Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

Maximum-entropy analysis of atomic compton profiles

The maximum-entropy formalism is used to obtain approximations to the atomic Compton profile, ??(q), in terms of the first few radial expectation values 〈Pⁿ〉 of the momentum density γ(p). This method leads to the least-biased results by the information not used. In particular, analytical and numerical approximations to the kinetic energy T and to the height of the peak ??(O) and the half-width q_0.5 of the Compton profile are obtained. Our results generalize and improve some approximations to ??(q) previously obtained by other authors. For illustration, the accuracy of these approximations are studied by means of near-Hartree–Fock wave functions. © 1995 John Wiley & Sons, Inc.     

Momentum space properties of atoms

A systematic investigation of momentum densities Π (p), Compton profiles J (q), and internally folded densities B (r) has been made for the ground states of the atoms from H to Kr. The data are presented in reduced form by means of the characteristic momentum p* = q* and length r* = 1/p*, where p* = [J (0)/2πΠ (0)]^½. The results indicate that p* and J (0) contain the gross qualitative behavior of the atomic properties in momentum space. They also show that subtle effects over and above the gross scale and size are mostly periodic.     

Structure of the electron momentum density of atomic systems

The present paper addresses the controversial problem on the nonmonotonic behavior of the spherically-averaged momentum density γ(p) observed previously for some ground-state atoms based on the Roothaan-Hartree-Fock (RHF) wave functions of Clementi and Roetti. Highly accurate RHF wave functions of Koga et al. are used to study the existence of extrema in the momentum density γ(p) of all the neutral atoms from hydrogen to xenon. Three groups of atoms are clearly identified according to the nonmonotonicity parameter μ, whose value is either equal to, larger, or smaller than unity. Additionally, it is found that the function p^?α γ(p) is (i) monotonically decreasing from the origin for α ≥ 0.75, (ii) convex for α ≥ 1.35, and (iii) logarithmically convex for α ≥ 3.64 for all the neutral atoms with nuclear charges Z = 1–54. Finally, these monotonicity properties are applied to derive simple yet general inequalities which involve three momentum moments 〈p ^t≥. These inequalities not only generalize similar inequalities reported so far but also allow us to correlate some fundamental atomic quantities, such as the electron-electron repulsion energy and the peak height of Compton profile, in a simple manner.     

Calculation of 2p 4(3 P)nl(l=s,d) Rydberg spectra of the fluorine isoelectronic sequence

The basic structure parameters of 2p ⁴(³ P)ns and 2p ⁴(³ P)nd (J=1/2, 3/2 and 5/2) Rydberg spectra for the fluorine isoelectronic sequence from FI to NiXX, as functions of effective nuclear charge, are calculated by using the eigenchannel quantum-defect theory. The results can be interpreted in terms of the variations of electrostatic and spin-orbit interactions along the sequence. A vast amount of basic atomic data can be obtained with these parameters as input. Some numerical examples are given, in which our results are in perfect agreement with experimental.     

Minimum cross‐entropy estimation of internally folded densities from Compton profiles

The internally folded density or reciprocal form factor B( r ) of many‐electron systems is tightly estimated from the knowledge of a small discrete set of values of the Compton profile J( q ). In doing so, the minimum cross‐entropy technique is employed. A numerical analysis of the approximations is carried out for the Helium atom. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

On the use of NDO approximate wavefunctions in the evaluation of momentum density and radial momentum density distributions in polyatomic molecules

The use of single determinantal approximate molecular wavefunctions of the LCAO MO NDO type for the calculation of the momentum densityρ(p) and the radial momentum density distributionJ(p) is discussed. In each case, these expressions should be orientationally invariant and the momentum density should be normalized. Combining these two requirements, it is shown that only two approximations are physically significant:

1. NDO wavefunctions are used andρ(p) andI(p) are approximated respectively up to an INDO and a CNDO level;
2. Overlap integrals are explicitly taken into account when solving the Roothaan SCF equations or deorthogonalized NDO functions are employed, together with the unapproximated expressions.

     

Small-angle X-ray scattering study on the microstructure evolution of zirconia nanoparticles during calcination

Zirconia nanoparticles have been synthesized from zirconium hydroxide precipitates followed by a supercritical CO₂ extraction. The microstructure evolution of these zirconia nanoparticles during the calcination at the moderate temperature has been investigated. Assisted by the analyses of TEM and XRD, small-angle X-ray scattering (SAXS) study offers possibilities to a comprehensive and quantitative characterization of the structural evolution on the nanometer scales. The as-synthesized zirconia sample exhibits a mass fractal structure constructed by the surface fractal particles. Such a structure can be preserved up to 300 °C. After calcination at 400 °C, considerable structural rearrangement occurs. In the interior of nanoparticles zirconia nanocrystallites emerge. It is the scattering from such zirconia nanoparticles that give rise to the broadened crossover in the ln[J(q)] vs. ln q plot and the scattering peak in the ln[q³J(q)] vs. q² plot. With a further increase in the calcination temperature, the power-law region at large-q in ln J(q) vs. ln q plot expands, and the peak in ln[q³J(q)] vs. q² plot shifts towards lower q values, indicating size increases in both the nanocrystallites and nanoparticles. Besides, the mass fractal structure constructed by zirconia nanoparticles can be largely preserved during the moderate temperature calcination.     

