Outer valence orbital momentum distributions of carbon dioxide by binary (e,2e) spectroscopy

The outer valence orbital momentum distributions of CO₂ have been reinvestigated using a high momentum resolution (0.1 a_o^?1 fwhm) binary (e,2e) spectrometer operated at 1200 eV impact energy under the non-coplanar symmetric scattering condition. Generally good agreement of the measured momentum distributions with theoretical momentum distributions calculated using literature SCF double-zeta quality wavefunctions has been obtained for the 1π_g, (1π_u + 3σ_u) and 4σ_g orbitals. Although there is a reasonable agreement of the measured momentum distributions with earlier low momentum resolution (0.4 a_o^?1 fwhm) non-coplanar measurements at 400 eV impact energy reported by Cook and Brion, given the large differences in the momentum resolutions much more definitive results are obtained in the present study. In particular, the significantly higher momentum resolution clearly shows the mixed s-p character of the 4σ_g orbital. The present study also gives a much better agreement with theory in the case of the 4σ_g momentum distribution. For each orbital the calculated and where possible the experimentally determined spherically averaged momentum distributions are compared and contrasted with their respective two-dimensional momentum and position density maps. These together with three-dimensional surface plots at selected constant density values of the four outermost orbitals are used to provide a detailed comparison of momentum-space bonding and orbital properties with their more familiar position-space counterparts in the CO₂ triatomic molecule. The calculated momentum-space density contour maps of the core orbitals exhibit rather large density oscillations and the feasibility of future experiments is discussed.     

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.     

Valence-shell momentum distributions and ionization energies of carbon disulfide

Valence-shell binding energy spectra and momentum distributions of CS₂ have been measured using non-coplanar symmetric binary (e,2e) spectroscopy. The present measurements are compared with previously published binding energy spectra calculated using the many body 2ph-TDA Green's function (GF) method and the symmetry-adapted cluster configuration-interaction (SAC CI) method. The measured and the calculated binding energy spectra both show extensive population splittings particularly above 20 eV, confirming a significant breakdown of independent particle ionization picture. A relatively strong-outer valence many-body state at 17.0 eV is shown to be satellite of the (2π₀)^?1 state, in accord with earlier conclusions of photoelectron studies. Momentum distributions measured at several carefully chosen binding energies are compared with the corresponding molecular orbital momentum distributions calculated using small and extended gaussian basis sets. The good qualitative agreement between momentum distributions measured in the inner-valence region wth theoretical 4σ_m and 5σ_g orbital momentum distributions confirms the qualitative predictions of satellite parentages by GF and SAC CI calculations. Momentum and position density contour maps of individual orbitals are used to interpret the shapes and atomic characters of the experimental momentum distributions. Momentum densities of the valence orbitals of CS₂ are compared with those of the respective valence isoelectronic species CO₂     

An investigation of the valence orbitals of water by high momentum resolution electron momentum spectroscopy

The momentum distributions of the valence orbitals for water well as the binding energy spectra in the region 10–45 eV have been reinvestigated with a high momentum resolution (≈0.1 a₀^?1 fwhm) binary (e.2e) spectrometer. The binding energy spectra show considerable satellite structure in the region > 25 eV which is consistent with theoretical predictions of final state configuration interaction (many-body effects) involving the (2a₁)^?1 hole state. An investigation of the momentum distribution in the satellite region confirms this assignment. This is in accord with a variety of recent theoretical studies and also consistent with earlier experiments. Differences suggested in earlier comparisons between theory and low momentum resolution experiments for the momentum distributions of the 1b₁ and 3a₁ orbitals have been verified. Several possible theoretical studies are suggested to investigate further this discrepancy between experiment and theory. Bonding effects and thenature of the molecular orbitals of H₂O in momentum space are also discussed.     

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.     

