An (e,2e) study of ammonia: Binding energies and momentum distributions of valence electrons

The valence shell electronic structure of NH₃ is studied in an (e,2e) experiment with symmetric non-coplanar geometry. The momentum distributions obtained for the separate orbitals are compared with those calculated from several approximate wavefunctions. The 3a₁ distribution is found to be particularly sensitive to the form of the wavefunction.     

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.     

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.     

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.     

Triple differential generalized oscillator strength of direct and resonance He(e, 2e)He+ reaction at high incident energies

The triple differential cross section and triple differential generalized oscillator strength of the direct and resonance He(e, 2e)He⁺ reaction in the first Born approximation for incident energiesE ₀≥4keV are calculated. For the direct (e, 2e) process our results obtained in definite structure models of the atom are found to be in good agreement with the available experimental data and theoretical estimates. The resonance profiles calculated in these models exhibit a complicated structure formation of overlapping¹ P and¹ D autoionization states (AIS) excited in the (e, 2e) reaction. The specific kine-matical conditions, when the overlap and interference of the¹ P and¹ D resonances are small and the¹ P and¹ D AIS yields can be measured separately, are discussed. It is also shown that in a certain range of ejection angles and at large momentum transfers (Q>2au) the yield of the¹ D AIS dominates over the¹ P resonance yield.     

Direct dynamics simulations of O(3P) + HCl at hyperthermal collision energies

The dynamics of the O(3P) + HCl reaction at hyperthermal collision energies were investigated using the quasiclassical trajectory method. Stationary points on the OClH 3A" and 3A' potential energy surfaces (PESs) were also examined. The lowest transition state leading to OCl + H on the 3A" surface is 2.26 eV above the reagents at the CCSD(T)/cc-pVTZ level of theory. This saddle point is bent and product-like. Direct dynamics calculations at the MP2/cc-pVTZ level of theory were used to investigate the excitation functions for OH + Cl, OCl + H, and O + H + Cl formation. OCl is formed mainly from small-impact-parameter collisions, and the OCl + H excitation function peaks around 5 eV, where it is similar in magnitude to the OH + Cl excitation function. The shape of the OCl + H excitation function is discussed, and features are identified that should be general to hyperthermal collision dynamics.     

On the self-consistent-field linear combination of atomic orbitals for bounded crystal orbitals (SCF-LCAO-BCO) method

The self-consistent-field linear combination of atomic orbitais for bounded crystal orbitais (SCF-LCAO-BCO) method can be used to study the electronic structure of bounded polymers and crystals if they have a significant amount of internal translational symmetry, at the ab initio Hartree-Fock level. The direct recursion (transfer matrix) method (DRM) is applied to its derivation, here only for certain simpler models. It is shown that the application of the free boundary condition instead of the periodic (Born-von Kármán) one halves the conventional one-dimensional Brillouin zone and resolves the double degeneracy of the Bloch states. A longitudinal bulk-state distortion (LBSD) is demonstrated for a linear bounded polymer model possessing perfect translational symmetry and symmetrical intercell interaction matrices. The block diagonalizability is discussed when free boundary conditions are applied. The non-existence of limit wave functions in the overlapping regions of bands is shown for the infinite size limit. The use of certain averaged wave functions is proposed for the calculation of the charge-bond order matrices in order to resolve the above difficulty.     

确定硼烷的杂硼烷价成键轨道对称性的拓扑方法

本文通过对硼烷的分子轨道的定域化分析, 建立了由硼烷或杂硼烷的骨架多面体的几何性质, 确定其价成键轨道对称性的拓扑方法。从以多面体骨架的三角面和缺顶点周围的边为基约化出的不同约表示中, 按建议的能量与节面数的对应规则,选定出分子的价成键轨道所属的不可约表示。     

Satellite structures and momentum distributions in binary (e, 2e) spectroscopy of N2O

The (e, 2e) coincidence technique has been applied in studying the valence shell of N₂O. The assignment of some satellite structures is discussed.     

