High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Hylleraas–configuration interaction (Hy–CI) method variational calculations with up to 4648 expansion terms are reported for the ground ¹S state of neutral helium. Convergence arguments are presented to obtain estimates for the exact nonrelativistic energy of this state. The nonrelativistic energy is calculated to be ?2.9037 2437 7034 1195 9829 99 a.u. Comparisons with other calculations and an energy extrapolation give an estimated nonrelativistic energy of ?2.9037 2437 7034 1195 9830(2) a.u., which agrees well with the best previous variational energy, ?2.9037 2437 7034 1195 9829 55 a.u., of Korobov (Phys Rev A 2000, 61, 64503), obtained using the universal (exponential) variational expansion method with complex exponents (Frolov, A. M.; Smith, V. H. Jr. J Phys B Atom Mol Opt Phys 1995, 28, L449). In addition to He, results are also included for the ground ¹S states of H^?, Li⁺, Be⁺⁺, and B⁺³. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

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.     

Studies on the effect of the cation nature on the kinetics of the isotopic exchange reaction between chloride ion and O,O-diphenylphosphorochloridothionate in acetonitrile

Rate constants and activation parameters for the isotopic exchange reactions between (PhO)₂PSCl and M³⁶Cl (M = Me₄N⁺, Et₄N⁺, n-Bu₄N⁺, Et₃HN⁺, EtH₃N⁺, Li⁺) in acetonitrile were measured in order to find the effect of the cation nature onthe kinetics of the reaction. The rate constants measured for a range of concentrations of Et₃HN³⁶Cl, EtH₃N³⁶Cl, and Li³⁶Cl were analyzed using the Acree equation. The equivalent conductance of LiCl in acetonitrile was determined. The nature of the cation has no effect on the mechanism of the reaction. The cation changes only the experimental rate constant proportionally to the dissociation degree of the salt. Smaller values of the rate constant and smaller activation parameters ΔH? and ΔS? for the reaction with Li³⁶Cl indicate the existenceof the intermolecular interaction between lithium ions and O,O-diphenylphosphorochloridothionate.     

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.     

Long- and intermediate-range interaction in three lowest sigma states of the HeH+ ion

Accurate variational energies have been calculated for three lowest sigma states of the HeH⁺ ion. This includes the ground state (5 ≤ R ≤ 9 a.u.) which dissociates into He + H⁺, as well as the A ¹Σ⁺ state (4 ≤ R ≤ 10) and the a ³Σ⁺ state (3 ≤ R ≤ 10) which both dissociate into He⁺ + H. The variational results are compared with those obtained using a perturbation theory expansion.     

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     

Osmotic Coefficients of the Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>+LiCl + H<Subscript>2</Subscript>O System at <Emphasis Type="Italic">T</Emphasis>=273.15 K

Osmotic coefficients and water activities for the Li₂B₄O₇+LiCl+H₂O system have been measured at T=273.15 K by the isopiestic method, using an improved apparatus. Two types of osmotic coefficients, φ _S and φ _E, were determined. φ _S is based on the stoichiometric molalities of the solute Li₂B₄O₇(aq), and φ _E is based on equilibrium molalities from consideration of the equilibrium speciation into H₃BO₃,B(OH)₄⁻ and B₃O₃(OH)₄⁻. The stoichiometric equilibrium constants K _m for the aqueous speciation reactions were estimated. Two types of representations of the osmotic coefficients for the Li₂B₄O₇+LiCl+H₂O system are presented with ion-interaction models based on Pitzer’s equations with minor modifications: model (I) represents the φ _S data with six parameters based on considering the ion-interactions between three ionic species of Li⁺, Cl⁻, and B₄O₇²⁻, and model (II) for represents the φ _E data based on considering the equilibrium speciation. The parameters of models (I) and (II) are presented. The standard deviations for the two models are 0.0152 and 0.0298, respectively. Model (I) was more satisfactory than model (II) for representing the isopiestic data.     