Valence electronic structure of CH3Br and CH3I: Electron momentum distributions and separation energies

Bromomethane (CH₃Br) and iodomethane (CH₃I) have been studied by binary (e,2e) coincidence spectroscopy at 1200 eV using non-coplanar symmetric kinematics. Separation energy spectra have been determined in the energy range up to 47 eV at azimuthal angles of 0° and 8° for CH₃Br and 0° and 6° for CH₃I. The separation energy spectra and the electron momentum distributions measured for each of the valence orbitals are compared with theoretical predictions employing SCF wavefunctions and outer valence type and extended 2 ph-TDA Green function calculations. Electron density and momentum density maps have been calculated for all the valence orbitals using the SCF wavefunctions, and they are used to explain trends and contrasts in the electronic structure and bonding properties of these halomethanes in both position and momentum space.     

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.     

Experimental and theoretical binding energy spectra and momentum distributions for the valence orbitals of H2O

The binding energy spectra (10–46 eV) and momentum distributions of the valence orbitals of H₂O have been measured using a new high-sensitivity binary (e,2e) electron spectrometer employing position-sensitive detectors. The binding energy spectrum shows a previously unreported feature at = 27 eV which is shown to be associated with the (2a₁)^?1 ionization process. The region between 25 and 46 eV is compared with previous (e,2e) and X-ray photoelectron measurements as well as with several existing and new many-body calculations indicating a splitting of the 2a₁ ionization pole strength. In addition the separate momentum distributions of the three outer valence orbitals of H₂O have been obtained from deconvoluted binding energy spectra run at a series of azimuthal angles. The results, which show considerably improved signal-to-noise ratio over earlier measurements using single-channel instrumentation are compared with spherically averaged momentum distributions calculated with a variety of wavefunctions.     

Intramolecular interactions of L‐phenylalanine: Valence ionization spectra and orbital momentum distributions of its fragment molecules

Intramolecular interactions between fragments of L ‐phenylalanine, i.e., phenyl and alaninyl, have been investigated using dual space analysis (DSA) quantum mechanically. Valence space photoelectron spectra (PES), orbital energy topology and correlation diagram, as well as orbital momentum distributions (MDs) of L ‐phenylalanine, benzene and L ‐alanine are studied using density functional theory methods. While fully resolved experimental PES of L ‐phenylalanine is not yet available, our simulated PES reproduces major features of the experimental measurement. For benzene, the simulated orbital MDs for 1e_1g and 1a_2u orbitals also agree well with those measured using electron momentum spectra. Our theoretical models are then applied to reveal intramolecular interactions of the species on an orbital base, using DSA. Valence orbitals of L ‐phenylalanine can be essentially deduced into contributions from its fragments such as phenyl and alaninyl as well as their interactions. The fragment orbitals inherit properties of their parent species in energy and shape (ie., MDs). Phenylalanine orbitals show strong bonding in the energy range of 14‐20 eV, rather than outside of this region. This study presents a competent orbital based fragments‐in‐molecules picture in the valence space, which supports the fragment molecular orbital picture and building block principle in valence space. The optimized structures of the molecules are represented using the recently developed interactive 3D‐PDF technique. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

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.     

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     

Unrestricted CNDO-MO calculations. II. MnO 4 2− and CrO 4 3−

The electronic structures of the tetrahedral molecule ions MnO ₄ ^2– and CrO ₄ ^3– have been investigated within an unrestricted CNDO-MO approximation [Theoret. Chim. Acta (Berl.)20, 317 (1971)]. Calculations assuming the unpaired electron occupies the 3a ₁, 2e, and 4t2 molecular orbitals indicate that the 3a ₁ and2e orbitals have similar orbital energies and that the 4t ₂ orbital is at a higher energy. The experimentally indicated2e orbital for the unpaired electron is obtained with expanded O^1– type atomic orbitals for oxygen and valence metal orbitals of the expanded 3d and plus one ion 4p types. The metal 4s orbitals must be held to the neutral atom type. The optimum valence orbitals above with a slightly contracted 4s type metal orbitals yield the minimum total energy and places the unpaired electron in the 3a ₁ orbital. Since the contracted 4s metal orbital produces results that are not in agreement with experimental data, the method used apparently does not adequately take into account the increased electron-electron repulsions that contracted 4s orbitals produce.     

