O₂) _n ^– showed a strong maximum at near-zero energy (0.5 eV) and also at 6.3, 8 and 14 eV. With the exception of the near-zero energy resonance, the (O₂) _n ^– anions at 6.3, 8 and 14 eV are attributed to nondissociative attachment of near-zero energy secondary electrons to O₂ clusters. The slow secondary electrons result predominantly from scattering via the O ₂ ^– negative ion states of incident electrons with energies in their respective regions. Similar results were obtained for the mixed O₂/rare gas clusters except that now a feeble and distinctly structured contribution in the yields of O^–(O₂) _n , (O₂) _n ^– (and Ar(O₂) _n ^– ) was observed at energies >10 eV. These anions are believed to have the lowest negative ion states of Ar*^– (Ne*^–) as their precursors.     

Unambiguous Determination of the Absolute Configurations of Acetylene Alcohols by Combination of the Sonogashira Reaction and the CD Exciton Chirality Method – Exciton Coupling between Phenylacetylene and Benzoate Chromophores

The CD exciton chirality method was applied to various phenylacetylene alcohols to determine their absolute configurations; the long axis polarized –^* transition (_max=252nm) of the 4-methoxyphenylacetylene chromophore couples with the transition (_max=257nm) of the 4-methoxybenzoate group to generate intense exciton split CD Cotton effects, from the signs of which the absolute configurations of phenylacetylene alcohols were unambiguously determined. As an extension of the results, a new methodology for determining the absolute configurations of acetylene alcohols having the HCCCH(OH)-moiety by combination of the Sonogashira reaction and the CD exciton chirality method has been developed and applied. Since the –^* transition of acetylene triple bond is located below 180nm, it is difficult to observe ideal bisignate CD Cotton effects due to the exciton coupling between acetylene and benzoate chromophores. To observe the ideal exciton split Cotton effects necessary for the unambiguous determination of absolute configuration, the terminal acetylene group was converted, by the Sonogashira reaction, to the 4-methoxyphenylacetylene moiety, which exhibits an intense –^* absorption band polarized along the long axis of the chromophore at 252nm. As a partner of exciton coupling, 4-methoxybenzoate showing a –^* band at 257nm was introduced into the alcohol moiety, and the benzoates formed showed intense bisignate CD Cotton effects, from the signs of which the absolute configurations of original acetylene alcohols could be determined in an unambiguous manner.     

Thermionic emission from fullerenes

We investigate the time dependence of carbon cluster ions, formed via thermionic emission from photoexcited fullerenes (C₆₀ and C₇₀). By pulsing the extraction field, we are able to observe delayed ions formed as late as 100 µs after excitation at 532 nm, 355 nm, or 266 nm. All even-sized clusters in the range 36 n 70 undergo thermionic emission.     

Mechanism of the cooperative vibronic emission of1δg singlet oxygen in solutions

The mechanism for inducing the probability of the ¹_g-X³_g ^– transition in an oxygen molecule with the simultaneous excitation of a vibration state of the solvent has been considered. The intensification of the 0-0 band of this transition under the influence of the solvent is attributed to the induction of the electric dipole moment of the b¹_g ⁺- ¹_g (m_ba) transition during a collision between O₂ and solvent molecules. It has been shown that m_ba is strongly dependent on the intermolecular distance and, consequently, on the normal coordinate of the vibrations of the solvent (Q) at a given collision parameter. Calculation of the derivative m_ba/Q (with consideration of the strong spin-orbit coupling of the b¹_g ⁺ and X³_g ^– states) makes it possible to account for the intensity of the new luminescence band of¹_g singlet oxygen, which is shifted toward longer wavelengths relative to the 0-0 band of the ¹_g-X³_g ^– by the value of the vibrational quantum of the solvent.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 5, pp. 594–596, September–October, 1985.     

Effects of an avoided crossing on linewidths of resonances in the H2 i3Π g state

We have investigated the influence of nonadiabatic effects on the linewidths of quasi-bound rovibrational levels in the i³ _g state of molecular hydrogen. This state has a potential barrier due to the interaction of then=3³ _g Rydberg series and the Q1³ _g valence state. The radial coupling with the higher lying³ _g states has been modelled into a diabatic problem. The widths of thev=4 and 5 levels, a measure for their lifetimes, have been determined both in the adiabatic i³ _g potential, and in the two-state system. The results show small shifts of the i³ _g (v=4,5;N=1) levels of a few wavenumbers, and a significant increase of 49% in the lifetimes of these levels. Both effects are large enough to be important in spectroscopic experiments. The magnitude of the effect is in accordance with observed linewidths obtained in recent experiments. Model calculations for differently shaped potential barriers have been carried out to study the generality of the above conclusions.     

