The confined helium atom: An information–theoretic approach

In this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius $r_0$. As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of $r_0$. We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime ( a.u.).     

Application of dynamical Lie algebraic method to atom–diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.     

Iron atom–nanoparticles for interactional enhancing the electrocatalytic reaction activity in Li-S batteries

The undesirable shuttle effect and sluggish redox kinetics of polysulfides seriously result in low sulfur utilization and poor capacity retention. Here, an integrated strategy is proposed by rational designing multifunctional architecture to manipulate the redox kinetics of polysulfides, specifically, by employing iron atoms (Fe-As) and iron-species nanoparticles (Fe-NPs) co-embedded nitrogen-doped carbon nanotube (Fe-NCNT) as catalyst and host for sulfur. The synergistic cooperation of Fe-As and Fe-NPs provides efficient active sites to facilitate the diffusion, strengthen the affinities, and promote the conversion reactions for polysulfides. Furthermore, the NCNT not only offers practical Li⁺ transport pathways but also immobilize the polysulfides effectively. Benefiting from these merits, the Fe-NCNT/S electrodes exhibit high initial specific capacity of 1502.6 mAh/g at 0.1 C, outstanding rate performance (830 mAh/g at 2 C), and good cycling performance (597.8 mAh/g after 500 cycles with an ultralow capacity fading rate of 0.069% per cycle). This work features the distinct interaction of iron atom-nanoparticles on facilitating immobilization-diffusion-transformation process of polysulfides, and it also expected to pave the way for the application in practical Li-S batteries.     

Hylleraas–Configuration Interaction calculations on the 11S ground state of helium atom

Hylleraas–Configuration Interaction (Hy–CI) calculations on the ground 1¹S state of helium atom are presented using s-, p-, d-, and f-Slater orbitals of both real and complex form. Techniques of construction of adapted configurations, optimization of the orbital exponents, and structure of the wave function expansion are explored. A new method to evaluate the two-electron kinetic energy integrals occurring in the Hy–CI method has been tested in this work and compared with other methods. The non-relativistic Hy–CI energy values are ≈10 picohartree accurate, about 2.2 × 10^?6 cm^?1. The Hy–CI calculations are compared with Configuration Interaction (CI) and Hylleraas (Hy) calculations employing the same orbital basis set, same computer code, and same computer machines. The computational required times are reported.     

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd–rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment. Received: 20 April 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Cationic iridium-catalyzed enantioselective activation of secondary sp3 C–H bond adjacent to nitrogen atom

A cationic Ir(I)–tolBINAP complex catalyzed an enantioselective C–C bond formation, which was initiated by secondary sp³ C–H bond cleavage adjacent to nitrogen atom. A wide variety of 2-(alkylamino)pyridines and alkenes were selectively transformed into the corresponding chiral amines with moderate to almost perfect enantiomeric excesses. Alkynes were also investigated as coupling partners. The effect of alkyl structure in substrates and directing groups were studied. This transformation represents the first example of a highly enantioselective C–H bond activation of a methylene group, not at allylic or benzylic position.     

Sol–gel chemistry: evidence of redistributionat silicon atom induced by NaOH as catalystduring ageing

The influence of the ageing conditions on the properties of organic-inorganic hybrid solids obtained by sol–gel route using NaOH catalysis has been studied. The cases of 1,4-bis(trimethoxysilyl)benzene 1 (‘rigid’ precursor) and 1,4-bis(trimethoxysilylethyl)benzene 2 (‘more flexible’ one) have been investigated. The ²⁹Si CP MAS NMR spectra of the silsesquioxanes clearly reveal that Si–O–Si bond cleavage and redistribution reactions occur when the ageing time is increased or is performed at higher temperatures. This particular behaviour observed only with NaOH is of importance in the choice of the catalyst.     

What does shape a topological atom?

In this pedagogical communication after demonstrating the legitimacy for using the quantum theory of atoms in molecules (QTAIM) to non-Coulombic systems, Hookean H₂ ⁺/H₃ ²⁺ species are used for AIM analysis. In these systems, in contrast to their Coulombic counterparts, electron density is atom-like and instead of expected two/three topological atoms, just a single topological atom emerges. This observation is used to demonstrate that what is really “seen” by the topological analysis of electron densities is the clustering of electrons. The very trait of monotonic decay of electron density around the “centers” of clustering guarantees the appearance of topological atoms as basin of attraction of the gradient vector field of the electron density. Although observations with Hookean molecules may seem disappointing at first glance, a careful reasoning points to the fact that the QTAIM methodology is extendable to novel domains, by a knowledge of the morphology of underlying densities, beyond the typical Coulombic systems.     

A Hartree–Fock approach to the Steklov eigenproblem for a two-electron atom in an s2 state

Two decades ago, in a brief note (Hinze and Hamacher, J Chem Phys 92:4372–4373, 1990), Hinze and Hamacher made a conjecture that the Hartree–Fock method may be applied to determine approximate solutions to a non-standard (Steklov-type) eigenproblem encountered in the non-relativistic eigenchannel R-matrix method. Later, this thread was mathematically pursued further by the present author (Szmytkowski, Phys Rev A 61:022725, 2000; erratum 66:029901, 2002). In the present paper, which is dedicated to the memory of Professor Jürgen Hinze, we make an attempt to elucidate the idea underlying the aforementioned works. To focus on the essence and avoid obscuring mathematical details, we consider the simplest system which is a two-electron atom in an s² state. Variational principles for pertinent Steklov eigenvalues (i.e., eigenvalues of a two-electron Dirichlet-to-Neumann integral operator) and for their reciprocals (i.e., eigenvalues of a two-electron Neumann-to-Dirichlet integral operator) are used to derive a radial integro-differential eigensystem of a Hartree–Fock type, in which both a Lagrange multiplier in an integro-differential equation and a Steklov eigenvalue appearing in a boundary condition are to be determined simultaneously at a fixed total energy of the atom. Mathematical similarities and (particularly) differences between the problem considered here and that of a spherically confined two-electron atom are highlighted.     

