Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

电子动量谱仪的研制和He原子结构的研究

前文指出，电子动量语学是研究原子和分子结构的一种新方法，其价值在于：它既能直接得到电子能级，又能相当直接和精细地得到各个电子态的动圭分布（屯就是动会表象中的电子波函数模方）．这些信息对量子化学等学科是极为有用的．在发达国家，电子动量语学已受到广泛的重视，但在国内还几乎是空白．虽然少数单位正在或准备开展这一工作，然而至今还没有成功的实验报导，其原因是国内还没有电子动量谱仪（Elec－tronM。nt。Spectro。ter，缩写为EMS），它是开展电子动量谱学实验的关键设备，在现阶段的国内外市场上均无产品出售，需要使…     

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.     

饱和烷烃分子C_nH_(2n+2)(n=4-6)的电子动量光谱(英文)

使用B3LYP/TZVP//B3LYP/aug-cc-pVTZ方法系统研究了饱和烷烃分子CnH2n+2(n=4-6)的轨道电子动量光谱,比较了同分异构体CnH2n+2(n=4-6)对轨道动量分布的影响.结合二维空间分析方法对电子在坐标空间中的密度分布进行了系统的研究.计算结果表明,最内价壳层电荷分布主要由s电子贡献,第二近邻芯价壳层则主要由p电子贡献,而其余的价壳层则为sp杂化.最内价轨道表现出最大的谱线强度并且远大于其它轨道的谱线强度,而且正烷烃的谱线强度要大于异烷烃等同分异构体的谱线强度,表现出了明显的与甲基移动的个数有关的性质.     

Stimulated emission at the sum-frequency generation of a bichromatic field interacting with a three-level atom

The Maximum-Entropy formalism is used to obtain approximations to the spherically averaged charge and momentum densities. The only information required is the first few radial expectation values. Analytical and numerical approximations to the central values of the densities are calculated. Moreover, the unused or unknown radial expectation values are estimated by means of the moments of these Maximum-Entropy densities. As illustration, the accuracy of these approximations are numerically studied in a Hartree-Fock framework. This method is complementary to the one which makes use of the Stieltjes-Chebyshev inequalities and leads to the least biased approximate densities compatible with the information we use.     

Density matrices from position and momentum densities

Summary One-electron density matrices, which are representable in single-centers-orbital basis sets, have been investigated with respect to their reconstruction from densities. The maximum allowed dimension for reconstruction from a combination of position & momentum density dependent properties is only slightly bigger than the dimension in the case of position (or momentum) densities only. Since for a given one-particle basis of dimensionM, the number of one-matrix elements which can be determined is also of orderM only, while the total number of one-matrix elements is of orderM ², it is in general necessary to introduce severe constraints and restrictions. The accuracy demands on the data and algorithms increase exponentially for linearly increasing size of basis set.     

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.     

He原子基态波函数的实验检验

以作者所在实验室最近完成的He原子基态的电子动全港学实验结果为基础，对三类He原子基态波函数进行了分析与检验．结果表明，电子动量话学是获取电子波西数信息的有用手段．且实验结果与理论计算的联系文＊已报导了本实验室最近完成的He原子基态的电子动量话学实验结果．此实验的条件满足准自由碰撞的要求问，平面波冲量近似是适用的，因而实验测定的（e，Ze）反应的符合计数N可表为问本文自始至终采用原子单位（an），除非另有说明．在（1）中，C是比例常数，只与实验条件有关；PO，PI和马分别是人射电子和两个出射电子的动量，Th是…     

Electron Momentum Spectroscopy of Ethanethiol Complete Valence Shell

The binding energy spectra and electron momentum distributions for the complete valence orbitals of ethanethiol were measured for the first time by binary (e, 2e) electron momentum spectroscopy employing non-coplanar symmetric kinematics at an impact energy of 1200 eV plus binding energy. The experimental results are generally consistent with the theoretical calculations using density functional theory and Hartree-Fock methods with various basis sets. A possible satellite line at 17.8 eV in binding energy spectrum was observed and studied by electron momentum spectroscopy.     

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.     

