Z dependence of electron scattering by single atoms into annular dark-field detectors

A simple parameterization is presented for the elastic electron scattering cross sections from single atoms into the annular dark-field (ADF) detector of a scanning transmission electron microscope (STEM). The dependence on atomic number, Z, and inner reciprocal radius of the annular detector, q(0), of the cross section σ(Z,q(0)) is expressed by the empirical relation [see formula in text] where A(q(0)) is the cross section for hydrogen (Z = 1), and the detector is assumed to have a large outer reciprocal radius. Using electron elastic scattering factors determined from relativistic Hartree-Fock simulations of the atomic electron charge density, values of the exponent n(Z,q(0)) are tabulated as a function of Z and q(0), for STEM probe sizes of 1.0 and 2.0 ?. Comparison with recently published experimental data for single-atom scattering [Krivanek et al. (2010). Nature 464, 571-574] suggests that experimentally measured exponent values are systematically lower than the values predicted for elastic scattering from low-Z atoms. It is proposed that this discrepancy arises from the inelastic scattering contribution to the ADF signal. A simple expression is proposed that corrects the exponent n(Z,q(0)) for inelastic scattering into the annular detector.     

Electron scattering from perfluorocyclobutane (c-C4F8)

We report experimental results for electron scattering from perfluorocyclobutane, c-C(4)F(8), obtained from measurements in our two laboratories. A set of differential, integral, and momentum transfer cross sections is provided for elastic scattering for incident electron energies from 1.5 to 100 eV. Inelastic scattering (vibrational excitation) cross sections have been measured for incident electron energies of 1.5, 2, 5, 6, and 7 eV. In order to investigate the role of intermediate negative ions (resonances) in the scattering process we have also measured an excitation function for elastic scattering and vibrational excitation of the ground electronic state of C(4)F(8) for incident energies between 0.6 and 20 eV. These results are compared with the limited amount of data available in the literature for scattering from this molecule.     

Organotellurium(VI) azides and halides

The reaction of azide with organotellurium(VI) halides Ph(5)TeBr and cis-(biphen)(2)TeF(2) (biphen = 2,2'-biphenyldiyl) resulted in the formation and isolation of Ph(5)TeN(3) (1) and cis-(biphen)(2)Te(N(3))(2) (2), which are the first tellurium(VI)-azide species. In addition to spectroscopic data, both crystal structures have been determined. Furthermore, the stability of possible Te(VI) species with higher azide contents Ph(x)()Te(N(3))(6)(-)(x)() and Me(x)()Te(N(3))(6)(-)(x)() as well as the syntheses and properties of their Ph/Me(x)()TeF(y)() precursors was investigated, including the crystal structure determination of trans-Ph(2)TeF(4) (3). Ab initio and density functional studies of all molecules regarding the structures and electronic populations were performed.     

Total atomic scattering factors for the ground states of the lithium isoelectronic sequence from Na8+ to Ca17+

In this work, total atomic scattering factors for the ground states of the lithium isoelectronic sequence are calculated by using the full core plus correlation wave function. For the ground state of the lithium atom, our results are compared with the previous theoretical values in the literature; the influence of electron correlation on total atomic scattering factors is analyzed systematically and our results agree with previous configuration interaction calculations very well. For the ground states of the lithium isoelectronic sequence from Na8+ to Ca17+, the general functional behavior of total atomic scattering factors is analyzed together for each state of the isoelectronic sequence.     

TeX(4) (X = F, Cl, Br) as Lewis acids - complexes with soft thio- and seleno-ether ligands

