Ground State Hydrogen Molecule Research Articles

Spectroscopic measurement of increases in hydrogen molecular rotational temperature with plasma-facing surface temperature and due to collisional-radiative processes in tokamaks

Spatially resolved rotational temperature of ground state hydrogen molecules desorbed from plasma-facing surface was measured in QUEST, LTX-β, and DIII-D tokamaks, and the increases of the rotational temperature with the surface temperature and due to collisional-radiative processes in the plasmas were evaluated. The increase due to collisional-radiative processes was calculated by solving rate equations considering electron and proton collisional excitation and deexcitation and spontaneous emission. The calculation results suggest a high sensitivity for the rotational temperature to electron and proton densities, but a negligible sensitivity to the electron, proton, and surface temperatures. In the three tokamaks with different plasma parameters and plasma-facing surface materials, the spatial profile of the rotational temperature was estimated using Fulcher-α emission lines (600–608 nm). In QUEST, the spatial profile of the rotational temperature was estimated from spatially resolved spectra. In the other tokamaks, the rotational temperature was evaluated assuming a single point emission with a location determined from the Fulcher-α emission profile as measured with a filtered camera. In metal-walled devices QUEST and LTX-β, the rotational temperature increased with the surface temperature, and the calculated collisional-radiative increase is consistent with measured increase assuming that the rotational temperature at the surface is approximately 500–600 K higher than the surface temperature. In DIII-D with carbon walls, a larger collisional-radiative increase than the other tokamaks was observed because of the higher density leading to a large difference from the calculated increase compared to the other smaller tokamaks. Measurement of the Fulcher-α emission profile with higher spatial resolution in DIII-D may reduce the difference and reveal the effect of the surface temperature on the rotational temperature. These results show the increases in the rotational temperature with the surface temperature and due to the collisional-radiative processes.

Setting benchmarks for modelling gas\u2013surface interactions using coherent control of rotational orientation states

The coherent evolution of a molecular quantum state during a molecule-surface collision is a detailed descriptor of the interaction potential which was so far inaccessible to measurements. Here we use a magnetically controlled molecular beam technique to study the collision of rotationally oriented ground state hydrogen molecules with a lithium fluoride surface. The coherent control nature of the technique allows us to measure the changes in the complex amplitudes of the rotational projection quantum states, and express them using a scattering matrix formalism. The quantum state-to-state transition probabilities we extract reveal a strong dependency of the molecule-surface interaction on the rotational orientation of the molecules, and a remarkably high probability of the collision flipping the rotational orientation. The scattering matrix we obtain from the experimental data delivers an ultra-sensitive benchmark for theory to reproduce, guiding the development of accurate theoretical models for the interaction of H2 with a solid surface.

Pseudopotential for ground state hydrogen molecule with nonadiabatic corrections

Nonadiabaticity cannot be entirely reduced to correcting a single potential energy surface. To still maintain this very simple and instructive concept, one can introduce coordinate-dependent corrections to the nuclear reduced mass. Recently, these R-dependent corrections, both vibrational and rotational, have been accurately determined for the hydrogen molecule in the ground electronic state. In this paper, using an inverse perturbational approach, an effective rotationless pseudopotential for the system was constructed, the vibrational levels of which exactly coincide with the experimental ones. The specifically rotational nonadiabatic effects can be taken into account by combining the R-dependent mass correction functions with specific state-dependent coordinate shifts of the rotationless potential. These characteristic parameters typically range from 0.0002 to 0.0003 Å, depending on the vibrational state (v) but being nearly independent of the rotational state (J). For example, shifting the rotationless potential by 0.0002125Å was found optimal for v = 0. Using this constant value, the zeroth vibrational levels for J = 0 to 11 can be determined with about 0.001 cm−1 accuracy, as has been shown by comparing with the available high-resolution experimental data.

Oscillations of the p–H2 single-electron capture cross sections due to two-centre interference

The single-electron capture process in the collision of fast protons with ground-state hydrogen molecules has been studied assuming an effective one-electron model. A Hartree–Fock molecular wavefunction, within a first-order Born approximation with correct boundary conditions, is employed to evaluate the transition amplitude. The dependence of the differential capture cross sections on the molecular orientation is examined. The oscillation of the cross sections, due to the interference between the scattering from two molecular nuclei, is investigated. Integrated cross sections are calculated and the results have been compared with available experimental data as well as other theoretical calculations.

