Electron momentum spectroscopy of sulphurhexafluoride

The SF₆ molecule has been studied using high-resolution electron momentum spectroscopy [EMS], at a total energy of 1200 eV and using non-coplanar symmetric kinematics. Binding-energy spectra ranging up to 62 eV were measured at out of plane azimuthal angles from 0° to 28°, and in the outer-valence region from 0° to 34°, corresponding to target electron momenta from about 0.1–2.8 au. The binding-energy spectra and electron momentum distributions obtained for the valence orbitals are compared with the results of Green function calculations for the ionization energies and their corresponding pole strengths and the spherically averaged momentum distributions obtained from the SCF wavefunction on which the Green function calculations are based. The SCF basis includes d components on both S and F atoms. In the outer-valence region, where the one-particle picture holds for the ionization process, there is very good agreement between the theoretical energies and pole strengths and the measured ones, but the orbital momentum distributions are given poorly by the SCF wavefunctions. The measured momentum distributions are significantly higher at low momentum (< 1 au), particularly for the 1t_2u and 3e_g orbitals. In the inner-valence region a substantial splitting of the lines occurs, which is only predicted in a qualitative way. The SCF momentum distribution for the 2e_g orbital is in poor agreement with the data, whereas that of the 3t_1u orbital is in very good agreement with the measurements.     

Electron momentum spectroscopy of the valence orbitals of H2O and D2O: Quantitative comparisons using Hartree—Fock limit and correlated wavefunctions

The large discrepancies found earlier between experimental measurements and calculations based on near Hartree—Fock wavefunctions for the valence orbital electron momentum distributions of H₂O are reinvestigated. New and improved electron momentum spectroscopy measurements for the valence orbitals of H₂O and D₂O, together with existing experimental data, have been placed on a common intensity scale using the binding energy spectra. Investigation of possible vibrational effects by means of new measurements of the momentum distributions of D₂O indicates no detectable differences with the H₂O results, within experimental error. A quantitative comparison of these experimental results with both the shapes and magnitudes of momentum distributions calculated in the PWIA and THFA approximations using new, very precise Hartree—Fock (single-configuration) wavefunctions is made. These wavefunctions, which include considerable polarization and which are effectively converged at the HF limit for total energy, dipole moment and momentum distribution permit establishment of basis set independence. The significant discrepancies between theory and experiment which still remain for the momentum distributions of the 1b₁, 3a₁ and 2a₁ orbitals at the THFA level are largely removed by CI calculations of the full ion—neutral overlap amplitude. These CI wavefunctions for the final ion and neutral ground states, generated from the accurate HF limit basis sets, recover up to 88% of the correlation energy. The present work clearly shows the need for adequate consideration of electron correlation effects in describing the low-momentum parts of the 1b₁, 3a₁ and 2a₁ electron distributions, a region which is of crucial importance in problems related to chemical bonding and reactivity. The high level of quantitative agreement obtained between experiment and calculations using sufficiently sophisticated wavefunctions provides support for the essential validity of the plane wave impulse approximation as used in the interpretation of EMS experiments on small molecules.     

Investigation of valence orbitals of propene by electron momentum spectroscopy

The binding energy spectra and momentum distributions of all valence orbitals of propene were studied by electron momentum spectroscopy (EMS) as well as Hartree-Fock and density functional theoretical calculations. The experiment was carried out at impact energies of 1200 eV and 600 eV on the state-of-the-art EMS spectrometer developed at Tsinghua University recently. The experimental momentum profiles of the valence orbitals were obtained and compared with the various theoretical calculations. Moreover, the experiment with a new analysis method presents a strong support for the correct ordering of the orbital 8a' and 1a', i.e., 9a' < 8a' < 1a' < 7a'.     