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.     

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.     

Mischligandenderivate des 1:1-Th(IV)—DTPA-Chelates mit Milchs?ure, Mandels?ure und o-Hydroxynaphthoes?uren

Potentiometric studies of the mixed ligand derivatives of 11-Th(IV)—DTPA chelate (whereDTPA=diethylene-triamine pentaacetic acid) with certain secondary ligands, such as lactic, mandelic and o-hydroxynaphthoic acids have been carried out. The pH-titrations of the reaction mixtures containing 111 molar ratio of metal ion toDTPA to secondary ligand have shown the formation of 111 ternary complexes at higher pH (8). The equilibrium constants of the resulting mixed complexes have been determined at 30±1°C and =0.1 (KNO₃) and the order of stability in terms of secondary ligands has been found to be o-hydroxy naphthoic acids>mandelic acid>lactic acid.     

Comparison of rate coefficients for rydberg electron and free electron attachment

New experimental results on attachment reactions involving free electrons at sub-meV resolution allow for the first time a conclusive comparison of measured rate coefficients for Rydberg electron attachment with those calculated from the measured free electron cross sections on the basis of the quasi-free electron model for Rydberg electron collisions. Using classical velocity distributions for the highn Rydberg electrons and our measured free electron attachment cross sections, we calculate Rydberg electron attachment rate coefficientsk _n for the two cases SF₆ and HI for Rydberg binding energies |E _n | of 0.1–40 meV. We find a significant increase ink _n towards lower binding energies, especially for HI, which is due to the deviation of the free electron cross section from the limitings-wave behaviour ₀E ^–1/2. The increase at |E _n |2 meV is in qualitative agreement with our highn Rydberg data (n80) if -mixing due to residual electric fields is taken into account. For low , Rydberg rate coefficientsk _n(|E _n |) are significantly larger than free electron rate coefficientsk _e (E=|E _n |), while for circular orbits (=n–1) they agree. On average, attachment reactions of Rydberg electrons in low orbits proceed with an effective collision energy substantially smaller than the binding energy |E _n |.     

Photoionization of oriented molecules in a gas phase

Use of a coincidence technique for registration of fragment ions and photoelectroms from dissociative ionization of molecules opens the possibility of studying the photoionization of oriented molecules in a gas phase. The first results obtained by this technique for O₂ molecules are presented. The angular distribution of photoelectrons as a function of an angle between molecular axis and a photoelectron momentum is measured for theB ² _g ^– final ionic state using the HeI resonance radiation. From measured data it follows that the ratio of channel cross sections is /=0.67±0.08.     

Collision induced dissociation of stored gold cluster ions

The stability of gold cluster ions Au _n ⁺ (2n23) has been investigated via collision induced dissociation in a Penning trap. Threshold energies and dissociation channels have been determined. The cluster stability exhibits a pronounced odd — even alternation: Clusters with an odd number of atoms,n, are more stable than the even-numbered ones. Enhanced stabilities are found for Au ₃ ⁺ , Au ₉ ⁺ , and Au ₁₉ ⁺ in accordance with the Clemenger-Nilsson and the deformed jellium model of delocalized valence electrons. Excited odd cluster ions withn15 predominantly decay by evaporation of dimers; all others decay by monomer evaporation. From the dissociation channels estimates of the binding energies are deduced.This publication comprises part of the thesis of St. Becker     

Fluorescence Quenching Studies of Curcumin by Hydrogen Peroxide in Acetonitrile Solution

Steady state quenching studies of curcumin, 1,7-bis(4-hydroxy-3-methoxyphenyl)-1,6-heptadiene-3,5-dione, fluorescence by hydrogen peroxide were conducted in acetonitrile solution. A quenching rate constant, k_q, of 1.05×10¹⁰M^–1·s^–1 was obtained with a short fluorescence lifetime of 347ps. The reaction rate constant, which is within the diffusion-limited regime, is activation-controlled. The rate constant of deactivation of the thermally excited curcumin was 1.2 orders of magnitude more nonradiative (2.67×10⁹s^–1) than radiative (2.16×10⁸s^–1). The reaction was exothermic with a G° of –1.97eV and solvent reorganization energy of 1.37eV. These values indicate that the electron transfer reaction is solvent-mediated with electron transfer rate constant, k_ET, of 2.16×10¹⁰s^–1.     

