Molecular formation and electron correlation in HeH+

A one-centre CI wave function for HeH⁺ reported by Stuart and Matsen for 0.1 ? R ? 5.0 has been analysed in detail from the viewpoint of molecular formation. Further, by means of a natural orbital analysis, it was possible to obtain some measure of the electron correlation contained within such wave functions for various R values. These effects were illustrated by means of a series of difference maps for the electron density. One- and two-particle expectation values were obtained as a function of R. Thus, it was possible to study several aspects of the influence of the proton on the electron charge cloud as we pass from He through to the united atom Li⁺. The occupation numbers within the natural expansions were compared with those which arise from a similar analysis of a two-centre wave function for HeH⁺. The “character” of such wave functions for HeH⁺, and also for He and Li⁺, were analysed and compared.     

Helium atom inside boxes with paraboloidal walls

The ground-state energy of the helium atom inside boxes with paraboloidal walls, with the nucleus at the common focus, is calculated variationally. The variational functions are products of geometry-adapted hydrogenic functions, and the interelectronic Coulomb repulsion is represented through its harmonic expansion in parabolic coordinates. The energy, pressure, quadrupole moment, and polarizability of the atom are determined as functions of the positions of the walls for symmetrical boxes. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 123–130, 1998     

On the behaviour of the wave function for the 23S state of the two-electron atom in the region where both electron–nuclear distances are small

The expansion of the wave function for the 2³S state of the two-electron atom in the neighbourhood of the singularity at r₁ = r₂ = 0 is considered. The restrictions imposed on the variational functions by this expansion are discussed. For the 2³S state of He, Li⁺, N⁵⁺ the behaviour of the variational function based on the Fock expansion in the neighbourhood of this singularity is investigated. The agreement of the variational coefficients with the theoretical coefficients is satisfactory. The calculated values of E and 〈δ(r₂)〉 for He, Li⁺, N⁵⁺ are given.     

Analytical Hartree–Fock wave functions subject to cusp and asymptotic constraints: He to Xe,Li+ to Cs+, H− to I−

Analytical, variational approximations to Hartree–Fock wave functions are constructed for the ground states of all the neutral atoms from He to Xe, the cations from Li⁺ to Cs⁺, and the stable anions from H⁻ to I⁻. The wave functions are constrained so that each atomic orbital agrees well with the electron–nuclear cusp condition and has good long‐range behavior. Painstaking optimization of the exponents and principal quantum numbers of the Slater‐type basis functions allows us to reach this goal while obtaining total energies that, at worst, are a few microHartrees above the numerical Hartree–Fock limit values. The wave functions are freely available by anonymous ftp from okapi.chem.unb.ca or upon request to the authors. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 491–497, 1999     

The Coulomb hole in the 23S state of the helium isoelectronic sequence

The pair distribution functions evaluated for the 2³S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree-Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree-Fock solution between He and Li⁺, the Coulomb hole has a different shape for He than for Li⁺ and the other isoelectronic ions.     

Supramolecular Polymer Ion Conductor with Weakened Li Ion Solvation Enables Room Temperature All-Solid-State Lithium Metal Batteries

Improved durability, enhanced interfacial stability, and room temperature applicability are desirable properties for all-solid-state lithium metal batteries (ASSLMBs), yet these desired properties are rarely achieved simultaneously. Here, in this work, it is noticed that the huge resistance at Li metal/electrolyte interface dominantly impeded the normal cycling of ASSLMBs especially at around room temperature (<30 °C). Accordingly, a supramolecular polymer ion conductor (SPC) with “weak solvation” of Li⁺ was prepared. Benefiting from the halogen-bonding interaction between the electron-deficient iodine atom (on 1,4-diiodotetrafluorobenzene) and electron-rich oxygen atoms (on ethylene oxide), the O-Li⁺ coordination was significantly weakened. Therefore, the SPC achieves rapid Li⁺ transport with high Li⁺ transference number, and importantly, derives a unique Li₂O-rich SEI with low interfacial resistance on lithium metal surface, therefore enabling stable cycling of ASSLMBs even down to 10 °C. This work is a new exploration of halogen-bonding chemistry in solid polymer electrolyte and highlights the importance of “weak solvation” of Li⁺ in the solid-state electrolyte for room temperature ASSLMBs.     

