Benchmark Dyson orbital study of the ionization spectrum and electron momentum distributions of ethanol in conformational equilibrium

An extensive study, throughout the valence region, of the electronic structure, ionization spectrum, and electron momentum distributions of ethanol is presented, on the ground of a model that focuses on a mixture of the gauche and anti conformers in their energy minimum form, using weight coefficients obtained from thermostatistical calculations that account for the influence of hindered rotations. The analysis is based on accurate calculations of valence one-electron and shakeup ionization energies and of the related Dyson orbitals, using one-particle Green's Function (1p-GF) theory in conjunction with the so-called third-order Algebraic Diagrammatic Construction scheme [ADC(3)]. The confrontation against available UPS (HeI) measurements indicates the presence in the spectral bands of significant conformational fingerprints at outer-valence ionization energies ranging from approximately 14 to approximately 18 eV. The shakeup onset is located at approximately 24 eV, and a shoulder at approximately 14.5 eV in the He I spectrum can be specifically ascribed to the minor anti (C(s)) conformer fraction. Thermally and spherically averaged Dyson orbital momentum distributions are computed for seven resolvable bands in model (e, 2e) ionization spectra at an electron impact energy of 1.2 keV. A comparison is made with results obtained from standard (B3LYP) Kohn-Sham orbitals and EMS measurements employing a high-resolution spectrometer of the third generation. The analysis is qualitatively in line with experiment and reveals a tremendously strong influence of the molecular conformation on the outermost electron momentum distributions. Quantitatively significant discrepancies with experiment can nonetheless be tentatively ascribed to strong dynamical disorder in the gas phase molecular structure.     

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.     

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.     

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.     

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.     

Study of the valence wave function of thiophene with high resolution electron momentum spectroscopy and advanced Dyson orbital theories

Results of an exhaustive experimental study of the valence electronic structure of thiophene using high resolution electron momentum spectroscopy at impact energies of 1200 and 2400 eV are presented. The measurements were performed using an electron momentum spectrometer of the third generation at Tsinghua University, which enables energy, polar and azimuthal angular resolutions of the order of DeltaE = 0.8 eV, Deltatheta = +/-0.53 degrees and Deltaphi = +/-0.84 degrees . These measurements were interpreted by comparison with Green's function calculations of one-electron and shake-up ionization energies as well as of the related Dyson orbital electron momentum distributions, using the so-called third-order algebraic diagrammatic construction scheme (ADC(3)). Comparison of spherically averaged theoretical electron momentum distributions with experimental results very convincingly confirms the presence of two rather intense pi-2 pi*+1 shake-up lines at electron binding energies of 13.8 and 15.5 eV, with pole strengths equal to 0.18 and 0.13, respectively. Analysis of the electron momentum distributions associated with the two lowest 2A2 (pi3-1) and 2B1 (pi2-1) cationic states provides indirect evidence for a symmetry lowering and nuclear dynamical effects due to vibronic coupling interactions between these two states. ADC(3) Dyson orbital momentum distributions are systematically compared with distributions derived from Kohn-Sham (B3LYP) orbitals, and found to provide most generally superior insights into experiment.     

Norbornane: an investigation into its valence electronic structure using electron momentum spectroscopy, and density functional and Green's function theories

We report on the results of an exhaustive study of the valence electronic structure of norbornane (C(7)H(12)), up to binding energies of 29 eV. Experimental electron momentum spectroscopy and theoretical Green's function and density functional theory approaches were all utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among all 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 of the 20 valence orbitals of norbornane. This experimentally validated quantum chemistry model was then used to extract some chemically important properties of norbornane. When these calculated properties are compared to corresponding results from other independent measurements, generally good agreement is found. Green's function calculations with the aid of the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than 22.5 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet photoemission and newly presented (e,2e) ionization spectra, except for the band associated with the 1a(2) (-1) one-hole state, which is probably subject to rather significant vibronic coupling effects, and a band at approximately 25 eV characterized by a momentum distribution of "s-type" symmetry, which Green's function calculations fail to reproduce. We note the vicinity of the vertical double ionization threshold at approximately 26 eV.     

