Nodal surfaces of the wave functions of the hydrogen molecule in the triplet state 3Σu +

For molecular hydrogen in the triplet state ³Σ_u ⁺, the nodal surfaces of the wave function corresponding to the minimum basis set of Slater orbitals in the Hartree—Fock approximation and those of the wave function used in calculations by the diffusion quantum Monte Carlo method were plotted and analyzed. Taking account of the condition for antisymmetrical wave function of the triplet state ³ S of He atom, the Hartree-Fock approximation in the minimum basis set of one-electron orbitals is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWF). An MWF quantum chemical method developed by the authors is outlined. The alternative nodal surfaces for H₂ (³Σ_u ⁺) a priori specified in this method are presented.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

The Origin of the Reactivity of the Criegee Intermediate: Implications for Atmospheric Particle Growth

The electronic structure of the simplest Criegee intermediate, H₂COO, is practically that of a closed shell. On the biradical scale (β), where 0 corresponds to the pure closed shell and 1 to a pure biradical, its β value is only 0.10, suggesting that its ground electronic state is best described as a H₂C=O^δ+?O^δ? zwitterion. However, this picture of a nearly inert closed shell contradicts its rich reactivity in the atmosphere. It is shown that the mixing of its ground state with the first triplet excited state, which is a pure biradical state of the type H₂C^.?O?O^., is responsible for the formation of strongly bound products during reactions inducing atmospheric particle growth.     

Quasiclassical trajectory study of the rotational distribution for the O+NO(v = 0) fundamental vibrational excitation

Quasiclassical trajectories have been run to study the fundamental one‐quantum vibrational transition formed from collisions of ground‐state nitric oxide with atomic oxygen at temperatures of 500, 750, and 1000 K. Two adiabatic potential energy surfaces of different symmetry (²A′ and ²A″ of NO₂) have been utilized. The rate constant for the title process is given along with the rotational distributions, and the results shown to corroborate previous atmospheric models that describe the nascent state by a Maxwell–Boltzmann distribution at the local temperature. © 2011 Wiley Peiodicals, Inc. Int J Chem Kinet 43: 345–352, 2011     

Valence-shell momentum distributions and ionization energies of carbon disulfide

Valence-shell binding energy spectra and momentum distributions of CS₂ have been measured using non-coplanar symmetric binary (e,2e) spectroscopy. The present measurements are compared with previously published binding energy spectra calculated using the many body 2ph-TDA Green's function (GF) method and the symmetry-adapted cluster configuration-interaction (SAC CI) method. The measured and the calculated binding energy spectra both show extensive population splittings particularly above 20 eV, confirming a significant breakdown of independent particle ionization picture. A relatively strong-outer valence many-body state at 17.0 eV is shown to be satellite of the (2π₀)^?1 state, in accord with earlier conclusions of photoelectron studies. Momentum distributions measured at several carefully chosen binding energies are compared with the corresponding molecular orbital momentum distributions calculated using small and extended gaussian basis sets. The good qualitative agreement between momentum distributions measured in the inner-valence region wth theoretical 4σ_m and 5σ_g orbital momentum distributions confirms the qualitative predictions of satellite parentages by GF and SAC CI calculations. Momentum and position density contour maps of individual orbitals are used to interpret the shapes and atomic characters of the experimental momentum distributions. Momentum densities of the valence orbitals of CS₂ are compared with those of the respective valence isoelectronic species CO₂     

Monte Carlo simulation of O(1D) + H2 and O(1D) + HCl — rotational excitation of product OH radicals

Experimental studies with molecular beam and LIF techniques have independently shown that the reaction O(¹D) + H₂ → OH + H passes through a long-lived complex and gives products with small translational and large rotational excitation. We have previously published a statistical algorithm, based on ordinary RRKM theory with angular momentum restrictions included, which was designed to simulate molecular beam experiments. It has now been modified and applied to simulate the experimental rotational OH distributions from O(¹D)+H₂, measured by Luntz et al. The present study also includes simulation of similar results by Luntz for O(¹D) + HCI → OH + Cl. The purely statistical algorithm successfully simulates the apparently non-statistical experimental rotational distributions. For these reactions the total angular momentum conservation. which is applied at the transition state, proves to be decisive for the product energy distributions.     

