2p Sigma Research Articles

Oscillator strengths and line widths of dipole-allowed transitions in N214 between 89.7 and 93.5nm

Line oscillator strengths in the 20 electric dipole-allowed bands of (14)N(2) in the 89.7-93.5 nm (111480-106950 cm(-1)) region are reported from photoabsorption measurements at an instrumental resolution of approximately 6 mA (0.7 cm(-1)) full width at half maximum. The absorption spectrum comprises transitions to vibrational levels of the 3p sigma(u) c(4)' (1)Sigma(u)(+), 3p pi(u) c(3) (1)Pi(u), and 3s sigma(g) o(3) (1)Pi(u) Rydberg states and of the b' (1)Sigma(u)(+) and b (1)Pi(u) valence states. The J dependences of band f values derived from the experimental line f values are reported as polynomials in J'(J'+1) and are extrapolated to J'=0 in order to facilitate comparisons with results of coupled Schrodinger-equation calculations. Most bands in this study are characterized by a strong J dependence of the band f values and display anomalous P-, Q-, and R-branch intensity patterns. Predissociation line widths, which are reported for 11 bands, also exhibit strong J dependences. The f value and line width patterns can inform current efforts to develop comprehensive spectroscopic models that incorporate rotational effects and predissociation mechanisms, and they are critical for the construction of realistic atmospheric radiative-transfer models.

Quantum calculations on the acid catalyzed rearrangements of norborn-5-en-2-one, 7-oxanorborn-5-en-2-one and 7-azanorborn-5-en-2-oneThe electron-releasing effect of homoconjugated carbonyl group

Protonation of norbom-5-en-2-one gives 6-oxo-2-norbomyl cation (2) as most stable C7H9O+ cation. Quantum calculations at B3LYP/6-31G(d) level (gas phase, 1 atm, 25 degrees C) predict a C-s-structure for 2 that can be represented as an intramolecular pi-complex (Dewar pi-complex model) of an acetylium ion with an alkene (cyclopent-3-enyl moiety). Isomeric 5-oxo-2-norbornyl (1) cation is calculated to be 16.7 kcal/mol less stable than 2. Part of the relatively high stability of 2 arises from the electron-releasing carbonyl group through n(C=O) sigma 2p(C+) hyperconjugation. This effect is also present in more stable 6-oxo-3-oxa (14) and 6-oxo-3-aza-2-norbornyl cation (19) as these ions are calculated to be 7.4 and 3.3 kcal/ mol, respectively, more stable than their 5-oxo isomers. (c) 2007 Elsevier B.V. All rights reserved.

Orbital Overlap and Chemical Bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).

Radiative decay modes of the antiprotonic helium atom

The authors discuss the decay modes of the 'exotic' He atom obtained by replacing one electron in ordinary He by an antiproton. They use the Born-Oppenheimer approximation as a first step in the description of this three-body Coulomb system, and concentrate on states with angular momentum approximately 20 to 40. The authors find that within the Born-Oppenheimer approximation strong correlations between the motion of the antiproton and electron are critical in determining the radiative lifetimes of "vibrationally" excited states. These correlations vastly increase the lifetimes of states formed in the potential determined by the electronic ground state. Going beyond the Born-Oppenheimer approximation, and including states based on excited electronic configurations leads to a new decay mechanism, a radiative transition with simultaneous electron excitation. Surprisingly this is the dominant radiative decay mode for highly excited states of antiprotonic helium. The inclusion of pi states can further alter the picture; strong angular coupling between the 2p sigma and 2p pi states leads to a complete breakdown of the Born-Oppenheimer approximation for states of total angular momentum <or approximately=20 and provides a spectacularly virulent example of Lambda doubling, so strong that the ground vibrational states of angular momentum <or approximately=20 are actually in an excited electronic state well. The auhtors discuss the implications for the long lived states observed experimentally in He.