Characterization of water-soluble,cationic polyelectrolytes as exemplified by poly(acrylamide-co-trimethylammoniumethylethacryate chloride) and the establishment of structure-property relationships

The cationic copolymerization products of poly (acrylamide-co-trimethylammoniumethylmethacrylate chloride (PTMAC) having cationic monomer percentages of 8%, 25%, and 50% as well as the cationic homopolymer, were characterized with respect to their molecular dimensions. The light-scattering and viscometric measurements were carried out for molecular weights ranging from 200 000 to 12 800 000 g/mol in 1 M NaCl solution at 25°C. It was possible to establish a relationship between the molecular weight and the two parameters: intrinsic viscosity and radius of gyration, for all four polymers.Rheological investigations of the flow properties in 1 M NaCl solution were also carried out using the polymer with a cationic monomer of 50% (PTMAC 50). Structure-property relationships were formulated which made it possible to describe and predict the shear viscosity, both in the zero-shear region (Newtonian region) and in the shear-dependent region (non-Newtonian region) as a function of the polymer concentration, the molecular weight, and shear rate.Abbreviations a exponent of the []-M relationship - A ₂ 2^nd virial coefficient/mol·cm³·g^–2 - AAm acrylamide - b slope of the flow-curve in the shear-rate dependent region - c concentration/g·cm^–3 - dn/dc refractive index increment/cm³·g^–1 - f function - K constant of the []-M relationship/cm³·g^t-1 - m _c proportion of cationic monomers/mol % - M molecular weight/g·mol^–1 - M _w weight-average molecular weight/g·mol^–1 - M _n number-average molecular weight/g·mol^–1 - NaCL sodium chloride - PAAm polyacrylamide - PS polystyrene - PTMAC poly(acrylamide-co-trimethylammoniumethylme thacrylate chloride) - R_G ^20.5 radius of gyration/nm - TMAC trimethylammoniumethylmethacrylate chloride - shear rate/s^–1 - critical shear rate/s^–1 - viscosity/Pa·s - 0 zero-shear viscosity/Pa·s - _s solvent viscosity/Pa·s - _sp specific viscosity - [] intrinsic viscosity/cm³·g^–1 - relaxation time/s     

Kinetics and mechanism of oxidation of bis(2,2′,6′,2″-terpyridine) iron(II) by manganese(IV)

A study has been made on the oxidation of bis(2,2,6, 2-terpyridine)-iron(II), Fe(tpy) ₂ ²⁺ by manganese (IV) using stopped-flow spectrophotometry in H₂SO₄–H₃PO₄ mixtures. The reaction is first order in each the substrate and the oxidant. The rate of the reaction increases with hydrogen ion concentration. A plausible mechanism is proposed considering the protonated forms of manganese(IV) as reactive oxidizing species. The reaction obeys the rate law

On the crystal chemistry of three copper(II)-arsenates: Cu3(AsO4)2-III,Na4Cu(AsO4)2, and KCu4(AsO4)3

