Leading‐order behavior of the correlation energy in the uniform electron gas

We show that, in the high‐density limit, restricted Møller‐Plesset (RMP) perturbation theory yields E = π^?2(1 ? ln 2) ln r_s + O(r) for the correlation energy per electron in the uniform electron gas, where r_s is the Seitz radius. This contradicts an earlier derivation which yielded E = O(ln|ln r_s|). The reason for the discrepancy is explained. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Redshifts and blueshifts of OH vibrations

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlations between these quantities, are presented for a water molecule and an OH^? ion in a uniform electric field of varying field strength. It is explained why a bound H₂O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH^? ion either a downshift or an upshift. The frequency-field variation is well accounted for by the expression Δν_OH ∝ ?E_∥·(dμ/dr_OH + 1/2 · ?μ/?r_OH). A frequency maximum occurs at the field strength where ?μ/?r_OH ～ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/dr_OH is negative (this is the situation for OH^?), and (2) the maximum frequency falls at a negative field when dμ/dr_OH is positive (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/dr_OH and ?μ/?r_OH. Correlation curves between the external linear force constant, k^ext, and r_OH,e are closely linear over the whole field range studied here, whereas the frequency vs. r_OH,e and force constants vs. r_OH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the v vs. r_OH,e curves has a slope of ～ ?16,000 cm^?1/Å. © 1993 John Wiley & Sons, Inc.     

Redshifts and blueshifts of OH vibrations

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlation between these quantities, are presented for a water molecule and an OH^? ion in a uniform electric field of varying field strength. It is explained why a bound H₂O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH^?1 ion, either a downshift or an upshift. The frequency-field variation is well accounted for by the expression Δν_OH α ?E‖ · (d μ/dr_OH + 1/2 · ?μ/?r_OH). A frequency maximum occurs at the field strength where ?μ‖^tot/?r_OH ～ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/dr_OH is positive (this is the situation for OH^?), and (2) the maximum frequency falls at a negative field when dμ/dr_OH is negative (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/dr_OH and ?μ/?r_OH. Correlation curves between the external linear force constant, k^ext, and r_OH,e are closely linear over the whole field range studied here, whereas the frequency vs. r_OH,e and force constants vs. r_OH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the ν vs. r_OH,e curves has a slope of ～ ? 16,000 cm^?1/Å. © 1993 John Wiley & Sons, Inc.     

Convergence accelerator approach for the evaluation of some three‐electron integrals containing explicit rij factors

A simplified analysis is presented for the evaluation of the three‐electron one‐center integrals of the form ∫rrrrrred r ₁d r ₂d r ₃, for the cases i, j, k, ≥−2, l=−2, m≥−1, n≥−1. These integrals arise in the calculation of lower bounds for energy levels and certain relativistic corrections to the energy when Hylleraas‐type basis sets are employed. Convergence accelerator techniques are employed to obtain a reasonable number of digits of precision, without excessive CPU requirements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 93–99, 1999     

Charge distributions and chemical effects. XXXIV. Concepts involved in an approximate,but accurate,description of bond energies

The concepts underlying the definition of bond energies in terms of potentials at the nuclei are outlined. The theory is rooted, first, in a definition of the energy, E_i, of “atom” i in the molecule in terms of the potential energy, V(i, mol), of nucleus Z_i in the field of all the electrons and nuclei of the molecule: E_i = K V(i, mol). The K parameter, which is not required to be a constant in the derivation of the energy expression describing the contribution of an ij bond, turns out to be virtually constant for each atomic species—a situation which is exploited in numerical applications. Second, the Hellmann—Feynman theorem is applied in the calculation of the derivative, δΔE/δZ_i, of the atomization energy, ΔE, using (i) the exact quantum-chemical definition of ΔE and (ii) the view that ΔE is the sum of bond energy contributions, ε_ij, plus a small interaction between nonbonded atoms. The individual bond energies derived in this manner necessarily depend on local charges at the bond-forming atoms. Numerical applications illustrate how this new bond-energy formula provides a simple link between typical saturated, olefinic, acetylenic, and aromatic hydrocarbons.     