Potential energy surface for interactions between two hydrogen molecules

Nonrelativistic clamped-nuclei energies of interaction between two ground-state hydrogen molecules with intramolecular distances fixed at their average value in the lowest rovibrational state have been computed. The calculations applied the supermolecular coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and very large orbital basis sets-up to augmented quintuple zeta size supplemented with bond functions. The same basis sets were used in symmetry-adapted perturbation theory calculations performed mainly for larger separations to provide an independent check of the supermolecular approach. The contributions beyond CCSD(T) were computed using the full configuration interaction method and basis sets up to augmented triple zeta plus midbond size. All the calculations were followed by extrapolations to complete basis set limits. For two representative points, calculations were also performed using basis sets with the cardinal number increased by one or two. For the same two points, we have also solved the Schrodinger equation directly using four-electron explicitly correlated Gaussian (ECG) functions. These additional calculations allowed us to estimate the uncertainty in the interaction energies used to fit the potential to be about 0.15 K or 0.3% at the minimum of the potential well. This accuracy is about an order of magnitude better than that achieved by earlier potentials for this system. For a near-minimum T-shaped configuration with the center-of-mass distance R=6.4 bohrs, the ECG calculations give the interaction energy of -56.91+/-0.06 K, whereas the orbital calculations in the basis set used for all the points give -56.96+/-0.16 K. The computed points were fitted by an analytic four-dimensional potential function. The uncertainties in the fit relative to the ab initio energies are almost always smaller than the estimated uncertainty in the latter energies. The global minimum of the fit is -57.12 K for the T-shaped configuration at R=6.34 bohrs. The fit was applied to compute the second virial coefficient using a path-integral Monte Carlo approach. The achieved agreement with experiment is substantially better than in any previous work.

A new theory of the molecular bond

In its simulation of the ground state hydrogen molecule, quantum mechanics, for example, assumes that the electrons repel. Though free electrons repel, the electrons in ground state H 2 are not free. We show then through careful computations that these electrons could attract.

Nonlocal theory of dissociative electron attachment toH2and HF molecules

We develop a method for calculation of dissociative electron attachment cross sections based on the Fano-Feshbach projection-operator approach. The coupling between the diabatic state and electron continuum is calculated with the inclusion of orthogonality scattering and long-range electron-molecule interaction. The dynamics of nuclear motion in the nonlocal complex potential is treated by semiclassical theory. We apply the theory to the calculation of dissociative attachment to the ${\mathrm{H}}_{2}$ and HF molecules. Our results for attachment to ground-state hydrogen molecules and the near-threshold vibrational enhancement of ${\mathrm{H}}_{2}$ are essentially the same as previous nonlocal results. However, the shape of the energy dependence of the cross section for attachment to vibrationally excited states of ${\mathrm{H}}_{2}$ is slightly different. The calculated value for the total attachment cross section to the ground state of HF is consistent with the little experimental data available; more definite conclusions are difficult because of the approximate nature of the experimental results. The results for the vibrational enhancement are in very good agreement with experiment.

Dissociative excitation of hydrogen in rf and dc glow discharges through H 2

The spectral and spatial profile of H β from the low pressure rf and dc glow discharges in hydrogen is studied in order to reveal the excitation mechanism of the fast excited H fragments. Measurements were performed both for the normal and abnormal dc glow discharges. Spatial distributions of the Balmer β radiation reflect the local plasma conditions in the discharge, especially the excitation efficiency which is used to determine the excitation kinetics in hydrogen discharges. Spectral H β profiles were measured and used to determine the kinetic energy of excited H atoms and to check which of the mechanisms describes best the results observed in our experiment. We have also calculated the number densities of vibrationally excited levels by solving a set of vibrational master equations for the conditions similar to those of our experiments, as excitation from the vibrationally excited ground-state hydrogen molecules may be used to explain the changes in the intermediate wing component of the line profile with the changing current.

Ratio of Balmer line intensities resulting from dissociative excitation of molecular hydrogen in an ionizing plasma

We have estimated the cross section for the production of excited hydrogen atoms from the emission cross sections for Lyman and Balmer lines when molecular hydrogen is dissociated into excited atoms. We have constructed a collisional-radiative model for the system of ground-state hydrogen molecules, excited hydrogen atoms, and protons, in a plasma and have calculated the population density distribution of the excited states. The resulting emission-line intensity ratios for the Balmer series lines are plotted against electron density. We expect these results to be useful for studies of plasmas containing molecular hydrogen, such as occur in the outer region of tokamak plasmas.