Orbital momentum distributions and binding energies for the complete valence shell of molecular chlorine by electron momentum spectroscopy

The complete valence shall binding energy spectrum (10–50 eV) of Cl₂ has been determined using electron momentum (binary (e,2e)) spectroscopy. The inner valence region, corresponding to 4σ_u and 4σ_g ionization, has been measured for the first time and shows extensive splitting of the ionization strength due to electron correlation effects. These measurements are compared with the results of many-body calculations using Green function and CI methods employing unpolarised as well as polarised wavefunctions. Momentum distributions, measured in both the outer and inner valence regions, are compared with calculations using a range of unpolarised and polarised wavefunctions. Computed orbital density maps in momentum and position space for oriented Cl₂ molecules are discussed in comparison with the measured and calculated spherically averaged momentum distributions.     

The outer valance orbital electron densities of cyclopentane by binary (e,2e) spectroscopy

The binding energy spectra and electron distributions in momentum space of the valence orbitals of cyclopentane (C(5)H(10)) are studied by Electron Momentum Spectroscopy (EMS) in a noncoplanar symmetric geometry. The impact energy was 1200 eV plus binding energy and energy resolution of the EMS spectrometer was 1.2 eV. The experimental momentum profiles of the outer valence orbitals are compared with the theoretical momentum distributions calculated using Hartree-Fock and density functional theory (DFT) methods. The shapes of the experimental momentum distributions are generally quite well described by both the Hartree-Fock and DFT calculations when the large and diffuse basis sets are used.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

An investigation of valence shell orbital momentum profiles of difluoromethane by binary (e,2e) spectroscopy

The electron binding energy spectra and momentum profiles of the valence orbitals of difluoromethane, also known as HFC32 (HFC-hydrofluorocarbon) (CH(2)F(2)), have been studied by using a high resolution (e,2e) electron momentum spectrometer, at an impact energy of 1200 eV plus the binding energy, and by using symmetric noncoplanar kinematics. The experimental momentum profiles of the outer valence orbitals and 4a(1) inner valence orbital are compared with the theoretical momentum distributions calculated using Hartree-Fock and density functional theory (DFT) methods with various basis sets. In general, the shapes of the experimental momentum distributions are well described by both the Hartree-Fock and DFT calculations when large and diffuse basis sets are used. However, the result also shows that it is hard to choose the different calculations for some orbitals, including the methods and the size of the basis sets employed. The pole strength of the ionization peak from the 4a(1) inner valence orbital is estimated.     

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.     

Looking at orbitals in the laboratory: The experimental investigation of molecular wavefunctions and binding energies by electron momentum spectroscopy

The experimental technique of electron momentum spectroscopy (EMS ) (i.e., binary (e, 2e) spectroscopy) is discussed together with typical examples of its applications over the past decade in the area of experimental quantum chemistry. Results interpreted within the framework of the plane wave impulse and the target Hartree—Fock approximations provide direct measurements of, spherically averaged, orbital electron momentum distributions. Results for a variety of atoms and small molecules are compared with calculations using a range of Fourier transformed SCF position space wavefunctions of varying sophistication. Measured momentum distributions (MD ) provide a “direct” view of orbitals. In addition to offering a sensitive experimental diagnostic for semiempirical molecular wavefunctions, the MD's provide a chemically significant, additional experimental constraint to the usual variational optimization of wavefunctions. The measured MD's clearly reflect well known characteristics of various chemical and physical properties. It appears that EMS and momentum space chemistry offer the promise of supplementary perspectives and new vistas in quantum chemistry, as suggested by Coulson more than 40 years ago. Binding energy spectra in the inner valence region reveal, in many cases, a major breakdown of the simple MO model for ionization in accord with the predictions of many-body calculations. Results are considered for atomic targets, including H and the noble gases. The measured momentum distribution for H₂ is also compared with results from Compton scattering. Results for H₂ and H are combined to provide a direct experimental assessment of the bond density in H₂, which is compared with calculations. The behavior of the outer valence MD ''s for small row two and row three hydride molecules such as H₂O and H₂S, NH₃, HF, and HCl are consistent with well known differences in chemical and physical behavior such as ligand-donor activity and hydrogen bonding. MD measurements for the outermost valence orbitals of HF, H₂O and NH₃ show significant differences from those calculated using even very high-quality wavefunctions. Measurements of MD's for outer σ_g orbitals of small polyatomic molecules such as CO₂, COS, CS₂, and CF₄ show clear evidence of mixed s and p character. It is apparent that EMS is a sensitive probe of details of electronic structure and electron motion in atoms and molecules.     