Dispersion coefficients for Li+–H and Li+–He systems with coulomb and screened coulomb potentials

Exploiting powerful computational aspects and highly correlated exponential wave functions for two‐electron atoms, we have investigated the effects of screened Coulomb interaction on the hexadecapole polarizability of Li⁺(1¹S), and the dispersion coefficients C₆, C₈, C₁₀, and C₁₂ for interaction of Li⁺ with H and He atoms in their ground states. The dispersion coefficients and hexadecapole polarizability for different screening parameters ranging from 0 to 1.0 a are reported. In the unscreened case, the hexadecapole polarizability of Li⁺, and the dispersion C₁₂ coefficients for Li⁺–H and Li⁺–He system are reported for the first time in the literature. The C₆, C₈, and C₁₀ coefficients for the unscreened cases are comparable with the reported results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Mechanism of Dissolution of a Lithium Salt in an Electrolytic Solvent in a Lithium Ion Secondary Battery: A Direct Ab Initio Molecular Dynamics (AIMD) Study

The mechanism of dissolution of the Li⁺ ion in an electrolytic solvent is investigated by the direct ab initio molecular dynamics (AIMD) method. Lithium fluoroborate (Li⁺BF₄^?) and ethylene carbonate (EC) are examined as the origin of the Li⁺ ion and the solvent molecule, respectively. This salt is widely utilized as the electrolyte in the lithium ion secondary battery. The binding of EC to the Li⁺ moiety of the Li⁺BF₄^? salt is exothermic, and the binding energies at the CAM–B3LYP/6‐311++G(d,p) level for n=1, 2, 3, and 4, where n is the number of EC molecules binding to the Li⁺ ion, (EC)_n(Li⁺BF₄^?), are calculated to be 91.5, 89.8, 87.2, and 84.0 kcal mol^?1 (per EC molecule), respectively. The intermolecular distances between Li⁺ and the F atom of BF₄^? are elongated: 1.773 Å (n=0), 1.820 Å (n=1), 1.974 Å (n=2), 1.942 Å (n=3), and 4.156 Å (n=4). The atomic bond populations between Li⁺ and the F atom for n=0, 1, 2, 3, and 4 are 0.202, 0.186, 0.150, 0.038, and 0.0, respectively. These results indicate that the interaction of Li⁺ with BF₄^? becomes weaker as the number of EC molecules is increased. The direct AIMD calculation for n=4 shows that EC reacts spontaneously with (EC)₃(Li⁺BF₄^?) and the Li⁺ ion is stripped from the salt. The following substitution reaction takes place: EC+(EC)₃(Li⁺BF₄^?)→(EC)₄Li⁺?(BF₄^?). The reaction mechanism is discussed on the basis of the theoretical results.     

Monohydration selectivity mechanism of alkali cations in the potassium channel of excitable biomembranes

Nonempirical quantum chemical method Hartree–Fock–Roothan LCAO SCF MO in a two-exponent Dunning basis with the use of an extended set of Gaussian functions by Huzinaga–Dunning with consideration of electron correlation according to the Meller–Plesset theory of excitations of the second order was used to study monohydrates of Li⁺, Na⁺, K⁺, and HCOO^? ions. The indicated basis was supplemented with polarization functions of d-type on the O atom and of p-type on the hydrogen atom as well as with diffusion functions of p-type on the oxygen atom. It has been found that binding energies of the water molecule with Li⁺, Na⁺ appeared to be higher and with K⁺ lower than with HCOO^? · H₂O. Potential curve shapes of K⁺ + H₂O and HCOO^? + H₂O reactions are shown to be similar. The molecular mechanism of K⁺ channel selectivity of an excitable membrane is explained on the basis of the obtained calculations.     

A comparison of coordination ability of hetero atoms: a Li and Na selective pyridinophane-based cryptand

A pyridinophane-based cryptand showed Li⁺ and Na⁺ selectivities. Crystallographic analysis of the Li⁺ cryptate indicates that the coordination ability of the heteroatoms is in the following order: unsaturated nitrogen>oxygen>saturated nitrogen atom.     

Doubly excited3Se,3De and3Ge states of two-electron atomic systems

Summary Time-dependent perturbation theory has been applied to calculate the doubly excited triplet statesNsns:³S^e,Npnp:³D^e andNdnd:³G^e (N=2, 3, 4,n=N+1, ... ,5) for He, Li⁺, Be²⁺ and B³⁺. A time-dependent harmonic perturbation causes simulataneous excitation of both the electrons with a change of spin state. The doubly excited energy levels have been identified as the poles of an appropriately constructed linearized variational functional with respect to the driving frequency. In addition to the transition energies, effective quantum numbers of these doubly excited states have been calculated and analytic representations of their wave functions are obtained. These are utilized to estimate the Coulomb repulsion term for these states which checks the consistency of the wave functions. These wave functions may also be used for calculating other physical properties of the systems.     

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ together with (ii) the anions F⁻, Cl⁻, Br⁻, NO₃⁻ and SO₄²⁻ with water clusters (H₂O)_n, n=1–8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.     