Properties of halogen atoms for representing intermolecular electrostatic interactions related to halogen bonding and their substituent effects

The electrostatic properties of halogen atoms are studied theoretically in relation to their ability of halogen bonding, which is an attractive intermolecular interaction of a covalently bonded halogen atom with a negatively charged atom of a neighboring molecule. The electric quadrupole (of electronic origin) with a positive zz component Θ_zz of a covalently bonded halogen atom, where the z axis is taken along the covalent bond involving the halogen atom, is mainly responsible for the attractive electrostatic interaction with a negatively charged atom. This positive Θ_zz is an intrinsic property of halogen atoms with the p_x²p_y²p_z configuration of the valence electronic shell, as shown by ab initio molecular orbital calculations for isolated halogen atoms with this electronic configuration, and increases in the order of F < Cl < Br < I, in parallel with the known general sequence of the strength of halogen bonding. For halogen‐containing aromatic compounds, the substituent effects on the electrostatic properties are also studied. It is shown that the magnitude of Θ_zz and the electric field originating from it are rather insensitive to the substituent effect, whereas the electric field originating from atomic partial charges has a large substituent effect. The latter electric field tends to partially cancel the former. The extent of this partial cancellation is reduced in the order of Cl < Br < I and is also reducible by proper substitution on or within the six‐membered ring of halobenzene. Perspectives on the development of potential function parameters applicable to halogen‐bonding systems are also briefly discussed. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

The band structure of one-dimensional (tetrazaporphyrinato)cobalt(II). A semi-empirical self-consistent field crystal orbital analysis

The band structure of (tetraporphyrinato)cobalt(II) (2) has been investigated by means of a semi-empirical INDO (intermediate neglect of differential overlap) crystal orbital approach. The simplest stoichiometric unit of the title compound contains an uneven number of electrons. We have considered metallic and insulating (Mott) electronic distributions in the “half-filled” band. The Hartree-Fock energies for two spatial symmetries have been determined: (i) singly occupied Co 3d_z² band (a_1g) and (ii) singly occupied ligand-centered (a_1u) linear combination. The mean-field energies of insulating “Mott” states have been calculated by means of a grand canonical (GC) averaging procedure. The electronic ground state is of spatial A_1g symmetry (“half-filled” Co 3d_z² dispersion) and corresponds to an insulating band occupation. The calculated width of the a_1g dispersion amounts to 0.13 eV. It is argued that the band structure results of 2 are in qualitative agreement with available experimental results derived for (phthalocyaninato(cobalt(II).     

Electronic structures of tetragonal nitrido and nitrosyl metal complexes

The standard oxidation states of central metal atoms in C _4v nitrido ([M(N)(L)₅] ^z ) complexes are four units higher than those in corresponding nitrosyls ([M(NO)(L)₅] ^z ) (L=CN: z = 3−, M = Mn, Tc, Re; z = 2−, M = Fe, Ru, Os; L = NH₃: z = 2+, M = Mn, Tc, Re; z = 3+, M = Fe, Ru, Os). Recent work has suggested that [Mn(NO)(CN)₅]³⁻ behaves electronically much closer to Mn(V)[b ₂(xy)]², the ground state of [Mn(N)(CN)₅]³⁻, than to Mn(I)[b ₂(xy)]²[e(xz,yz)]⁴. We have employed density functional theory and time-dependent density functional theory to calculate the properties of the ground states and lowest-lying excitations of [M(N)(L)₅] ^z and [M(NO)(L)₅] ^z . Our results show that [M(N)(L)₅] ^z and [M(NO)(L)₅] ^z complexes with the same z value have strikingly similar electronic structures.     

Quantum chemistry of many-electron systems: high-priority aspects

The review generalizes the studies devoted to the development of a new quantum chemistry method representing an alternative to the Hartree–Fock approximation. Based on the hypothesis of prohibition of equipotential surfaces, which clarifies the physical sense of the Pauli exclusion principle, and taking account of the condition for antisymmetrical wave function of the triplet state (3S) of He atom, the Hartree–Fock approximation is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWFs) for the test systems traditionally used in quantum chemistry, namely, excited triplet state of H₂ molecule and the ground electronic states of Li atom and LiH molecule. The nodal surfaces of the wave functions corresponding to the minimum basis set of Slater orbitals in the Hartree–Fock approximation are constructed and analyzed. An alternative to the Hartree–Fock approximation is provided by the MWF quantum chemical method being developed by the authors. In the MWF method, the nodal surfaces for H₂(³Σ _u ^v ) and Li(²S) are specified a priori. Some aspects of geometric interpretation of the Pauli exclusion principle are discussed. Unlike the MWF method, the Hartree–Fock approximation is unsuitable for taking account of the dependence of the MWF nodal surfaces on the nuclear charges and on correlation effects related to the motion of electrons with antiparallel spins because such nodal surfaces are predefined by the mathematical properties of Slater determinants rather than by physically clear and more practically valuable algebraic products of electrostatic potential differences.     

