丙烷分子的价轨道(2b2)电子的动量分布测量

电子动量谱学（EMS）是在原子、分子和固体物理中研究电子结构的一种强有力的工具，它基于运动学条件完全确定的（e，2e）碰撞电离反应[1-3]．本文报告用高分辨电子动量谱仪首次测量得到丙烷门3H8）分子的价轨道电子（252）的动量分布·丙烷（C3Hs）价轨道电子的动量分布实验是     

Electron Momentum Spectroscopy Investigation on Electronic Structure of Iso-dichloroethylene Valence Shell

Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a₂ and 5b₂ Cl lone-pair orbitals.     

Electron momentum density and band structure calculations of α- and β-GeTe

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a ¹³⁷Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree–Fock/DFT.     

C4H10分子的价电子的结构研究

We report here the measurements of valence electron structure for the n-butane (C4H10) using high resolution (ΔE=0.9 eV FWHM, ΔP=0.1 a.u.) (e,2e) spectrometer. The impact energy was 1200eV plus binding energy (i.e. 1206 to 1232 eV) and symmetric non-coplanar kinematics was employed. The inner-and outer-valence energy spectrum is in agreement with published Photoelectron data. The experimental momentum profiles have been compared with calculations obtained using Hartree-Fock method with the minimum basis set and a high-level basis set, and also using density functional theory (DFT) density methods with a high level basis set. The agreement between theory and experiment for shape of orbital electron momentum distributions is generally good.     

Coexistence of 1,3-butadiene conformers in ionization energies and Dyson orbitals

The minimum-energy structures on the torsional potential-energy surface of 1,3-butadiene have been studied quantum mechanically using a range of models including ab initio Hartree-Fock and second-order M?ller-Plesset theories, outer valence Green's function, and density-functional theory with a hybrid functional and statistical average orbital potential model in order to understand the binding-energy (ionization energy) spectra and orbital cross sections observed by experiments. The unique full geometry optimization process locates the s-trans-1,3-butadiene as the global minimum structure and the s-gauche-1,3-butadiene as the local minimum structure. The latter possesses the dihedral angle of the central carbon bond of 32.81 degrees in agreement with the range of 30 degrees-41 degrees obtained by other theoretical models. Ionization energies in the outer valence space of the conformer pair have been obtained using Hartree-Fock, outer valence Green's function, and density-functional (statistical average orbital potentials) models, respectively. The Hartree-Fock results indicate that electron correlation (and orbital relaxation) effects become more significant towards the inner shell. The spectroscopic pole strengths calculated in the Green's function model are in the range of 0.85-0.91, suggesting that the independent particle picture is a good approximation in the present study. The binding energies from the density-functional (statisticaly averaged orbital potential) model are in good agreement with photoelectron spectroscopy, and the simulated Dyson orbitals in momentum space approximated by the density-functional orbitals using plane-wave impulse approximation agree well with those from experimental electron momentum spectroscopy. The coexistence of the conformer pair under the experimental conditions is supported by the approximated experimental binding-energy spectra due to the split conformer orbital energies, as well as the orbital momentum distributions of the mixed conformer pair observed in the orbital cross sections of electron momentum spectroscopy.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

环己烯分子2b和3a轨道的电子动量谱学研究

The electron momentum profile for inner valence orbitals 2b and 3a of cyclohexene (C6H10) was firstly studied by the binary (e,2e) electron momentum spectroscopy (EMS), at the impact energy of 1200 eV plus binding energy using symmetric non-coplanar kinematics. The complete valence shell binding energy spectrum of C6H10 was also obtained. The experimental momentum profile of the summed orbitals was compared with Hartree Fock (HF) and density functional theory (DFT) methods with various basis sets. The experimental measurement was well described by the HF and DFT calculations except for the low-p region (p<0.25 a.u.). Experimental small “turn-up” effects of momentum profile in the low-p region could be due to the distorted wave effects.     

High Resolution Electron Momentum Spectroscopy Study on Ethanol: Orbital Electron Momentum Distributions for Individual Conformers

The outer-valence binding energy spectra of ethanol in the energy range of 9-21 eV are measured by a high-resolution electron momentum spectrometer at an impact energy of 2.5 keV plus the binding energy. The electron momentum distributions for the ionization peaks corresponding to the outer-valence orbitals are obtained by deconvoluting a series of azimuthal angular correlated binding energy spectra. Comparison is made with the theoretical calculations for two conformers, trans and gauche, coexisting in the gas phase of ethanol at the level of B3LYP density functional theory with aug-cc-pVTZ basis sets. It is found that the measured electron momentum distributions for the peaks at 14.5 and 15.2 eV are in good agreement with the theoretical electron momentum distributions for the molecular orbitals of individual conformers (i.e., 8a' of trans and 9a of gauche), but not in accordance with the thermally averaged ones. It demonstrates that the high-resolution electron momentum spectrometer, by inspecting the molecular electronic structure, is a promising technique to identify different conformers in a mixed sample.     