An electrolyte electroreflectance study of FeS2

We report an electrolyte electroreflectance (EER) study of synthetic pyrite FeS2 single crystals in the energy range 1-6 eV. The EER spectrum exhibits derivative-like structures in the vicinity of the interband transitions. The transition energies are determined accurately and a probable energy band structure near the Fermi level is constructed. It is proposed that FeS2 has a completely filled 3d t2g band occupied by six electrons in the low-spin configuration, separated from empty S 3p sigma * and Fe 3d eg* bands, and that the bottom of the conduction band corresponds to the S 3p sigma * antibonding states.

Electron capture by doubly charged ions from laser-excited alkali atoms: II. He2+-Li*(2p) collisions

For pt. I, see ibid., vol. 26, p. 2137-51 (1993b). Single electron capture in collisions of slow (keV amu-1) He2+ ions with aligned Li*(2p) atoms has been investigated by means of translational energy spectroscopy. A single mode cw dye laser beam has been modified by using an electro-optical modulator in order to pump both hyperfine ground states of Li simultaneously, thus maximizing the fraction of excited target atoms. Cross sections for electron capture from Li(2s), Li*(2p Sigma ) and Li*(2p Pi ) initial states into He+(n = 3 4, 5) final states have been determined for different impact energies and compared with 68-state atomic orbital (AO) close coupling calculations.

Electron capture by doubly charged ions from laser-excited alkali atoms: I. He2+-Na*(3p) collisions

State-selective single electron capture in slow (0.5-3 keV amu-1) collisions of He2+ with laser-excited Na*(3p) atoms has been studied by means of translational energy spectroscopy and the results compared with 64-state atomic orbital (AO) close coupling calculations, considering cross sections for electron capture into He+(n=3,4,5) final states for different impact energies. In addition, alignment effects have been studied by controlling the polarization of the exciting laser light. The experimentally observed dependence on Na*(3p Sigma ) and Na*(3P Pi ) initial state preparation is quantitatively reproduced by the AO calculations.

Integral alignment of Na(3p) in resonant charge transfer collisions

Experimental results for the integral alignment of Na(3p) in resonant charge transfer collisions with Na+ for collision energies in the range 90 to 2500 eV are presented. Among the three possible configurations 3p sigma , 3p pi + and 3p pi - the 3p sigma turns out to be most efficient for the charge transfer process at all investigated energies. At 90 eV its relative cross section is approximately 50% and decreases to approximately 33% at higher energies.

Electronic excitation of carbon dioxide in the 10.5-18 eV range studied by inelastic electron scattering spectroscopy

Electronic excitation of carbon dioxide has been studied in the 10.5-18 eV energy range by electron impact energy-loss spectroscopy. The experimental conditions (various impact energies ranging between 60 and 1.35 eV above thresholds and various detection angles between 4 and 50') enabled the authors to show evidence for most of the g to or from g forbidden transitions predicted by theoretical calculations to lie in the same region as the Rathenau progressions. The first three members of four new Rydberg series converging to the ionic ground state have been identified, two being triplets and the two others being symmetry-forbidden. In addition, the symmetry-forbidden character of two series, one converging to the A 2 Pi u state and the other to the B 2 Sigma u state, has been obtained experimentally; the triplet component of the 2 pi u to 3p sigma u transition is observed with a singlet-triplet splitting of 0.26 eV.

A coincidence analysis of the excitation mechanisms for two electrons in low-energy collisions of Li+ and He

The authors have performed a coincidence analysis of two-electron excitation in the Li+-He collision system at low energies (1 keV<or=Ep<or=3 keV). They measured the emitted autoionisation electrons in coincidence with the scattered projectiles. The results show that excitation takes place via two mechanisms: the (1s sigma 22p sigma 2) 1 Sigma -(1s sigma 22p pi 2)1 Sigma , 1 Delta and (1s sigma 22p sigma 2)1 Sigma -(1s sigma 22s sigma 2p pi )1 Pi rotational coupling. Because two excitation mechanisms participate in this system one cannot use the simple MO model to derive predictions for the transition amplitudes for this case, in contrast with the cases of one- and two-electron excitation in the He+-He system. The authors confine themselves to a discussion of the important points that an elaborate theoretical description should take into account. The results show that the primary population of the Sigma , Pi and Delta states is shared at large internuclear distance between the M=0, M=1 and M=2 levels of the He(2p2)1D and He(2s2p)1P states.

