Minima and maxima in the generalized oscillator strengths for the lithium isoelectronic sequence

We have calculated the ionization generalized oscillator strengths (GOS) f(K,k) as a function of the momentum transfer K for the allowed dipole transitions ns → kp (with n = 2) in the lithium isoelectronic sequence through Z = 10, in the Hartree-Fock (HF) approximation. Our results clearly show (i) the regular and systematic trends of the occurrence of the extrema, (ii) the shift of their positions towards the higher values of K with increase of K, and finally, the gradual decrease of the magnitude of f(K,k) with increase of atomic number Z. The results are discussed qualitatively.     

Effects of the environmental factors on the casein micelle structure studied by cryo transmission electron microscopy and small-angle x-ray scattering/ultrasmall-angle x-ray scattering

Casein micelles are colloidal protein-calcium-transport complexes whose structure has not been unequivocally elucidated. This study used small-angle x-ray scattering (SAXS) and ultrasmall angle x-ray scattering (USAXS) as well as cryo transmission electron microscopy (cryo-TEM) to provide fine structural details on their structure. Cryo-TEM observations of native casein micelles fractionated by differential centrifugation showed that colloidal calcium phosphate appeared as nanoclusters with a diameter of about 2.5 nm. They were uniformly distributed in a homogeneous tangled web of caseins and were primarily responsible for the intensity distribution in the SAXS profiles at the highest q vectors corresponding to the internal structure of the casein micelles. A specific demineralization of casein micelles by decreasing the pH from 6.7 to 5.2 resulted in a reduced granular aspect of the micelles observed by cryo-TEM and the existence of a characteristic point of inflection in SAXS profiles. This supports the hypothesis that the smaller substructures detected by SAXS are colloidal calcium phosphate nanoclusters rather than putative submicelles.     

Experimental and theoretical study on generalized oscillator strengths of the valence-shell electronic excitations in CF4

We report an angle-resolved electron energy loss spectroscopy (EELS) study on the valence-shell electronic excitations in CF(4). Experimentally momentum-transfer-dependent generalized oscillator strengths (GOSs) or GOS profiles for low-lying electronic excitations at 12.6, 13.8, and 14.8 eV are derived from EELS spectra measured at an incident electron energy of 3 keV. We also calculate GOS profiles using theoretical wave functions at the equation-of-motion coupled cluster singles and doubles level. There are good agreements between experiment and theory except for a significant discrepancy at small momentum transfer for the 1t(l) → 3s Rydberg excitation at 12.6 eV. The experimental GOS profile for 1t(l) → 3s exhibits a shape that is typical of a dipole allowed transition, while the excitation is formally dipole forbidden. This symmetry breaking behavior is rationally accounted for by qualitatively analyzing the nature of vibronic coupling effects. For the excitation band at 13.8 eV, a shoulder and extrema are observed in the GOS profile and are then found to be mainly due to the 2(1)T(2) transition. Furthermore, the theoretical GOS profile for the 2(1)T(2) transition exhibits a remarkable oscillatory pattern; its origin is discussed by considering multicenter interference effects. For the 14.8 eV excitation band, the predominant nondipole nature of the underlying transitions are revealed and comparisons with the theoretical calculations show that major contributions to this band come from the 4t(2) → 3p excitation.     

On the classical behavior, coherent and incoherent contributions to scattering of atoms from a surface

In this work we calculate the coherent and incoherent contributions to the diffraction probability of atoms scattered by a surface. We are interested in exploring the relative importance of each of these contributions, and compare them with results obtained from molecular dynamics calculations. To achieve this goal, we employed a method developed by Heller that consists of writing the incident plane wave as a sum of Gaussian wave packets, propagating them independently by using the time dependent Schrödinger equation, and constructing the scattered wave function by adding coherently the scattered packets. For the system studied, the molecular dynamics results show the largest intensity in the specular region and also display a classical rainbow structure. On the other hand, the quantum results exhibit diffraction features, with the coherent contribution accounting for most of the total intensity probability.     