Ion‐Pair SN2 Reaction of OH− and CH3Cl: Activation Strain Analyses of Counterion and Solvent Effects

We have theoretically studied the non‐identity S_N2 reactions of M_nOH^(n?1)+CH₃Cl (M⁺=Li⁺, Na⁺, K⁺, and MgCl⁺; n=0, 1) in the gas phase and in THF solution at the OLYP/6‐31++G(d,p) level using polarizable continuum model (PCM) implicit solvation. We want to explore and understand the effect of the metal counterion M⁺ and solvation on the reaction profile and the stereoselectivity of these processes. To this end, we have explored the potential energy surfaces of the backside (S_N2‐b) and frontside (S_N2‐f) pathways. To explain the computed trends, we have carried out analyses with an extended activation strain model (ASM) of chemical reactivity that includes the treatment of solvation effects.     

Activation Strain Analyses of Counterion and Solvent Effects on the Ion-Pair SN2 Reaction of and CH3Cl

We have computationally studied the bimolecular nucleophilic substitution (S_N2) reactions of M_nNH₂⁽ⁿ⁻¹⁾ + CH₃Cl (M⁺ = Li⁺, Na⁺, K⁺, and MgCl⁺; n = 0, 1) in the gas phase and in tetrahydrofuran solution at OLYP/6-31++G(d,p) using polarizable continuum model implicit solvation. We wish to explore and understand the effect of the metal counterion M⁺ and of solvation on the reaction profile and the stereochemical preference, that is, backside (S_N2-b) versus frontside attack (S_N2-f). The results were compared to the corresponding ion-pair S_N2 reactions involving F⁻ and OH⁻ nucleophiles. Our analyses with an extended activation strain model of chemical reactivity uncover and explain various trends in S_N2 reactivity along the nucleophiles F⁻, OH⁻, and , including solvent and counterion effects. © 2019 Wiley Periodicals, Inc.     

Potential energy curve of 1Σ+ Li+/He

The potential energy curve of the system Li⁺/He has been determined with moderately large basis sets for 0.5 ? r ? 10.0 a₀ both at the SCF level and including correlation. The present SCF results predict a deeper well (?0.00248 au) at a smaller r(3.66 a₀) compared with earlier calculations. Correlation deepens the well further (?0.00274 au), but pulls it inward slightly (3.63 a₀). In the repulsive part the calculated curve lies above the experimental one, especially at shorter distances. A similar behavior has been noted in the systems Li⁺/H₂, Li⁺/CO and Li⁺/N₂, suggesting that the experimental determinations may underestimate the interaction in this region by 10–20%.     

Ion‐Pair SN2 Substitution: Activation Strain Analyses of Counter‐Ion and Solvent Effects

The ion‐pair S_N2 reactions of model systems M_nF^n?1+CH₃Cl (M⁺=Li⁺, Na⁺, K⁺, and MgCl⁺; n=0, 1) have been quantum chemically explored by using DFT at the OLYP/6‐31++G(d,p) level. The purpose of this study is threefold: 1) to elucidate how the counterion M⁺ modifies ion‐pair S_N2 reactivity relative to the parent reaction F^?+CH₃Cl; 2) to determine how this influences stereochemical competition between the backside and frontside attacks; and 3) to examine the effect of solvation on these ion‐pair S_N2 pathways. Trends in reactivity are analyzed and explained by using the activation strain model (ASM) of chemical reactivity. The ASM has been extended to treat reactivity in solution. These findings contribute to a more rational design of tailor‐made substitution reactions.     

Theoretical study of interaction of 2,6-dithiopurine with Li+, Na+, K+, Be2+, Mg2+, and Ca2+ metal cations