Atomic integrals containing rrr with λ, μ, ν ≥ −2

In this paper, the efficient evaluation of the atomic integrals I =∫rrrrrre^{?αr1?βr2?γr3}dτ with one or two factors r is described. These integrals are necessary for a lower-bound calculation for Li-like systems using the method of variance minimization or Temple's formula. © 1993 John Wiley & Sons, Inc.     

The kinetics of the interaction of peroxy radicals. I. The Tertiary Peroxy Radicals

Existing data on the self-reactions of tertiary peroxy radicals RO₂ has been reanalyzed and corrected to deduce Arrhenius parameters for both termination and nontermination paths. For R = t-Butyl, these are logk_t(M^?1sec^?1) = 7.1 - (7.0/θ) and logk_nt(M^?1sec^?1) = 9.4 - (9.0/θ), respectively, different from those recommended by other authors. The higher magnitudes observed for termination processes of tertiary peroxy radicals like those of cumyl and 1,1-diphenylethyl have been discussed in terms of a much greater cage recombination of cumyloxy radicals as contrasted with t-butoxy radicals. It is shown that for benzyl peroxy radicals, the R—O bond dissociation energy is sufficiently low (18–20 kcal) that reversible dissociation into R^˙ + O₂ opens a competing second-order path to fast recombination R^˙ + RO → ROOR. This path is probably not important for cumyl peroxy radicals under usual experimental conditions but can become important for 1,1-diphenyl ethyl peroxy radicals at (O₂) < 10^?3M. At very low RO concentrations (<10^?5M), in the absence of added O₂, an apparent first-order disappearance of RO can occur reflecting the rate determining breaking of the cumyl—O bond followed by the second step above. The thermochemistry of RO is used to show that the reaction of R₂O₄ → 2RO + O₂ must be concerted and cannot proceed via RO which is too unstable and cannot form even from RO^˙ + O₂.     

Evaluation of two‐center,three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

An algorithm for evaluation of two‐center, three‐electron integrals with the correlation factors of the type rr and rrr as well as four‐electron integrals with the correlation factors rrr and rrr in the Slater basis is presented. This problem has been solved here in elliptical coordinates, using the generalized and modified form of the Neumann expansion of the interelectronic distance function r for k ≥ ?1. Some numerical results are also included. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Slater's nonlocal exchange potential and beyond

The local density approximation (LDA) to the exchange potential V_x( r ), namely the ρ^1/3 electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density ? _x( r ), the Slater (Sl) nonlocal exchange potential V( r ) is defined by 2? _x( r )/ρ( r ). In spherical atomic ions, say the Be or Ne‐like series, this form V( r ) already has the correct behavior in both r → 0 and r → ∞ limits when known properties of the exchange energy density ? _x( r ) and the ground‐state electron density ρ( r ) are invoked. As examples, some emphasis will first be given to the use of the so‐called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both ? _x( r ) and ρ( r ) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two‐level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential V( r ) is a valuable starting point, even though it needs appreciable quantitative corrections reflecting directly atomic shell structure. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of torsional stiffness upon temperature response of a polymeric chain

The influence of torsional stiffness upon the temperature dependence of the mean square end-to-end polymer chain distance 〈r〉 was studied parametrically for six different polymer chain models. The equations for 〈r〉, expressed in terms of the torsional potential energy, were differentiated with respect to temperature and the resulting equations were evaluated numerically. The magnitudes and locations of the secondary barrier heights, angular location and magnitudes of the energy minima, angular location of the maximum barrier U₀, spacing of the extrema, and the number of extrema were all found to play a significant role in the value of the predicted thermal expansion coefficients. The coefficients were also found to critically depend upon the relative energy ratio and were usually a highly nonlinear function of this ratio. Transitions between positive and negative values of the thermal expansion coefficients were found to exist and to depend upon the torsional potential shape, energy ratio, and the polymer chain model.     