A bound2Σg+ground state for H2-? A valence-bond study

By constructing wavefunctions of the form Psi (H2-)= Psi (H2, e)+ mu ( Psi (H-H)+ Psi (HH-))+ nu ( Psi (H2-H (HH2-)) for H2-, it is calculated that the ground state for this species, with 2 Sigma g+ symmetry, is bound relative to the 1 Sigma g+ ground state of H2 and a free electron. The Psi (H2, e) accommodates an electron in a diffuse 1s orbital, which is centred midway between the protons. When the Weinbaum wavefunction with (STO-5G) 1s orbitals is used to describe H2, the minimum energy for each of these species is calculated to occur at an internuclear separation of 1.43 au. The resulting electron affinity (De(H2-)-De(H2)) for H2 is 2.0 kJ mol-1. A similar calculation with nuclear-centred 2p sigma orbitals also included gives an electron affinity of 6.5 kJ mol-1.

The dissociative ionisation of hydrogen by 5-25 keV protons: energy spectra and angular distribution of fragment ions

The energy and angular distributions of fragment protons produced in H+-H2 collisions have been investigated within the energy range 5-25 keV. The observed energetic protons arise from at least four repulsive states, the 2p sigma u, 2p pi u and 2s sigma g states of H2+ and the unbound H+H+ state. No significant contribution from autoionisation is observed. Analysis of the angular distributions has been performed to distinguish the separate degenerate channels available to the ejected electron. The results show a remarkable similarity to photoionisation data.

Theoretical study of associative ionisation in H+-H-collisions at low energy (0.001-5 eV)

A simple mechanism responsible for H+-H- associative ionisation is proposed which selects the (2p sigma u)2 1 Sigma g+ configuration state as the autoionising state relevant to this process. According to results on mutual neutralisation, the HH1 Sigma g+ and B"B1 Sigma u+ adiabatic states of H2 are assumed to be the way of entering the transition region. Quantal calculations have been performed including all dissociation and ionisation channels. The calculated cross section is found to be in agreement with the previous experimental results of Poulaert et al. (1978).

Small impact parameter studies of 2pσ vacancy production in high-Z heavy-ion-atom collisions

K-shell ionisation probabilities were measured for impact parameters between about 10 and 100 fm in collisions between Xe40+ and Sn, Sm, Au and Th. The present data are compared with measurements of ionisation probabilities and total 2p sigma cross sections for other collisions with united-atom atomic numbers up to Zu=184. Also, comparison is made with theories of direct ionisation from the 2p sigma molecular orbital and with a proposed theory involving the two-step transfer of projectile M vacancies into the 2p sigma molecular orbital. The bulk of the high-Z data are in better agreement with the direct ionisation theory.

Theoretical study of population sharing between n=2 levels in the Li++He collision

Presents a theoretical study of the relative populations of Sigma and Pi states associated with Li*(n=2)+He+ and Li++He*(n=2) products that are formed in Li++He collisions at keV energies. A half-collision model is considered where the (1s sigma 22p sigma 2p pi ) 1 Pi molecular state is assumed to be prepared initially (as a result of a primary 2p sigma -2p pi rotational coupling step) and the population-sharing processes occur as the collisional system breaks apart. The corresponding calculations involve six-state and twelve-state atomic-like diabatic representations and are carried out using the impact parameter method. the differential electron capture probability and the Stokes' parameters for Li*(22P) and He*(21P) excitations are determined. The calculated alignment angles gamma (Li,He) and shape parameters are slowly oscillating functions of the collision energy. The differences between the results for Li and He are discussed in terms of the various electron transition mechanisms. Qualitative agreement between theory and experiment is found for gamma (Li) but the comparison for gamma (He) is disappointing.