Probing molecular conformations in momentum space: the case of n-pentane

A comprehensive study, throughout the valence region, of the electronic structure and electron momentum density distributions of the four conformational isomers of n-pentane is presented. Theoretical (e,2e) valence ionization spectra at high electron impact energies (1200 eV+electron binding energy) and at azimuthal angles ranging from 0 degrees to 10 degrees in a noncoplanar symmetric kinematical setup are generated according to the results of large scale one-particle Green's function calculations of Dyson orbitals and related electron binding energies, using the third-order algebraic-diagrammatic construction [ADC(3)] scheme. The results of a focal point analysis (FPA) of relative conformer energies [A. Salam and M. S. Deleuze, J. Chem. Phys. 116, 1296 (2002)] and improved thermodynamical calculations accounting for hindered rotations are also employed in order to quantitatively evaluate the abundance of each conformer in the gas phase at room temperature and reliably predict the outcome of experiments on n-pentane employing high resolution electron momentum spectroscopy. Comparison with available photoelectron measurements confirms the suggestion that, due to entropy effects, the trans-gauche (tg) conformer strongly dominates the conformational mixture characterizing n-pentane at room temperature. Our simulations demonstrate therefore that experimental measurements of (e,2e) valence ionization spectra and electron momentum distributions would very consistently and straightforwardly image the topological changes and energy variations that molecular orbitals undergo due to torsion of the carbon backbone. The strongest fingerprints for the most stable conformer (tt) are found for the electron momentum distributions associated with ionization channels at the top of the inner-valence region, which sensitively image the development of methylenic hyperconjugation in all-staggered n-alkane chains.     

The band 12 issue in the electron momentum spectra of norbornane: a comparison with additional Green's Function calculations and ultraviolet photoemission measurements

In continuation of a recent study of the electronic structure of norbornane [J. Chem. Phys., 2004, 121, 10525] by means of electron momentum spectroscopy (EMS), we present Green's Function calculations of the ionization spectrum of this compound at the ADC(3) level using basis sets of varying quality, along with accurate evaluations at the CCSD(T) level of the vertical (26.5 eV) and adiabatic (22.1 eV) double ionization thresholds under C(2v) symmetry. The obtained results are compared with newly recorded ultraviolet photoemission spectra (UPS), up to binding energies of 40 eV. The theoretical predictions are entirely consistent with experiment and indicate that, in a vertical depiction of ionization, shake-up states at binding energies larger than approximately 26.5 eV tend to decay via emission of a second electron in the continuum. A band of s-type symmetry that has been previously seen at approximately 25 eV in the electron impact ionization spectra of norbornane is entirely missing in the UPS measurements and theoretical ADC(3) spectra. With regard to these results and to the time scales characterizing electron-electron interactions in EMS (10(-17) s) as compared with that (10(-13) s) of photon-electron interactions in UPS, and considering the p-type symmetry of the electron momentum distributions for the nearest 1b(1) and 1b(2) orbitals, this additional band can certainly not be due to adiabatic double ionization processes starting from the ground electronic state of norbornane, or to exceptionally strong vibronic coupling interactions between cationic states derived from ionization of the latter orbitals. It is therefore tentatively ascribed to autoionization processes via electronically excited and possibly dissociating states.     

High resolution electron momentum spectroscopy of the valence orbitals of water

The development of a third-generation electron momentum spectrometer with significantly improved energy and momentum resolutions at Tsinghua University (ΔE = 0.45–0.68 eV, Δθ = ±0.53° and Δ? = ±0.84°) has enabled a reinvestigation of the valence orbital electron momentum distributions of H₂O with improved statistical accuracy. The measurements have been conducted at impact energies of 1200 eV and 2400 eV in order to check the validity of the plane wave impulse approximation. The obtained ionization spectra and electron momentum distributions have been compared with the results of computations carried out with Hartree Fock [HF] theory, density functional theory in conjunction with the standard B3LYP functional, one-particle Green’s function [1p-GF] theory along with the third-order algebraic diagrammatic construction scheme [ADC(3)], symmetry adapted cluster configuration interaction [SAC-CI] theory, and a variety of multi-reference [MR-SDCI, MR-RSPT2, MR-RSPT3] theories. The influence of the basis set on the computed momentum distributions has been investigated further, using a variety of basis sets ranging from 6-31G to the almost complete d-aug-cc-pV6Z basis set. A main issue in the present work pertains to a shake-up band of very weak intensity at 27.1 eV, of which the related momentum distribution was analyzed for the first time. The experimental evidences and the most thorough theoretical calculations demonstrate that this band borrows its ionization intensity from the 2a₁ orbital.     

