Note on the electron–electron counterbalance hole

The electron–electron counterbalance hole implies that two parallel spin electrons cannot be at opposite positions with respect to the spatial inversion center, if it exists. The hole is known to appear for any approximate and exact wave functions with an even inversion parity. We point out that for particular cases, the counterbalance hole also appears when wave functions have an odd inversion parity and two electrons with anti-parallel spins are involved.     

Structure of water (H2O) 6 − and ammonium (NH3) 13 − clusters with an excess electron: Quantum chemical studies

The B3LYP method within DFT and the ab initio MP2 method with an extended 6-311++G(3df,3pd) basis set are employed to calculate the adiabatic bound state of an excess electron in (H₂O) ₆ ^? water and (NH₃) ₁₃ ^? . ammonium clusters. Adiabatic electron affinity of (H₂O)₆ and (NH₃)₁₃ clusters is 0.03–0.18 eV and 0.18 eV respectively. The calculated vertical binding energies of the excess electron in anionic clusters ((H₂O) ₆ ^? 0.37÷0.66 eV and (NH₃) ₁₃ ^? 0.26 eV) agree well with the experimental values of 0.50 eV and 0.22 eV obtained from photoelectron spectra. A cavity model of solvated electrons in water and ammonium is considered.     

Tracking lithiation with transmission electron microscopy

Li-ion batteries(LIBs) have dominated energy-storage techniques for portable electronic devices and electric cars, and are expanding their territory into the large-scale energy storage. The energy storage of LIBs is realized by the reversible shuttle of lithium ions between electrodes. It is essential to track the lithium diffusion and obtain a profound insight into the lithiation mechanism during the work cycle of LIBs. Transmission electron microscopy(TEM) is a powerful tool for the structural...     

Can a dipole-bound electron form a pseudo-atom? An atoms-in-molecules study of the hydrated electron

Non-nuclear local maxima, or attractors, of electron density are a rare but very interesting feature of the electron density distribution in molecules and solids. Recently, non-nuclear attractors (NNAs) and the corresponding pseudoatoms of electron density have been identified with the quantum theory of atoms in molecules for some anionic clusters formed by several polar solvent molecules and an excess electron bound in either a solvated-electron or dipole-bound fashion. This contribution reports a detailed study of the topology of the electron density for a series of dipole-bound water cluster anions, as calculated with Hartree-Fock, M?ller-Plesset perturbation theory, and coupled-cluster methods together with basis sets augmented with extra diffuse basis functions to accommodate the excess electron. For dipole-bound clusters, electron densities obtained with insufficient inclusion of electron correlation effects and tight basis sets feature a well-pronounced pseudoatom due to the excess electron, which ultimately disappears when a higher level of electronic structure theory and a more diffuse basis set are used. On the other hand, for solvated-electron clusters, where the excess electron is surrounded by solvent molecules, the existence of NNAs does not seem to be an artifact of the method employed, but rather a genuine feature of the electron density distribution. Pseudoatoms of electron density thus appear to be an exclusive feature of confined environments and are unlikely to be found on the tip of a cluster dipole or on solid surfaces.     

The response electron–electron repulsion energy and energy component analysis in CC/MBPT methods

Molecular properties are computed as responses to perturbations (energy derivatives) in coupled-cluster (CC)/many-body perturbation theory (MBPT) models. Here, the CC/MBPT energy derivative with respect to a general two-electron (2-e) perturbation is assembled from gradient theory for 2-e property evaluation, including the electron repulsion energy. The correlation energy (?E) is shown to be the sum of response kinetic (?T), electron–nuclear attraction (?V), and electron repulsion (?V _ee ) energies. Thus, evaluation of total V _ee for energy component analysis is simple: For total energy (E), total 1-e responses T and V, and nuclear–nuclear repulsion energy (V _NN ), V _ee  = E ? V _NN  ? T ? V is the true 2-e response value. Component energy analysis is illustrated in an assessment of steric repulsion in ethane’s rotational barrier. Earlier SCF-based results (Bader et al. in J Am Chem Soc 112:6530, 1990) are corroborated: The higher-energy eclipsed geometry is favored versus staggered in the two repulsion energies (V _NN and V _ee ), while decisively disfavored in electron–nuclear attraction energy (V). Our best quality calculations (CCSD/cc-pVQZ) attain practical Virial Theorem compliance (i.e., agreement among the kinetic energy, potential energy, and total energy representations) in assigning 2.70 ± 0.06 to the barrier height; ?195.80 kcal/mol is assigned to the drop in “steric” repulsion upon going to the eclipsed geometry. Steric repulsion is not responsible for any fraction of the ~3 kcal/mol barrier.     

