Average inner product sums of electron linear momenta for atoms and ions

From the second moments of the electron-pair densities in momentum space, accurate Hartree–Fock values of the average inner product sum 〈∑ _i<j p _i ·p _j 〉 of electron linear momenta are evaluated for the 102 neutral atoms from He to Lr, the 53 singly charged cations from Li⁺ to Cs⁺, and the 43 stable anions from H⁻ to I⁻ in their experimental ground states. The present results are new for 38 species and improve the literature values for 68 species. Received: 18 July 2002 / Accepted: 4 September 2002 / Published online: 8 November 2002 Acknowledgement. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: H. Matsuyama e-mail: hisashi@mmm.muroran-it.ac.jp     

Ground-state multiplicities of atoms and positive ions

A procedure is developed to establish the ground-state multiplicities for atoms with any number of electrons. The procedure is applied to two- and three-electron systems. The results are that all neutral and positive two- and three-electron atoms have singlet (S=0) and doublet (S=1/2) ground states, respectively. Received: 10 August 1999 / Accepted: 6 October 1999 / Published online: 15 December 1999     

Electrostatic potentials and fields from density expansions of deformed atoms in molecules

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.     

Isoelectronic changes in energy of quark atoms and molecules via the Levy equation

Summary Z-transition state calculations based on the Levy equation suggest that the isoelectronic changes in energy of quark atoms,Q, (ordinary atoms with extra nuclear charge in units of ±1/3 and/or ±2/3) can be expressed quantitatively in terms of the electrostatic potential at the nucleus of an isoelectronic ordinary atom. Numerical tests within the local density functional theory are presented for the quark atoms of Li-F. Theab initio MO (molecular orbital) calculations using STO-5G basis on the C₂ molecule and its quark derivatives lead to similar conclusions.     

Different van der Waals radii for organic and inorganic halogen atoms: a significant improvement in IMOMM performance

The discrepancies between X-ray and integrated molecular orbital molecular mechanics computed geometries for Os(H)₂Cl₂(PⁱPr₃)₂ and Ir(H)₂Cl(P^tBu₂ Ph)₂ are explained by the inadequacy of the default molecular mechanics van der Waals radii for halogen elements. A simple procedure is proposed for the calculation of corrected van der Waals radii, and the application of the corrected radius for chloride is shown to improve substantially the results for the systems under test. Received: 25 February 1997 / Accepted: 7 April 1997     

Properties of atoms in electronically excited molecules within the formalism of TDDFT

The topological analysis of the electron density for electronic excited states under the formalism of the quantum theory of atoms in molecules using time‐dependent density functional theory (TDDFT) is presented. Relaxed electron densities for electronic excited states are computed by solving a Z‐vector equation which is obtained by means of the Sternheimer interchange method. This is in contrast to previous work in which the electron density for excited states is obtained using DFT instead of TDDFT, that is, through the imposition of molecular occupancies in accordance with the electron configuration of the excited state under consideration. Once the electron density of the excited state is computed, its topological characterization and the properties of the atoms in molecules are obtained in the same manner that for the ground state. The analysis of the low‐lying singlet and triplet vertical excitations of CO and C₆H₆ are used as representative examples of the application of this methodology. Altogether, it is shown how this procedure provides insights on the changes of the electron density following photoexcitation and it is our hope that it will be useful in the study of different photophysical and photochemical processes. © 2014 Wiley Periodicals, Inc.     

One and two body densities for excited states of the helium confined atom

A study of the first excited states of the helium atom confined under impenetrable spherical walls is carried out. Both single particle and two body, intracule and extracule, densities are constructed. Crossing levels and Hund's rule are analyzed in terms of the contribution to the total energy from kinetic, electron–nucleus, and electron–electron energies. A study about the behavior of the single particle and two body densities is carried out. The Multiconfiguration Parameterized Optimized Effective Potential method is employed with a cut-off factor to account for Dirichlet boundary conditions. Single particle density is analytically constructed whereas the Monte Carlo algorithm is used to calculate two body densities.     

Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates

The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination.     