The Kohn-Sham kinetic energy density as indicator of the electron localization: atomic shell structure

In this report, it is shown that the Kohn-Sham (KS) kinetic energy density (KED) contains the average local electrostatic potential (ALEP) and the average local ionization energy (ALIE); the shell structure in atomic systems is presented as one application of the KS-KED. By writing the KS-KED from the KS equations, this quantity was divided in three contributions: orbital, Coulomb, and exchange correlation. By studying several closed and open shell atoms, the shell structure was established by the maxima presented by the Coulomb contribution and the minima in the orbital contribution of the KS-KED. The exchange-correlation contribution to the KS-KED does not show maxima or minima, but this quantity shows bumps where the division between shells is expected. The results obtained in this work were compared with other shell structure indicators such as the electron localization function, the ALEP, the ALIE, and the radial distribution function. The most important result in this work is related to the fact that even when the ALEP and the ALIE functions were built with different arguments to each other, they are contained in the KS-KED. In this way, the KS-KED shows its importance to reveal the electron localization in atomic systems.     

Generalized nonlocal kinetic energy density functionals based on the von Weizsäcker functional

We generalize the ideas behind the procedure for the construction of kinetic energy density functionals with a nonlocal term based on the structure of the von Weizs?cker functional, and present several types of nonlocal terms. In all cases, the functionals are constructed such that they reproduce the linear response function of the homogeneous electron gas. These functionals are designed by rewriting the von Weizs?cker functional with the help of a parameter β that determines the power of the electron density in the expression, a strategy we have previously used in the generalization of Thomas-Fermi nonlocal functionals. Benchmark calculations in localized systems have been performed with these functionals to test both their relative errors and the quality of their local behavior. We have obtained competitive results when compared to semilocal and previous nonlocal functionals, the generalized nonlocal von Weizs?cker functionals giving very good results for the total kinetic energies and improving the local behavior of the kinetic energy density. In addition, all the functionals discussed in this paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, resulting in a quasilinear scaling for the computational cost.     

Gradient expansion of the kinetic energy density functional: Local behavior of the kinetic energy density

Calculations with Hartree—Fock electron densities for the rare gas atoms He through Xe show that the gradient expansion for the kinetic energy functional, T[] = T₀[] + T₂[] + T₄[] + … = ∫t() dτ, approximates the kinetic energy by averaging over the shell structure present in the true local kinetic energy density, t(), and that the accuracy of the gradient expansion improves with increasing atomic number. Components of t(), t₀(), t₂() and t₄(), are exhibited and discussed. The defined function t() is everywhere positive.     

Bond length and local energy density property connections for non-transition-metal oxide-bonded interactions

For a variety of molecules and earth materials, the theoretical local kinetic energy density, G(r(c)), increases and the local potential energy density, V(r(c)), decreases as the M-O bond lengths (M = first- and second-row metal atoms bonded to O) decrease and the electron density, rho(r(c)), accumulates at the bond critical points, r(c). Despite the claim that the local kinetic energy density per electronic charge, G(r(c))/rho(r(c)), classifies bonded interactions as shared interactions when less than unity and closed-shell when greater, the ratio was found to increase from 0.5 to 2.5 au as the local electronic energy density, H(r(c)) = G(r(c)) + V(r(c)), decreases and becomes progressively more negative. The ratio appears to be a measure of the character of a given M-O bonded interaction, the greater the ratio, the larger the value of rho(r(c)), the smaller the coordination number of the M atom and the more shared the bonded interaction. H(r(c))/rho(r(c)) versus G(r(c))/rho(r(c)) scatter diagrams categorize the M-O bonded interactions into domains with the local electronic energy density per electron charge, H(r(c))/rho(r(c)), tending to decrease as the electronegativity differences for the bonded pairs of atoms decrease. The values of G(r(c)) and V(r(c)), estimated with a gradient-corrected electron gas theory expression and the local virial theorem, are in good agreement with theoretical values, particularly for the bonded interactions involving second-row M atoms. The agreement is poorer for shared C-O and N-O bonded interactions.     