Gauging away the electron–electron interaction by the local phase of complex wave functions in two-electron systems

The electron–electron interaction is eliminated in the expectation values of the electronic Hamiltonian for two-electron systems. The part of the Hamiltonian referring to the repulsive interaction is gauged away by the local phase of the complex wave functions, much like a gauge field transformation, thereby leading to a one-electron Hamiltonian. Despite the appearance of complex wave functions, the expectation values of the total momentum operator vanish and Löwdin’s criterion holds for the stationary states.     

High resolution electron attachment to CO₂ clusters

Electron attachment to CO? clusters performed at high energy resolution (0.1 eV) is studied for the first time in the extended electron energy range from threshold (0 eV) to about 10 eV. Dissociative electron attachment (DEA) to single molecules yields O(-) as the only fragment ion arising from the well known (2)Π(u) shape resonance (ion yield centered at 4.4 eV) and a core excited resonance (at 8.2 eV). On proceeding to CO? clusters, non-dissociated complexes of the form (CO?)(n)(-) including the monomer CO?(-) are generated as well as solvated fragment ions of the form (CO?)(n)O(-). The non-decomposed complexes appear already within a resonant feature near threshold (0 eV) and also within a broad contribution between 1 and 4 eV which is composed of two resonances observed for example for (CO?)(4)(-) at 2.2 eV and 3.1 eV (peak maxima). While the complexes observed around 3.1 eV are generated via the (2)Π(u) resonance as precursor with subsequent intracluster relaxation, the contribution around 2.2 eV can be associated with a resonant scattering feature, recently discovered in single CO? in the selective excitation of the higher energy member of the well known Fermi dyad [M. Allan, Phys. Rev. Lett., 2001, 87, 0332012]. Formation of (CO?)(n)(-) in the threshold region involves vibrational Feshbach resonances (VFRs) as previously discovered via an ultrahigh resolution (1 meV) laser photoelectron attachment method [E. Leber, S. Barsotti, I. I. Fabrikant, J. M. Weber, M.-W. Ruf and H. Hotop, Eur. Phys. J. D, 2000, 12, 125]. The complexes (CO?)(n)O(-) clearly arise from DEA at an individual molecule within the cluster involving both the (2)Π(u) and the core excited resonance.     

Photoinduced intramolecular electron transfer between fluorescein and carbazole

Several dyads consisting of a fluoreseein covalently linked with a carhazole at site 2 or site 6 have been synthesized and characterized.Studies of absorption spectra,emission spectra and fluorescence lifetime quern hing Indicate that the ground-state interaction between fluorescein and carhazole in dyads is negligible and the intramolecular electron transfer (ET) reactions are mainly of dynamic process.Moreover,the efficiency and raie conslam of lectron transfer reactions in ZFO4 (carbazole linked at site 2'of fluorescein) are larg er than those in 4FOZ (carbazole linked at site 6 of fluorescein) 0 74; KET 11×108S-1),because the mutual orientation of donor and acceptor in ZFO4 is nearly face-to-face,which is more favorable to the process than the shoulder-to-shoulder mutual orientation in 4FOZ.Estimations are also formed of the free energy change of the photomduced electron transfer and the back reactions in the dyads.     