The geometries of the complexes of Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ metal cations with different possible 2,6-dithiopurine anions (DTP) were studied. The complexes were optimized at the B3LYP level and the 6-311++G(d, p) basis set. The interactions of the metal cations at different nucleophilic sites of various possible 2,6-dithiopurine anions were considered. It was revealed that metal cations would interact with 2,6-dithiopurine anions in a bicoordinate manner. In the gas phase, the most preferred position for the interaction of Li⁺, Na⁺, and K⁺ cations is between the N₃ and S₂ sites, while all divalent cations Be²⁺, Mg²⁺, and Ca²⁺ prefer binding between the N₇ and S₆ sites of the corresponding 2,6-dithiopurine. The influence of aqueous solvent on the relative stability of different complexes has been examined using the Tomasi’s polarized continuum model. The basis set superposition error (BSSE) corrected interaction energy was also computed for complexes. The AIM theory has been applied to analyze the properties of the bond critical points (electron densities and their Laplacians) involved in the coordination between 2,6-dithiopurine anions and the metal cations. It was revealed that aqueous solution would have significant effect on the relative stability of complexes obtained by the interaction of 2,6-dithiopurine anions with Mg²⁺ and Ca²⁺ cations. The effect of metal cations on different NH and CS stretching vibrational modes of 2,6-dithiopurine has also been discussed.     

Isopiestic Determination of the Osmotic Coefficients and Pitzer Model Representation for the Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>+LiCl + H<Subscript>2</Subscript>O System at <Emphasis Type="Italic">T</Emphasis>=298.15 K

Isopiestic molalities and water activities have been measured for the Li₂B₄O₇+LiCl + H₂O system at T=298.15 K using an improved isopiestic apparatus. Two types of osmotic coefficients, φ _S and φ _E, were determined, where φ _S is based on the stoichiometric molalities of the solute Li₂B₄O₇(aq) and φ _E is based on equilibrium molalities calculated by consideration of the equilibrium speciation of Li₂B₄O₇ to partially form H₃BO₃, B(OH)₄⁻ and B₃O₃(OH)₄⁻. The stoichiometric equilibrium constant K _m for the aqueous speciation reaction was estimated. Two representations of the osmotic coefficients of Li₂B₄O₇ + LiCl + H₂O were made with Pitzer’s ion-interaction model. Model (1) involved representing the φ _S values with six parameters based on considering the ionic interactions between Li⁺, Cl⁻, and B₄O₇²⁻; and model (2) involved representing the φ _E values based on the calculated equilibrium speciation. Reasonable agreements were obtained between the experimental osmotic coefficient data and those calculated using the above models, with standard deviations of 0.075 and 0.0229, respectively, for these two models. The thermodynamic osmotic coefficients for the complex system containing polymeric boron anions and lithium cation was modelled and explained by use of Pitzer’s ion-interaction model, with minor modifications in combination with speciation reaction equilibria.     

Statistical evaluations of single-ion Gibbs energies of transfer

A statistical approach for the evaluation of single-ion Gibbs energies of transfer of the cations Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Ba²⁺, Ag⁺, Tl⁺, Cu⁺, Zn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ into 40 solvents based on the principal component analysis is presented. It is shown that the Gibbs energies of transfer depend both on the nature of the cation and on the donor site of the respective solvent molecule. Correlation of the data for the investigated cations required separating the solvents into subgroups according to their donor atoms in the solvent molecule. Gibbs energies of transfer into oxygen donor solvents could be correlated with the Born term [N _L(z _i e ₀)²/(8πε₀ r _i )]. Several cation parameters were investigated with respect to the transfer data into nitrogen and sulfur donor solvents. No correlations were found. Thus the use of cation parameters derived from the statistical analysis are proposed to account for the Gibbs energies of transfer into nitrogen and sulfur donor solvents. Published in Russian in Elektrokhimiya, 2008, Vol. 44, No. 1, pp. 9–17. The text was submitted by the authors in English.     

固体电解质Li9-nxMn+xN2Cl3(M=Na、Mg、Al)的合成及表征

高温固相反应合成了固体电解质Ｌｉ９－ｎｘＭ＾ｎ＋ｘＮ２Ｃｌ３（Ｍ＝Ｎａ、Ｍｇ、Ａｌ）。利用粉末Ｘ射线衍射测定样品结构,测定了离子电导率,分解电压和电子电导。得出掺杂可以提高快离子快离子导体材料Ｌｉ９Ｎ２Ｃｌ３中的Ｌｉ＾＋离子可以很大程度的提高其电导率。     

Complexation Properties of a Carbon-Bridged Cryptand with Metal Ions in Aqueous Solution at 25°C

