Experimental and Theoretical Study of Hydrogen Atom Abstraction from C2H6 and C4H10 by Zirconium Oxide Clusters Anions

The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H- and Zr3O7H- are observed after the reaction. Den-sity functional theory calculations indicate that the hydrogen abstraction is favorable in the reaction of Zr2O5- with C2H6, which supports that the observed Zr2O5H- and Zr3O7H- are due to hydrogen atom abstraction from the alkane molecules. This work shows a newpossible pathway in the reaction of zirconium oxide cluster anions with alkane molecules.

Determination of a Safe Distance for Atomic Hydrogen Depositions in Hot-Wire Chemical Vapour Deposition by Means of CFD Heat Transfer Simulations

A heat transfer study was conducted,in the framework of Computational Fluid Dynamics(CFD),on a Hot-Wire Chemical Vapour Deposition(HWCVD)reactor chamber to determine a safe deposition distance for atomic hydrogen produced by HWCVD.The objective of this study was to show the feasibility of using heat transfer simulations in determining a safe deposition distance for deposition of this kind.All CFD simulations were set-up and solved within the framework of the CFD packages of OpenFOAM namely;snappyHexMesh for mesh generation,buoyantSimpleFoam and rhoSimpleFoam as the solvers and paraView as the post-processing tool.Using a standard set of deposition parameters for the production of atomic hydrogen by HWCVD,plots of the gas temperature in the deposition region were produced.From these plots,we were able to determine a safe deposition distance in the HWCVD reactor to be in the range between 3 and 4 cm from the filament.

A preliminary experiment of determining the geopotential difference using two hydrogen atomic clocks and TWSTFT technique

General relativity theory(GRT)concludes that a precise clock ticks at different running rates if it is under the influence of different geopotentials.Therefore,by comparing the running rates of clocks at arbitrary two stations,the geopotential difference between them can be determined.In this study,with the help of two hydrogen atomic clocks(noted as H-masers),using the two-way satellite time and frequency transfer(TWSTFT)technique,we carried out experiments of the geopotential difference determination at the China Aerospace Science&Industry Corporation(CASIC),Beijing.Here the ensemble empirical mode decomposition(EEMD)method is adopted to remove periodic signals included in the original observations.Finally,the clock-comparison-determined geopotential difference in the experiments is determined.Results show that the difference between the geopotential difference determined by GRT and that determined by measuring tape is about 1316.1±931.0 m2s-2,which is equivalent to 134.3±95.0 m in height,and in consistence with the stability of the H-masers applied in the experiments(at the level of10-15/day).With the rapid improvement of atomic clocks’accuracy,the geopotential determination by accurate clocks is prospective,and it is promising to realize the unification of the world vertical height system(WVHS).

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

Adsorption of hydrogen atoms on Pd (211), (311) and (511) stepped defective surfaces

Using embedded-atom-method potential for Pd and MORSE potential for the interaction between H and Pd atoms, the adsorption properties of H atoms on Pd (211), (311) and (511) stepped defective surfaces were calculated systematically. For Pd (311) surface, it is found that the four-fold hollow sites H4 are the preferable sites for H atoms being adsorbed on these Pd defective surfaces. The sites H4 are the most stable adsorbed sites and the three-fold hollow sites Hf and Hh are metastable ones. The calculated results are in reasonable agreement with the HREELS experiment results. For the (211) and (511) stepped defective surfaces of Pd, our calculation shows that the most stable adsorption sites are H5 and H2 respectively, both of them are four fold hollow sites.

On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom

The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.

Single-Atom Catalysts for Electrochemical Hydrogen Evolution Reaction: Recent Advances and Future Perspectives

Hydrogen,a renewable and outstanding energy carrier with zero carbon dioxide emission,is regarded as the best alternative to fossil fuels.The most preferred route to large-scale production of hydrogen is by water electrolysis from the intermittent sources(e.g.,wind,solar,hydro,and tidal energy).However,the efficiency of water electrolysis is very much dependent on the activity of electrocatalysts.Thus,designing high-effective,stable,and cheap materials for hydrogen evolution reaction(HER)could have a substantial impact on renewable energy technologies.Recently,single-atom catalysts(SACs)have emerged as a new frontier in catalysis science,because SACs have maximum atom-utilization efficiency and excellent catalytic reaction activity.Various synthesis methods and analytical techniques have been adopted to prepare and characterize these SACs.In this review,we discuss recent progress on SACs synthesis,characterization methods,and their catalytic applications.Particularly,we highlight their unique electrochemical characteristics toward HER.Finally,the current key challenges in SACs for HER are pointed out and some potential directions are proposed as well.

Conjugate addition‐enantioselective protonation to forge tertiary stereocentresαto azaarenes via cooperative hydrogen atom transfer and chiral hydrogen‐bonding catalysis

Cooperative hydrogen atom transfer and chiral hydrogen‐bonding catalysis as a new platform for the asymmetric synthesis of azaarene derivatives is reported.By using a tetrabutylammonium decatungstate as the photocatalyst and a chiral phosphoric acid as the hydrogen‐bonding catalyst,transformations of a variety of commercially available hydrocarbons and silanes with diverseα‐branched 2‐vinylazaarenes could efficiently experience a tandem radical conjugate addition and enantioselective protonation process,providing a convenient and fully atom economical approach to access a range of valuable enantioenrichedα‐tertiary azaarenes in high yields with good to excellent enantioselectivities(up to 93%ee).Through the direct use of tert‐butyl methylcarbamate as the feedstock,this method enables a highly practical and concise synthesis of the enantiomerically pure medicinal molecule pheniramine(Avil).

