Valence Orbital Momentum Distributions Research Articles

A joint experimental and theoretical study of the valence electron momentum distributions of trans-stilbene

This paper reports an experimental and theoretical study on the valence orbital momentum distributions of trans-stilbene. Experimentally, an (e, 2e) electron-impact ionization measurement is performed to obtain momentum profiles of the outer valence orbitals. Theoretically, calculations of the momentum profiles are carried out at the level of density functional theory, including the influences of thermally induced torsional motions of phenyl rings as well as contributions from other vibrational modes. The theoretical analysis shows that despite the structural flexibility of trans-stilbene, molecular vibration does not significantly affect the momentum profiles. The experimental results for the high-lying occupied π orbitals reveal that the position of the maximum in each momentum profile reflects the bonding character of the corresponding orbital. It provides a basis to apply electron momentum spectroscopy to large π-conjugated molecules, such as oligomers of conducting polymers.

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.

Inheritance and correlation of nucleic acid pyrimidine bases

Valence electronic structures of pyrimidine (P, C4N2H4) and nucleic acid (NA) pyrimidine bases, including cytosine (C, C4N3OH5), thymine (T, C5N2O2H6), and uracil (U, C4N2O2H4), are studied using B3LYP/aug-cc-pVTZ, B3LYP/TZVP, SAOP/et-pVQZ, and OVGF/TZVP. The highest occupied molecular orbital (HOMO) and the next HOMO (NHOMO) of pyrimidine are conclusively assigned as 7b2 and 2b1, respectively. The ionization energy spectra and valence orbital momentum distributions studies reveal that the NA bases, that is, cytosine, thymine, and uracil, exhibit a larger degree of similarity to each other than to pyrimidine, although they do inherit certain properties from pyrimidine. © 2013 Wiley Periodicals, Inc.

Vibrational effects on the electron momentum distributions of valence orbitals of formamide

The ionization energy spectra and electron momentum distributions of formamide were investigated using the high-resolution electron momentum spectrometer in combination with high level calculations. The observed ionization energy spectra and electron momentum distributions were interpreted using symmetry adapted cluster-configuration interaction theory, outer valence Green function, and DFT-B3LYP methods. The ordering of 10a(') and 2a(") orbitals of formamide was assigned unambiguously by comparing the experimental electron momentum distributions with the corresponding theoretical results, i.e., 10a(') has a lower binding energy. In addition, it was found that the low-frequency wagging vibration of the amino group at room temperature has noticeable effects on the electron momentum distributions. The equilibrium-nuclear-positions-approximation, which was widely used in electron momentum spectroscopy, is not accurate for formamide molecule. The calculations based on the thermal average can evidently improve the agreement with the experimental momentum distributions.

Electron momentum spectroscopy study on valence electronic structures of pyrimidine

The momentum distributions of valence orbitals of pyrimidine were measured at various impact energies. The observed distributions were compared with HF, DFT-B3LYP, and OVGF calculations. The HOMO was unambiguously assigned to the 7b 2 symmetry. It was found that the pole strength of the outer valence orbital 2b 1 was 0.8. Moreover, the present study indicated that we should be very cautious in using the (e, 2e) reaction to investigate the molecular conformational population by comparing the PWIA theoretical results with the experimental results at a single impact energy.

Orbital based electronic structural signatures of the guanine keto G-7H/G-9H tautomer pair as studied using dual space analysis

