Ground State Of H2 Research Articles

Electronic excitation in collisions of H2+ on He.

Ab initio cross sections have been calculated for electronic excitation resulting from single collisions in the keV energy range between ${\mathrm{H}}_{2}^{+}$ initially in the ground electronic and vibrational state incident on He targets. These collisional excitation studies are based on ab initio calculations of the three lowest adiabatic states of the (${\mathrm{HeH}}_{2}$${)}^{+}$ quasimolecular system and ab initio calculations of the nonadiabatic gradient coupling matrix elements between these three adiabatic states. With use of straight-line trajectories in the classical trajectory approximation, cross sections have been obtained for (1) charge exchange into the ground state of He and (2) collisional dissociation via electronic excitation 1${\mathrm{\ensuremath{\sigma}}}_{\mathit{g}}$\ensuremath{\rightarrow}1${\mathrm{\ensuremath{\sigma}}}_{\mathit{u}}$ of the ${\mathrm{H}}_{2}^{+}$ projectile. Furthermore, with a knowledge of the diabatic structure of the (${\mathrm{HeH}}_{2}$${)}^{+}$ energy levels, (3) the sum of the cross sections for Rydberg excitation of the He target or Rydberg excitation of the ${\mathrm{H}}_{2}^{+}$ projectile or charge exchange into the repulsive state of ${\mathrm{H}}_{2}$ was also obtained. The calculated cross sections are in reasonable agreement with available experimentally measured cross sections. The energy thresholds for these cross sections are found to be determined by excitation at level crossings between the ground electronic state and the ${\mathrm{H}}_{2}^{+}$(1${\mathrm{\ensuremath{\sigma}}}_{\mathit{u}}$)+He(1${\mathit{s}}^{2}$) at R\ensuremath{\simeq}1.2 a.u. and the ${\mathrm{H}}_{2}^{+}$(1${\mathrm{\ensuremath{\sigma}}}_{\mathit{g}}$)+He(1s,2l) at R\ensuremath{\simeq}0.7 a.u.

Near-zero energy proton production mechanisms from the three-body dissociation of H3+

The laboratory energy distribution of H+ from the dissociation of H3+ in low-keV H3+-He collisions is measured at a 0\ifmmode^\circ\else\textdegree\fi{} laboratory angle. An inelastic energy loss of Q=26\ifmmode\pm\else\textpm\fi{}2 eV has been determined for the excited states of H3+ that produce low-energy protons upon dissociation. An approximate projectile-frame energy distribution of H+ is also presented. Our results suggest that the near-zero projectile-frame energy protons are produced by either an electronic singlet excitation of the ground state of H3+ to a distribution of 2 E1\ensuremath{'}, 1 E1\ensuremath{''}, and 2 A12\ensuremath{''}, or as an alternative mechanism, a triplet excitation of H3+ to 1 E3\ensuremath{'} accompanied by a simultaneous triplet excitation of the He target. In either case, the near-zero energy protons are produced by a three-body dissociation of the excited (H3+)*. In the case of the triplet excitation, there are no long-range correlations for the motion of the neutral H atoms. For the singlet excitation, the neutral H atoms' motion is correlated and the angle between them is near 180\ifmmode^\circ\else\textdegree\fi{}. The effects of the long-range nature of the total potential between the fragments is discussed in terms of the hyperspherical coordinates.

On the treatment of the center of mass motion in nuclear mean field theories

It is shown how the spurious components due to the center of mass motion can be eliminated from general Hartree-Fock-Bogoliubov quasi-particle configurations with the help of projection techniques. The problem how to restore the additional symmetries being broken by such configurations is discussed. An explicit formulation is given for the spherical Hartree-Fock problem with center of mass momentum projection before the variation. As an example for the application of this method the ground state of4He is studied using two different interactions, a microscopic two-body one as well as a phenomenological one including a Skyrme-type three-body force. The results are compared to those of the usual approximate treatment of the center of mass motion in Hartree-Fock calculations. It turns out that, at least for the chosen example, the latter yields a rather reasonable approximation to the correct total energy, single particle energy and even the mass density provided that it is calculated from a translationally invariant density operator.

The H2 molecule in a magnetic field

The authors calculated the spectrum of highly excited H2 molecules in a laboratory strength magnetic field (B=4.7 T) including both the linear and the quadratic Zeeman interactions in the range E=-300 to -20 cm-1. The lowest major feature of the field-free photoabsorption spectrum of ground-state H2 results from the interaction between two Rydberg series corresponding to the H2+ core in its N=0 and N=2 rotational states (these are usually termed the np0 and np2 series respectively). In the presence of the field, the character of the spectrum differs dramatically depending on the degree of interaction between neighbouring N=0 and N=2 lines. The quadratic Zeeman interaction is also known to be associated with chaotic behaviour in the hydrogen atom.

