All-electron calculations with plane waves in solid lithium hydride

Calculations of the directional Compton profiles and the anisotropies of Compton scattering are reported, based on the density functional theory in the local density approximation, performed in the plane-wave basis, and using full, unscreened Coulomb potentials for both Li and H atoms. It is shown that converged results can be obtained without employing pseudopotentials, and the Compton profiles obtained are in excellent agreement with experiment. The influence of correlation on Compton profiles in LiH is found to be very weak. Possibilities (and limits) of extending the plane-wave calculations with the full Coulomb potentials to other atoms and substances are discussed. © 1997 John Wiley & Sons, Inc.     

Experimental investigation of multiple scattering of 662 keV gamma rays in zinc at 90°

Compton scattering investigations usually examine the case when photon has undergone only one Compton collision in the sample. The probability of a photon being scattered several times may be significant for a target of finite dimensions both in depth and lateral dimensions. The present experiment is undertaken to study the intensity and energy distributions of 662 keV gamma rays multiply scattered from a zinc target of various thicknesses at a scattering angle of 90° with the scattered photons being detected by an HPGe gamma detector. We observe that with an increase in target thickness, the number of multiply scattered photons also increases and saturates at a particular value of the target thickness (saturation depth). This supports the work of Paramesh, L., Venkataramaih, L., Gopala, K., Sanjeevaih, H. [1983. Z-dependence of saturation depth for multiple scattering of 662 keV photons from thick samples. Nucl. Instrum. Methods 206, 327–230]. The double Compton scattered peak is also observed in the experimental spectra, with a position in agreement with the predictions of Fernandez, J.E. [1991. Compton and Rayleigh double scattering of unpolarized radiation. Phys. Rev. A44, 4232–4248] and Barnea, G., Dick. C.E., Ginzburg. A.E., Seltzer. S.M. [1995. A study of multiple scattering background in Compton scatter imaging. NDT E Int. 28. 155–162].     

Bethe surface and compton profile for CO2 obtained by use of 35 keV incident electrons

Electron impact spectra for CO₂ have been obtained at 25 different scattering angles ranging from 1.12° to 14.06°. The measured intensities were converted to generalized oscillator strengths and normalized by use fo the Bethe sum rule, leading to the mapping of the Bethe surface over large momentum transfer K and energy loss E ranges. Substantial deviations from the binary encounter theory were observed for K values smaller than 3 au. A discussion is given on the possibility of extracting partial Compton profiles from the data. The total Compton profile was obtained at large K values and found to be in good agreement with recent calculations, within the experimental uncertainties.     

Electron momentum density and compton profiles: an accurate check of overlap models

Directional Compton profiles of single crystal LiH have been measured for the scattering vector parallel to 〈100〉 and 〈110〉. These two directions are of prime importance because 〈100〉 is the direction of the LiH molecular bond and 〈110〉 that of the interactions between ions of the same species. These measurements have been performed using X-Ray inelastic scattering with the highest ever achieved resolution. Because of Synchrotron Radiation, this technique has now reached the point of routine and reliable execution. Compton scattering is a very accurate test of calculated wave functions. Our results are compared with two different calculations. None is found to be satisfactory over the entire momentum range. Best agreement is obtained at large momentum values with a calculation where the overlap between hydrogen ions is treated, but the existing discrepancy at small momentum invites to more sophisticated models.     

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.     

Bremsstrahlung spectra from lead and tantalum at 6 MeV electron energy

Bremsstrahlung spectral distributions have been experimentally measured for thick targets of lead and tantalum at 6 MeV electron energy, using Compton scattering technique. The experimental results are in agreement with the theoretical results.     

