Bound states of helium atom in dense plasmas

We have obtained the bound 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies of helium atom in dense plasma environments in accurate variation calculations. A screened Coulomb potential to represent the Debye model is used for the interaction between the charged particles. A correlated wave function consisting of a generalized exponential expansion has been used to take care of the correlation effect. The 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies along with the ionization potential, the energy splitting between the 1s2s ³S, and 1s2s ¹S states, transition energies between the ground state and low‐excited states of He estimated for various Debye lengths, are reported. The results show high degree of accuracy even under strong plasma conditions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Berechnung der Röntgen- und Auger-Linien des Methans mit Hilfe des Pseudo-Neon-Modells

Zusammenfassung Mit Hilfe des Pseudoneonmodells wurden die Energien der aus den folgenden Konfigurationen hervorgehenden Terme bzw. Mittelwerte dieser Energien für das Methanmolekül bestimmt: [(1s)² (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶ (3p)¹], [(1s)¹ (2s)² (2p)⁶ (4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] und [(1s)² (2s)⁰ (2p)⁶].Die Energien wurden mit Hilfe der Slater-Condonschen Regeln analytisch berechnet und dann mit einer elektronischen Rechenmaschine (Zuse 23) minimisiert.Aus den erhaltenen Energiewerten wurde die Lage der Röntgen- und Auger-Linien des Methans berechnet. Die von Mehlhorn [8] gemessenen Auger-Elektronenenergien konnten zugeordnet werden.Die Rechenergebnisse stimmen mit den von Chun aus Röntgenabsorptionsmessungen ermittelten experimentellen Werten befriedigend überein.

---

The pseudo neon model is used to calculate the energies of the levels deriving from the following configurations (or their mean values) of the methane molecule: [(1s)² (2s)² (2p)⁶], [(1s)¹(2s)²(2p)⁶], [(1s)¹(2s)²(2p)⁶(3p)¹], [(1s)¹ (2s)² (2p)⁶ (4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] and [(1s)² (2s)² (2p)⁶].The energy expressions are given by the Slater-Condon rules; the minimization is done with a digital computer (Zuse 23). Prom the energy values obtained the X-ray and Auger lines of methane are calculated. An interpretation of the experimental Auger electron energies of Mehlhorn [8] is made.Calculated and measured (by Chun) values are in satisfactory agreement with each other.

---

Résumé A l'aide du modèle du pseudo-atome de néon, les énergies des niveaux dérivant des configurations suivantes (ou leurs moyens) ont été calculées: [(1s)² (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶], [(1s)¹(2s)²(2p)⁶(3p)¹], [(1s)¹(2s)²(2p)⁶(4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] et [(1s)² (2s)⁰ (2p)⁶].Les énergies sont données par les règles de Slater et Condon et minimisées à l'aide d'une machine à calculer électronique (Zuse 23).On en dérive les spectres X et d'Auger du méthane. Nous pouvions interpréter les énergies des électrons Auger mesurées par Mehlhorn [8]. Les calculs s'accordent assez bien aux valeurs expérimentales de Chun.

---

---

Auszug aus der Dissertation von T. K. Ha, Frankfurt am Main, 1963.     

Self-consistent calculation of 1s2s1S state wave function of helium

A simple self consistent variation perturbation method in the coupled Hartree–Fock scheme has been proposed to calculate 1s2s ¹S state of the He atom. The present paper deals with an 1s2s ¹S wave function in which all the relevant orthogonality conditions are imposed in successive stages. The resulting wave functions together with some interesting features are discussed.     

Synthesis,purification and spectroscopic characterization of potential impurities of hexamethylmelamine

The syntheses and spectroscopic properties (ir, ¹H nmr, ¹³C nmr, uv and ms) of pure samples of 2-chloro-4,6-bis(dimethylamino)-s-triazine 1 , 4,6-dichloro-2-dimethylamino-s-triazine 2 , 4,6-bis(dimethylamino)-s-triazin-2(lH)-one 3 , 4-chloro-6-dimethylamino-s-triazin-2(1H)-one 4 , 6-dimethylamino-s-triazine-2,4(1H,3H)-dione 5 , and 2,4,6-tris(dimethylamino)-s-triazine (altretamine, HMM) are reported. Evidence for enol-keto equilibria are also presented for 3 , in which the enol form exhibits as an H-bonded dimer structure similar to the dimer of organic carboxylic acids.     