Abstract

Thermodynamic quantities (log K, ΔH, and ΔS) for the interactions of a carbon-bridged cryptand with Li⁺, Na⁺, K⁺, Ca²⁺, Sr²⁺, Ba²⁺, and Pb²⁺ were determined at 25° C by calorimetric titration in aqueous solution. The cryptand forms complexes with Na⁺, Sr²⁺, Ba²⁺, and Pb²⁺ with log K ≤ 2. Complexation was not detected for Li⁺, K⁺, and Ca²⁺. Weak interactions with Li⁺ and K⁺ and a log K value of 2.4 for Na⁺ suggest that the cavity size of the cryptand is close to that of Na⁺ but too small for K⁺ and too large for Li⁺. The carbon-bridged cryptand selectively binds Sr²⁺ (log K = 3.2) over Ca²⁺ and Ba²⁺ by more than one order of magnitude.     

Complexing ability of pesticides and related compounds. Formation and stability in aqueous solution of H+ , Li+, Na+, K+, Mg2+ and Ca2+ phenoxyacetate complexes at different temperatures and ionic strengths

The formation constants of Li⁺, N⁺, K⁺, Mg²⁺ and Ca²⁺ phenoxyacetate complexes were determined potentiometrically using an (H⁺)-glass electrode at 10, 25, 37 and 45°C, at several ionic strengths, in the range 0.04?I? 0.9 mol 1^?1. Simple empirical equations for the dependence of the formation constants on ionic strength were derived. From the temperature coefficients, estimates of ΔH^o and ΔS^o were obtained.     

Properties and derivation of the fourth and sixth coefficients of the characteristic polynomial of molecular graphs—New graphical invariants

Some previously unknown relationships for determining the a ₄ and a ₆ coefficients of the characteristic polynomial for polycyclic aromatic hydrocarbons are presented for the first time. The structural information contained in these coefficients is more fully revealed. The equations derived for a ₄ and a ₆ allow one to determine the characteristic polynomial by inspection for many small molecular graphs. Some relationships for a ₈ and a ₁₀ are presented. The set of known graphical invariants (GI) or properties that remain unchanged in isomeric PAH6s is now shown to be GI={a ₄, a ₆+n ₀+2r ₆, a ₈ ^c , d _s+N_Ic, N_c, N_h, N_Ic+N_Pc, q, r}.Part VIII: A periodic table for polycyclic aromatic hydrocarbons     

Helium states II. Perturbation treatment of the ground state using the coordinates r< and r>

In an attempt to improve upon the convergence properties of the Hylleraas-Scherr-Knight-Midtdal perturbation expansion for the ground-state energies and eigenfunctions of the helium isoelectronic sequence, the term r is included in the zeroth-order Hamil-tonian. This term dominates the usual perturbation r for the ground state of these systems, and by removing it from H⁽¹⁾ we substantially reduce, in some sense, its size. In order to find the exact eigenfunction of the resulting zeroth-order Hamiltonian it was found necessary to include in H⁽⁰⁾ two additional terms involving the delta function δ(r₁ ? r₂) = δ(r_< ? r_>) and one such term in H⁽¹⁾. Approximate first- and second-order eigenfunctions are calculated variationally giving the energies to fifth order. The results are disappointing. The errors in the energies to fifth order for He, Li⁺, and Be²⁺, although quite small, are significantly larger than the corresponding errors in the more conventional perturbation treatment. Reasons for the failure to improve upon the earlier results are discussed. A “paradox” noted some time ago by Snyder and Parr is examined in an Appendix.     

Long-Range interaction coefficients between H,He+, He,and Li+

Using the new expression for the dynamic multipole polarizabilities in terms of effective oscillator strengths and effective transition energies derived from the variational procedure based on the total energy expansion in terms of induced multipole moments, we have calculated the long-range dispersion force coefficients and the leading relativistic correction to the long-range potential between H, He⁺, He, and Li⁺. We have in addition calculated the oscillator strength sum rules for the above systems. Our results are comparable with those obtained using both a hydrodynamic model to quantum mechanics and double perturbation theory.