Compton profiles and momentum space inequalities

Rigorous upper and lower bounds to the atomic Compton profileJ(q) are obtained for any value of the momentum transferredq in terms of radial expectation values 〈p ⁿ 〉 of the atomic momentum density γ(p). In doing so, a procedure based on moment-theoretic techniques and Chebyshev inequalities has been used. This type of results can be employed to study the compatibility of diverse information obtained by using different models, techniques, numerical calculations or experimental data. The same method allows also to obtain approximations to the Compton profile and to bound other relevant characteristics ofJ(q). A comparison of the approximations with some previously known Maximum Entropy Approximations is done. In order to test the accuracy of the bounds, a numerical study of the results is carried out in a Hartree-Fock framework for atomic systems.     

Compton profiles of solvated electrons

The importance of applying a variety of experimental techniques to unravel the nature of solvated electrons is emphasized. Compton profiles are evaluated for these species from a range of models. Some comparisons are made with positron annihilation studies.     

Compton profiles by the 1. Born approximation

Analytic formulas for K, L and M subshell Compton profiles (CP's) within the first Born approximation are given for relativistic scattering kinematics.     

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.     

Calculation of isotropic Compton profiles with Gaussian basis sets

In this paper we present an adaptive algorithm for calculating the isotropic Compton profile (ICP) for any type of Gaussian basis set. The ICP is a measure of the momentum density of electrons and it can be obtained from inelastic X-ray scattering experiments employing synchrotron radiation. We have performed calculations of the ICP for water and helium monomers and dimers using density-functional theory, Hartree-Fock and post-Hartree-Fock methods, with Dunning-type ((d-)aug-)cc-p(C)VXZ basis sets. We have examined the convergence of the Compton profile as a function of the basis set and the level of theory used for the formation of the density matrix. We demonstrate that diffuse basis functions are of utmost importance to the calculation of Compton profiles. Basis sets of at least triple-ζ quality appended by diffuse functions should be used in Compton profile calculations in order to obtain sufficient convergence with regard to the current, experimentally feasible accuracy for systems consisting of light elements.     

Electronic structure,Compton profiles and optical properties of TaC and TaN

Isotropic Compton profiles of TaC and TaN have been measured for the first time, at an intermediate resolution, using 662 keV γ-radiation. Energy bands, density of states and Fermi surface topology of TaC and TaN have been computed using linear combination of atomic orbitals with density functional theory and full potential linearised augmented plane wave method. Both band structure calculations predict the metallic character of TaC and TaN. The electron momentum densities calculated using various approaches of density functional theory are compared with the present measurements. On the basis of Mulliken’s population, it is also seen that TaC has more covalent bonding than TaN. The optical properties computed using full potential linearised augmented plane wave method are explained in terms of intraband transitions.     

Compton profiles for ejected electrons: Determination of momentum densities

Electron Compton scattering effects usually lead to the determination of momentum densities in atoms and molecules by cross-section measurements on scattered electrons. Similar information is also shown to be directly available from the study of ejected electrons. The proposed treatment results from a simple alteration of the impulse assumptions and appears to give a satisfactory representation of ejected profiles for medium and high energy electron scattering. Preliminary investigations are discussed here for hydrogen and helium atoms.     

Methods for the calculation of spherically averaged Compton profiles with GTOs

For the first time, an analytical and efficient algorithm for the evaluation of spherically averaged reciprocal form factors B(s)=〈B( s )〉_Ω using Gauss-type basis functions is presented. The spherically averaged Compton profile is available by Fourier transformation of the reciprocal form factor. The algorithm has been successfully implemented in connection with the quantum chemistry codes GAMESS and CRYSTAL92, which perform Hartree–Fock calculations for molecules and solids. In addition, an analytical algorithm for the direct evaluation of spherically averaged Compton profiles and the moments 〈p^ν〉 (ν≥−1) via the momentum density is proposed for Gauss-type basis functions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 213–223, 1997     

Evidence of instantaneous electron correlation from Compton profiles of crystalline silicon

The combination of new experimental and theoretical techniques provides evidence of instantaneous electron correlation effects in directional Compton profiles of crystalline silicon, which cannot be reproduced when reference is made to a density matrix obtained from a single-determinantal wavefunction. These effects are instead accounted for by a recently implemented post-Hartree-Fock periodic scheme, which gives results in quite good agreement with the high-quality experimental data.     

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     

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.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

团簇研究中的原子间势函数

原子间势函数在团簇结构和性质的理论研究中十分重要.本文将模拟团簇原子间相互作用的势函数划分成三类,对各类势函数的发展状况进行了综述;并对原子间势函数与最优化方法和分子动力学相结合,在团簇结构和性能研究中的应用和发展方向进行了讨论.     

Interatomic contributions to high-energy electron-molecule scattering

Within the independent atom scattering model, we derive an approximate formula for the rotationally and vibrationally averaged three-atom terms in the series expansion of the electron scattering cross section. This formula uses the atomic scattering factors as well as the atomic scattered wavefunctions as input, and rotational averaging is performed numerically. We compare our results to previous theoretical multiple scattering approaches for the molecules F(3), F(4), and SF(6) and to experimental data for TeF(6). Our results are consistent with those of previous calculations and inclusion of the three-atom term produces a dramatically better least squares fit of the TeF(6) data. The algorithm presented here is sufficiently fast and simple to be incorporated easily into existing electron diffraction codes.     

Interatomic potential-based semiclassical theory for Lennard-Jones fluids

An interatomic potential based semiclassical theory is proposed to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid confined in a channel. The inputs to the semiclassical formulation are the LJ parameters of the fluid and the wall, the density of channel wall atoms, and the average concentration of the fluid inside the channel. Using the semiclassical formulation, fluid confinement in channel with widths ranging from 2sigma ff to 100sigma ff, where sigma ff is the fluid-fluid LJ distance parameter, is investigated. The concentration and potential predicted by the semiclassical formulation are found to be in good agreement with those from equilibrium molecular dynamics simulations. While atomistic simulations in large channels are computationally expensive, the proposed semiclassical formulation can rapidly and accurately predict the concentration and potential profiles. The proposed semiclassical theory is thus a robust and fast method to predict the interfacial and "bulk" fluid phenomena in channels with widths ranging from the macroscale down to the scale of a few atomic diameters.     

Interatomic correlation in partially oriented polymer fibers

The atomic ordering in materials possessing cylindrical symmetry can be investigated by an approximation of the cylindrical distribution function in a given direction. The approximation gives correctly the extent of the interatomic correlation for a wide class of polymer fibers and reduces considerably the amount of the experimental and computational times.