Photoelectrochemical oxygen atom transfer enabling efficient selective oxygenation

Photoelectrochemical(PEC)technique represents a promising approach to chemical transformation by harvesting sustainable solar energy.Despite the wide applications of PEC systems such as environmental remediation and solar energy conversion,the reported PEC reactions are dominated by the radical-based processes that are initiated by the single electron transfer between photo-induced carriers and adsorbed species on photoelectrode surface[1,2].For instance,hydroxyl radicals are often involved in the PEC oxidation reactions.As well known,it is a grand challenge to control the formation and evolution rates of radicals,which inevitably leads to the unsatisfactory product selectivity of PEC reactions.Naturally,such a circumstance brings about a question to the research community whether a different mechanism can be established to sustain efficient and selective oxygenation.Recently,based on their previous findings on PEC water oxidation[3,4],Zhao and coworkers[5]reported that many substrates can be oxidized in an oxygen atom transfer(OAT)pathway,a non-radical two electron process,to oxygenated products byα-Fe2O3 photoanodes.     

What is an atom in a molecule?

The derivation of the Hirshfeld atoms in molecules from information theory is clarified. The importance for chemistry of the concept of atoms in molecules (AIM) is stressed, and it is argued that this concept, while highly useful, constitutes a noumenon in the sense of Kant.     

Perspective on “Semiclassical theory of atom–diatom collisions: path integrals and the classical S matrix”

Miller's papers on classical S-matrix theory had a profound influence on the understanding of inelastic atom–molecule collisions. This perspective discusses the historical background, the content, some applications, and new developments. Received: 26 February 1999 / Accepted: 5 April 1999 / Published online: 21 June 1999     

H atom transfer of collinear OH…O system

A quantum mechanical calculation was performed to study the hydrogen atom transfer of collinear OH…O/OD…O system, for which Delves' coordinates and R- matrix propagation method were applied in a Melius-Blint potential energy surface. The calculation result showed that the state-state H atom transfer probability comported strong oscillation phenomena and collision delay time of the title system was in the fs-ps time scale. The kinetic isotope effect was calculated in this work too.     

Is the dominance of even carbon atom molecules odd?

The unexpected higher frequency of occurrence of even carbon atom molecules over odd carbon atom ones revealed through previous database searches is shown to be a consequence of the predominantly bimolecular nature of bond formation processes and the fact that combinations of odd and odd as well as even and even atom molecules result in even atom products whereas odd and even atom molecule combinations alone lead to odd atom products.     

Excited state intramolecular hydrogen atom transfer of phenylethynyl-substituted 2′-hydroxychalcones

(E)-1-[2-Hydroxy-4-(phenylethynyl)phenyl]-3-[4-(phenylethynyl)phenyl]prop-2-en-1-one (1), (E)-1-[2-hydroxy-4-(phenylethynyl)phenyl]-3-phenylprop-2-en-1-one (2), and (E)-1-(2-hydroxyphenyl)-3-[4-(phenylethynyl)phenyl]prop-2-en-1-one (3), which belong to a new class of 2′-hydroxychalcones with phenylethynyl group(s) at the para position of the phenyl ring, were synthesized, and their photochemical properties were investigated. The lowest energy absorption band of 1 peaks at a longer wavelength (383 nm) with a much larger molar extinction coefficient (5.0 × 10⁴ M ^?1 cm^?1) than that of the parent 2′-hydroxychalcone (2′HC) (2.0 × 10⁴ M ^?1 cm^?1 at 318 nm). Upon photoexcitation, all three compounds underwent excited-state intramolecular hydrogen atom transfer (ESIHT) to produce an excited tautomer that emitted fluorescence with a large Stokes shift in the longer wavelength region at 600–700 nm. The quantum yield of the tautomer fluorescence of 1 was not high at 298 K (Φ _f = 9.1 × 10^?5), but was highest among 2′HC and its analogues. The Φ _f values of 1–3 increased 10–30 fold upon reducing the temperature from 298 to 77 K.     

Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

We present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

     

Photochemical naphthylation at(α-carbon atom of carbonyl and its equivalences

The photostimulated reaction of halonaphthalene with a series of carbanions derived from,propionic acid derivatives in liquid ammonia led to the naphthylation at a-carbon of the carbanions inan isolated yield ranging from 25％ to 86％.In all cases,the dehalonaphthalenes were found to,be by-products and the reaction was inhibited by p-dinitrobenzere.An electron transfer from thecarbanion to the halonaphthalene followed by ejection of halogen led to naphtbyl radical,as predictedby comparing the LUMOs of the carbanions and the halonaphthalenes,was involved in the process.Absence of the alkylnaphthalene and 1,2-dinaphthylalkane in the products indicates the smoothelectron transfer between(Naph-Nu)~+ and Naph-X.C-vs.O-naphthylation is fully addressed interms of MNDO calculations and acid-base principle.     

Analysis of cation—macrocycle complexation by fast atom bombardment mass spectrometry

Abstract

Fast atom bombardment mass spectrometry has been used to analyse the cation complexation behaviour of a systematically varied array of crown and lariat ethers having one or two sidearms. Sandwich complexation. apparent when the cation is somewhat larger than the crown cavity, is observed for several systems but the presence of donor-group-containing sidearms in lariat ethers suppresses this phenomenon. Calcium cation complexation proved to be especially interesting.