TeF(4) reacts with OPR(3) (R = Me or Ph) in anhydrous CH(2)Cl(2) to give the colourless, square based pyramidal 1?:?1 complexes [TeF(4)(OPR(3))] only, in which the OPR(3) is coordinated basally in the solid state, (R = Me: d(Te-O) = 2.122(2) ?; R = Ph: d(Te-O) = 2.1849(14) ?). Variable temperature (19)F{(1)H}, (31)P{(1)H} and (125)Te{(1)H} NMR spectroscopic studies strongly suggest this is the low temperature structure in solution, although the systems are dynamic. The much softer donor ligands SMe(2) and SeMe(2) show a lower affinity for TeF(4), although unstable, yellow products with spectroscopic features consistent with [TeF(4)(EMe(2))] are obtained by the reaction of TeF(4) in neat SMe(2) or via reaction in CH(2)Cl(2) with SeMe(2). TeX(4) (X = F, Cl or Br) causes oxidation and halogenation of TeMe(2) to form X(2)TeMe(2). The Br(2)TeMe(2) hydrolyses in trace moisture to form [BrMe(2)Te-O-TeMe(2)Br], the crystal structure of which has been determined. TeX(4) (X = Cl or Br) react with the selenoethers SeMe(2), MeSe(CH(2))(3)SeMe or o-C(6)H(4)(SeMe)(2) (X = Cl) in anhydrous CH(2)Cl(2) to give the distorted octahedral monomers trans-[TeX(4)(SeMe(2))(2)], cis-[TeX(4){MeSe(CH(2))(3)SeMe}] and cis-[TeCl(4){o-C(6)H(4)(SeMe)(2)}], which have been characterised by IR, Raman and multinuclear NMR ((1)H, (77)Se{(1)H} and (125)Te{(1)H}) spectroscopy, and via X-ray structure determinations of representative examples. Tetrahydrothiophene (tht) can form both 1?:?1 and 1?:?2 Te?:?L complexes. For X = Br, the former has been shown to be a Br-bridged dimer, [Br(3)(tht)Te(μ-Br)(2)TeBr(3)(tht)], by crystallography with the tht ligands anti, whereas the latter are trans-octahedral monomers. Like its selenoether analogue, MeS(CH(2))(3)SMe forms distorted octahedral cis-chelates, [TeX(4){MeS(CH(2))(3)SMe}], whereas the more rigid o-C(6)H(4)(SMe)(2) unexpectedly forms a zig-zag chain polymer in the solid state, [TeCl(4){o-C(6)H(4)(SMe)(2)}](n), in which the dithioether adopts an extremely unusual bridging mode. This is in contrast to the chelating monomer, cis-[TeCl(4){o-C(6)H(4)(SeMe)(2)}], formed with the analogous selenoether and may be attributed to small differences in the ligand chelate bite angles. The wider bite angle xylyl-linked bidentates, o-C(6)H(4)(CH(2)EMe(2))(2) behave differently; the thioether forms cis-chelated [TeX(4){o-C(6)H(4)(CH(2)SMe)(2)}] confirmed crystallographically, whereas the selenoether undergoes C-Se cleavage and rearrangement on treatment with TeX(4), forming the cyclic selenonium salts, [C(9)H(11)Se](2)[TeX(6)]. The tetrathiamacrocycle, [14]aneS(4) (1,4,8,11-tetrathiacyclotetradecane), does not react cleanly with TeCl(4), but forms the very poorly soluble [TeCl(4)([14]aneS(4))](n), shown by crystallography to be a zig-zag polymer with exo-coordinated [14]aneS(4) units linked via alternate S atoms to a cis-TeCl(4) unit. Trends in the (125)Te{(1)H} NMR shifts for this series of Te(iv) halides chalcogenoether complexes are discussed.     

Electron scattering from tetrafluoroethylene

We report experimental results for electron scattering from tetrafluoroethylene, C2F4, obtained from measurements in two laboratories. An extensive set of differential, integral, and momentum transfer cross sections is provided for elastic scattering for incident electron energies from 1 to 100 eV and inelastic (vibrational excitation) scattering for incident electron energies at 3, 6, 7.5, 8, and 15 eV, and for scattering angles ranging from 10 degrees to 130 degrees. To highlight the role of intermediate negative ions (resonances) in the scattering process we have also measured excitation functions for elastic scattering and vibrational excitation of the ground electronic state of C2F4 for incident energies between 1.5 and 20 eV. Our results are compared with recent theoretical calculations and a limited number of other experimental results.     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Quasielastic electron scattering from methane, methane-d4, methane-d2, ethylene, and 2-methylpropane

Quasielastic electron scattering from gaseous species at high momentum transfer was recently reported for the first time [Cooper et al., J. Electron Spectrosc. Relat. Phenom. 155, 28 (2007)]. The first results for CH(4) and CD(4) were well explained by a classical electron Compton scattering picture in which the electron scatters independently from each atom rather than the molecule as a whole. However, an alternative possible interpretation in terms of nondipole molecular vibrational excitation is suggested by previously published quantum mechanical calculations on high momentum transfer electron scattering from diatomic molecules [Bonham and de Souza, J. Chem. Phys. 79, 134 (1983)]. In order to determine which of these two interpretations best fits the experimental results, we have measured the quasielastic spectra of gaseous 2-methylpropane, ethylene, methane, and two isotopically substituted methanes, CH(2)D(2) and CD(4), at a momentum transfer of approximately 20 a.u. (2.25 keV impact energy and 100 degrees scattering angle). The experimental spectra are found to be composed of as many peaks as there are different atomic isotopes in the molecule (two for CH(4), C(2)H(4), 2-methylpropane, and CD(4) and three for CH(2)D(2)). The peak positions are predicted accurately by the independent atom electron Compton scattering model, and the relative intensities are in reasonable agreement. The experimental results thus support classical electron Compton scattering as the origin of the signal.     