An empirical relation between oscillator strengths calculated from the dipole length and dipole velocity formalisms in the optical absorption of conjugated molecules

It is found that a ratio between the oscillator strengths of the optical absorption calculated from the dipole length formalism and those calculated from the dipole velocity formalism is almost constant for many conjugated molecules if the calculation is made using the theoretically obtained transition energy. The value of the ratio becomes very sensitive to the molecular geometry if the calculation is made using the experimentally obtained transition energy. The origin of the constancy of the ratio is discussed.     

Dynamics of water studied by coherent and incoherent inelastic neutron scattering

This paper reviews the more recent results obtained on the dynamics of water by neutron scattering and shows that some information can be obtained by this technique at the microscopic level of the hydrogen bond. It also accounts for some very recent results obtained with the hydrated protein C-phycocyanin.

Incoherent quasi-elastic and inelastic neutron scattering by water has been performed in a temperature range extending to the supercooled state. The analysis of the quasi-elastic spectrum separates two main components and gives two characteristic times, one of them being related to the hydrogen-bond lifetime. The inelastic spectra extend until 600 meV, i.e. covering the intramolecular vibration region, showing for the first time the stretching band.

Collective excitations propagating at 3310 m s⁻¹ have been observed by coherent inelastic neutron scattering. This result was predicted by previous computer molecular dynamics simulations of water. The data are interpreted as a manifestation of short wavelength collective modes propagating within patches of highly bonded water molecules, and distinct from the ordinary sound wave.     

The determination of absolute anion formation cross sections from electron beam scattering data

Using recent low energy electron scattering data for CCl4 and SF6, and accompanying theory illustrating the coupling of attachment and elastic scattering, absolute cross sections are derived for electron attachment to CCl4 and SF6 between impact energies, respectively, of 8-52 meV and 7-42 meV. Values of attachment cross sections are compared with those obtained by laser and threshold photoionization techniques, which include normalization to rate coefficient data. Excellent agreement with the latest CCl4 data is obtained, with less precise agreement for SF6, but still lying within experimental uncertainties.     

Absolute quantitative electron microscopy of thin biological specimens by energy-dispersive x-ray microanalysis and densitometric mass determination

The method described is capable of measuring both the absolute mass and the mass fraction of elements is isolated thin biological specimens. To determine the elemental mass, characteristic x-rays emitted under electron irradiation are used, whereas the total mass of the specimen is found from electron scattering. Comparison with measurements on standards allows the calculation of the absolute elemental mass and elemental mass fraction values. The number of x-ray quanta per atom of a particular element, detected under strictly standardized procedural conditions, is given by a unit x-ray count value. Such values were determined for magnesium, phosphorus, sulfur and calcium using spray droplets as standard specimens.     

Structural dynamics of surfaces by ultrafast electron crystallography: experimental and multiple scattering theory

Recent studies in ultrafast electron crystallography (UEC) using a reflection diffraction geometry have enabled the investigation of a wide range of phenomena on the femtosecond and picosecond time scales. In all these studies, the analysis of the diffraction patterns and their temporal change after excitation was performed within the kinematical scattering theory. In this contribution, we address the question, to what extent dynamical scattering effects have to be included in order to obtain quantitative information about structural dynamics. We discuss different scattering regimes and provide diffraction maps that describe all essential features of scatterings and observables. The effects are quantified by dynamical scattering simulations and examined by direct comparison to the results of ultrafast electron diffraction experiments on an in situ prepared Ni(100) surface, for which structural dynamics can be well described by a two-temperature model. We also report calculations for graphite surfaces. The theoretical framework provided here allows for further UEC studies of surfaces especially at larger penetration depths and for those of heavy-atom materials.     