A systematic study of the D-state probability of 4He using eight different realistic N-N interactions

The D-state probability of the ground state of 4He has been calculated using the shell model with these eight N-N interactions: RSC, ARGONNE V 14, TRSB, PARIS, SSC-B, SSC-C, URBANNA, BONN-OBEPR. The results range from about 9% to 17% for all interactions and from 10% to 15% for modern potentials. Our results are compared with other calculations that use these potentials where possible.

Optimized trial functions for quantum Monte Carlo

An algorithm to optimize trial functions for fixed-node quantum Monte Carlo calculations has been developed based on variational random walks. The approach is applied to wave functions that are products of a simple Slater determinant and correlation factor explicitly dependent on interelectronic distance, and is found to provide improved ground-state total energies. A modification of the method for ground-states that makes use of a projection operator technique is shown to make possible the calculation of more accurate excited-state energies. In this optimization method the Young tableaux of the permutation group is used to facilitate the treatment of fermion properties and multiplets. Application to ground states of H2, Li2, H3, H+3, and to the first-excited singlets of H2, H3, and H4 are presented and discussed.

Calculation of helium photoionization with excitation including angular distribution and resonance structure.

A nine-channel coupled-equation calculation for photoionization of the 1s/sup 2/ ground state of He is performed within the framework of many-body perturbation theory. Partial cross sections for leaving the ion in 1s, 2s, 2p, 3s, 3p, and 3d levels are obtained together with the angular asymmetry parameter for leaving the ion in n = 2 states. The resonance structure in the 1s, 2s, and 2p cross sections and in the n = 2 angular asymmetry parameter due to doubly excited autoionizing states below the n = 3 threshold is calculated. Also, parameters describing the resonances in the 1s cross section below the n = 2 threshold are obtained.

ON THE INTERACTION OF H2 (X1∑g+)—H2(E1∑g+) SYSTEM

A perturbative calculation for the long-range and intermediate interactions between excited state H2(E1∑g+) and ground state H2(X1∑g+) in the crossed geometry is performed by using a trial wavefunction depending on the interelectronic distance explicitly. According to the results, there is a potential energy barrier around the inter-molecular separation D = 6.5α0. Inside the barrier, there shows a strong chemical bond behavior.

Theoretical study of single-electron capture in He2+ ?H? collision

We present a detailed theoretical treatment of single-electron transfer between He2+ and H−. The total cross section is calculated using stationary molecular states which are appropriate in the energy range covered by the experiments (between 0.5 and 2250 eV in the centre of mass frame). We use an expansion on a two-electron basis built with one-electron diatomic molecule (OEDM) orbitals and including the common translation factor of Errea et al. All coupling terms are calculated explicitly. Because of the small binding energy of H− compared to that of the ground state of He+, capture occurs into highly excited states of He+. Results obtained with a straight-line quasiclassical calculation are in good agreement with the experimental data. At low energy, He+ (n=5) +H(1s) is the dominant capture channel; at higher energy, the He+ (n=4) + H(1s) channel becomes important. The rise in the cross section below 6 eV can be attributed to the Coulomb attraction in the incoming channel. To account for this effect, a fully quantal calculation has been performed. The agreement with the low-energy measurements is then excellent.

The energy dependence of polarization observables in the 2H(d, γ) 4He reaction

Measurements of the tensor and vector analyzing powers, A yy (130°) and A y (130°), have been obtained for the 2H(d, γ ) 4He reaction for energies ranging from E d(lab) = 0.3 MeV to E d(lab) = 50 MeV. The A yy (130°) data are sensitive to the D-state present in the ground state of 4He and are observed to have their maximum value near E d = 30 MeV. The vector analyzing power data show a maximum near E d = 3 MeV. The data are compared to the results of a microscopic multi-channel resonating group model calculation.

Gaussian functions in hylleraas-CI calculations. I. Ground state energies for H2, HeH+, and H+3

Gaussian basis functions have been used in explicitly correlated configuration interaction calculations for the ground states of H2, HeH+, and H+3. Due to the use of rij, the polarization functions are found to be much less important in comparison with their effectiveness in the convectional CI methods. Our lowest ground state energies for H2 and HeH+ are 1.8 and 8 cm−1, respectively, above the best literature values obtained by using generalized James–Coolidge expansion in terms of confocal elliptical coordinates. With 10s and 2p contracted functions, the calculated ground state energy for H+3 is −1.343 500 hartrees, which is believed to be the lowest variational energy in the literature.

Electron Impact Ionisation of the Ground State of He+

Electron impact ionisation of the ground state of He+ is studied by using the distorted wave polarised orbital (DWPO) method in the energy range 61�2-272�0 eV. The present results for the total cross section are in good agreement with the measured values.

CAS SCF/CI calculations of potential energy surfaces of He 3+ and He 2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the 2Σ g + ground state of He 3 +. The potential minimum for the 2Σ g + state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He 3 + with respect to He + He + + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He 3 + ( 2Σ g +) into He 2 + ( 2Σ u +) and He( 1S) is calculated to be 0.14 eV. The same level of SOCI calculations of He 2 + yield a D e value of 2.36 eV.

