A Closed-Form Relation for Dimension-Dependent Two-Electron Matrix Elements of the Interelectronic Distance

The evaluation of matrix elements of two electron atoms is fundamental for the study of the electronic properties of those systems. We add to this knowledge by presenting an explicit expression for the matrix elements of the inverse of the interelectronic distance of two-electron atoms in any spatial dimension D. The basis functions used are the D-dependent hydrogenic wavefunctions {1s ²,2p ²,3d ²,4f ²,5g ²,...,21y ²,...}, extending and including, in this way, the results of the previous basis set {1s ²,2p ²,3d ²,4f ²}. The methodology used does not employ Fourier integral transforms as in previous works but hypergeometric transformation formulas.     

Two-electron atomic wave functions which satisfy proportionality relations between one-and two-electron moments

Based on momentum- and position-space analyses of the moment operators for two-electron atoms, it is shown that there exists a family of two-electron wave functions which satisfy a proportionality relation, r/ ₁ ^v /r ₁₂ ^v =p/ ₁ ^v /p ₁₂ ^v =2^–v/2, between the one and two-electron moments in position and momentum spaces, where v is an arbitrary number for which the moments are well-defined.     

Quantum Size Effects on Two Electrons and Two Holes in Double-Layer Quantum Dots

We propose a procedure to solve exactly the Schrodinger equation for a system of two electrons and two holes in a double-layer quantum dot by using the method of few-body physics. The features of the low-lying spectra have been deduced based on symmetry. The binding energies of the ground state are obtained as a function of the electron-to-hole mass ratio σ for a few values of the quantum dot size.     

Electroprotic reactions

Reactions involving the coupled transfer of electrons and protons are called electroprotic reactions. In this article we briefly describe some of our experiences with electroprotic reaction as a tool for executing interesting chemical transformations.     

双回碰机制下双电子谐波发射的特点

本文数值研究了阿秒分辨下双电子He原子发射高次谐波的特点.数值计算结果表明,双电子谐波光谱的截止能量与单电子相比有较大延伸,并且我们发现了一些新的截止能量.随后分析显示,这些新的截止能量是由双电子的双回碰机制所导致的,并且电子相关效应在里面起到了很重要的作用.     

Carborane Substituents Promote Direct Electrophilic Insertion over Reduction–Metalation Reactions

Two‐electron reduction of 1,1′‐bis(o‐carborane) followed by reaction with [Ru(η‐mes)Cl₂]₂ affords [8‐(1′‐1′,2′‐closo‐C₂B₁₀H₁₁)‐4‐(η‐mes)‐4,1,8‐closo‐RuC₂B₁₀H₁₁]. Subsequent two‐electron reduction of this species and treatment with [Ru(η‐arene)Cl₂]₂ results in the 14‐vertex/12‐vertex species [1‐(η‐mes)‐9‐(1′‐1′,2′‐closo‐C₂B₁₀H₁₁)‐13‐(η‐arene)‐1,13,2,9‐closo‐Ru₂C₂B₁₀H₁₁] by direct electrophilic insertion, promoted by the carborane substituent in the 13‐vertex/12‐vertex precursor. When arene=mesitylene (mes), the diruthenium species is fluxional in solution at room temperature in a process that makes the metal–ligand fragments equivalent. A unique mechanism for this fluxionality is proposed and is shown to be fully consistent with the observed fluxionality or nonfluxionality of a series of previously reported 14‐vertex dicobaltacarboranes.     

Two-electron excitation of calcium, strontium, and barium atoms on exposure to electron impact

The absolute effective excitation cross-sections for the spectral transitions of alkaline-earth atoms under the action of electron impact are determined, which correspond to simultaneous excitation of s²-valence electrons. The results were obtained on a setup with intersecting atomic and electron beams. It is established that the effective cross-sections of one- and two-electron excitation of valence subshells into states with the same effective principal and orbital quantum numbers are equal. The results obtained are compared with the available theoretical data. Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetskaya St., Uzhgorod, 294016, Ukraine. Translated from Zhurnal Prikladnoi, Spektroskopii, Vol. 65, No. 3, pp. 433–436, May–June, 1998.     

离散变分x_α的双电子计算及MgF_2Ni~(2+)的晶场能级

使用离散变分x_a双电子计算方法计算了激光晶体MgF_2:Ni~(2+) 的部分双电子积分,并由此获得晶体的单态和三重态分裂值.结合离散变分x_a自旋计算,获得了MgF_2:Ni~(2+)的晶场能级.     

Chemical model of oxidases. CuI-catalyzed oxidation of secondary alcohols by dioxygen

Oxidation of secondary alcohols (2-propanol, 2-butanol, and cyclohexanol) by dioxygen, catalyzed by Cu^I ando-phenanthroline complexes, in the presence of alkali, was studied. The conditions under which oxidative dehydrogenation of secondary alcohols result in fast formation of ketones as the only primary oxidation products were found. Bis-phenanthrolinates [Cu(phen)₂]⁺ are the active forms of the catalyst. The catalytic turnover number for complexes between copper(i) ando-phenanthroline is 1 to 2 s^–1 at room temperature.Kinetic regularities of the reaction are similar to those of the oxidation of alcohols in the presence of oxidases. The mechanism of the process is proposed, suggesting that the oxidation of secondary alcohols occursvia a concerted two-electron mechanism involving a stage of formation of the ternary complex [O₂...Cu(phen)₂ ⁺...^–OCHR¹R²]. It is significant for the oxidation mechanism that a hydrogen atom is transferred from the anionic form of a substrate to oxygen, which is confirmed by the value of the kinetic isotope effectk _H/k _D = 2.1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1952–1958, October, 1995.The work was financially supported by the Russian Foundation for Basic Research (Project No. 94-03-08733a) and the International Science Foundation (Grant MN4 000).