A proper account of core-polarization with pseudopotentials: single valence-electron alkali compounds

A polarization potential is incorporated into semi-empirical and Hartree-Fock adjusted pseudopotentials. For molecules, the pseudopotentials become geometry-dependent. The omission of this effect has been the reason for too smallR_e values in earlier semi-empirical work. Very accurate results are obtained for the dimer and hydride ions of alkali elements up to K.     

On the Activation of Methane and Carbon Dioxide by [HTaO]+ and [TaOH]+ in the Gas Phase: A Mechanistic Study

The thermal reactions of [Ta,O,H]⁺ with methane and carbon dioxide have been investigated experimentally and theoretically by using electrospray ionization mass spectrometry (ESI MS) and density functional theory calculations. Although the activation of methane proceeds by liberation of H₂, the activation of CO₂ gives rise to the formation of [OTa(OH)]⁺ under the elimination of CO. Computational studies of the reactions of methane and carbon dioxide with the two isomers of [Ta,O,H]⁺, namely, [HTaO]⁺ and [Ta(OH)]⁺, have been performed to elucidate mechanistic aspects and to explain characteristic reaction patterns.     

An unusual eight‐coordinated copper complex: bis­(4,7‐diphenyl‐1,10‐phenanthroline)dinitratocopper(II)

In the title monomer, [Cu(NO₃)₂(C₂₄H₁₆N₂)₂], the copper(II) cation is eight‐coordinate within an octa­hedral‐like polyhedron. The coordination polyhedron is formed by two chelating diphenyl­phenanthroline groups that define the highly distorted CuN₄ equatorial plane and two weakly bound bidentate (chelating) nitrate groups in the apical or axial positions. The complex crystallizes in the monoclinic space group C2/c; a twofold axis passes through the copper(II) cation and bis­ects the two nitrate ligands. This gives the mol­ecule C₂ point‐group symmetry, rendering only half of the mol­ecule independent.     

Hyperbolic-like solutions for singular Hamiltonian systems

We study the existence of unbounded solutions of singular Hamiltonian systems: where is a potential with a singularity. For a class of singular potentials with a strong force , we show the existence of at least one hyperbolic-like solutions. More precisely, for given and , we find a solution q(t) of (*) satisfying Received October 1998     

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.     

An electron localization function and catastrophe theory analysis on the molecular mechanism of gas-phase identity SN2 reactions

A set of four reactions, XCH₃+X^? (X=F, Cl, Br) and ClSiH₃+Cl^?, is investigated by means of the joint use of the electron localization function (ELF) and catastrophe theory (CT) analysis in order to obtain new insights into the bond breaking/forming processes for identity S_N2 gas-phase reactions. Using DFT calculations at the OLYP/6-311++G(d,p) level, the effect of nucleophile (F, Cl, and Br anions) and the role of reacting centers (C or Si) on the reaction mechanisms are investigated. The charge-shift character of carbon–halogen bonds is studied by determination of the weights of the Lewis resonance structures. In all S_N2 reactions at the carbon atom, there is a progressive reduction on the covalent character of the C–X bond from the reactant complex (0.41, 0.57, 0.58 for F, Cl, and Br, respectively) until the bond-breaking process, occurring before the transition structure is reached. On the other hand, the Si–Cl bond maintains its degree of covalent character (0.51) from the isolated fragments to the formation of a stable transition complex, presenting two silicon–chlorine charge-shifted bonds. The analysis of the ELF topology along the reaction path reveals that all reactions proceed via the same turning points of fold-type but the order is inverted for reactions taking place at C or Si atoms.     

Electronic structure of first and second row atoms under harmonic confinement

Atoms under pressure undergo a number of modifications of their electronic structure. Good examples are the spontaneous ionization, stabilization of excited-state configurations, and contraction of atomic-shells. In this work, we study the effects of confinement with harmonic potentials on the electronic structure of atoms from H to Ne. Dynamic and static correlation is taken into account with coupled cluster with single and double excitations and CASSCF calculations. Because the strength of harmonic confinement cannot be translated into pressure, we envisioned a “calibration” method to transform confinement into pressure. We focused on the effect of confinement on: (a) changes of electron distribution and localization within the K and L shells, (b) confinement-induced ionization pressure, (c) level crossing of electronic states, and (d) correlation energy. We found that contraction of valence and core-shells are not negligible and that the use of standard pseudopotentials might be not adequate to study solids under extreme pressures. The critical pressure at which atoms ionize follows a periodic trend, and it ranges from 28 GPa for Li to 10.8 TPa for Ne. In Li and Be, pressure induces mixing of the ground state configuration with excited states. At high pressure, the ground states of Li and Be become a doublet and a triplet with configurations 1s²2p and 1s²2s2p, respectively, which could change the chemistry of Be. Finally, it is observed that atoms with fewer electrons correlation increases, but for atoms with more electrons, the increasing of kinetic energy dominates over electron correlation.     

Equilibrium of an Inverted Mathematical Double-Link Pendulum with a Follower Force

A discrete model of an elastic pendulum with a follower force is studied. This model is an inverted mathematical two-link pendulum with viscoelastic hinges. It is shown that divergent bifurcations are possible for some absolute values of the follower force and the stiffness of the restraint of the pendulum's upper end. As a result, the vertical position of the equilibrium becomes unstable and two new nonvertical stable equilibrium states (fork bifurcation) occur.