A coherence study of 2pσ-2pπ rotational coupling: Li(22P) and He(21P) orientation and alignment in 1-25 keV Li+-He collisions

The authors have studied the alignment and orientation of the electron cloud of the Li(22P) and He(21P) states excited by 2p sigma -2p pi rotational coupling for impact parameters between 0.2 and 1.1 au in 1-25 keV Li+-He collisions by coherence and correlation analysis techniques. It is found that for collision energies below 5 keV the shape of the excited electron cloud is very nearly that of a p orbital, aligned perpendicular to the asymptotic internuclear axis, independent of impact parameter and of whether the electron stays on the He core or is transferred to the Li centre during the collision. These findings agree with the predictions based on an analysis of the simple diabetic MO diagram for the Li-He system. At energies above 5 keV, the shape changes significantly. Also, the alignment angle deviates from the perpendicular direction, being larger than 90 degrees for Li and smaller for He. The angular momentum perpendicular to the collision plane shows a pronounced variation with collision energy but is only weakly dependent on impact parameter. Possible origins for this behaviour are discussed.

Excited states of HCl and DCl and their negative ions between 12.5 and 28 eV

The electron impact ionisation efficiency curves of HCl and DCl have been measured with a high signal-to-noise ratio, in the energy range immediately above the first ionisation threshold (12.75-26 eV). Many structures from HCl*, DCl*, HCl-* and DCl-* are seen. Vibrating Rydberg states related to the configurations (3p sigma )(3p pi )44s, 3d and their corresponding negative-ion states are observed. Furthermore the pair of states related to the (3s sigma )(3p sigma )2(3p pi )44s and 4p levels are reported.

Alignment and orientation of atomic orbitals in Na(3p)+Na+interactions

The authors use an efficient matrix propagator method to solve the coupled equations describing populations of the adiabatic states of Na2+ during a collision of Na+ with laser-excited Na(3p). Both straight-line and curved energy-conserving classical trajectories for the nuclei are used. Electronic motion is treated explicitly with a common translation factor. The radius at which the electronic angular momentum of a partially coherent mixture of Na(3p sigma u) and (3p pi u) becomes locked at the molecular axis is evaluated and the dependence of differential cross sections for inelastic transitions on the initial orbital alignment and orientation is discussed. The elementary mechanisms responsible for the observed effects are analysed numerically. Results are in qualitative agreement with recent experimental findings.

Non-adiabatic effects beyond the rotational coupling in H++H collisions

The H+-H collisional system is revisited in order to study the nature and the effects of the non-adiabatic 2p sigma u-np sigma u radial couplings in the range of internuclear distances 0<R<2 a0. To investigate whether these couplings reflect pseudo-crossings caused by the 'super-promotion' of an exotic state the authors build alternatively diabatic representations that preserve the characteristics of the two-centre separated-atom wavefunctions or those of the single-centre united-atom wavefunctions. It is found that none of the considered approaches supports a curve-crossing view. They demonstrate that the common bell-shaped form of the (2p sigma u mod delta / delta R mod np sigma u) matrix elements is not an exclusive property of the 2p sigma u state and the authors uncover a duplication property of all the (np sigma u mod delta / delta R mod n'p sigma u) non-adiabatic couplings. Finally, calculations of the probabilities of electron transitions due to these couplings show that a 10% leakage from the adiabatic 2p sigma u state does occur at small impact parameters at collision energies above 1 keV.

The direct dissociative recombination of the hydrogen molecular ion at low energies

The electronic collisions of ground-state H2+ followed by capture into the (2p sigma u)(nlm) state (n>or=2) are investigated theoretically by means of a configuration interaction theory. Emphasis is put on the investigation of the domain of very low energy. The mean energy in the chosen mix of molecular-ion-hydrogen configurations is evaluated and, consequently, the corresponding capture radius, which appears to depend approximately linearly on the energy. Finally the cross section is evaluated. It diverges around zero, as expected. For capture into the n=2 states, it has an approximately E-1 dependence for a large range of energies, having values of above 10-16 cm2 for less than 2 eV, in good agreement with experimental results. For capture into the 3s states, the authors give evidence of a dip of 2*10-20 cm2 at 0.2 eV and a peak of 1.4*10-17 cm2 at 6.6 eV, in good agreement with previous calculations.