Relativistic calculation of autoionization widths of 1s2s2pjJ, 1s2s2 2S1/2, and 1s2pJ 2pj′J levels

The autoionization widths of levels 1s 2s 2p_jJ, 1s2s^{2 2}S_1/2, and 1s2p_j2p_j′ J have been calculated for ions with Z = 6–30. The calculation has been carried out in intermediate coupling. The decay amplitudes have been calculated in a relativistic approximation.     

Säurekatalysierte Dienon-Phenol-Umlagerungen von 6-Propargyl-6-methyl-cyclohexa-2,4-dien-1-onen; ladungskontrollierte,aromatische [1s, 2s]- und [3s, 4s]-sigmatropische Reaktionen

The acid catalysed dienone-phenol rearrangement of methyl substituted o-propargyl-cyclohexadienones (scheme 3) was investigated. The rearrangements were carried out in acetic anhydride containing about 1⁰/₀₀ sulfuric acid. Under these conditions acetoxy benzenium ions are formed as intermediates. These then undergo charge-controlled [3s, 4s]- and [1s, 2s]-sigmatropic rearrangements. Thus, the [3s, 4s]-process leads to the formation of the corresponding allenyl-phenol acetates ( 19 , 21 , 23 , 25 , 28 , 30 ) whereas the [1s, 2s]-process yields propargyl-phenol acetates ( 20 , 22 , 24 , 26 , 29 ), respectively (cf. scheme 4).     

3S- Versus 1s-type Gaussian primitives: Modifications of the 3-21G(*) basis set for the sulfur atom

The complete set of second-order Gaussian functions (6D) includes a totally symmetric second-order Gaussian function (3s-type) in addition to the five d-type functions. This 3s-type function in the 3–21G(*) basis set for the sulfur atom is described (1) in terms of its geometric and electronic effects observed in the sulfur atom and in four sulfur-containing molecules and (2) by the ability of a single zero-order 1s-type Gaussian function (with various exponents) to replace it in ab initio Hartree–Fock calculations. The geometry of the molecules (dihydrogen sulfide, dihydrogen thioketone, dihydrogen disulfide, and methanesulfonamide) were obtained using various semiempirical and ab initio methods. It is found that the 3s-type function lowers the energy relative to that calculated with the 3–21G(*) basis set with only five second-order Gaussian functions by ca. 46–48 kcal/mol per sulfur atom. Only small changes in geometry are observed when the latter basis set is augmented with a 3s or 1s function. When the exponent of the 1s replacement function is chosen so that the resulting function has a location similar to that of the 3s function as measured by the degree of overlap or the coincidence of radial distribution maxima, the corresponding drop in energy is less than 8 kcal/mol per sulfur atom. However, when the shape of the radial distribution of the 1s function is similar to that of the 3s, i.e., when the value of the 1s exponent is ca. equal to that of the 3s function (a local maximum in the 1s energy profile), the energy lowering is similar to that produced with the 3s function. The electronic effects observed in the molecules differ from those in the atom, the largest deviations being found in the methanesulfonamide calculations.     

Die Dienol-Benzol-Umlagerung von Propargylcyclohexadienolen: aromatische [1,2]-, [3,3]- und [3,4]-sigmatropische Umlagerungen

The acid catalysed dienol-benzene rearrangement of methyl substituted o- and p-propargylcyclohexadienols ( 18–22 , 34 and 35 ) was investigated. In the first step water is eliminated to yield the corresponding methyl propargyl benzonium ions (cf. scheme 6, a ), which undergo [1s, 2s] sigmatropic rearrangements to give propargylbenzenes ( 28 , 29 , 30 , 38 ) and [3s, 4s] sigmatropic rearrangements to give allenylbenzenes ( 24–27 , 40) (cf. schemes 2, 3, 5, 6). [3s, 3s] sigmatropic rearrangements occur only to a small extend. In the rearrangement of 2-propargyl-2,4,6-trimethylcyclohexa-3,5-dien-1-ol ( 18 ) a [1s, 2s] sigmatropic methyl shift is observed (4%).     

Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

A general synthesis of s-triazolo[1,5-x] diazines

Treatment of 2-aminopyrimidime, a 4-aminopyrimidine, aminopyrazine, and 3-aminopyridazines with O-mesilylenesulfonylhydroxylamine gave the corresponding N-aminodiazinium salts in high yields. These salts could be transformed into s-triazolo[1, 5-a] pyrimidines, s-triazolo[1, 5-a]-pyrazines, s-triazolo[1, 5-c]pyrimidines, and s-triazolo[1, 5-b]pyridazines hy treatment with acylating agents.     

Molecular mechanics simulation studies of dienoic hydrocarbons: From alkenes to 1-Palmitoyl-2-linoleoyl-phosphatidylcholines

Although no crystal structures of mixed-chain phosphatidylcholines with unsaturated sn-2 acyl chains exist, the force field method in conjunction with the experimentally determined structure of saturated identical-chain phosphatidylcholine can be applied to simulate molecular structure for mixed-chain phosphatidylcholines. In this study, the packing models of mixed-chain 1-palmitoyl-2-linoleoyl-phosphatidylcholines in bilayers at temperatures below the gel-liquid crystalline phase transition temperature or T < T_m are simulated by using Allinger's MM3(92) force field. Our results indicate that the unsaturated sn-2 acyl chains of the mixed-chain lipid can fold into two energy-minimized topologies: the crankshaftlike and the U-shaped motifs. The folded region in the crankshiftlike sn-2 acyl chain is characterized by a sequence s⁻ Δs⁺s⁺Δs⁻, and the U-shaped chain arises from the characteristic sequence s⁻Δs⁺s⁻Δs⁺, where s^± denotes the ± skew conformation and Δ the cis carbon-carbon double bond. These modeled structures of 1-palmitoyl-2-linoleoyl-phosphatidylcholines in the bilayer at T < T_m should not be regarded as highly rigid structures, since torsion angles of carbon-carbon bonds associated with sequences s Δs⁺s⁺Δs and s Δs⁺s⁻Δ s⁺ can fluctuate somewhat without appreciably affecting the steric energy of the corresponding lipid bilayer. © 1996 by John Wiley & Sons, Inc.     

New approach to the effects of pressure dependence on sedimentation velocity experiments

A theory is developed for sedimentation velocity experiments when the sedimentation coefficient s_p depends on pressure P as s_p/s_o = (1 + γP)^?1, where γ is a constant. In contrast to the more usually analyzed from s_p/s_o = 1 ? γP, this model does not lead, in extreme cases, to a negative sedimentation rate. A theory is presented for homogeneous macromolecules sedimenting with no diffusion. It leads to estimations of s_o and γ from a knowledge of the point of maximum concentration gradient as a function of time. Results of these calculations are compared with accurate numerical solutions of the Lamm equation with diffusion included.     

Sign Reversal of a Large Circularly Polarized Luminescence Signal by the Twisting Motion of a Bidentate Ligand