Statistics and Correlation Properties of Diamagnetic High Rydberg Hydrogen Atom

The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.

Interaction of intense laser pulses with hydrogen atomic clusters

The interaction between intense femtosecond laser pulses and hydrogen atomic clusters is studied by a simplified Coulomb explosion model. The dependences of average proton kinetic energy on cluster size, pulse duration, laser intensity and wavelength are studied respectively. The calculated results indicate that the irradiation of a femtosecond laser of longer wavelength on hydrogen atomic clusters may be a simple, economical way to produce highly kinetic hydrogen ions. The phenomenon suggests that the irradiation of femtosecond laser of longer wavelength on deuterium atomic clusters may be easier than that of shorter wavelength to drive nuclear fusion reactions. The product of the laser intensity and the squared laser wavelength needed to make proton energy saturated as a function of the squared cluster radius is also investigated. The proton energy distribution calculated is also shown and compared with the experimental data. Our results are in agreement with the experimental results fairly well.

Circular Rydberg States of Atomic Hydrogen in an Arbitrary Magnetic Field

We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and valid for an arbitrary magnetic field. Energy levels of hydrogen are presented for circular Rydberg states with azimuthal quantum numbers ｜m｜ =10-70 as a function of magnetic field strengths ranging from zero to 2.35 × 10^9 T. The variation of spatial distributions of electron probability densities with magnetic field strengths is discussed and competition between Coulomb and magnetic interactions is illustrated.

Magic Wavelengths for the 1S-2S and 1S-3S Transitions in Hydrogen Atoms

The dynamic dipole polarizabilities for 1S, 2S and 3S states of the hydrogen atom are calculated using the finite B-spline basis set method, and the magic wavelengths for 1S-2S and 1S-3S transitions are identified. In comparison of the solutions from the Schr6dinger and Dirac equations, the relativistic corrections on the magic wavelengths are of the order of 10-2 nm. The laser intensities for a 300-Er-deep optical trap and the heating rates at 514 and 1371 nm are estimated. The reliable prediction of the magic wavelengths would be helpful for the experimental design on the optical trapping of the hydrogen atoms, and in turn, it would be helpful to improve the accuracy of the measurements of the hydrogen 1S-2S and 1S-3S transitions.

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

Semiclassical and Quantum-Mechanical Formalism Applied in Calculating the Emission Intensity of the Atomic Hydrogen

The energy spectrum of the hydrogen atom has been applied in calculating the time rate of energy transitions between the quantum states of the atom. The formal basis of the approach has been provided by the quantum properties of energy and time deduced from the Joule-Lenz law. The rates of the energy transitions obtained in this way were compared with the quantum-mechanical probabilities of transitions calculated earlier by Bethe and Condon and Shortley for the same pairs of the quantum states.

Formation and Transport of Atomic Hydrogen in Hot-Filament Chemical Vapor Deposition Reactors

In this paper we focus on diamond film hot-filament chemical vapor deposition reactors where the only reactant is hydrogen so as to study the formation and transport of hydrogen atoms. Analysis of dimensionless numbers for heat and mass transfer reveals that thermal conduction and diffusion are the dominant mechanisms for gas-phase heat and mass transfer, respectively. A simplified model has been established to simulate gas-phase temperature and H concentration distributions between the filament and the substrate. Examination of the relative importance of homogeneous and heterogeneous production of H atoms indicates that filament-surface decomposition of molecular hydrogen is the dominant source of H and gas-phase reaction plays a negligible role. The filament-surface dissociation rates of H2 for various filament temperatures were calculated to match H-atom concentrations observed in the literature or derived from power consumption by filaments. Arrhenius plots of the filament-surface hydrogen dissociation rates suggest that dissociation of H2 at refractory filament surface is a catalytic process, which has a rather lower effective activation energy than homogeneous thermal dissociation. Atomic hydrogen, acting as an important heat transfer medium to heat the substrate, can freely diffuse from the filament to the substrate without recombination.

Time Intervals of the Electron Transitions between the Energy States in the Hydrogen Atom Calculated in a Non-Probabilistic Way

Definitions of the mechanical parameters entering the Bohr model of the hydrogen atom allowed us to calculate the time intervals connected with the electron transitions between the nearest-neighbouring energy levels in the atom. This is done in a strictly non-probabilistic way. The time results are compared with those derived earlier on the basis of the classical Joule-Lenz law for the energy emission adapted to the case of the electron transfer in the quantum systems. A similar formalism has been next applied to the harmonic oscillator and a particle moving in the one-dimensional potential box.

Properties of Coherent State for Hydrogen Atom

We construct the coherent state for the two-dimensional hydrogen atom,for which the averaged motion of position describes a Kepler ellipse.The coherent state can be expanded with respect to the eigenstates of 2D hydrogen atom,from which we evaluate the binding energy of the wave packet for this state.