Theoretical study on nonlinear optical properties of the Li+[calix[4]pyrrole]Li−dimer,trimer and its polymer with diffuse excess electrons

The static (hyper)polarizabilities of the dimer and trimer with diffuse excess electrons, [Li⁺[calix[4]pyrrole]Li^?]_n, are firstly investigated by the DFT(B3LYP) method in detail. For the dimer and trimer, a Li atom inside each calix[4]pyrrole unit is ionized to form a diffuse excess electron. The results show that the dimer and trimer containing two and three excess electrons, respectively, have very large first hyperpolarizablities as 2.3 × 10⁴ and 4.0 × 10⁴ au, which are 30 and 40 times larger than that of the corresponding [calix[4]pyrrole]_n (n = 2, 3) without Li atom. Also, β values of dimer and trimer are twice and four times as large as that of monomer containing one excess electron. Obviously, not only excess electron but also the number of excess electron plays an important role in increasing the first hyperpolarizability. Moreover, the (hyper)polarizabilities of the [Li⁺[calix[4]pyrrole]Li^?]_n polymer are investigated at ab initio level by using the elongation finite‐field (elongation FF) method. All the oligomers of the [Li⁺[calix[4]pyrrole]Li^?]_n with many excess electrons exhibit very large first hyperpolarizability and large second hyperpolarizability. The present investigation shows that by introducing several and more excess electrons into the nonlinear optical (NLO) materials will be an important strategy for improving their NLO properties, which will be helpful for design of NLO materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Polarographic and voltammetric investigations in N-methylpyrrolidinone(2) and N-methylthiopyrrolidinone(2)

Polarographic and voltammetric methods were employed to study the influence of N-methylpyrrolidinone(2) (NMP) and N-methylthiopyrrolidinone(2) (NMTP) towards a series of cations. In NMP reversible electrode reactions were observed for Na⁺, K⁺, Tl⁺, Zn²⁺, Cd²⁺, Cu²⁺, Ag⁺ and irreversible reductions for Ba²⁺, Mn²⁺, Co²⁺ and Ni²⁺. 0.1 mol l^?1 tetraethylammoniumperchlorate solutions served as supporting electrolytes. Li⁺ was not electroactive in the supporting electrolyte mentioned, but yielded an irreversible cathodic wave in tetra-n-butylammonium perchlorate. In NMTP, Li⁺, Na⁺, Tl⁺, Zn²⁺, Cd²⁺, Cu⁺ and Ag⁺ gave reversible cathodic waves on the DME, while Mn²⁺, Co²⁺ and Ni²⁺ were reduced in an irreversible electrode process. Bisbiphenylchromium iodide serving as a reference system throughout this study showed reversible behaviour in both solvents. A comparison of E_1/2 for given ions in both solvents showed a shift of about 0.5 V to more positive values in the case of a typically hard cation such as Na⁺ whereas soft cations such as Ag⁺ and Cu⁺ shifted by more than 0.8 V to more negative values. The effects of these two solvents on the cations studied is discussed in terms of donor acceptor interactions between the cation and the solvent molecules with special respect to the changes caused by replacing the oxygen atom in NMP by a sulphur atom.     

Lithium redox-responsive ferrocene bis-tertiary amide derivatives

The addition of Li⁺ to ferrocene bis-tertiary amide derivatives in acetonitrile results in a shift of the ferrocene oxidation wave to more positive potentials and the appearance of a new redox couple associated with a Li⁺ complex.     

Aluminum phosphate dispersed on a cellulose acetate fiber surface: Preparation, characterization and application for Li, Na and K separation

Cellulose acetate fibers with supported highly dispersed aluminum phosphate were prepared by reacting aluminum-containing cellulose acetate (Al₂O₃=3.5 wt.%; 1.1 mmol g⁻¹ aluminum atom per gram of the material) with phosphoric acid. Solid-state NMR spectra (CPMAS ³¹P NMR) data indicated that HPO₄²⁻ is the species present on the fiber surface. The specific concentration of acidic centers, determined by ammonia gas adsorption, is 0.50 mmol g⁻¹. The ion exchange capacities for Li⁺, Na⁺ and K⁺ ions were determined from ion exchange isotherms at 298 K and showed the following values (in mmol g⁻¹): Li⁺=0.03, Na⁺=0.44 and K⁺=0.50. The H⁺/Li⁺ exchange corresponds to the model of the ideal ion exchange with a small value of the corresponding equilibrium constant K=1.1×10⁻². Due to the strong cooperative effect, the H⁺/Na⁺ and H⁺/K⁺ ion exchange is non-ideal. These ion exchange equilibria were treated with the use of models of fixed bi- or tridentate centers, which consider the surface of the sorbent as an assemblage of polyfunctional sorption centers. Both the observed ion exchange capacities with respect to the alkaline metal ions and the equilibrium constants were discussed by taking into consideration the sequence of the ionic hydration radii for Li⁺, Na⁺ and K⁺. The matrix affinity order for the ions decreases as the hydration radii of the cations increase, i.e. Li⁺>Na⁺>K⁺. The high values of the separation factors S_Na⁺/Li⁺ and S_K⁺/Li⁺ (up to several hundred) provide quantitative separation of Na⁺ and K⁺ from Li⁺ from a mixture containing these three ions.     