Electronic structural signatures of the guanine-7H and guanine-9H tautomers have been investigated on an orbital by orbital basis using dual space analysis. A combination of density functional theory (B3LYP/TZVP), the statistical average of model orbital potentials (SAOP/TZ2P) method and outer valence Green's function theory (OVGF/TZVP) has been used to generate optimal tautomer geometries and accurate ionization energy spectra for the guanine tautomer pair. The present work found that the non-planar form for both of the guanine keto pair possesses lower energies than their corresponding planar counterparts, and that the canonical form of the guanine-7H tautomer has slightly lower total energy than guanine-9H. This latter result is in agreement with previous experimental and theoretical findings. In the planar guanine pair the geometric parameters and anisotropic molecular properties are compared, focusing on changes caused by the mobile proton transfer. It is demonstrated that the mobile proton only causes limited disturbance to isotropic properties, such as geometry and the energetics, of the guanine keto tautomer pair. The exception to this general statement is for related local changes such as the N (7)–C (8) and C (8)–N (9) bond length resonance between the single and double bonds, reflecting the nitrogen atom being bonded with the mobile proton in the tautomers. The mobile proton distorts the electron distribution of the tautomers, which leads to significant changes in the molecular anisotropic properties. The dipole moment of guanine-7H is altered by about a factor of three, from 2.23 to 7.05 D (guanine-9H), and the molecular electrostatic potentials also reflect significant electron charge distortion. The outer valence orbital momentum distributions, which were obtained using the plane wave impulse approximation (PWIA), have demonstrated quantitatively that the outer valence orbitals of the tautomer pair can be divided into three groups. That is orbitals 1a″–7a″ and 18a′, which do not have visible alternations in the tautomeric process (which consist of either π orbitals or are close to the inner valence shell); a second group comprising orbitals 19a′–22a′, 25a′, 26a′, 28a′, 29a′ and 31a′, which show small perturbations as a result of the mobile hydrogen locations; and group three, orbitals 23a′, 24a′, 27a′, 30a′ and 32a′, which demonstrate significant changes due to the mobile proton transfer and are therefore considered as signature orbitals of the G-7H/G-9H keto tautomeric process.

Assessment of Quantum Mechanical Models Based on Resolved Orbital Momentum Distributions of n-Butane in the Outer Valence Shell.

Fully resolved outer valence orbital momentum distributions (MDs) of n-butane (C4H10) in the ground electronic state (X1Ag) are studied quantum mechanically using RHF/TZVP, density functional theory (DFT) DFT-BP/TZVP, and B3LYP/TZVP methods. The orbital MDs are simulated to reflect the recent experimental conditions with the plane wave impulse approximation (PWIA) and are compared favorably with the available experimental orbital cross sections. However, the majority of the outer valence molecular orbitals (MOs) of n-butane has been only partially resolved experimentally, forming into three clustered MOs of 7ag + 2bg + 6ag, 2au + 6bu and 1bg + 5bu + 5ag. Deconvolution of the clustered MOs is a challenge experimentally but rather straightforward theoretically, as the inversion is a multiple channel process. The outer valence MOs are crucial to understanding the chemical bonding mechanism and the unresolved outer valence orbitals cause significant bonding information loss. This work provides an orbital based assessment to the quality of the RHF/TZVP, DFT-BP/TZVP, and B3LYP/TZVP models using orbital MD information, by decomposing the clustered outer valence MOs of n-butane, which also reveals the bonding mechanism of the species.

Electron momentum spectroscopy of the isoelectronic species hydrogen fluoride and neon

The authors report new electron momentum spectroscopy (EMS) measurements on hydrogen fluoride (HF) and neon (Ne) at 1500 eV. The present HF data for the 1 pi , 3 sigma and 2 sigma orbitals are compared in detail with the results of an earlier EMS study at 400 and 1200 eV and with the results of a recent calculation of the valence orbital momentum distributions given by (i) SCF calculations at the Hartree-Fock limit and (ii) CI calculations of the complete molecule-ion overlap amplitude. The current Ne 2p and 2s momentum distributions are compared with the results of both the plane wave and a new, fully distorted wave Born approximation (DWBA) calculation. The results of the DWBA calculation in Ne have direct relevance to HF, in particular to the inner valence (2 sigma ) cross section.

Hartree-Fock limit and configuration interaction calculations of the ion-molecule overlap amplitude for hydrogen fluoride: Comparison with EMS experiments

The valence orbital momentum distributions of HF have been calculated using extended Gaussian basis sets at the SCF limit and CI levels and with a numerical Hartree-Fock procedure. The basis sets and CI methodologies were capable of recovering approximately 85% of the estimated correlation energy. Comparison with previously published experimental results shows a disagreement with these calculations for the shape of the 1π momentum distribution, as well as a considerable difference between the measured and calculated intensity of the 2σ momentum distribution.