CFCl3分子2e和4a1轨道的电子动量谱研究

由于工业的迅速发展,使得空气质量急剧下降,因此对影响大气的分子进行深入研究变得非常必要．本实验室已经对影响环境的甲烷[1]、丙烷[2]、CO2[3]等分子进行了电子动量谱研究,为环保提供了有用的数据．CFCl3作为工业广泛应用的气雾剂和制冷剂原料,它的大量使用导致了大气中臭氧的减少[4]．前人已用光电子谱学的方法[5-8]研究了CFCl3,我们又用电子动量谱的手段对CFCl3分子进行了进一步的研究,即从波函数的层次上详细了解CFCl3的电子结构．     

Conformational stability of 1-butene: an electron momentum spectroscopy investigation

The valence-shell electron momentum distributions for 1-butene are measured by electron momentum spectroscopy (EMS) employing non-coplanar symmetric geometry. The experimental electron momentum distributions are compared with the density functional theory (DFT) calculations using different-sized basis sets. Although the two conformers of 1-butene in the gas phase, namely the skew and syn, have very close ionization potentials, the electron momentum distributions, especially in the low momentum region, can show prominent differences for some of the valence orbitals. By comparing the experimental electron momentum profiles with the theoretical ones, the skew conformer is found to be more stable than the syn and their relative abundances at room temperature are estimated to be (69 +/- 6)% and (31 +/- 6)%, respectively. It demonstrates that EMS has the latent potential to study the relative stability of conformers.     

Study of the photoelectron and electron momentum spectra of cyclopentene using benchmark Dyson orbital theories

A complete study of the valence electronic structure and related electronic excitation properties of cyclopentene in its C(s) ground state geometry is presented. Ionization spectra obtained from this compound by means of photoelectron spectroscopy (He I and He II) and electron momentum spectroscopy have been analyzed in details up to electron binding energies of 30 eV using one-particle Green's function (1p-GF) theory along with the outer-valence (OVGF) and the third-order algebraic diagrammatic construction [ADC(3)] schemes. The employed geometries derive from DFT/B3LYP calculations in conjunction with the aug-cc-pVTZ basis set, and closely approach the structures inferred from experiments employing microwave spectroscopy or electron diffraction in the gas phase. The 1p-GF/ADC(3) calculations indicate that the orbital picture of ionization breaks down at electron binding energies larger than approximately 17 eV in the inner-valence region, and that the outer-valence 7a' orbital is also subject to a significant dispersion of the ionization intensity over shake-up states. This study confirms further the rule that OVGF pole strengths smaller than 0.85 foretell a breakdown of the orbital picture of ionization at the ADC(3) level. Spherically averaged (e, 2e) electron momentum distributions at an electron impact energy of 1200 eV that were experimentally inferred from an angular analysis of EMS intensities have been interpreted by comparison with accurate simulations employing ADC(3) Dyson orbitals. Very significant discrepancies were observed with momentum distributions obtained from several outer-valence ionization bands using standard Kohn-Sham orbitals.     

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.     

Electron momentum spectroscopy of CF2Cl2: experimental and theoretical momentum profiles for outer valence orbitals

Electron momentum distributions for outer valence orbitals of CF2Cl2 have been obtained by (e,2e) electron momentum spectroscopy at an incident energy of 1200 eV + binding energy. The experimental electron momentum profiles are compared with Hartree-Fock and density functional theory (DFT) calculations using B3LYP hybrid functional with the 6-31G and 6-311+G* basis sets. Generally, the shapes of the experimental momentum profiles are well reproduced by DFT calculations using larger basis sets 6-311 + G*. An attempt has been made to clarify the ordering of the outer valence orbitals, which have been in controversy, by comparing experimental results with B3LYP/6-311 + G* calculations.     