This work demonstrates sign reversal of large circularly polarized luminescence (CPL) signal based on the hinge‐like twisting motion of a bidentate ligand, 3,3‐bis(diphenylphosphoryl)‐2,2‐bipyridine (BIPYPO), in a cis–trans isomerization of chiral europium(III) complexes. X‐ray diffraction analysis revealed that twisting motion of BIPYPO provides s‐cis and s‐trans geometries of a chiral Eu^III complex containing either tris[3‐(trifluoromethylhydroxymethylene)‐(+)‐camphorate] (D ‐ 1 ) or tris[3‐(heptafluoropropylhydroxymethylene)‐(+)‐camphorate] (D ‐ 2 ). The s‐cis Eu^III complexes show eight‐coordinate geometry around the Eu^III ion, in which the chelate between the phosphoryl oxygen and the Eu^III ion forces the s‐cis geometry of BIPYPO. In contrast, the phosphorus–nitrogen interaction provides a conformational lock for the s‐trans geometry of the BIPYPO ligand, inducing a quasi‐seven‐coordinate Eu^III complex. The difference in coordination geometry causes the sign change of the CPL signals between the s‐cis and s‐trans isomers, whereby the s‐cis and s‐trans isomers of Eu^III complexes exhibit the positive and negative CPL signals, respectively, for the ⁵D₀→⁷F₁ transition. The proportion of the s‐trans‐D ‐ 1 against s‐cis‐D ‐ 1 increases upon changing the solvent from [D₃]acetonitrile to [D₆]acetone, inducing a sign change of the CPL signals. The complexes D ‐ 1 and D ‐ 2 show a biexponential decay with two different lifetimes, suggesting two emitting species, that is, the s‐cis and s‐trans isomers of Eu^III complexes. In both cases, the proportions of the longer lifetime components (τ₁) decrease and instead the shorter lifetime components (τ₂) increase upon changing the solvent from [D₃]acetonitrile to [D₆]acetone.     

The kinetics and mechanisms of gas phase elimination of primary,secondary, and tertiary 2‐hydroxyalkylbenzenes

2‐Phenylethanol, racemic 1‐phenyl‐2‐propanol, and 2‐methyl‐1‐phenyl‐2‐propanol have been pyrolyzed in a static system over the temperature range 449.3–490.6°C and pressure range 65–198 torr. The decomposition reactions of these alcohols in seasoned vessels are homogeneous, unimolecular, and follow a first‐order rate law. The Arrhenius equations for the overall decomposition and partial rates of products formation were found as follows: for 2‐phenylethanol, overall rate log k₁(s⁻¹)=12.43−228.1 kJ mol⁻¹ (2.303 RT)⁻¹, toluene formation log k₁(s⁻¹)=12.97−249.2 kJ mol⁻¹ (2.303 RT)⁻¹, styrene formation log k₁(s⁻¹)=12.40−229.2 kJ mol⁻¹(2.303 RT)⁻¹, ethylbenzene formation log k₁(s⁻¹)=12.96−253.2 kJ mol⁻¹(2.303 RT)⁻¹; for 1‐phenyl‐2‐propanol, overall rate log k₁(s⁻¹)=13.03−233.5 kJ mol⁻¹(2.303 RT)⁻¹, toluene formation log k₁(s⁻¹)=13.04−240.1 kJ mol⁻¹(2.303 RT)⁻¹, unsaturated hydrocarbons+indene formation log k₁(s⁻¹)=12.19−224.3 kJ mol⁻¹(2.303 RT)⁻¹; for 2‐methyl‐1‐phenyl‐2‐propanol, overall rate log k₁(s⁻¹)=12.68−222.1 kJ mol⁻¹(2.303 RT)⁻¹, toluene formation log k₁(s⁻¹)=12.65−222.9 kJ mol⁻¹(2.303 RT)⁻¹, phenylpropenes formation log k₁(s⁻¹)=12.27−226.2 kJ mol⁻¹(2.303 RT)⁻¹. The overall decomposition rates of the 2‐hydroxyalkylbenzenes show a small but significant increase from primary to tertiary alcohol reactant. Two competitive eliminations are shown by each of the substrates: the dehydration process tends to decrease in relative importance from the primary to the tertiary alcohol substrate, while toluene formation increases. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 401–407, 1999     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.     

Bound states of a more general exponential screened Coulomb potential

An alternative approximation scheme has been used in solving the Schr?dinger equation to the more general case of exponential screened Coulomb potential, V(r) = −(a/r)[1 + (1 + br)e ^−2br ]. The bound state energies of the 1s, 2s and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.      