Statistical mechanics in rotationally inelastic scattering of molecules from surface within the dynamical Lie algebraic method

The dynamical Lie algebraic (DLA) method of Alhassid and Levine [Phys. Rev. A 18 (1978) 89] is applied to statistical mechanics in rotationally inelastic scattering of molecules from surfaces. Specifically, the method is generalized to include the motion of surface atoms, i.e., phonons. For given Hamiltonian and initial state, the set of constraints required to obtain the solution of the motion equations is determined by an algebraic procedure. It is furthermore found possible to derive the motion equations for the mean values of the constraints. Application of the method to the scattering of NO molecules from a Pt(1 1 1) surface is made. The mean values of the final energies of NO molecules scattered from the surface obtained using the DLA method are in good agreement with experimental results in qualitative trends. The DLA method thus appears to have a wide range of validity for describing the statistical mechanics of the gas-surface scattering.     

Compton profiles and polarizability as two similar probes of the electronic structure of 14 electron diatomic molecules: An ab initio study

High‐ and low‐energy scattering properties, namely, Compton profiles and polarizability, respectively, were calculated at the configuration interaction (CI) level from molecular orbitals expressed in the linear combination of atomic orbitals (LCAO) model for 14 electron diatomic molecules. Extended atomic basis sets including about 100 Gaussian‐type functions (GTFs) were used. The isotropic and directional Compton profiles and the polarizability show that the behavior of CO and N₂ is rather similar but very different from that of BF. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 63–74, 1999     

A DFT computational study of spin crossover in iron(III) and iron(II) tripodal imidazole complexes. A comparison of experiment with calculations

B3LYP* functionals were used to model the sixteen iron(II) (1A, LS and 5T, HS) and iron(III) (2T, LS and 6A, HS) complexes of the 1 : 3 Schiff base condensate of tris(2-aminoethyl)amine and imidazole-4-carboxaldehyde, H3L1, and its deprotonated forms, [H2L1]1-, [HL1]2-, and [L1]3-. This ligand system is unusual in that [FeH3L1]3+, [FeH3L1]2+ and [FeL1]- all exhibit a spin crossover between 100-300 K. This makes these complexes ideal for a hybrid DFT computational approach and provides an opportunity to refine the value of the exact exchange admixture parameter, c3, and to predict properties of partially protonated complexes that are not experimentally available. The accepted value of 0.20 is larger than the value of approximately 0.13 that was found to best reproduce experimental data in terms of spin state predictions. With iron(III) B3LYP calculations showed that all of the complexes were low spin at 298 K with the exception of [FeH3L1]3+ which is spin crossover in agreement with experimental results. It was also shown for iron(III) that the ligand field increased as the number of protons decreased.In contrast all of the iron(II) complexes were close to the spin crossover region regardless of protonation state. Experimental structures are fairly well modeled by this system in regard to the key structural indicators of spin state, which are the bite and trans angles. The calculated iron to nitrogen atom distances are always larger in the high spin form than the low spin form but all iron to nitrogen bond distances are larger than the experimental values. In general non-bonded interactions are not well modeled by this methodology.     

Electron momentum density in ZnSe: Theory and experiment

We present experimental Compton profiles of ZnSe along [1 0 0] and [1 1 0] directions using our 740 GBq ¹³⁷Cs Compton spectrometer. We have also computed the momentum densities, energy bands, density of states (DOS) and band gaps using density functional theory (local density and generalized gradient approximations) and pseudopotential (PP) approach. The anisotropy in the momentum density is well reproduced by the density functional calculations. The energy bands and bond length are interpreted in terms of the anisotropies.     

Asymmetries and anisotropies in the Compton scattering from the hydrogen molecule

The Compton energy loss spectra of atomic targets exhibits usually a specific asymmetry due to the postcollisional electrostatic interaction between the remaining ion and the ejected electron. This asymmetry, or Compton defect, also exists in the scattering by molecules or solids. The first attempt to describe the Compton defect for the hydrogen molecule is proposed here. The Compton energy loss spectra depends particularly on the relative orientation of the momentum transferred by the incident particle and the molecular axis. A comparison between the respective magnitudes of Compton profiles and Compton defects was one of the aims of this article. The results emphasize the particular interest of a simultaneous interpretation of both symmetrical and antisymmetrical contributions in the study of molecular or solid-state electronic structures. © 1995 John Wiley & Sons, Inc.     