On the structure of glassy polymers. IV. Small-angle x-ray scattering from rigid polyvinyl chloride

The small-angle x-ray scattering (SAXS) from quenched and annealed rigid polyvinyl chloride (PVC) has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference. The scattering from annealed (6 days at 75°C) and unannealed PVC was identical within experimental error, varying with scattering angle in a manner similar to the SAXS from other amorphous polymers. The intensity decreases rapidly with increasing scattering angle over the ranges from 20 sec to 20 min. Beyond 20 min the intensity is fairly constant, decreasing only slightly with increasing angle. At the largest angles of measurement (in the range of 120 min), the measured intensity is close to the value calculated for thermal density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 50 to 4500 Å and, assuming the crystalline excess density, the total concentration of heterogeneities is less than 0.5%. The mean-square fluctuation in density, determined from the measured intensity invariant, is also consistent with such a distribution of heterogeneities. The present SAXS results on rigid PVC are inconsistent with the presence of nodular features as representative of the bulk polymer. Rather, it is suggested that they are associated with surface effects. It is further suggested that previously indicated volume fractions of crystallinity in rigid PVC (generally in the range of 5–12%) are incorrect, and that the model of a three-dimensional network of crystallites used to explain the rheological behavior of this material should be re-examined.     

On the structure of glassy polymers. III. Small-angle x-ray scattering from amorphous polyethylene terephthalate

The small-angle x-ray scattering (SAXS) from glassy polyethylene terephthalate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 15 min, decreases more gradually in the range between 15 min and 45 min, and reaches a nearly constant asymptotic value over the range between 45 min and 2 deg. The magnitude of the scattering in the constant range, about 0.4 (electrons)² Å^?3, is very close to the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass-transition temperature [0.34 (electrons)² Å^?3]. The increase in intensity at angles smaller than about 45 min cannot be described by structures on the scale and volume fraction of the nodules reported in amorphous PET (50–100 Å), but can be well represented by small concentrations of heterogeneities, ranging in size from 100 to 2000 Angstroms, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material seems well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration (<1 vol-%) of heterogeneities covering a range of sizes. The heterogeneities in the small end of the range may well be crystallites which formed on cooling.     

On the length,velocity and acceleration expressions for the calculation of accurate oscillator strengths in many-electron systems

The problem of deciding which of three equivalent forms of electric dipole transition probabilities is the most “proper” or “accurate” to use, has been discussed in recent papers from various points of view. Here we examine this question and also certain conditions which have to be satisfied for the three forms to give the same results. Regarding the question of accuracy, we suggest that, on the whole, arguments based on the importance of regions of configuration space are still the most convincing, in spite of recent attempts to select only one form as the proper one. A number of many-body calculations are carried out for transitions in BI, CII, OI, OIV and SiX. For the CII, OIV 1s²2s²2p ²p⁰ → 1s²2s2p²²D oscillator strengths, good agreement between all three expressions is obtained for the first time.     

Solvent and lipid dynamics of hydrated lipid bilayers by incoherent quasielastic neutron scattering

The microscopic dynamics of the planar, multilamellar lipid bilayer system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) has been investigated using quasielastic neutron scattering. The DMPC was hydrated to a level corresponding to approximately nine water molecules per lipid molecule. Selective deuteration has been used to separately extract the dynamics of the water, the acyl chains, and the polar head groups from the strong incoherent scattering of the remaining hydrogen atoms. Furthermore, the motions parallel and perpendicular to the bilayers were probed by using two different sample orientations relative to the incident neutron beam. For both sample orientations, the results showed an onset of water motions at 260 K on the experimental time scale of about 100 ps. From lack of wave-vector dependence of the onset temperature for water motions, it is evident that the observed water dynamics is of mainly rotational character at such low temperatures. At 290 K, i.e., slightly below the gel-to-liquid transition around 295 K, the nature of the water dynamics had changed to a more translational character, well described by a jump-diffusion model. On the limited experimental time and length (about 10 A) scales, this jump-diffusion process was isotropic, despite the very anisotropic system. The acyl chains exhibited a weak onset of anharmonic motions already at 120 K, probably due to conformational changes (trans-gauche and/or syn-anti) in the plane of the lipid bilayers. Other anharmonic motions were not observed on the experimental time scale until temperature had been reached above the gel-to-liquid transition around 295 K, where the acyl chains start to show more substantial motions.     