On the variation of the distances of Nd3+−Cl− and Tm3+−Cl− in mixed system of dimethyl sulfoxide and water

The stability constants, β₁, of each monochloride complex of Ln(III) (Ln=Nd or Tm) have been determined in the mixed system of dimethyl sulfoxide (DMSO) and water with 1.0 mol·dm⁻³ ionic strength using a solvent extraction technique. The values of β₁ of Ln(III) decrease to about 0.2 mole fraction of DMSO (X _s) in the mixed solvent system and then increase withX _s (>about 0.2). However, the variation mode of β₁ of Nd(III) withX _s somewhat differs from that of Tm(III). Calculation of Ln³⁺−Cl⁻ distance using a Born-type equation of the Gibbs' free energy derived from the β₁ evealed the followings: (1) For Tm³⁺ with coordination number 8, the estimated distance between Tm³⁺ and Cl⁻ (d _Tm-Cl) increases linearly withX _s in 0.00≤X _s≤0.17. This means an enlargement of the primary solvation sphere size of Tm³⁺ withX _s. On the other hand, thed _Tm-Cl shows a decrease withX _s in 0.17<X _s<0.28. (2) The estimatedd _Nd-Cl increases linearly withX _s in 0.00≤X _s<0.06 and 0.06<X _s≤0.17, but their slopes are different. The larger slope againstX _s in 0.06<X _s≤0.17 is attributable to a lowering of the β₁ by a coordination of ClO₄ ⁻ into the secondary solvation sphere of Nd³⁺ and/or by an increase in the solvation number of the primary solvation sphere of Nd³⁺.     

(1-Methoxyvinyl)boronic and (1-chlorovinyl)boronic esters

(s)-Pinanediol (1-methoxyvinyl)boronate ( 1 ) was prepared from (1-methoxyvinyl)-lithium and triisopropyl borate followed by (s)-pinanediol. Attempted reaction with (dichloromethyl)lithium failed, and reaction with butylmagnesium chloride followed by acetic acid yielded a mixture of diastereomers of (s)-pinanediol (1-methoxy-1-methyl-pentyl)boronate ( 2 ). (s)-Pinanediol (1-chlorovinyl)boronate ( 4 ) has been prepared by dehydrochlorination of (s)-pinanediol 1,1-dichloroethylboronate ( 3 ) with lithium chloride in dimethylformamide. Reaction of 4 with (dichloromethyl)lithium yielded (s)-pinanediol (1S)-(1,2-dichloroallyl)boronate ( 5 ) in 92% diastereomeric excess. Reaction of 5 with RMgX resulted in a 3 : 1 ratio of displacement of the 1-Cl from carbon by R to displacement of the entire 1,2-dichloroallyl group from boron by R. With lithium benzyl oxide, displacement of the 1-Cl from 5 failed entirely. Reaction of 4 with (dibromomethyl)lithium was inefficient and yielded a gross mixture of diastereomers.     

Thermally stimulated depolarization currents of films obtained from supernatant layer of mixed solutions of stereoregular polymethyl methacrylates

Summary Thermally stimulated depolarization currents were investigated for films obtained from supernatant layer of mixed solutions ofi- ands-PMMA ini/s weight ratio of 1/1 and 1/2. The results showed that the degree of stereocomplex formation is not uniform: the mixed solutions contain the insoluble and the soluble stereocomplex aggregates and in some case the residual (free)i-PMMA. The stereocomplex is formed ini/s weight ratio of 1/2.     

Anion-lnduced Fluorescence Quenching of a New Zwitterionic Biacridine Derivative

The effect of halides and different buffer anions on the quenching of the fluorescence of the new probe 10,10′-bis(3-sulfopropyl)-9,9′-biacridine (SPBA) has been studied using fluorescence and decay time measurements. The linearity of the Stern-Volmer plot indicates that fluorescence quenching by halides can be described reasonably well by a single-exponential decay with a K of 4.06 times 10⁶M^-1s^-1for chloride, 7.83 times 10⁶M^-1s^-1for bromide and 1.12 times 10⁷M^-1s^-1for iodide. We have found that SPBA is collisionally quenched also by the buffers 3-(N-mor-pholino)propanesulfonic acid (MOPS) and N-2-hydroxy-ethylpiperazine-N′-ethansulfonic acid (HEPES). The bi-molecular rate constants are 1.67 × 10⁶M^-ls^-1for HEPES and 1.44 times 10⁶M^-1s^-1for MOPS.