Accurate potential for the ground state of the hydrogen molecule

Starting from the spectroscopic constants, an electronic potential for the ground state hydrogen molecule is presented. Self-consistence is checked by numerical integration of the radial wave equation. The mean eigenvalue deviation is about 1 cm −1. Comparison with the latest theoretical work is considered. New revised spectroscopic constants and vibrational quanta are calculated.

Resonance-enhanced multiphoton ionization for diagnosis of a weakly ionized plasma

We describe an experimental setup in which resonance-enhanced multiphoton ionization (REMPI) is used for diagnosis of neutral particles (atoms or molecules) effusing from a plasma. Quantum-state-specific detection, achieved by selective ionization with the help of REMPI, yields the distribution over their internal degrees of freedom. Discrimination against nonlaser-produced ions is performed by means of the combination of an electric and a magnetic field. The applicability of the setup is demonstrated by the determination of the rotational temperature of ground-state hydrogen molecules in a multicusp ion source. Under nondischarge conditions a detection limit is achieved of ≊2×1010 state-selected hydrogen molecules/cm3, corresponding to a value of ≊7×108/cm3 at the analysis region. Under discharge conditions, this detection limit is deteriorated by the presence of metastable hydrogen molecules, which are ionized in a one-photon process.

Exchange effects in the independent-atom model for electron-hydrogen-molecule elastic scattering

It is shown that all the previous procedures to include exchange effects in the elastic scattering of electrons by the ground-state hydrogen molecule within the framework of the independent-atom model are improper. The proper way to include exchange has been pointed out. The direct scattering amplitudes for the scattering of electrons by the hydrogenlike atom are obtained in the modified Glauber approximation and by the eikonal Born series method. Exchange scattering amplitude is calculated in the Ochkur approximation. The differential cross sections for the hydrogen molecule are then obtained in the independent-atom model. The results are in very good agreement with the absolute experimental data for impact energies $E\ensuremath{\ge}100$ eV.

Charge overlap effects and the validity of the multipole results for first-order molecule-molecule interaction energies. Formalism and an application to H2-H2

For the interaction of two molecules, the first-order coulomb energy, E e (1), is expressed as a sum of non-expanded partial wave components which exhibit the orientation dependence of the energy explicitly. By comparing these non-expanded results with the analogous multipolar results for the first-order energy, the effects of charge overlap on the multipole representation of the energy can be investigated as a function of intermolecular separation and orientation, and the validity of the multipole results for E e (1) assessed. The interaction of two ground-state hydrogen molecules is considered as a specific example of this approach for studying the validity of the multipole expansion as a representation of molecular first-order Coulomb energies. All calculations are presented as a function of four molecular wave functions of varying degrees of sophistication in order to assess the sensitivity of (1) the representation of charge overlap effects and (2) the calculated quadrupole and hexadecapole moments o...

Degenerate autoionization processes in the photoionization of molecular hydrogen

The contribution of both autoionization and direct ionization processes to the photoionization continuum of hydrogen has been examined experimentally in order to ascertain the relative importance of the above two processes, to determine the final state to which a particular autoionizing Rydberg state decays, and to see if there are any preferred routes for the two types of processes. Autoionization processes which produce electrons with energies in the range 0 to 0.003 eV, so-called degenerate autoionization processes, have been studied here by means of a new type of threshold electron analyzer which has an identically zero transmission probability for energetic electrons. It was found that degenerate autoionization processes are not uncommon and that there is a preference in such autoionization processes for J=K between the ground state hydrogen molecule and the final state of the molecular ion. Direct ionization also appears to be favored for J=K. The detailed routes of several degenerate autoionization processes are examined and other inferences made.

Scmielassical Calculation of the Vibrational Transition Probabilities of Diatomic Molecules in Collision. The Effect of Vibrational Anharmonicity

Abstract The multi-state semiclassical method proposed by Sharp and Rapp for calculating the vibrational transition probabilities of harmonic oscillators in collision was extended to Morse oscillators. Model calculations have been carried out for the excitation of a vibrational ground-state hydrogen molecule colliding with a helium atom at varying relative velocity. It has been shown that the Morse oscillator model gives greater transition probabilities than the corresponding harmonic oscillator model.