Electron Momentum Distributions for 4a1 Orbitals of CFxCl4-x in Low Momentum Region： a Possible Evidence of Molecular Geometry Distortion

Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentum region. The tentative calculations using equilibrium geometries of molecular ions have exhibited a great improvement in agreement with the experimental data, which suggests that the molecular geometry distortion may be responsible for the observed high intensities at p〈0.5 a.u.. Further analyses show that the severe discrepancies at low momentum region mainly arise from the influence of molecular geometry distortion on C-Cl bonding electron density distributions.     

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.     

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.     

Angle-resolved photoelectron spectroscopy of the chloro-substituted methanes

The angular distribution parameter, β, was determined for the valence orbitals (IP ′ 21.2 eV) of CCl₄, CHCl₃, CH₂Cl₂, and CH₃Cl in the 10–30 eV photon energy range using dispersed polarized synchrotron radiation. The energy dependence of β in the photoelectron energy range of 2 to 10 eV for the non-bonding chlorine n(Cl) orbitals of these molecules was found to be similar for all n(Cl) orbitals investigated. The energy dependence of β for the σ orbitals in these molecules was similar to that observed previously for other σ orbitals. The experimental CCl₄ results were compared with theoretical CCl₄ results obtained using the Xα multiple scattering formalism. Theory predicts the existence of two strong shape resonances in each of the valence orbitals of CCl₄. The overall agreement between experiment and theory is evaluated along with the experimental evidence concerning the verification of the predicted shape resonances.     

Probing molecular conformations with electron momentum spectroscopy: the case of n-butane.

High-resolution (e,2e) measurements of the valence electronic structure and momentum-space electron density distributions of n-butane have been exhaustively reanalyzed in order to cope with the presence of two stable structures in the gas phase, namely the all-staggered and gauche conformers. The measurements are compared to a series of Boltzmann-weighted simulations based on the momentum-space form of Kohn-Sham (B3LYP) orbital densities, and to ionization spectra obtained from high-level [ADC(3)] one-particle Green's Function calculations. Indubitable improvements in the quality of the simulated (e,2e) ionization spectra and electron momentum profiles are seen when the contributions of the gauche form of n-butane are included. Both the one-electron binding energies and momentum distributions consistently image the distortions and topological changes that molecular orbitals undergo due to torsion of the carbon backbone, and thereby exhibit variations which can be traced experimentally. With regard to the intimate relation of (e,2e) cross sections with orbital densities, electron momentum spectroscopy can therefore be viewed as a very powerful, but up to now largely unexploited, conformational probe. The study also emphasizes the influence of thermal agitation in photoionization experiments of all kind.     

Momentum space properties of various orbital basis sets used in quantum chemical calculations

Momentum expectation values (p^k), values of the momentum density P(p) at selected points, and coefficients in the MacLaurin and asymptotic expansions of P(p) are used to test the quality of various orbital basis sets previously used for the atomic helium Hartree-Fock problem. The wellknown position-space defects of Gaussian-type orbital expansions are shown to have their momentum-space counterparts. Expansions of even-tempered Slater-type orbitals are found to be rather accurate. The exponentially damped rational function is found to be the outstanding two-parameter unconventional orbital.     

A CNDO study of the electronic structure of oxyanions XO4n− with X = Si,P, S,Cl, Ge,As, Se and Br

The orbital order, the bonding properties of the orbitals and the orbital populations are discussed. It is concluded that the orbital order in the valence shell in all the ions is 1a₁, 1t₂, 2a₁, 2t₂, 1e, 3t₂ and 1t₁. The results are compared when possible with experimental data and ab initio results.     

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.