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.     

Imaging momentum orbital densities of conformationally versatile molecules: a benchmark theoretical study of the molecular and electronic structures of dimethoxymethane

The main purpose of the present work is to predict from benchmark many-body quantum mechanical calculations the results of experimental studies of the valence electronic structure of dimethoxymethane employing electron momentum spectroscopy, and to establish once and for all the guidelines that should systematically be followed in order to reliably interpret the results of such experiments on conformationally versatile molecules. In a first step, accurate calculations of the energy differences between stationary points on the potential energy surface of this molecule are performed using Hartree-Fock (HF) theory and post-HF treatments of improving quality (MP2, MP3, CCSD, CCSD(T), along with basis sets of increasing size. This study focuses on the four conformers of this molecule, namely the trans-trans (TT), trans-gauche (TG), gauche-gauche (G+G+), and gauche-gauche (G+G-) structures, belonging to the C2v, C1, C2, and Cs symmetry point groups, respectively. A focal point analysis supplemented by suited extrapolations to the limit of asymptotically complete basis sets is carried out to determine how the conformational energy differences at 0 K approach the full CI limit. In a second step, statistical thermodynamics accounting for hindered rotations is used to calculate Gibbs free energy corrections to the above energy differences, and to evaluate the abundance of each conformer in the gas phase. It is found that, at room temperature, the G+G+ species accounts for 96% of the conformational mixture characterizing dimethoxymethane. In a third step, the valence one-electron and shake-up ionization spectrum of dimethoxymethane is analyzed according to calculations on the G+G+ conformer alone by means of one-particle Green's function [1p-GF] theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. A complete breakdown of the orbital picture of ionization is noted at electron binding energies above 22 eV. A comparison with available (e,2e) ionization spectra enables us to identify specific fingerprints of through-space orbital interactions associated with the anomeric effect. At last, based on our 1p-GF/ADC(3) assignment of spectral bands, accurate and spherically averaged (e,2e) electron momentum distributions at an electron impact energy of 1200 eV are computed from the related Dyson orbitals. Very significant discrepancies are observed with momentum distributions obtained for several outer-valence levels using standard Kohn-Sham orbitals.     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Binary (e,2e) spectroscopic study of carbonyl sulfide and the momentum-space chemistry of CO2, CS2 and OCS

The valence-shell binding energy spectra (8–44 eV) and molecular orbital momentum distributions of OCS have been studied by non-coplanar symmetric binary (e,2e) spectroscopy. Existing theoretical binding energy spectra calculated using the many-body 2ph-TDA Green's function (GF) method and using the symmetry-adapted cluster (SAC) on method are compared with the experiment. Intense many-body structure in the measured and calculated binding energy spectra indicates the general breakdown of the independent particle ionization picture. Experimental momentum distributions are compared with those calculated using ab initio SCF wavefunctions of minimal basis set quality and of near Hartree—Fock quality. Excellent agreement between the experimental momentum distributions and those calculated by the near Hartree—Fock wavefunction is obtained for the three innermost valence orbitals: 8σ, 7σ and 6σ. The correct order of the close lying outer-valence 2π and 9σ orbitals is unambiguously identified from the shapes of the measured momentum distributions. Momentum and position contour density maps computed from theoretical wavefunctions of near Hartree—Fock quality are used to interpret the shapes and atomic characters of the observed momentum distributions. The momentum densities of the outermost-valence antibonding π orbitals and of the outermost-valence bonding σ orbitals of the linear triatomic group: CO₂, CS₂ and OCS are compared respectively with each other. The associated chemical trends are discussed within the existing framework of momentum-space chemical principles.     

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.