The three copper(II)-arsenates were synthesized under hydrothermal conditions; their crystal structures were determined by single-crystal X-ray diffraction methods:Cu₃(AsO₄)₂-III:a=5.046(2) Å,b=5.417(2) Å,c=6.354(2) Å, =70.61(2)°, =86.52(2)°, =68.43(2)°,Z=1, space group ,R=0.035 for 1674 reflections with sin / 0.90 Å^–1.Na₄Cu(AsO₄)₂:a=4.882(2) Å,b=5.870(2) Å,c=6.958(3) Å, =98.51(2)°, =90.76(2)°, =105.97(2)°,Z=1, space group ,R=0.028 for 2157 reflections with sin / 0.90 Å^–1.KCu₄(AsO₄)₃:a=12.234(5) Å,b=12.438(5) Å,c=7.307(3) Å, =118.17(2)°,Z=4, space group C2/c,R=0.029 for 1896 reflections with sin / 0.80 Å^–1.Within these three compounds the Cu atoms are square planar [4], tetragonal pyramidal [4+1], and tetragonal bipyramidal [4+2] coordinated by O atoms; an exception is the Cu(2)^[4+1] atom in Cu₃(AsO₄)₂-III: the coordination polyhedron is a representative for the transition from a tetragonal pyramid towards a trigonal bipyramid. In KCu₄(AsO₄)₃ the Cu(1)^[4]O₄ square and the As(1)O₄ tetrahedron share a common O—O edge of 2.428(5) Å, resulting in distortions of both the CuO₄ square and the AsO₄ tetrahedron. The two Na atoms in Na₄Cu(AsO₄)₂ are [6] coordinated, the K atom in KCu₄(AsO₄)₃ is [8] coordinated by O atoms.Die drei Kupfer(II)-Arsenate wurden unter Hydrothermalbedingungen gezüchtet und ihre Kristallstrukturen mittels Einkristall-Röntgenbeugungsmethoden ermittelt:Cu₃(AsO₄)₂-III:a = 5.046(2) Å,b = 5.417(2) Å,c = 6.354(2) Å, = 70.61 (2)°, = 86.52(2)°, = 68.43(2)°,Z = 1, Raumgruppe ,R = 0.035 für 1674 Reflexe mit sin / 0.90 Å^–1.Na₄Cu(AsO₄)₂:a = 4.882(2) Å,b = 5.870(2) Å,c = 6.958(3) Å, = 98.51(2)°, = 90.76(2)°, = 105.97(2)°,Z = 1, Raumgruppe ,R = 0.028 für 2157 Reflexe mit sin / 0.90 Å^–1.KCu₄(AsO₄)₃:a = 12.234(5) Å,b = 12.438(5) Å,c = 7.307(3) Å, = 118.17(2)°,Z = 4, Raumgruppe C2/c,R = 0.029 für 1896 Reflexe mit sin / 0.80 Å^–1.Die Cu-Atome in diesen drei Verbindungen sind durch O-Atome quadratisch planar [4], tetragonal pyramidal [4 + 1] und tetragonal dipyramidal [4 + 2]-koordiniert; eine Ausnahme ist das Cu(2)^{[4 + 1]}-Atom in Cu₃(AsO₄)₂-III: Das Koordinationspolyeder stellt einen Vertreter des Übergangs von einer tetragonalen Pyramide zu einer trigonalen Dipyramide dar. In KCu₄(AsO₄)₃ haben das Cu(1)^[4]O₄-Quadrat und das As(1)O₄-Tetraeder eine gemeinsame O—O-Kante von 2.428(5) Å, was eine Verzerrung der beiden Koordinationsfiguren CuO₄-Quadrat und AsO₄-Tetraeder bedingt. Die zwei Na-Atome in Na₄Cu(AsO₄)₃ sind durch O-Atome [6]-koordiniert, das K-Atom in KCu₄(AsO₄)₃ ist [8]-koordiniert.

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Zur Kristallchemie dreier Kupfer (II)-Arsenate: Cu₃(AsO₄)₂-III, Na₄Cu(AsO₄)₂ und KCu₄(AsO₄)₃

     

An estimation of the surface ionization constant of oleic acid in aqueous sodium chloride solution

The zeta potential () measurements and the site binding theory were utilized for calculations of the parameters of the electrical double layer (edl), ionization, and complexation constants for oleic acid-aqueous sodium chloride solution interface. Assuming that is equal to the diffuse layer potential ( _d ) of the edl, the charge of the diffuse part of the edl was calculated from the Gouy-Chapman equation. The intrinsic ionizaiton constant was then determined by an extrapolation method to be . Subsequently, the surface potential ( ₀) was calculated, and it was found that ₀ changes by 50 mV per pH unit (50 mV/pH) or 42.5 mV/pH for 10^–3 and 10^–2 M NaCl, respectively. For further calculations, the integral capacity of the outer zone of the compact part of the edl was assumed to be for both ionic strengths. It was established that the intrinsic complexation constant for the binding of Na⁺ ions with the surface of oleic acid ispK _Na ^int = 2.9±0.5 if the integral capacity of the inner zone of the compact edl (K ₁) is 80 for 10^–3 M NaCl, but 280 for 10^–2 M NaCl. The use of the sameK ₁ value for both ionic strengths gives a differentpK _Na ^int for different NaCl concentrations, and also provides unrealistic surface charge ( _o ) values greaterfor 10^–3 M NaCl than for 10^–2 M NaCl, at the same pH of the solution.     

TPD of ammonia from H-ZSM-5 zeolites deactivated during coupled methanol hydrocarbon cracking (CMHC)

The deactivation of H-ZSM-5 zeolite samples during coupled methanol/hydrocarbon cracking (CMHC) with n-butane as feed has been investigated in two different reaction modes (with intermediate regeneration and without regeneration). TPDA was used to characterize strong Brönsted acidity of fresh, regenerated and steamed H-ZSM-5 zeolite. The prevention of dealumination by blocking the acid centers with carbonaceous products could be proved, but the conversion rate of n-butane and the olefin selectivity declined drastically with increasing coking rate. H-ZSM-5 - / - - ( -). , - H-ZSM-5. - , , - - .