The electrical neutrality of atoms

An atomic beam deflection experiment is described which establishes upper limits to the electrical charges of potassium and cesium atoms ofq(K)<2.4×10^?18 q _e andq(Cs)<3.0×10^?18 q _e at the 90% confidence level, in whichq _e is the electron charge magnitude. If we assume that the electron neutrino charge is zero and that charge conservation holds in neutron beta decay, then the difference δq in the electron and proton charge magnitudes has the upper limit δq<1.3×10^?20 q _e at the 90% confidence level. The possibility of a more sensitive atomic beam deflection experiment using a laser-cooled atomic beam is suggested. A brief review of the topic of the electrical neutrality of atoms is given.     

Molecular momentum distributions and compton profiles. Effects of bonding on some small molecules

Electronic momentum distributions and Compton profiles have been calculated from minimum basis set SCF wavefunctions for H₂O, H₂O₂, CO, CO₂ and H₂CO. Radial distributions and profiles have also been estimated for these molecules from localized molecular orbitals. The results suggest that (a) the height of the Compton peak, <p^?1>, may be as sensitive to the effects of chemical bonding as the kinetic energy, <p²>/2, and that (b) the virial theorem may provide a more useful criterion than energy minimization in assessing the accuracy of calculated bonding effects and Compton profiles.     

A coupled-states approximation study of Li+-H2 collisions

The recently developed coupled-states approximation for describing atom-molecule collisions is applied in a slightly modified form to the Li⁺-H₂ system. Due to the large anisotropy in the potential, a preferred orientation for rotational excitation exists which suggests the use of l = J-j rather than l = J as the angular momentum quantum number in approximating the eigenvalue of 1² by l(l + 1). Here, J and j are respectively the total and rotator angular momentum quantum numbers. The coupled-states integral and differential cross sections are compared with results of close-coupling calculations at 0.6, 0.9, and 1.2 eV.     

A proton and carbon-13 nuclear magnetic resonance study of neopentylmercury compounds

Substituent effects on ¹⁹⁹Hg¹H and ¹⁹⁹Hg¹³C spinspin coupling constants have been studied for neopentylmercury derivatives, (CH₃)₃CCH₂HgR(or X), where R is covalently bonded Me, Et, t-Bu, neopentyl, and vinyl, and X is easily ionizable CN, Br, Cl, OCOCH₃, and ONO₂. Linear relationships exist between the methylene J(¹³CH) and ²J(HgH), ⁴J(HgC) and ²J(HgC) and ³J(HgC); but deviations from linearity occur for the chloride, bromide, acetate, and nitrate in the relationships between ²J(HgH) and ⁴J(HgH), ²J(HGH) and ²J(HGC). These deviations are discussed in terms of hyperconjugative p_πd_π bonding between the methylene CH bonds and mercury.     

The nodal structure of the momentum distributions of molecules

The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H₂⁺ momentum distribution, it is shown that an infinite sequence of nodes does exist along the p_z axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the p_z axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the p_z axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J( q ) are discussed.     

Experimental and theoretical cross sections for photoionization of metastable Xe*. (6s 3 P 2, 3 P 0) atoms near threshold

Using high resolution laser photoelectron spectrometry we have determined absolute cross sections σJ ₀ J ₁ and the electron angular distribution parameter for one photon ionization of metastable Xe^*(6s ³ P _J0, J ₀ = 2, 0) atoms to the resolved Xe₊ (² P _J1, J ₁ = 3/2, 1/2) ion states at several wavelengths near threshold. For comparison with the present and future experimental data we have calculated partial cross sections and ß-parameters for photoionization of Xe^*(6s ³ P _J0, J ₀ = 2, 0) and of the analogous alkali atom Cs(6s) over the photoelectron energy range (0–5) eV. We have used both a term-dependent Pauli-Fock (PF) approach and a configuration interaction method involving Pauli-Fock atomic orbitals (CIPF). Through the PF method we include relativistic effects on the atomic orbitals; the CIPF method was designed to take into account the important electron correlation effects which are found to be essential for obtaining good agreement between the theoretical and experimental results.     