Photophysical and photochemical processes in zeolite cavities: The effects of ion-exchanged alkalimetal cations on the excited states of xanthone and the photolysis of 2-pentanone

The characteristics properties of xanthone phosphorescence and of 2-pentanone photolysis in alkali metal cation-exchanged zeolites have been investigated to clarify the effect of the micro-environment of host-adsorbents on the photophysical and photochemical properties of guest-molecules in restricted void spaces. The enhancement of the phosphorescence yields of xanthone included in zeolites is observed by changing the exchangeablealkali metal cation from Li⁺ to Cs⁺. Simultaneously, the phosphorescence lifetimes were observed to continuously shorten by changing the cation from Li⁺ to Cs⁺. These results suggest that the external heavy-atom effect deriving from the alkali metal cations on the singlet-triplet transitions of xanthone molecules stabilized on alkali metal cations in the order of Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺. The yields for the photolysis of 2-pentanone included in zeolites increase with changing the alkali metal cation from Li⁺ to Cs⁺. IR investigations of the adsorption state of 2-pentanone indicate that strength of the interaction between the alkali metal cations and 2-pentanones decreases by changing the cation from Li⁺ to Cs⁺, which results in a longer lifetime of 2-pentanone. The selectivity of propylene formation is dramatically increased by changing the cation from Li⁺ to Cs⁺. The enhanced formation of propylene is asociated with the hydrogen absorption from propyl radicals by lattice oxygen, their basicity increasing by changing the cation from Li⁺ to Cs⁺. Thus, these changes in the zeolite cavities modified by exchanging cations caused significant effects not only on the excited state but also on the following chemical reactions of ketones.     

Self-consistent calculation of excited 3P state wave functions of atoms

A variation perturbation method in the Hartree–Fock scheme has been described to calculate excited ³P state wave functions of atoms. The starting wave functions are obtained from a study of the singularities in the dynamic polarizability calculation [1]. The 2³P, 3³P and 4³P states of He, Li⁺, Be²⁺, B³⁺ and C⁴⁺ are studied. The results obtained are in satisfactory agreement with experimental values and with other accurate theoretical estimates.     

Structure and Stability of Endohedral Complexes X@（HBNH）12

Using quantum chemistry methods B3LYP/6-31＋＋G（d,p） to optimize endohedral complexes X@（HBNH）12 （X=Li^0/＋, Na^0/＋, K^0/＋, Be^0/2＋, Mg^0/2＋, Ca^0/2＋, H and He）, the geometries with the lowest energy were achieved. Inclusion energy, standard equilibrium constant, natural charge, spin density, ionization potentials, and HOMO-LUMO energy gap were also discussed. The calculation predicted that X=Na^0/＋, K^0/＋, Mg^0/2＋, Ca^0/2＋, H and He are nearly located at the center of （HBNH）12 cluster. Li^＋ lies in less than 0.021 nm departure from the center. Li and Be^0/2＋ dramatically deviate from the center. （HBNH）12 prefers to enclose Li^＋, Be^2＋, Mg^2＋, and Ca^2＋ in it than others. Moreover, M@（HBNH）12 （M=Li, Na, K） species are ＂superalkalis＂ in that they possess lower first ionization potentials than the Cs atom （3.9 eV）.     

Intra- and inter-atomic auger processes in collisions of low energy He++, He+, He* (23,S, 21 S) and Li+ with Li covered W(110) surfaces

Electron spectra from He⁺⁺, He⁺ and Li⁺ (10 to 1500 eV) ions colliding under grazing incidence with Li covered W (110) surfaces are reported. The results are compared with those obtained from thermal collisions of (2³ S; 2¹ S) metastable He atoms. In these collisions 1s vacancies are either produced during the collision event (energetic He⁺ (Li ⁺) collisions) or are brought into the collision (slow He⁺⁺ (He⁺, He*) collisions). Population of the 2s orbitals by two electrons produces states which decay by intraatomic Auger processes: we observe autoionization of He** (2s ²) and Li** (1s 2s ²) as well as autodetachment of He^?* (1s 2s ²). Alternatively the 1s-holes in the projectile or target (Li) can be filled by Auger processes involving one or two surface electrons. The processes leading to electron emission are studied as a function of the Li coverage in the submonolayer region (0≦Θ_Li≦1Ml) and as a function of the projectile energy. It is concluded that with one or two 1s vacancies present in the projectile the double capture of two surface electrons constitutes an important process responsible for electron emission of low work function surfaces.