The valence orbital momentum distributions and binding energy spectra of methane by electron momentum spectroscopy: Quantitative comparisons using near Hartree-Fock limit and correlated wavefunctions

The binding energies and electron momentum distributions of the two valence orbitals of CH 4 have been measured at high momentum resolution. The measured binding energy spectrum compares favourably with the results of previously published Green's function calculations, which predict some small splitting of the 2a 1 pole strength. At least four distinct satellite peaks (of dominantly 2a 1 symmetry) are identified in the inner valence region. The measured momentum profiles have been quantitatively compared with momentum distributions predicted using SCF wavefunctions up to near the Hartree-Fock limit in quality and also with ion-neutral overlap calculations using correlated wavefunctions obtained by the method of configuration interaction. Excellent agreement is found with theory at the Hartree-Fock limit level and inclusion of relaxation and electron correlation is found to have minimal effect on the calculated electron momentum distributions. Density maps for oriented CH 4 molecules in position and momentum space are presented.

An experimental and theoretical investigation of the valence orbital momentum distributions and binding energy spectra of nitrogen

We have carried out an accurate and detailed EMS and a many-body theoretical study of the complete valence region of N 2. The 1500 eV EMS momentum distributions show that they provide a sensitive test for orbital wavefunctions of SCF calculations, and of correlation effects. The momentum distribution of the outermost 3σ g orbital is more sharply peaked at the origin than predicted by the orbital wavefunction. There is a 2σ u state at 25 eV with a spectroscopic strength of approximately 0.07 in agreement with the results of the many-body calculations. There may be significant 2σ u and or 1π u strength (up to 0.1) as well as 2σ g strength (0.07–0.12) in the region 27–34.5 eV. Peaks observed at about 29 and 32 eV, previously attributed only to the 2σ g orbital, could contain considerable 2σ u or 1π u contributions. If the predicted 3σ g component of the σ g poles in this region are all out of phase with the 2σ g components, only small σ u or π u strength would be required to explain the momentum distributions in this region. The many-body calculations tend to predict too much 2σ g strength in the region 27–34 eV.

The valence orbital momentum distributions and binding energy spectra of dimethyl ether by electron momentum spectroscopy: An investigation of the methyl inductive effect

The high momentum resolution experimental momentum profiles of some of the valence orbitals of (CH 3) 2O have been measured by electron momentum spectroscopy. Good agreement is obtained between the measurements and the momentum distributions calculated from relatively simple wavefunctions except in the case of the outermost 2b 1 orbital. The effects of diffuse and polarization functions in the basis sets and also the influence of molecular geometry have been investigated. The observed features of the binding energy spectra including the inner valence region are quite well reproduced by earlier published Green function calculations. Comparison of the XMPs of the outermost (HOMO and NHOMO) orbitals of H 2O, CH 3OH, and (CH 3) 2O shows an increase in low momentum components with increasing methyl substitution. The results are discussed in relation to commonly held views of the methyl inductive effect.

The valence orbital momentum distributions and binding energy spectra of silane by electron momentum spectroscopy: Quantitative comparisons using Hartree-Fock limit and correlated wavefunctions

The binding energies and momentum distributions of the two valence orbitals of SiH 4 have been measured by electron momentum spectroscopy. The measured binding energy spectrum is compared with ADC(3) and ADC(4) many-body Green function calculations. The momentum distributions are compared on a quantitative basis with SCF wavefunctions near the Hartree-Fock limit and also with full ion-neutral overlap calculations carried out using correlated wavefunctions by the method of configuration interaction. Quite good agreement with theory is found at the Hartree-Fock limit and inclusion of electron correlation has minimal effect on the calculated momentum distributions. A study of the angular dependence of the satellite structure in the inner valence region shows that these processes arise predominantly from final state correlations associated with the production of the 3a 1 −1 hole state.

The valence orbital momentum distributions and binding energy spectra of H 2CO: A comparison of electron momentum spectroscopy and quantum chemical calculations using near-Hartree-Fock quality and correlated wavefunctions

The high momentum resolution experimental momentum profiles (XMPs) of the valence orbitals of H 2CO have been measured by electron momentum spectroscopy (EMS). Good quantitative agreement is obtained between the measured XMPs and the momentum distributions calculated from a near-Hartree-Fock wavefunction except for the outermost 2b 2 orbital. A configuration interaction study suggests that the difference between theory and experiment observed for the outermost 2b 2 orbital cannot be accounted for by inclusion of electron correlation and electronic relaxation effects. The measured 5a 1 and 1b 2 XMPs confirm earlier orbital assignments made by Hood et al. Extensive many-body structures are observed in the inner valence binding energy region and these are assigned predominantly to the (3a 1) −1 process.