用对称透射二维WAXS强度研究PET取向非晶态结构

用对称透射法，测试聚酯（ＰＥＴ）取向非晶试样的二维广角Ｘ射线散射相干强度Ｉ（Ｋ，α），将不同方位角α上的Ｉ（Ｋ，α）非晶重叠峰曲线进行计算分解，获得分子链间原子散射引起的二个峰为Ａ（Ｋ＝０．１２６），Ｂ（Ｋ＝０．１６９），分子链内原子散射引起五个峰分别为Ｃ（Ｋ＝０．３０４），Ｄ（Ｋ＝０．５５３），Ｅ（Ｋ＝０．３７４），Ｆ（Ｋ＝０．４６５），Ｇ（Ｋ＝０．６０６），Ｋ单位为ｎｍ＾－１，分析了它们的结构     

Low-energy electron attachment to SF6. II. Temperature and pressure dependences of dissociative attachment

Low-energy electron-molecule collisions, leading to dissociative attachment through metastable anionic states, are kinetically modeled within the framework of statistical unimolecular rate theory. The reaction e(-)+SF(6)-->SF(5)(-)+F is used as an illustrative example. The modeling is applied to new measurements of branching fractions for SF(5)(-) formation in the bath gas He between 360 and 670 K at 1 and 2 Torr, and between 490 and 620 K over the range of 0.3-9 Torr. The analysis of the data follows the previous kinetic modeling of the nondissociative electron attachment, e(-)+SF(6)-->SF(6)(-), from Part I of this series. Experimental results from the present work and the literature on branching fractions and total cross sections for anion formation as functions of electron energies, bath gas temperatures and pressures, as well as observation times are analyzed. The assumption of a participation of the electronic ground state of SF(6)(-) alone suffices to model the available experimental data. A value of the dissociation energy of SF(6)(-) into SF(5)(-)+F of E(0,dis)=1.61(+/-0.05) eV is determined, which may be compared to the electron affinity of SF(6), EA=1.20(+/-0.05) eV, such as derived in Part III of this series.     

Contributions from radiation damping and surface scattering to the linewidth of the longitudinal plasmon band of gold nanorods: a single particle study

The scattering spectra of single gold nanorods with aspect ratios between 2 and 4 have been examined by dark field microscopy. The results show that the longitudinal plasmon resonance (electron oscillation along the long axis of the rod) broadens as the width of the rods decreases from 14 to 8 nm. This is attributed to electron surface scattering. Analysis of the data using gamma = gamma(bulk) + Anu(F)/L(eff), where L(eff) is the effective path length of the electrons and nu(F) is the Fermi velocity, allows us to determine a value for the surface scattering parameter of A = 0.3. Larger rods with widths of 19 and 30 nm were also examined. These samples also show spectral broadening, which is attributed to radiation damping. The relative strengths of the surface scattering and radiation damping effects are in excellent agreement with recent work on spherical gold nanoparticles by S?nnichsen et al., Phys. Rev. Lett., 2002, 88, 077402; and by Berciaud et al., Nano Lett., 2005, 5, 515.     

Effective monkey saddle points and berry and lever mechanisms in the topomerization of SF(4) and related tetracoordinated AX(4) species