Electron Momentum Spectroscopy of Valence Orbitals of Cyclopentene: Nuclear Dynamics and Distorted Wave Effect

We report a measurement of electron momentum distributions of valence orbitals of cyclopentene employing symmetric noncoplanar (e, 2e) kinematics at impact energies of 1200 and 1600 eV plus the binding energy. Experimental momentum profiles for individual ionization bands are obtained and compared with theoretical calculations considering nuclear dynamics by harmonic analytical quantum mechanical and thermal sampling molecular dynamics approaches. The results demonstrate that molecular vibrational motions including ring-puckering of this flexible cyclic molecule have obvious influences on the electron momentum profiles for the outer valence orbitals, especially in the low momentum region. For π*-like molecular orbitals 3a'', 2a'', and 3a', the impact-energy dependence of the experimental momentum profiles indicates a distorted wave effect.     

二氟甲烷分子3a1和2b2轨道的电子动量谱

The electron momentum spectroscopy of the inner valence orbitals 3a1 and 2b2 of methylene fluoride was studied by electron momentum spectroscopy（EMS）. The experiment was performed using a high resolution（ΔE=1.15 eV FWHM,Δp=0. 1 a. u.）（e,2e）EMS spectrometer. The experimental momentum profiles of these two orbitals are compared with those calculated by Hartree-Fork method and Density Functional Theory.     

Rovibrational momentum densities of diatomic molecules in the rigid rotor-harmonic oscillator approximation

The rigid rotor-harmonic oscillator model in the momentum representation is used to examine the rovibrational momentum density of a diatomic molecule. The effects on this function of rotational and vibrational excitation, thermal averaging, and nuclear spin statistics are exhibited in calculations on N₂ and thehydrogen halides, and a brief comparison with electron momentum densities is made.     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Electron densities from the Brueckner Doubles method

Summary The concept of the Brueckner orbital is examined, following a resurgence of interest in wavefunctions constructed from them. The distinction between Self Consistent Field, Natural and Brueckner orbitals are discussed. Total electron densities are calculated for several examples, and correlation densities are studied. It is found that the Brueckner orbitals are more localised than SCF orbitals. The total electron density constructed from the Brueckner reference determinant with Brueckner orbitals gives qualitatively similar pictures as other correlated methods. Brueckner orbitals are found to show dissociation well.     

Atomic quantum similarity indices in position and momentum spaces

Quantum similarity for atoms is investigated using electron densities in position and momentum spaces. Contrary to the results in position space, the analysis in the momentum space shows how the momentum density carries fundamental information about periodicity and structure of the system and reveals the pattern of Mendeleev's table. A global analysis in the joint r-p space keeps this result.     

1-碘丙烷分子的电子动量谱学研究：自旋-轨道耦合效应与分子内轨道相互作用

利用不对称不共面电子动量谱仪,在2.5 keV碰撞能量下,采用高精度的SAC-CI方法计算了1-碘丙烷分子束缚能谱,同时采用Hartree-Fock、B3LYP/aug-cc-pVTZ（C,H）6-311G＊＊（I）方法计算其电子动量分布. 并对电离能峰进行了标示. 结合非相对论与相对论计算方法以及自然键轨道分析,对最外层两个轨道（碘的5p孤对）的自旋-轨道耦合效应与分子内轨道相互作用进行了比较. 两种相互作用对电子动量分布的不同影响是可观的. 实验结果与相对论计算的结果一致,表明1-碘丙烷分子内自旋-轨道耦合效应占主导.     

CF2BrCl分子近域轨道的电子动量谱学研究

The frontier molecular orbitals (HOMO and NHOMO) of CF2BrCl molecule have been firstly investigated by (e,2e) electron momentum spectroscopy. The experimental momentum profiles are compared with the theoretical profiles employing Hartree-Fock and density functional theory with 6-31G and 6-311+G(d) basis sets. Both HF and DFT calculations using 6-311+G(d) basis set can well describe the experiment, whereas those calculated using 6-31G basis set largely underestimate the experiment at the low momentum region. Furthermore, orbital electron density images show that HOMO and NHOMO have a mixed character of the bromine and chlorine lone pairs.     

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.     

Observation of Interference Effects in (e, 2e) Electron Momentum Spectroscopy of SF6 (cited: 1)

Two-dimensional electron density map (2D map) of binding energy and relative azimuthal angle (i.e., momentum) for the outer-valence molecular orbitals of SF₆ has been measured by a highly sensitive electron momentum spectrometer with noncoplanar symmetric geometry at the impact energy of 1.2 keV plus binding energy. The experimental electron momentum profiles for the relevant molecular orbitals have been extracted from the 2D map and interpreted on the basis of the quantitative calculations using the density functional theory with B3LYP hybrid functional. For the outermost F2p nonbonding orbitals of SF₆, the interference patterns are clearly observed in the ratios of the electron momentum profiles of molecular orbitals to that of atomic F2p orbital.