Electron momentum spectroscopy of trisubstituted amines: The valence shell orbitals of triethylamine

The ionization potentials of the valence shell orbitals (up to 40 eV) of triethylamine have been measured by means of the binary (e,2e) technique. Satellite structure, due to transitions to ionic excited states, has been observed in the outer valence shell for binding energies larger than 15 eV. The electron momentum distributions of the valence orbitals have been measured on ionization peaks corresponding to main and satellite transitions. Results are compared with SCF calculations. The electron momentum distribution of the most external orbital, formed mostly by the N 2p lone pair, is discussed in detail.     

Green's function study of the one-electron and shake-up ionization spectra of unsaturated hydrocarbon cage compounds

The valence one-electron and shake-up ionization spectra of stella-2,6-diene, stella-2,6-dione, bicyclo-[2.2.2]-octane-2,5-dione, and bicyclo-[2.2.1]-heptane-2,5-dione have been exhaustively studied, up to the double ionization threshold and beyond, by means of one-particle Green's function theory. This study is based on calculations employing the outer-valence Green's function and the third-order algebraic diagrammatic construction schemes, along with a variety of basis sets. A comparison is made with available ultraviolet (He I) photoelectron and (e, 2e) electron-impact ionization spectra, with main focus on the identification of spectral fingerprints for cyclic strains and through-bond pi-conjugation. As a byproduct, our results demonstrate that it is impossible to reliably assign complex (e, 2e) ionization spectra by resorting only to Hartree-Fock or Kohn-Sham orbital energies and to the related electron momentum distributions.     

Experimental and theoretical electron momentum spectroscopic study of the valence electronic structure of tetrahydrofuran under pseudorotation

The most populated structure of tetrahydrofuran (THF) has been investigated in our previous study using electron momentum spectroscopy (EMS). Because of the relatively low impact energy (600 eV) and low energy resolution (DeltaE = 1.20 eV) in the previous experiment, only the highest occupied molecular orbital (HOMO) of THF was investigated. The present study reports the most recent high-resolution EMS of THF in the valence space for the first time. The binding energy spectra of THF are measured at 1200 and 2400 eV plus the binding energies, respectively, for a series of azimuthal angles. The experimentally obtained binding energy spectra and orbital momentum distributions (MDs) are employed to study the orbital responses of the pseudorotation motion of THF. The outer valence Greens function (OVGF), the OVGF/6-311++G** model, and density function theory (DFT)-based SAOP/et-pVQZ model are employed to simulate the binding energy spectra. The orbital momentum distributions (MDs) are produced using the DFT-based B3LYP/aug-cc-pVTZ model, incorporating thermodynamic population analysis. Good agreement between theory and experiment is achieved. Orbital MDs of valence orbitals exhibit only slight differences with respect to the impact energies at 1200 and 2400 eV, indicating validation of the plane wave impulse approximation (PWIA). The present study has further discovered that the orbital MDs of the HOMO in the low-momentum region (p < 0.70 a.u) change significantly with the pseudorotation angle, phi, giving a v-shaped cross section, whereas the innermost valence orbital of THF does not vary with pseudorotation, revealing a very different bonding mechanism from the HOMO. The present study explores an innovative approach to study pseudorotation of sugar puckering, which sheds a light to study other biological systems with low energy barriers among ring-puckering conformations.     

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.     

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.     

Electron Momentum Spectroscopy of Outer Valence Orbitals of 2-Fluoroethanol

The binding energy spectra and electron momentum distributions for the outer valence molecular orbitals of gaseous 2-fluoroethanol have been measured by the non-coplanar asymmetric (e, 2e) spectrometer at impact energy of 2.5 keV plus binding energy. The quantitative calculations of the ionization energies and the relevant molecular orbitals have been carried out by using the outer-valence Green’s function method and the density functional theory with B3LYP hybrid functional. The observed ionization bands in binding energy spectra, as well as the previous photoelectron spectrum which was not assigned, have been assigned for the first time through the comparison between experiment and theory. In general, the theoretical electron momentum distributions calculated by B3LYP method with aug-cc-pVTZbasis set are in line with the experimental ones when taking into account the Boltzmannweighted thermo-statistical abundances of five conformers of 2-fluoroethanol.     

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.     

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.     

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'.