The topomerization mechanisms of the SF(4) and SCl(2)F(2) sulfuranes, as well as their higher (SeF(4), TeF(4)) and isoelectronic analogues PF(4)(-), AsF(4)(-), SbF(4)(-), SbCl(4)(-), ClF(4)(+), BrF(4)(+), BrCl(2)F(2)(+), and IF(4)(+)), have been computed at B3LYP/6-31+G and at B3LYP/6-311+G. All species have trigonal bipyramidal (TBP) C(2)(v)() ground states. In such four-coordinated molecules, Berry rotation exchanges both axial with two equatorial ligands simultaneously while the alternative "lever" mechanism exchanges only one axial ligand with one equatorial ligand. While the barrier for the lever exchange in SF(4) (18.8 kcal mol(-1)) is much higher than that for the Berry process (8.1 kcal mol(-1)), both mechanisms are needed for complete ligand exchange. The F(ax)F(ax) and F(eq)F(eq) isomers of SF(2)Cl(2) have nearly the same energy and readily interconvert by BPR with a barrier of 7.6 kcal mol(-1). The enantiomerization of the F(ax)F(eq) chiral isomer can occur by either the Berry process (transition state barrier 8.3 kcal mol(-1)) or the "lever" mechanism via either of two C(s)() transition states, based on the TBP geometry: Cl(ax) <--> Cl(eq) or F(ax) <--> F(eq) exchanges with barriers of 6.3 and 15.7 kcal mol(-1), respectively. Full scrambling of all ligand sites is possible only by inclusion of the lever mechanism. Planar, "tetrahedral", and triplet forms are much higher in energy. The TBP C(3)(v) structures of AX(4) either have two imaginary frequencies (NIMAG = 2) for the X = F, Cl species or are minima (NIMAG = 0) for the X = Br, I compounds. These "effective monkey saddle points" have degenerate modes with two small frequencies, imaginary or real. Although a strictly defined "monkey saddle" (with degenerate frequencies exactly zero) is not allowed, the flat C(3)(v) symmetry region serves as a "transition state" for trifurcation of the pathways. The BPR mechanism also is preferred over the alternative lever process in the topomerization of the selenurane SeF(4) (barriers 5.9 vs. 12.1 kcal mol(-1)), the tellurane TeF(4) (2.1 vs. 6.4), and the interhalogen cations ClF(4)(+) (2.5 vs 14.8), BrF(4)(+) (4.7 vs. 11.3), BrF(2)Cl(2)(+) (14.6 vs. 17.4), and IF(4)(+) (1.4 vs. 6.0), as well as for the series PF(4)(-) (7.0 vs. 9.0), AsF(4)(-) (9.3 vs. 17.2), and SbF(4)(-) (3.8 vs. 5.3 kcal mol(-1)), all computed at B3LYP/6-311+G with the inclusion of quasirelativistic pseudopotentials for Te, I, and Sb. The heavier halogens increasingly favor the lever process, where the barrier (2.6 kcal mol(-1)) pertaining to the effective monkey saddle point (C(3)(v) minimum for SbCl(4)(-)) is less than that for the Berry process (8.2 kcal mol(-1)).     

Examination of (e,2e) scattering models by comparison of momentum profiles of noble gases between experiment and theory

Momentum profiles have been measured for the two outermost atomic orbitals of noble gases, Ar, Kr and Xe, at incident electron energy of about 2 keV using a newly developed multichannel (e,2e) spectrometer. The experimental results exhibit significantly improved statistics compared with those achieved in previous studies while covering a wide range of momenta up to 3.6 a.u. The results are compared with theoretical calculations using four (e,2e) scattering models, the plane-wave impulse and Born approximations (PWIA and PWBA), and the distorted-wave impulse and Born approximations (DWIA and DWBA). The DWIA and DWBA scattering models have been found to satisfactorily reproduce the experimental momentum profiles in terms of both shape and intensity over the entire momentum range covered, indicating the importance of distorted wave effects for quantitatively describing (e,2e) reaction.     

Crystal structure of ClF(4)(+)SbF(6)(-), normal coordinate analyses of ClF(4)(+), BrF(4)(+), IF(4)(+), SF(4), SeF(4), and TeF(4), and simple method for calculating the effects of fluorine bridging on the structure and vibrational spectra of ions in a strongly interacting ionic solid.

The crystal structure of the 1:1 adduct ClF(5).SbF(5) was determined and contains discrete ClF(4)(+) and SbF(6)(-) ions. The ClF(4)(+) cation has a pseudotrigonal bipyramidal structure with two longer and more ionic axial bonds and two shorter and more covalent equatorial bonds. The third equatorial position is occupied by a sterically active free valence electron pair of chlorine. The coordination about the chlorine atom is completed by two longer fluorine contacts in the equatorial plane, resulting in the formation of infinite zigzag chains of alternating ClF(4)(+) and cis-fluorine bridged SbF(6)(-) ions. Electronic structure calculations were carried out for the isoelectronic series ClF(4)(+), BrF(4)(+), IF(4)(+) and SF(4), SeF(4), TeF(4) at the B3LYP, MP2, and CCSD(T) levels of theory and used to revise the previous vibrational assignments and force fields. The discrepancies between the vibrational spectra observed for ClF(4)(+) in ClF(4)(+)SbF(6)(-) and those calculated for free ClF(4)(+) are largely due to the fluorine bridging that compresses the equatorial F-Cl-F bond angle and increases the barrier toward equatorial-axial fluorine exchange by the Berry mechanism. A computationally simple model, involving ClF(4)(+) and two fluorine-bridged HF molecules at a fixed distance as additional equatorial ligands, was used to simulate the bridging in the infinite chain structure and greatly improved the fit between observed and calculated spectra.     