Selective oxidation of CO in excess hydrogen on copper—cerium-containing catalysts

Selective oxidation of CO that is in mixtures enriched in H₂ was studied to investigate catalytic properties of the 0.5—80% CuO/Ce_0.7Zr_0.3O₂ system. The catalysts were prepared by the combined decomposition of copper, cerium, and zirconyl nitrates at 300 °C. The systems studied are active and stable under mild conditions of the process (80—160 °C) and at high space velocities (to 100000 h^–1) of the reaction mixture (2% CO, 1% O₂, 40—50% H₂). With an increase in the CuO content in the catalysts up to 20%, the degree of CO removal achieves 60% (120 °C and V = 35000 h^–1) and further does not change appreciably. The contribution of oxygen participation into CO oxidation is virtually independent of the copper concentration in the sample and ranges from 65 to 75%. The dependences of the Arrhenius equation parameters for CO and H₂ oxidation on the catalyst composition were determined, which makes it possible to calculate the conversion of reactants and selectivity of CO conversion under the specified conditions of the process. The addition of CO₂ and H₂O (12—15%) to the reaction mixture decreases the catalyst activity and simultaneously increases the selectivity of CO oxidation to 100%. It is shown by the TPR and X-ray diffraction methods that the combined decomposition of the starting Cu²⁺, Ce³⁺, and ZrO²⁺ nitrates produces solid solutions of oxides with a high content of CuO. The reductive pre-treatment of fresh samples of the studied catalysts results in the destruction of the solid solution and formation of highly dispersed Cu particles on the surface of Ce—Zr—O. These particles are active in CO oxidation.     

Rapid determination of enantiomeric excess of α-chiral cyclohexanones using circular dichroism spectroscopy

Ketone handedness was discriminated using circular dichroism (CD) spectroscopy by monitoring the metal-to-ligand charge transfer (MLCT) bands of complexes between [Cu(I)((S)-1)(CH(3)CN)(2)]PF(6) and derivatized α-chiral cyclohexanones (4). This method was able to quantify the enantiomeric excess of unknown samples using a calibration curve, giving an absolute error of ±7%. The analysis was fast, allowing potential application of this assay in high-throughput screening (HTS).     

2-Methoxyethanol–Tetrahydrofuran–Binary Liquid System. Viscosities,densities, excess molar volumes and excess Gibbs activation energies of viscous flow at various temperatures

Densities (d ₁₂) and viscosities (η₁₂) have been measured for 2-methoxyethanol (ME) with tetrahydrofuran (THF) binary liquid mixtures over the whole composition range at various temperatures ranging from 291.15 to 308.15 K. The experimental data were used to test some empirical equations of the type: y ₁₂=y ₁₂(t) and y ₁₂=y ₁₂(X ₁) [where: y ₁₂−d ₁₂ or η₁₂]. From all these data, the excess molar volumes (V ₁₂ ^E), the excess viscosities (η₁₂ ^E) and excess Gibbs activation energies (ΔG ^*) of viscous flow were calculated. These structural parameters as a function of concentration suggest the formation of 3ME⋅THF and 2ME⋅THF types of intermolecular complexes. This revised version was published online in August 2006 with corrections to the Cover Date.     

An investigation of basis set effects in the characterization of electron – atom scattering resonances using the dilated electron propagator method

 The effects of basis set variations on resonance attributes are investigated using systematically augmented basis sets by correlating the resulting changes in resonance energy and width with the alterations induced in the radial probability density profile of the resonant orbital. Applications to ²P Be⁻ and ²P Mg⁻ shape resonances reveal that basis sets capable of describing both electron density accumulation near the target nucleus to facilitate resonance formation and sufficiently large electron density away from the target nucleus to provide for its decay are necessary for effective characterization of these resonances. A comparison of radial probability density profiles from the bivariational self-consistent field, the second-order, the diagonal two particle–one hole Tamm–Dancoff approximation and quasiparticle decouplings reveals that relaxation effects dominate in resonance formation. Received: 3 January 2000 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Dimension‐dependent two‐electron Hamiltonian matrix elements

Since the birth of quantum mechanics the ground state electronic energy of the twoelectron atom has received special attention. This is because the twoelectron system is the simplest atom to include electron–electron interactions. These interactions are key to understanding manyelectron systems. This paper adds to the knowledge of twoelectron atoms by presenting closed form solutions for Hamiltonian matrix elements at arbitrary spatial dimension, . The basis functions are the dependent hydrogenic wavefunctions: . The electron–electron repulsion integrals are solved by the Fourier integral transform.     