The valence orbitals of NH 3 by electron momentum spectroscopy: Quantitative comparisons using Hartree-Fock limit and correlated wavefunctions

The complete valence shell binding energy spectra and valence orbital electron momentum distributions for NH 3 have been measured by high-momentum-resolution electron momentum spectroscopy (EMS). The results are quantitatively compared with theoretical calculations using SCF wavefunctions ranging from DZ quality to a newly developed 126-GTO wavefunction essentially at the Hartree-Fock limit. The 3a 1 and to a lesser extent the 2a 1 valence orbital are not adequately described even at the Hartree-Fock limit with basis set saturation including diffuse functions. The differences between theory and experiment are largely resolved by ion-neutral overlap calculations using CI wavefunctions to incorporate the effects of electron correlation. The 126-G (CI) wavefunctions provide accurate calculation of a wide range of electronic properties of NH 3 and also give good quantitative prediction of the three valence orbital momentum distributions as well as a reasonable prediction of the many-body pole strength distribution observed in the (2a 1) −1 inner valence binding energy spectrum. The present EMS results are compared with recent investigations of wavefunction tails by exterior electron distribution calculations and Penning ionization electron spectroscopy measurements reported by Ohno et al.

Valence orbital momentum distributions in s-triazine

Valence orbital momentum distributions, ρ(q), are obtained for s-triazine, C3H3N3, from (e,2e) spectroscopy and split valence SCFMO calculations. The separation energy spectrum simulated using the calculated ρ(q) and ionization energies from Green’s function calculations is in good agreement with experiment from 9–20 eV, but at higher energy the simulated spectrum has higher intensity than experiment, indicating that the Green’s function calculation underestimates the complexity of the inner valence region. The calculated momentum distributions have their maxima at higher values than observed experimentally for the outermost valence orbitals, but the difference in momentum distributions between the antisymmetric 4e′ N2p lone pair orbital of s-triazine and the N2p lone pair orbital of ammonia is reproduced well by the calculations. Similarly, calculated and experimental differences of Fourier transformed ρ(q) for the 4e′ and 3a′1 N2p lone pair orbitals of triazine are in agreement and can be interpreted using plots of 4e′ and 3a1 orbital averages and differences from the SCFMO calculations. The Fourier transformed momentum distribution of the 4e′ orbital clearly shows the presence of both nearest-neighbor C and second-nearest-neighbor N interactions.

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

The outer valence orbital momentum distributions of CO 2 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 CO 2 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.

Experimental investigation of the valence orbital momentum distributions and ionization energies of the noble gases by binary (e, 2e) spectroscopy

A binary (e. 2e) spectrometer has been modified to obtain significantly improved momentum resolution ▪. Using this apparatus a systematic study of the ionization of all the valence orbitals of the noble gases: He, Ne, Ar, Kr and Xe has been carried out at an impact energy of 1200 eV plus the binding energy. Binding-energy spectra have been obtained at a series of azimuthal angles (corresponding to different electron momenta) for each target gas. In Ar, Kr and Xe the pole strength for ns ionization is severely split among several final ion states and the intensities are compared with earlier results from (e, 2e) spectroscopy. X-ray photoelectron spectroscopy and theoretical calculations. The ns and np atomic orbital (AO) electron-momentum distributions have been measured for the noble gases and the results, which give directly the squares of the AO momentum-spade wavefunctions, are compared with the square of Fourier transformed position-space wavefunctions of Hartree-Fock (HF), double-zeta (DZ) and single-zeta (SZ) quality. Excellent agreement is obtained between the experiment and Hartree-Fock calculations. Atomic orbital momentum density and position density contour maps have also been generated using Hartree-Fock wavefunctions. The maps have been used to provide a complementary discussion of position-and momentum-space properties of the noble-gas group of elements in the periodic table. Trends are discussed in the momentum distributions, density maps in position and momentum space and also the binding-energy spectra with reference to the electronic structure of the noble gases.

Ionization of fluorinated methanes and ethylenes through (e,2e) process and green's function approach to predict ionization potentials

(e,2e) spectra of fluoromethanes and fluoroethylenes are here reported and compared with Green's function calculation. Furtherly measured electron momentum distributions of valence orbitals of the same compounds, yielding information on, each single molecular bond are discussed. In this way a full analysis of each molecular orbital is performed for the studied systems.