Metastable H+3 formation and decay in the reaction of highly excited H+2 with H2

This paper presents the detailed results of a quasiclassical trajectory surface hopping study of reaction of highly vibrationally excited H+2 with ground state H2 (and isotopic counterparts H+2 +D2, D+2 +H2, and D+2 +D2 ), with particular emphasis on the formation and decay of metastable H+3 products. A diatomics-in-molecules surface is used which has been successful in previous studies of H+2 (v) + H2 at low v. In the present study, we consider v=0–17, and find that metastable H+3 ’s are a major product for v≥13. Some of these metastables decay rapidly, showing exponential lifetime distributions with 2–7 ps lifetimes depending on v and on isotope. The remaining H+3 ’s have much longer lifetimes, and a number of methods are used to determine the origin of their stability. In no cases are any of these molecules found to be quasiperiodic, but a Fourier spectral analysis reveals some decoupling of H+ –H2 orbital motion from H2 rotational motion, and we find that many molecules have long lifetimes even though they have energies which are above any rigorous centrifugal barrier. The relation of these results to recent infrared absorption measurements on highly excited H+3 ’s is discussed.

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.

Momentum space correlation effects in the 23S, 21P and 23P states of He

A Dirac-Fourier transformation of correlated and Hartree-Fock wavefunctions for some (1s, nl) states of He allowed the authors to analyse electron correlation effects in momentum space for excited states of differing symmetry and spin multiplicity. For the 2 3S, 2 1P and 2 3P states, Coulomb shifts and partial Coulomb shifts were determined, as well as certain radial and angular distribution functions. For 2 3S and 2 1P it was established that, like the ground state of He, angular and radial correlation have opposing effects on the momentum distributions. In contrast to this, for 2 3P these two components of correlation work in unison, as occurs in position space. A rationalisation of this behaviour is given, along with an interpretation of the complex nature of the corresponding partial Coulomb shifts. The latter revealed significant changes in the relative importance of angular and radial correlation as the momentum of a test electron was increased. The success of this analysis rested essentially on a detailed knowledge of the inter-vectorial angular shifts. For these excited states, the use of angular expectation values alone proved to be too insensitive to explain the quite marked differences in the correlation characteristics.

Effects on H− production in a multicusp ion source by mixtures of H2 with H2O, NH3, CH4, N2H4, and SF6

Effects of H− production in a multicusp ion source are measured by separately mixing with hydrogen small amounts (0.33%–10%) of water, ammonia, methane, and hydrazine—molecules which produce large amounts of H− via dissociative attachment (DA) resonances at higher electron energies. The mixing was done in a separate reservoir, with careful measurement of individual pressures. Experimental enhancements of 1.4 and less were observed, whereas calculated enhancements, using accurate DA cross sections for ground-state H2, should have produced factors of 1.5, 3.0, 1.3, and 2.4 enhancements for water, ammonia, methane, and hydrazine, respectively, at a mean electron energy of 1.0 eV in the extraction region. The difference is accounted for by including, in the enhancement calculation, vibrationally and rotationally excited H2 molecules, with v″=5–11, and J″=0–5, and the large DA cross sections for the excited H2(v″,J″). The relative populations of H2(v″,J″) thus obtained are found to be substantially smaller than those predicted by theoretical calculations. The effect on H− current was also studied by mixing small amounts of SF6 with H2. A 1.5% mixture was found to reduce the H− output by one half.

Charge transfer in He+-He+collisions

Cross sections for charge transfer in He+-He+ collisions have been measured in the centre-of-mass energy range 7-112 keV, using crossed beams and coincident detection of the reaction products. The results obtained are in excellent agreement with previous measurements by Peart et al in the CM energy range 19-57 keV. A two-state coupling calculation with asymptotically correct pseudomolecular states shows that the capture into the ground state of He is approximately only 50% of the total capture cross section at energies below the cross section maximum.

Expectation values of p1

We examine expectation values of p/sub 1/xp/sub 2/ in ground states of He and H/sup -/, the singly and doubly excited states of He, and the ground and low-lying valence states of the alkaline-earth-metal atoms. A simple commutator relation derived by Froese Fischer and Smentek-Mielczarek (J. Phys. B 16, 3479 (1983)) can be used to explain the sign and relative magnitudes of in the ground states of He and H/sup -/ and singly excited states of He. In the doubly excited states of He and in the ground and low-lying valence states of the alkaline-earth metals, the molecular model, which treats the electron--core-electron system as a floppy, linear triatomic ''molecule,'' correctly predicts signs and general trends for . These results represent an important test of the molecular model. The ability of this model to make intuitive predictions about quantities like is a strong confirmation of its validity and utility.

Minimum cross-entropy inference of molecular momentum densities

The principle of minimum cross entropy, instead of the principle of maximum entropy, of information theory is employed to estimate a molecular radial momentum density I(p) under the constraint of a given moment 〈pn〉. An application to the ground-state H2 system shows that the minimum cross-entropy inference is superior to the maximum entropy inference.