Bonding in ammonia borane: an analysis based on the natural orbitals for chemical valence and the extended transition state method (ETS-NOCV)

In the present study the natural orbitals for chemical valence (NOCVs) combined with the energy decomposition scheme (ETS) were used to characterize bonding in various clusters of ammonia borane (borazane): dimer D, trimer TR, tetramer TE, and the crystal based models: nonamer N and tetrakaidecamer TD. ETS-NOCV results have shown that shortening of the B-N bond (by ~0.1 ?) in ammonia borane crystal (as compared to isolated borazane molecule) is related to the enhancement of donation (by 6.5 kcal/mol) and electrostatic (by 11.3 kcal/mol) contributions. This, in turn, is caused solely by the electrostatic dipole-dipole interaction between ammonia borane units; dihydrogen bonding, BH···HN, formed between borazane units exhibits no direct impact on B-N bond contraction. On the other hand, formation of dihydrogen bonding appeared to be very important in the total stabilization of single borazane unit, namely, ETS-based data indicated that it leads to significant electronic stabilization ΔE(orb) = -17.5 kcal/mol, which is only slightly less important than the electrostatic term, ΔE(elstat) = -19.4 kcal/mol. Thus, both factors contribute to relatively high melting point of the borazane crystal. Deformation density contributions (Δρ(i)) obtained from NOCVs allowed to conclude that dihydrogen bonding is primarily based on outflow of electron density from B-H bonding orbitals to the empty σ*(N-H) (charge transfer component). Equally important is the covalent contribution resulting from the shift of the electron density from hydrogen atoms of both NH and BH groups to the interatomic regions of NH···HB. Quantitatively, averaged electronic strength of dihydrogen bond per one BH···HN link varies from 1.95 kcal/mol (for the crystal structure model, N), 2.47 kcal/mol (for trimer TR), through 2.65 kcal/mol (for tetramer TE), up to 3.95 kcal/mol (for dimer D).     

Ionization potentials and electron momentum distributions for SiF4 valence-shell orbitals: an (e,2e) spectroscopic investigation and Green's function study

Ionization potentials and electron momentum distributions of SiF₄ valence-shell orbitals have been measured by means of (e,2e) spectroscopy. SCF calculations and a Green's function study have been performed on the same molecule. A comparison between experimental and theoretical results shows that a significant interaction of 2p F with 3d Si orbitals occurs.     

(e,2e) Spectroscopy of methane

Measurements are reported on the spectroscopy of methane using the symmetric (e,2e) technique at energies of 600 eV and 1200 eV. The angular correlations of the states with separation energies of 14.2 and 23.1 eV have been measured and compared with the orbital wavefunctions of Snyder and Basch and with some earlier data at 400eV. The angular correlation of the configuration interaction state at 31 eV shows that this state definetely results from the removal of an electron in the 2a₁ orbital. Other structure at high separation energy is also identified with this orbital. Relative strengths of the It₂ and 2a₁ states are compared and found to be in agreement with the theory at 1200eV.     

Triple-differential cross sections of helium for (e, 2e) processes

The triple differential cross sections for electron impact ionization of helium in a symmetric coplanar energy-sharing geometry at incident energies from 45–500 eV and an angle of 45° are calculated by use of the modified BBK model. A comparison with other theoretical results has been performed. It has been found that the present results give an excellent agreement with the absolute experimental measurement for the energy range considered.     

Experimental and calculated momentum densities for the valence orbitals of carbon tetrafluoride

Carbon tetraflouoride has been investigated by binary (e,2e) spectroscopy at 1200 eV impact energy. Binding energy spectra (10–60 eV) at azimuthal angles of 0° and 8° are reported and are found to be in quantitative agreement with a previous Green's function calculated spectrum. Momentum distributions corresponding to individual orbitals are also reported and compared with theoretical momentum distributions evaluated using double-zeta quality SCF wavefunctions. Excellent agreement between experimental and theories is found for the strongly bonding 3t₂ orbital and the antibonding 4a₁ orbital but agreement is less good for the outermost non-bonding orbitals. Intense structure due to molecular density (bond) oscillation is observed experimentally in the region above 1.0 a_o^?1 in the case of the non-bonding 4t₂ orbital. It is also notable that the measured 4a₁ momentum distribution exhibits an extremely well-defined “p” character with clear separation between the s and p components. Contour maps of the position-space and momentum-space orbital densities in the F-C-F plane of the molecule are used to provide a qualitative interpretation of the features observed in the momentum distribution. In order to further extend momentum-space chemical concepts to three-dimensional systems, constant density surface plots are also used to give a more comprehensive view of the density functions of the CF₈ molecule.     

Recoil-ion momentum distribution for He(e,2e)He+-and He(e,3e)He++-reactions

Using Recoil-Ion Momentum Spectroscopy (RIMS) we have measured the momenta of recoiling target ions in He(e,2e)He⁺- and He(e,3e)He⁺⁺-reactions at impact energies between 270 ev and 3200 eV. The recoil-ion momentum reflecting the sum momentum of all outgoing electrons was determined for the first time in all three spatial dimensions separately for single and double ionization by electron impact. The data are compared to results of a nCTMC-calculation.