Crystal Structures of {[Cd(phen)](C6H8O4)3/3} and {[Cd(phen)](C7H10O4)3/3} · 2H2O with C6H10O4 = Adipic Acid and C7H12O4 = Pimelic Acid

Two coordination polymers {[Cd(phen)](C₆H₈O₄)_3/3} ( 1 ) and {[Cd(phen)](C₇H₁₀O₄)_3/3} · 2H₂O ( 2 ) were structurally characterized by single crystal X‐ray diffraction methods. In 1 (C2/c (no. 15), a = 16.169(2)Å, b = 15.485(2)Å, c = 14.044(2)Å, β = 112.701(8)°, U = 3243.9(7)ų, Z = 8), the Cd atoms are coordinated by two N atoms of one phen ligand and five O atoms of three adipato ligands to form mono‐capped trigonal prisms with d(Cd‐O) = 2.271‐2.583Å and d(Cd‐N) = 2.309, 2.390Å. The [Cd(phen)] moieties are bridged by adipato ligands to generate {[Cd(phen)](C₆H₈O₄)_3/3} chains, which, via interchain π—π stacking interactions, are assembled into layers. Complex 2 (P1¯(no. 2), a = 9.986(1)Å, b = 10.230(3)Å, c = 11.243(1)Å, α = 66.06(1)°, β = 87.20(1)°, γ = 66.71(1)°, U = 955.7(2)ų, Z = 2) consists of {[Cd(phen)](C₇H₁₀O₄)_3/3} chains and hydrogen bonded H₂O molecules. The Cd atoms are pentagonal bipyramidally coordinated by two N atoms of one phen ligand and five O atoms of three pimelato ligands with d(Cd‐O) = 2.213—2.721Å and d(Cd‐N) = 2.329, 2.372Å. Through interchain π—π stacking interactions, the {[Cd(phen)](C₇H₁₀O₄)_3/3} chains resulting from [Cd(phen)] moieties bridged by pimelato ligands are assembled in to layers, between which the hydrogen bonded H₂O molecules are sandwiched.     

Hylleraas–CI with linked correlation terms

Hylleraas–CI calculations with linked correlation terms of the form rr are discussed. Formulas for the integration of the angular part are deduced and a method for the reduction of the radial part to auxiliary integrals is given. In the case of the Li atom, it is shown that for the calculation of the ground-state energy an ansatz for the wave function with at most two factors rr is sufficient to achieve spectroscopic accuracy. © 1993 John Wiley & Sons, Inc.     

Motion of a particle in a ring-shaped potential: An approach via a nonbijective canonical transformation

The problem of a particle in the three-dimensional ring-shaped potential ησ²(2a₀/r ? ηa/r² sin² θ)ε₀ introduced by Hartmann is transformed into the problem of a coupled pair two-dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring-shaped potential is obtained in a straightforward way from the one for the two-dimensional potential — (4Eρ² + η²σ²a ε₀/ρ²).     

Conformational Analysis and Chromic Acid Oxidation. Oxidation Rates and Equilibrium Constants of Epimeric Alcohols

The linear free energy relationship of Sicher for relative reactivity towards chromic acid oxidation (ΔΔG) as a function of thermodynamic stability (ΔG) has been reexamined with 23 pairs of epimeric alcohols. The plot of ΔG vs. ΔG has a slope of 0.8, a correlation coefficient of 0.97 and a standard deviation of 0.23 kcal/mol on ΔΔG_Ox. The limitations of the relationship and the exceptions are discussed.     

Kinetics and mechanism of the reaction of aqueous sulfite with N-chloroalanylalanylalanine

The rate of the reaction of aqueous sulfite with the N-chloropeptide N-chloroalanylalanylalanine has been studied as a function of pH, temperature, and ionic strength. The results of this work suggest that the mechanism of the reaction involves the interaction of the neutral chloramine with the three ionic forms of sulfite, SO, HSO, and H₂SO₃, with the rate of reaction increasing rapidly with increasing protonation. The estimated second-order rate constants for each ionic species as a function of temperature are where the activation energies are in units of cal/mol.     