An investigation of the valence orbitals of water by high momentum resolution electron momentum spectroscopy

The momentum distributions of the valence orbitals for water well as the binding energy spectra in the region 10–45 eV have been reinvestigated with a high momentum resolution (≈0.1 a₀^?1 fwhm) binary (e.2e) spectrometer. The binding energy spectra show considerable satellite structure in the region > 25 eV which is consistent with theoretical predictions of final state configuration interaction (many-body effects) involving the (2a₁)^?1 hole state. An investigation of the momentum distribution in the satellite region confirms this assignment. This is in accord with a variety of recent theoretical studies and also consistent with earlier experiments. Differences suggested in earlier comparisons between theory and low momentum resolution experiments for the momentum distributions of the 1b₁ and 3a₁ orbitals have been verified. Several possible theoretical studies are suggested to investigate further this discrepancy between experiment and theory. Bonding effects and thenature of the molecular orbitals of H₂O in momentum space are also discussed.     

一系列d8配合物1,3[(dz2)(pz)]激发态和金属间相互作用的理论研究

采用MP2和CIS方法分别优化trans-[M₂(CN)₄(PH₂CH₂PH₂)₂] [M＝Pt (1), Pd (2)和Ni (3)]和trans-[M(CN)₂(PH₃)₂] [M＝Pt (4), Pd (5)和Ni (6)]的基态和^1,3[(d_z2)(p_z)]激发态结构. CIS计算显示1的激发态Pt-Pt距离相对基态变短, 而2和3的金属间距离却增长. TD-DFT方法合理地预测了1～6发射能, 如: 1在CH₂Cl₂溶液中分别拥有348和404 nm的荧光和磷光发射, 与实验的386和448 nm相对应. 在1～3的激发态中, d⁸-d⁸相互作用依次递减, 相应的发射跃迁能增加; 与单核配合物4～6相比, 金属间相互作用使得双核Pt配合物的发射波长红移, 而对双核Pd和Ni配合物影响很小.     

First-principles calculation of temperature-dependent electronic transitions mechanism in V or Nb substituted BiFeO3

Here, we present a simulation study of temperature-dependent electronic transitions in BiVO₃ (BVO) and BiNbO₃ (BNO) using density functional theory (DFT) together with generalized gradient approximation (GGA) and two-dimensional correlation analysis (2D-CA). The results indicate that heat accumulation can accelerate the degeneracy of V-3d orbital in BVO and the splitting of Nb-4d orbital in BNO at 750 K. We found changes in the type of d–p hybrid orbital as follows, for BVO: V-d_x²_+y² + d_Z²-O-2p_z → V-d_x²_+y²-O-2p_z; and for BNO: Nb-d_x²_+y²-O-2p_z → Nb-d_x²_+y² + d_Z²-O-2p_z. Furthermore, we found changes in the type of hybrid orbital leading to the following electron–electron interactions, for BVO: t_2g (V-d_Z²-O-2p_z) + e_g (V-d_x²_+y²-O-2p_z) → t_2g (V-d_x²_+y²-O-2p_z); and for BNO: t_2g + e_g (Nb-d_x²_+y² + d_Z²-O-2p_z) → t_2g (Nb-d_x²_+y²-O-2p_z) + e_g (Nb-d_z²-O-2p_z). The electronic transitions are determined by a charge-transfer from the occupied O-2p⁴ orbitals to the unoccupied V-3d³ (or Nb-4d³) and Bi-6p³ orbitals. Due to the temperature-dependent electronic structure closely related to these electronic transitions, this study provides a new perspective for the design and improvement of BFO-based temperature-sensitive devices.     