A DFT computational study of spin crossover in iron(III) and iron(II) tripodal imidazole complexes. A comparison of experiment with calculations

B3LYP* functionals were used to model the sixteen iron(II) (1A, LS and 5T, HS) and iron(III) (2T, LS and 6A, HS) complexes of the 1:3 Schiff base condensate of tris(2-aminoethyl)amine and imidazole-4-carboxaldehyde, H3L1, and its deprotonated forms, [H2L1]1-, [HL1]2-, and [L1]3-. This ligand system is unusual in that [FeH3L1]3+, [FeH3L1]2+ and [FeL1]- all exhibit a spin crossover between 100-300 K. This makes these complexes ideal for a hybrid DFT computational approach and provides an opportunity to refine the value of the exact exchange admixture parameter, c3, and to predict properties of partially protonated complexes that are not experimentally available. The accepted value of 0.20 is larger than the value of approximately 0.13 that was found to best reproduce experimental data in terms of spin state predictions. With iron(III) B3LYP calculations showed that all of the complexes were low spin at 298 K with the exception of [FeH3L1]3+ which is spin crossover in agreement with experimental results. It was also shown for iron(III) that the ligand field increased as the number of protons decreased. In contrast all of the iron(II) complexes were close to the spin crossover region regardless of protonation state. Experimental structures are fairly well modeled by this system in regard to the key structural indicators of spin state, which are the bite and trans angles. The calculated iron to nitrogen atom distances are always larger in the high spin form than the low spin form but all iron to nitrogen bond distances are larger than the experimental values. In general non-bonded interactions are not well modeled by this methodology.     

Measurement of the Compton profiles of CH4 and C2H4 by high energy electron impact spectroscopy

We present a new experimental determination of the Compton profiles of CH₄ and C₂H₄ molecules using high energy electron impact. The observable q range has been extended up to 10 au (6 au for C₂H₄). Good agreement is found with an earlier X-ray scattering experiment and with new theoretical calculations.     

Measurement of Compton scattering on bound electrons by the coincidence method

A review of results of the new method for measuring the Compton scattering on bound electrons in germanium, introduced by the presented authors, is given. It is based on the application of two detectors that operate in the coincidence mode. One detector is used as the scatterer and the other as the detector of scattered radiation. Two conditions, simultaneity of pulses from the two detectors and constant energy sum, result in very clean spectra in broad energy regions. Normalization of the Compton spectra to the Ge K X-ray escape peaks, which are measured simultaneously with the Compton spectrum, gives reliable double-differential Compton-scattering cross sections on an absolute scale. Several versions of the impulse approximation are compared to the cross sections obtained by the present method for incident photon energies in the range from 60 to 105 keV. The non-relativistic impulse approximation gives the best agreement to the experimental data. We point out the suitability of the new method for an investigation of the incoherent scattering function at small photon momentum transfer.     

Electronic structure,Compton profiles and cohesive properties of Cs-halides

We have reported energy bands, density of states, valence electron charge densities and Compton profiles of CsCl, CsBr and CsI using linear combination of atomic orbitals with Hartree–Fock and density functional theories. We have also computed these properties, except the momentum densities, using full potential linearized augmented plane wave method. The general features of the energy bands and the density of states in these halides are found to be almost similar. To interpret the theoretical data on Compton line shapes, we have also measured the Compton profiles using our 20 Ci ¹³⁷Cs spectrometer. It is seen that the Hartree–Fock calculations give relatively a better agreement with the experimental momentum densities. On the basis of equal-valence-electron-density profiles, a comparison of relative nature of bonding is made which is in agreement with the valence charge densities and atomic charges by means of Mulliken analysis. Using our experimental and theoretical Compton profiles, we have also computed the cohesive energy of the halides.     

Experimental compton profile of water

Experimental Compton profiles of water have been corrected for multiple scattering effects and compared with calculated profiles available from wavefunctions of various types. Small but still existing differences between the experimental result and the result obtained from a near Hartree—Fock function (less than 2% at J(0)) suggest the inclusion of the effects of intermolecular bonding into the calculation.     