Empirical penetration functions and two-center electron repulsion integrals for semiempirical calculations of electronic structure

Explicit functional forms for both the two-electron Coulomb integral, (aa∣bb), and the one-center core–orbital integrals, Z (aa∣Z_A), are derived which permit the penetration integrals to be fully derived and calculated. With these forms the ³Σ of the H₂ molecule is unstable. These forms are generalized so that they are suitable for optimizing semiempirical predictions of experimental one-electron properties.     

Temperature and pressure effects on the kinetics of the Bromate ion-iodide ion-L-ascorbic acid clock reaction

The kinetics of the bromate ion-iodide ion-L-ascorbic acid clock reaction was investigated as a function of temperature and pressure using stopped-flow techniques. Kinetic results were obtained for the uncatalyzed as well as for the Mo(VI) and V(V) catalyzed reactions. While molybdenum catalyzes the BrO-I^? reaction, vanadium catalyzes the direct oxidation of ascorbic acid by bromate ion. The corresponding rate laws and kinetic parameters are as follows. Uncatalyzed reaction: r₂ = k₂[BrO] [I^?][H⁺]², k₂ = 38.6 ± 2.0 dm⁹ mol^?3 s^?1, ΔH? = 41.3 ± 4.2 kJmol^?1, ΔS? = ?75.9 ± 11.4 Jmol^?1 K^?1, ΔV? = ?14.2 ± 2.9 cm³ mol^?1. Molybdenum-catalyzed reaction: r′₂ = k₂[BrO] [I^?] [H⁺]² + k_Mo[BrO] [I^?] [ H⁺]²[M₀(VI)], k_Mo = (2.9 ± 0.3)10⁶ dm¹² mol^?4 s^?1, ΔH? = 27.2 ± 2.5 kJmol^?1, ΔS? = ?30.1 ± 4.5 Jmol^?1K^?1, ΔV? = 14.2 ± 2.1 cm³ mol^?1. Vanadium-catalyzed reaction: r′₁ = k_V[BrO] [V(V)], k_V = 9.1 ± 0.6 dm³ mol^?1 s^?1, ΔH? = 61.4 ± 5.4 kJmol^?1, ΔS? = ?20.7 ± 3.1 Jmol^?1K^?1, ΔV? = 5.2 ± 1.5 cm³ mol^?1. On the basis of the results, mechanistic details of the BrO-I^? reaction and the catalytic oxidation of ascorbic acid by BrO are elaborated. © 1995 John Wiley & Sons, Inc.     

Synthese und Kristallstruktur von [N(Hex)4][Cu2(CN)3]

Synthesis and Crystal Structure of [N(Hex)₄] [Cu₂(CN)₃] [N(Hex)₄][Cu₂(CN)₃] has been prepared by solvothermal reaction of CuCN with Tetra‐n‐hexylammoniumiodide in acetone. The crystal structure is built up by condensed (CuCN)₆ and (CuCN)₇ rings, forming a zeolith type cyanocuprate(I) framework [Cu₂(CN)₃^—]. Space group R3; α = 44.482(6), c = 21.283(4) Å, V = 36471(9) ų; Z = 9.     

The elastic potential function of slightly compressible rubberlike materials

In order to obtain an analytical expression for the stored energy function W of slightly compressible rubberlike materials, two recent results are used to obtain a unified expression where Γ_i are a new set of invariants, and H(Γ₁,Γ₂) is the shear part of the stored energy function which is now assumed to be a separate symmetric function of the modified stretch ratio, λ = λ_i/I, i.e., Various analytical forms of h(λ) are proposed. Also, a straightforward transformation technique is formulated such that one can easily relate the stress-strain relation in terms of modified stretch ratio λ to the new invariants Γ_i. Thus, by a combination of the above equations and the transformation technique, one may readily determine the elastic strain energy function of slightly compressible materials from careful measurements of the volume change in multiaxial deformations.