A computational study of tetrafluoro-[2.2]cyclophanes

A computational study of the isomers of tetrafluorinated [2.2]cyclophanes persubstituted in one ring, namely F4-[2.2]paracyclophane (4), F4-anti-[2.2]metacyclophane (5a), F4-syn-[2.2]metacyclophane (5b), and F4-[2.2]metaparacyclophane (6a and 6b), was carried out. The effects of fluorination on the geometries, relative energies, local and global aromaticity, and strain energies of the bridges and rings were investigated. An analysis of the electron density by B3PW91/6-31+G(d,p), B3LYP/6-31+G(d,p), and MP2/6-31+G(d,p) was carried out using the natural bond orbitals (NBO), natural steric analysis (NSA), and atoms in molecules (AIM) methods. The analysis of frontier molecular orbitals (MOs) was also employed. The results indicated that the molecular structure of [2.2]paracyclophane is the most affected by the fluorination. Isodesmic reactions showed that the fluorinated rings are more strained than the nonfluorinated ones. The NICS, HOMA, and PDI criteria evidenced that the fluorination affects the aromaticity of both the fluorinated and the nonfluorinated rings. The NBO and NSA analyses gave an indication that the fluorination increases not only the number of through-space interactions but also their magnitude. The AIM analysis suggested that the through-space interactions are restricted to the F4-[2.2]metacyclophanes. In addition, the atomic properties, computed over the atomic basins, gave evidence that not only the substitution, but also the position of the bridges could affect the atomic charges, the first atomic moments, and the atomic volumes.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

Theoretical investigation on electron scattering by benzene in the intermediate-energy range

We present a theoretical investigation on electron scattering by benzene (C₆H₆) in the intermediate-energy range. Calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and total absorption cross sections are reported for impact energies ranging from 20 to 500 eV. A complex optical potential is used to represent the electron-molecule interaction dynamics. A theoretical method based on the single-center-expansion close-coupling framework and corrected by the Padé approximant [F.A. Gianturco, R.R. Lucchese, N. Sanna, J. Chem. Phys. 102 (1995) 5743] is used to solve the scattering equations. The comparison of our calculated results with the experimental and theoretical data available in the literature is encouraging.     

Combined spectroscopic and topographic characterization of nanoscale domains and their distributions of a redox protein on bacterial cell surfaces

Redox protein nanoscale domains on the cell surface of a bacterium, Shewanella oneidensis MR1, grown in the absence and presence of electron acceptors, is topographically characterized using combined atomic force microscopy (AFM) and confocal surface enhanced Raman scattering (SERS) spectroscopy. The protruding nanoscale domains on the outer membrane of S. oneidensis were observed, as was their disappearance upon exposure to electron acceptors such as oxygen, nitrate, fumarate, and iron nitrilotriacetate (FeNTA). Using SERS spectroscopy, a redox heme protein was identified as a major component of the cell surface domains. This conclusion was further confirmed by the disappearance of Raman vibrational frequencies, characteristic of heme proteins, upon exposure of the cells to electron acceptors. Our experimental results from our AFM imaging and SERS spectroscopy, consistent with the literature, suggest the protruding nanoscale surface domains as heme-containing secretions. Our results on the distributions of redox proteins on microbial cell surfaces will be helpful for a mechanistic understanding of the behaviors of surface proteins and their interactions with redox environments.     

Inner shell excitation of SF6 by 2.5 keV electron impact

The S 2p, S 2s and F 1s inner shell excitation spectra of SF₆ have been examined by small angle, inelastic scattering of 2.5 keV electrons. While the main features of the spectra are in agreement with previous photoabsorption spectra, a number of new features have been observed. A detailed investigation of the S 2p spectrum below the ionization limit has been performed. The weak Rydberg structure in this region has been interpreted on the basis of a comparison of the present electron energy loss results with previous photoabsorption studies. Part of the Rydberg structure in the electron impact spectrum has been identified as arising from electric quadrupole transitions.     

X-ray and electron scattering factors for many-electron atomic system

Analytical expressions are developed for the x-ray and electron scattering factors for a many-electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater-type orbitals (STO 's). The expressions so developed have been used to calculate the coherent and incoherent x-ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree–Fock wave functions for the evaluation of “one-electron properties” of many-electron atomic systems.