Chemistry and the near-sighted nature of the one-electron density matrix

Two different macrospopic pieces of copper have different external potentials and, because of the unique functional relationship between the electron density and the external potential as demanded by density functional theory, should possess different electron density distributions. Experimentally, however, an atom in the bulk exhibits the same electron density in both samples and they possess identical sets of intensive properties. Density functional theory does not account for the fundamental observation underlying the theory of atoms in molecules: that what are apparently identical distributions of charge can be observed for an atom or a grouping of atoms in systems with different external potentials and that these atoms contribute essentially identical amounts to the energies and all other properties of the systems in which they occur. It is shown that, unlike the external potential, the kinetic energy density and the potential energy density, defined by the virial of the Ehrenfest force acting on electron density, are short-range functions. As recorded in the first article on atoms in molecules, they exhibit a local dependence on the electron density that causes them to faithfully mimic the transferability of the atomic charge distributions from one system to another. The electron, the kinetic energy, and the virial densities are all determined directly by the one-electron density matrix, a function termed near-sighted by Professor Kohn. It is this near-sighted property of the one-matrix that underlies the working hypothesis of chemistry—that of a functional group exhibiting a characteristic set of properties. The observations obtained from the theory of atoms in molecules and the atomic theorems it determines demonstrate the existence of a local relationship between the electron density and all properties of a system. © 1995 John Wiley & Sons, Inc.     

Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions

The kinetic energy is the center of a controversy between two opposite points of view about its role in the formation of a chemical bond. One school states that a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism of covalent bonding. In contrast, the opposite school holds that a chemical bond is formed by a decrease in the potential energy due to a concentration of electron density within the binding region. In this work, a topographic analysis of the Hamiltonian Kinetic Energy Density (KED) and its laplacian is presented to gain more insight into the role of the kinetic energy within chemical interactions. This study is focused on atoms, diatomic and organic molecules, along with their dimers. In addition, it is shown that the laplacian of the Hamiltonian KED exhibits a shell structure in atoms and that their outermost shell merge when a molecule is formed. A covalent bond is characterized by a concentration of kinetic energy, potential energy and electron densities along the internuclear axis, whereas a charge-shift bond is characterized by a fusion of external concentration shells and a depletion in the bonding region. In the case of weak intermolecular interactions, the external shell of the molecules merge into each other resulting in an intermolecular surface comparable to that obtained by the Non-covalent interaction (NCI) analysis.     

Investigation into the valence electronic structure of norbornene using electron momentum spectroscopy, Green's function, and density functional theories

Results of a study of the valence electronic structure of norbornene (C(7)H(10)), up to binding energies of 30 eV, are reported. Experimental electron momentum spectroscopy (EMS) and theoretical Green's function and density functional theory approaches were utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all 19 valence orbitals of norbornene. This experimentally validated model was then used to extract other molecular properties of norbornene (geometry, infrared spectrum). When these calculated properties are compared to corresponding results from independent measurements, reasonable agreement is typically found. Due to the improved energy resolution, EMS is now at a stage to very finely image the effective topology of molecular orbitals at varying distances from the molecular center, and the way the individual atomic components interact with each other, often in excellent agreement with theory. This will be demonstrated here. Green's Function calculations employing the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than about 22 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet emission and newly presented (e,2e) ionization spectra. Finally, limitations inherent to calculations of momentum distributions based on Kohn-Sham orbitals and employing the vertical depiction of ionization processes are emphasized, in a formal discussion of EMS cross sections employing Dyson orbitals.     

Improved local density functional approach for atomic systems

Through a new local density approximation to the kinetic energy density functional introduced by us recently, a simple Thomas–Fermi-like scheme for the direct calculation of electron density in atoms is proposed. The calculated density is nonsingular at the nucleus and the energy values are in very good agreement with the corresponding Hartree–Fock results for atoms. © 1994 John Wiley & Sons, Inc.     

Kinetic energy density study of some representative semilocal kinetic energy functionals

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.     

Electron Momentum Spectroscopy Study on Inner Orbitals of Methyl iodide

The binding energy spectrum and electron momentum profiles of the inner orbitals of methyl iodide have been measured using an electron momentum spectrometer at the impact energy of 1200 eV plus binding energy. Two peaks in the binding energy spectrum, arising from the spin-orbit splitting, are observed and the corresponding electron momentum profiles are obtained. Relativistic density functional calculations are performed to elucidate the experimental electron momentum profiles of two spin-orbit splitting components, showing agreement with each other except for the intensity in low momentum region. The measured high intensity in the low momentum region can be further explained by the distorted wave calculation.