The structure of water in the hydration shell of cations from x-ray Raman and small angle x-ray scattering measurements

X-ray Raman scattering (XRS) spectroscopy and small angle x-ray scattering (SAXS) are used to study water in aqueous solutions of NaCl, MgCl(2), and AlCl(3) with the particular aim to provide information about the structure of the hydration shells of the cations. The XRS spectra show that Na(+) weakens the hydrogen bonds of water molecules in its vicinity, similar to the effect of increased temperature and pressure. Mg(2+) and Al(3+), on the other hand, cause the formation of short and strong hydrogen bonds between the surrounding water molecules. The SAXS data show that Mg(2+) and Al(3+) form tightly bound hydration shells that give a large density contrast in the scattering data. From the form factors extracted from the SAXS data, we found that Mg(2+) and Al(3+) have, respectively, an equivalent of one and one and a half stable hydration shells that appear as a density contrast. In addition, we estimated that the density of water in the hydration shells of Mg(2+) and Al(3+) is, respectively, ～61% and ～71% higher than in bulk water.     

Joint experimental and theoretical study of vibrationally inelastic electron scattering on propane

Vibrational electron energy loss spectra were measured for propane at incident energies of 3, 6, 10, 15, 20, and 25 eV at scattering angles of 40 degrees, 55 degrees, 70 degrees, 85 degrees, and 100 degrees . The spectra are compared with the results of ab initio calculations using a recently developed two-channel discrete momentum representation method. Good agreement between theory and experiment was found for large scattering angles and energies above the resonant region.     

On the determination of bond angles of triatomic radicals from electron spin resonance

The s and the p density of the sp hybrid orbital of the unpaired electron on the central nucleus of CO^?₂ and BF₂ are calculated as a function of the bond angle by the INDO molecular orbital method. The theory yields a dependence of the ratio of the p density to the s density on bond angle markedly different from a dependence derived from the orthogonality of sp hybrid orbitals and commonly used to determine the bond angle from ESR data.     

On the structure of glassy polymers. II. Small-angle x-ray scattering from poly(methyl methacrylate)

The small-angle x-ray scattering (SAXS) from glassy poly(methyl methacrylate) has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.6 (electrons)² Å^?3, is within a factor of 1.5 of the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in highly isotactic PMMA (150–200 Å), but can be well represented by small concentrations of heterogeneities, several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material is well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

On the theoretical determination of the electron affinity of ozone

Summary Multiconfigurational electron correlation methods have been analyzed in order to theoretically compute the electron affinity (EA) of ozone. The near-degeneracy correlation effects, which are so important in O₃ and O ₃ ^– , have been described using complete active space (CAS) SCF wave functions. Remaining dynamic correlation effects are computed using second-order perturbation theory (the CASPT2 method). The best calculated adiabatic value (including zero-point energy corrections), 2.19 eV, is about 0.09 eV larger than the experimental value. Comparative studies using size-consistent coupled pair functional approaches (CPF and ACPF) have also been performed. The harmonic frequencies in O ₃ ^– have been determined to be: ₁=992, ₂=572, and ₃=879 cm^–1, which gives a zero-point energy of 0.151 eV.     

To the theory of electron scattering by polyatomic molecules

Within the Born-Oppenheimer adiabatic perturbation theory, an equation was obtained for the intensity of fast electron scattering by polyatomic molecules. All of its parameters are explicitly defined by vibronic interaction in a molecule; due to this, quantum chemical calculations are fully applicable to electron diffraction studies of molecular geometries. Engels Anti-Aircraft Missile Higher Military School. Translated fromZhurmal Strukturnoi Khimii, Vol. 35, No. 2, pp. 40–45, March–April, 1994. Translated by L. Smolina