Maximum-entropy analysis of momentum densities in diatomic molecules

The one-particle density in momentum space γ(p) is studied for diatomic molecules by using the maximum-entropy technique. The knowledge of one or more momentum expectation values <p"> provides approximations on the density γ(p) for any value of the momentum, which are convergent when increasing the number of known moments. Other unknown expectation values are estimated in terms of the constructed maximum-entropy densities. A numerical study of the quality of the approximations is carried out by means of experimental and theoretical data for the momentum expectation values involved. Experimental errors are also taken into account to have an idea of the sensibility of the results to the information from which they are obtained. © 1997 John Wiley & Sons, Inc.     

Electronic structure,optical properties and Compton profiles of Bi2S3 and Bi2Se3

In this paper, we present the Compton profiles of Bi₂S₃ and Bi₂Se₃ using our 20 Ci ¹³⁷Cs Compton spectrometer. To compare our experimental data, we have computed the Compton profiles, energy bands and density of states using linear combination of atomic orbitals with density functional theory (DFT) and Hartree-Fock (HF) scheme. It is seen that hybrid functional involving HF and DFT approximations gives a relatively better agreement with experimental momentum densities than other approximations of DFT. We have also reported the band structure, density of states, valence charge densities, dielectric functions and electron energy loss spectra using full potential linearized augmented plane wave scheme. On the basis of charge densities, Mulliken’s population data and equal-valence-electron-density profiles, Bi₂S₃ is found to be more ionic than Bi₂Se₃. The calculated dielectric functions for the parallel and perpendicular polarizations show a small anisotropic effect. The electron energy loss spectrum for Bi₂Se₃ is found to be in good agreement with the available experimental data.     

Fluorescence lifetime studies of no a 2Σ+(ν = 5, N = 9), B2Π32(ν = 8, J = 8.5), CwΠ32(ν = 1, J = 8.5), D2Σ+ (ν = 0, N = 5) and D2Σ+(ν = 1, N = 9)

Fluorescence decay profiles of NO excited levels slightly above the dissociation limit have been measured by a single-photon counting technique with nanosecond pulse excitation using an iodine flash lamp. Three iodine atomic lines in the vicinity of 180 nm are found to bring NO molecules into the levels A²Σ⁺(ν = 5, N = 9), B²²Π_{$\text{3}\text{2}$}(ν = 8, J = 8.5), C²Π_{$\text{3}\text{2}$}(ν = 1, J = 8.5), D²Σ⁺(ν = 0, N = 5) and D²Σ⁺(ν = 1, N = 9). Extrapolated zero-pressure lifetimes for single rotational levels are obtained, except for the C state where only a lifetime of ⩽0.4 ns was obtained. Self-quenching rate constants are also determined under higher-pressure conditions. Helium was found to quench the NO A²Σ⁺(ν′ = 5) fluorescence very efficiently.     

Calculation of the 1J(PP) angular dependence in P2H4

Using the results obtained from an MO SCF ab initio calculation on P₂H₄ in four different conformations, the ¹J(PP) NMR coupling constants have been calculated. The ¹J(PP) values are highly dependent upon the rotational angle φ (?238.0 Hz in the eclipsed conformation, 10.9 Hz in the staggered one). The shape of the theoretical ¹J(PP) plot seems to be in good agreement with experimentally measured ¹J(PP) values.     

Interet de la deuteriation des molecules organostanniques en rmn de 119Sn : I. Acces aux constantes de couplage nJ(SnD) et application a l'etude structurale de vinyl et d'allyletains

The selective deuteration of organotin compounds gives FT ¹¹⁹Sn NMR a new proficiency, since it allows direct access to ⁿJ(SnD) coupling constants. Usually ⁿJ(SnD) is easily apparent for n  1, 2, 3 and sometimes 4 (allyltin compounds). This criterion has been successfully applied for qualitative and subsequently quantitative analysis of vinyltin and allyltin compounds.In the first series, the stereochemistry of alkyne deuterostannation has been easily explored, the assignments of configurations being made directly from ³J(SnD) on the basis of ³J(SnD)_trans > ₃J(SnD)_cis. In the second series, the method appears to be the best tool for simultaneous study of regiochemistry and stereochemistry in the substitution of 3-deutero-5-methyl-2-cyclohexenyl toluene sulphonates by trialkylstannyl anions. The choice between regioisomers was made on the basis of ₂J(SnD) >- ⁴J(SnD).A further aspect of this work is the observation of isotopic effects on ¹¹⁹Sn chemical shifts which were tentatively rationalized considering inductive, steric or hyperconjugative contribution of deuterium.