Electron momentum distributions and compton profiles of some alkali halides with FSGO model

The electron momentum distributions (EMD's) and Compton profiles (CP's) of LiF, LiCl, NaF and NaCI have been calculated using the floating spherical gaussian orbital (FSGO) model wavefunctions. The calculated FSGO Compton profiles are in good agreement with the available experimental data considering the simplicity of the model used. The calculated EMD and CP values in these systems are nearly equal to the sum of the contributions of respective cations and anions.     

Experimental observation of energy dependence of saturation thickness of multiply scattered gamma photons

The gamma photons continue to soften in energy as the number of scatterings increases in the target having finite dimensions both in depth and lateral dimensions. The number of multiply scattered photons increases with an increase in target thickness, and saturates at a particular value of the target thickness known as saturation thickness (depth). The present measurements are carried out to study the energy dependence of saturation thickness of multiply scattered gamma photons from targets of various thicknesses. The scattered photons are detected by a properly shielded NaI(Tl) gamma ray detector placed at 90° to the incident beam. We observe that the saturation thickness increases with increasing incident gamma photon energy. Monte Carlo calculations based upon the package developed by Bauer and Pattison [Compton scattering experiments at the HMI (1981), HMI-B 364, pp. 1–106] support the present experimental results.     

Strong antiferromagnetism in the dinuclear 2-pyridone complex with N–C–O bridges: A paddle-wheel analogue of the dinuclear tetracarboxylates

A novel dinuclear complex [Cu₂(μ-L)₄(HL)₂] (1) was isolated from starting 2-pyridone (HL) via a resonance and a tautomeric transformation. Each copper centre is in a square-pyramidal coordination sphere, defined by two oxygen atoms (Cu–O4 1.978(5), Cu–O11 1.964(4) Å) and two nitrogen atoms (Cu–N2 2.003(5), Cu–N3 2.007(5) Å) of four bridging deprotonated pyridin-2-olates and an oxygen atom on the top from a neutral 2-pyridone (Cu–O2 2.227(5) Å), analogous to tetracarboxylate paddle-wheel complexes. Compound 1 was compared with mixed pyridin-2-olato/methanoato analogues [Cu₂(μ-HCO₂)₂(μ-L)₂(HL)₂] · 2CH₃CN (2) and [Cu₂(μ-HCO₂)₂(μ-L)₂(HL)₂] (2a) (2a is an air stable form obtained from 2 outside mother-liquid). The EPR spectra of air stable 1 and 2a show three signals H_z1, H₂ and H_z2, typical for the binuclear systems with spin S = 1, both revealing strong antiferromagnetism 2J = −334 (1) and −324 cm⁻¹ (2a). Interestingly, only for 1 additional H₁ signal at 100 mT is noticed (D(1) = 0.293 cm⁻¹ < hν = 0.320 cm⁻¹ < D(2a) = 0.347 cm⁻¹). On the other hand, several broad signals in the 100–450 mT region, only in the high temperature spectrum for 2a are observed. These results are in agreement with the magnetic susceptibility analysis.     

X-ray scattering by water molecules studied by using synchrotron radiation

The energy spectra of free water molecules were measured at scattering angles 2θ ranging from 10.5° to 75.7°, using an angle-dispersive-type diffractometer and synchrotron radiation as an X-ray source. A silicon (111) monochrometer was used to obtain incident X-rays with the wavelengths of (1.543/n) Å (n = 1,3,4,5). Observed inelastic scattering peaks are clearly separated from eleastic ones at s values [s = (4π/λ) sin Å] larger than 8 Å^?1. The increase of the separation with an increasing s value was consistent with the classical theory of the Compton shift. The total (elastic plus inelastic) intensities were obtained over a range of s = 0.74–5.0 Å^?1. Experimental difference intensities Δσ_ee and Δσ_ne were obtained separately by combining the X-ray and high-energy electron scattering data. The experimental results are in reasonable agreement with the theoretical intensities calculated from SCF and CI molecular wave functions with a basis set of double-zeta plus polarization functions. © 1994 John Wiley & Sons, Inc.