Radial and angular correlation in heliumlike ions

In the framework of nonrelativistic variational formalism a new type of basis set is proposed, to estimate separately the effect of radial and angular correlations on the ground‐state energy for helium isoelectronic sequence H^? to Ar¹⁶⁺. Effect of radial correlation is incorporated by using multiexponential functions arising from product basis sets suitably formed out of Slater‐type one‐particle orbitals. The angular correlation can be switched on by incorporating an expansion in terms of basis involving interparticle coordinates. With a set of six‐term Slater‐type one‐particle basis and five‐term interparticle expansion, the ground‐state energy of helium is estimated as ?2.9037236 (a.u.) compared with the multiterm variational estimates ?2.9037244 (a.u.) due to Pekeris and Thakkar and Smith and Drake. Matrix elements of different operators in the ground state have been calculated and found to be in good agreement with available accurate results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Variational Monte Carlo calculations for some cations and anions of the first‐row atoms using explicitly correlated wave functions

The variational Monte Carlo method is applied to calculate ground‐state energies of some cations and anions of the first‐row atoms. Accurate values providing between 80 and 90% of the correlation energy are obtained. Explicitly correlated wave functions including up to 42 variational parameters are used. The nondynamic correlation due to the 2s ? 2p near degeneracy effect is included by using a multideterminant wave function. The variational free parameters have been fixed by minimizing the energy that has shown to be a more convenient functional than the variance of the local energy, which is the most commonly employed method in variational Monte Carlo calculations. The energies obtained improve previous works using similar wave functions. © 2002 Wiley Periodicals, Inc.; DOI 10.1002/qua.10125     

Description of correlated densities for few‐electron atoms by simple functional forms

Simple analytical functional forms for the electron density of two‐ and three‐electron atoms which reproduce fairly the correlated (exact) values are presented. The procedure is based on the fitting of an auxiliary f(r) function which has adequate properties for this purpose and can be extended to more complex atoms. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 443–454, 1999     

Electron density properties and metallophilic interactions of gold halides AuX2 and Au2X (X = F–I): Ab Initio calculations

We present ab initio calculations of the electron density properties and metallophilic interactions of the gold halide series, AuX₂ and Au₂X (X = F–I) as well as their anions performed at MP2 theoretical level with extended basis sets. The gold halide's structure, stability, and interactions with alkali metal atoms were investigated. The mechanisms of metallophilic interactions were explored by natural bond orbital analyses, electron localization function, electron density deformation, atoms in molecules, and reduced density gradient analyses. © 2016 Wiley Periodicals, Inc.     

Update of the AIM2000-program for atoms in molecules

The second version of the program package AIM2000 is presented. AIM2000 makes use of the well established theory of atoms in molecules. AIM2000 analyzes the molecular structure and calculates properties of atoms in molecules as well as properties of interatomic surfaces. The program has an interactive, context-sensitive help component and extensive 2D and 3D visualization components.     

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals

Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1-C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H-H interaction, rather than denoting the presence of "nonbonded steric repulsions", makes a stabilizing contribution of up to 10 kcal mol(-1) to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules-the physics of an open system-demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H-H interatomic surface is shown to account for the resulting stability. It is pointed out that H-H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H-H bonding is shown to be distinct from "dihydrogen bonding", a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.     

Factored wave function for bound S-type states of two-electron atomic systems

A simple and accurate variational wave function in which the dependence in the interelectronic distance is factored is proposed to describe S-type states of two-electron atomic systems. We introduce a parameterization which generalizes the previous ones used in this same framework and which allows us to obtain in a simple way the wave function of both symmetric and antisymmetric excited states. We performed a systematic analysis of some exact properties such as the virial theorem and the cusp conditions and a study of both the one- and two-body densities. Finally, a comparison among the different correlation functions for these states was performed for helium. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 405–413, 1998     

Participation of preadsorbed atoms in heterogeneous recombination of hydrogen atoms on semiconductor surfaces

Atoms trapped from the vapor phase in the preadsorbed state were found to provide the catalytic activity of semiconductors in the heterogeneous recombination of hydrogen atoms.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

Aufbau principle and singlet-triplet gap in spherical Hooke atoms

Singlet and triplet spin state energies for three-dimensional Hooke atoms, that is, electrons in a quadratic confinement, with even number of electrons (2, 4, 6, 8, 10) is discussed using Full-CI and CASSCF type wavefunctions with a variety of basis sets and considering perturbative corrections up to second order. The effect of the screening of the electron–electron interaction is also discussed by using a Yukawa-type potential with different values of the Yukawa screening parameter (λ_ee = 0.2, 0.4, 0.6, 0.8, 1.0). Our results show that the singlet state is the ground state for two and eight electron Hooke atoms, whereas the triplet is the ground spin state for 4-, 6-, and 10-electron systems. This suggests the following Aufbau structure 1s < 1p < 1d with singlet ground spin states for systems in which the generation of the triplet implies an inter-shell one-electron promotion, and triplet ground states in cases when there is a partial filling of electrons of a given shell. It is also observed that the screening of electron–electron interactions has a sizable quantitative effect on the relative energies of both spin states, specially in the case of two- and eight-electron systems, favoring the singlet state over the triplet. However, the screening of the electron–electron interaction does not provoke a change in the nature of the ground spin state of these systems. By analyzing the different components of the energy, we have gained a deeper understanding of the effects of the kinetic, confinement and electron–electron interaction components of the energy.