Coupling matrix element of electron self-exchange reactions in solution

On the basis of the common feature among the electron transfer process and the ion hydration process as well as the relevant experimental kinetic data of electron transfer reaction,a new accurate hydration potential function scheme for the determination of electron transfer coupling matrix element is presented.The coupling matrix element between two hydrated ions of the reacting system in solution is calculated.The results and the applicability of this scheme are discussed.     

Theoretical study on electron transfer in biological systems (Ⅲ)——Intramolecular electron transfer in metal-containing spiro π-electron system

Intramolecular electron transfer of metal-containing spiro π-electron system was studied by AM1 method in the MOPAC-ET program developed by the present group. The results indicated that with the increasing of the outer electric field F, the activation energy of the reaction decreased. When F reaches a certain threshold value, the activation energy barrier becomes zero and the rate of reaction achieves the largest value. The results also indicated that electron transfer matrix elements V_(AB) and reorganization energy λ were not obviously affected by outer electric field while the exothermicity ΔE was directly proportional to it.     

Where does the electron go? Electron distribution and reactivity of peptide cation radicals formed by electron transfer in the gas phase

We report the first detailed analysis at correlated levels of ab initio theory of experimentally studied peptide cations undergoing charge reduction by collisional electron transfer and competitive dissociations by loss of H atoms, ammonia, and N-C alpha bond cleavage in the gas phase. Doubly protonated Gly-Lys, (GK + 2H) (2+), and Lys-Lys, (KK + 2H) (2+), are each calculated to exist as two major conformers in the gas phase. Electron transfer to conformers with an extended lysine chain triggers highly exothermic dissociation by loss of ammonia from the Gly residue, which occurs from the ground ( X ) electronic state of the cation radical. Loss of Lys ammonium H atoms is predicted to occur from the first excited ( A ) state of the charge-reduced ions. The X and A states are nearly degenerate and show extensive delocalization of unpaired electron density over spatially remote groups. This delocalization indicates that the captured electron cannot be assigned to reduce a particular charged group in the peptide cation and that superposition of remote local Rydberg-like orbitals plays a critical role in affecting the cation-radical reactivity. Electron attachment to ion conformers with carboxyl-solvated Lys ammonium groups results in spontaneous isomerization by proton-coupled electron transfer to the carboxyl group forming dihydroxymethyl radical intermediates. This directs the peptide dissociation toward NC alpha bond cleavage that can proceed by multiple mechanisms involving reversible proton migrations in the reactants or ion-molecule complexes. The experimentally observed formations of Lys z (+*) fragments from (GK + 2H) (2+) and Lys c (+) fragments from (KK + 2H) (2+) correlate with the product thermochemistry but are independent of charge distribution in the transition states for NC alpha bond cleavage. This emphasizes the role of ion-molecule complexes in affecting the charge distribution between backbone fragments produced upon electron transfer or capture.     

Rapid determination of enantiomeric excess of α-chiral aldehydes using circular dichroism spectroscopy

A method for enantiodiscrimination of α-chiral aldehydes is reported. The method utilizes circular dichroism (CD) spectroscopy and a sensing ensemble composed of 2-(1-methylhydrazinyl) pyridine (1) and Fe(II)(TfO)₂. Aldehydes react rapidly with hydrazine (1) to form chiral imines, which form complexes with Fe(II). By monitoring the CD bands above 320 nm, one can determine the enantiomeric excess (ee) values of α-chiral aldehydes with an average absolute error of ±5%. The analysis was fast, and thus can have potential applications in high-throughput screening (HTS) of catalytic asymmetric induction.