Ionization equilibrium in salt‐containing aqueous solutions of synthetic polyampholytes

The peculiarities of ionic equilibrium in salt‐containing aqueous solutions of polyampholytes (acrylic acid–2‐methyl‐5‐vinylpyridine copolymers) of various compositions and molecular weights were studied. The protonation degree of base groups (β_iep), the dissociation degree of acid groups (α_iep), and the ionization constant of methylvinylpyridine groups (pK_b) for the isoelectric points of the studied polyampholytes under various ionic strength values (I) were assessed spectrophotometrically. The dependencies of α_iep and pK_b versus the copolymer composition in the absence of low molecular weight electrolyte are described by the following equations: pK_b = 6.2–0.037z and lg α_iep = 0.27–0.0215z, where z is the molar content of the acrylic acid units. The basicity of methylvinylpyridine groups increases in proportion to the content of acid groups at a constant ionic strength and is independent of the molecular weight and molecular weight distribution of the copolymer. The relationship between pK_b and the ionic strength of the solution for acrylic acid–methylvinylpyridine copolymers was established: pK_b(I) = pK + B · I^1/2, where pK is the thermodynamic ionization constant of base groups and B is 0.21 + 0.0065z. A good agreement between the experimental and theoretical (calculated from the given equation) values of the ionization constant, pK_b, of methylvinylpyridine groups for other polyampholytes (copolymers of methacrylic acid with 2‐methyl‐5‐vinylpyridine) demonstrated that the ionic state of polyampholytes is determined by the basicity of methylvinylpyridine groups, which depends on the copolymer composition and solution ionic strength. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1824–1831, 2000     

Laser-induced photodissociation of He+2

The momentum distributions of He⁺ fragments from photodissociation of He⁺₂ ions have been recorded in a crossed-beams experiment. The discrete values of the kinetic energy releases can be predicted from the vibrational spacings in the ground state of the primary ions.     

Diatomic interactions in momentum space. The effect of polarization and floating functions

The method of momentum density for interatomic interactions is used to investigate the pictures and roles of the polarization and floating functions in momentum (p-) space. Referring to the previous results from the minimal LCAO (Finkelstein-Horowitz) momentum density, we quantitatively discuss the effect of these functions for the bonding process in the ground state of H ₂ ⁺ system. The essence of the polarization and floating effects is found to be a modulation of the oscillation in the two-center part of the momentum density. The polarization function introduces a term with a phase and the floating function enlarges the period of the oscillation. An increased migration of the density from the one-center to the two-center part is also important. As a result, both the functions contribute to emphasize the contraction and expansion of momentum density observed previously. However, the floating function disturbs the density distribution in high momentum region, reflecting the destruction of cusps in position (r-) space. We point out an error in the pioneer work of Duncanson.     

Evaluation of Eigenvalues by Successive Variations

A successive variation method was studied and tested on the hydrogen molecular ion H₂⁺. Results show that it takes less computational time than conventional method. It was also found that ground state wavefunction of H₂⁺ can be well approximated by the linear combination of the simplest Gaussian orbitals e^?I(T-a)3     

Slater Sum in Cylindrically Symmetric Inhomogeneous Electron Liquids: Towards A Differential Equation for the Stark Effect in Hydrogen Atom

Abstract

Attention is focussed here on a variety of cylindrically symmetric inhomogeneous electron liquids. These include separable potentials in which a general variation along the (z) axis of cylindrical symmetry is combined with isotropic harmonic confinement in the (x, y) plane. in this case, an explicit differential equation is derived for the Slater sum along the z axis by projecting out of the (off-diagonal) canonical density matrix the states with zero angular momentum about the axis of symmetry. Some attention is then given to the calculation of the Slater sum for a hydrogen-like atom in a uniform electric field of arbitrary strength. the model of a separable potential with harmonic confinement, though no longer exact, is shown to lead directly to a (now approximate) equation for the Slater sum along the z axis for the Stark effect in hydrogen. Finally some further progress is shown to be possible in the extreme high field limit.     

Charge Separation in Triafulvenes: Application of the Para-Fluorophenyl Tag 19f NMR Method

Triafulvene (1) is the simplest [n]fulvene. Interest in triafulvenes centered on the potential contributions (in the ground state) of dipolar ‘aromatic’ structures of the type la, in which three-membered ring assumes ‘cyclopropenium’ character^2-5). Various attempts have been made to increase these dipolar contributions by introducing electron withdrawing substituents at the exocyclic carbon atom (C₄) of the triafulvene skeleton^2-6). A striking illustration of this trend is the study of the triapentafulvalene (2) system, motivated by the search for aromatic ‘cyclopropenium-cyclopentadienide’ structures (2a)³⁾. Cyclopropenone (3), the simplest [n]annulenone, may also fall within the category of triafulvenes formally being viewed upon as 4-oxatriafulvene with a potential contribution of a cyclopropenium oxide (3a) structure to the ground state resonance hybride^5,7,8).