Ground State Of Hydrogen Molecule Research Articles

Application of $$\hbox {GK}^{{\mathbf {1}}} \Sigma ^{+}_{\mathbf {g}}$$, $$\nu ' = 0 \rightarrow \hbox {B}^{1} \Sigma ^{+}_{\mathbf {u}}$$, $$\nu '' = 0$$ hydrogen band for the axial temperature measurement in the cathode sheath region of an abnormal glow discharge

In this paper, optical emission spectroscopy technique was used to measure rotational and gas temperature distribution in the cathode-sheath region of an abnormal glow discharge operated in hydrogen and hydrogen–argon mixtures. The rotational temperature of excited electronic states of H $$_{\mathrm {2}}$$ was determined from the R-branch of the $$\hbox {GK}^{\mathrm {1}}\Sigma ^{\mathrm {+}}_{g}$$ , $$\nu '= 0 \rightarrow \hbox {B}^{\mathrm {1}}\Sigma ^{\mathrm {+}}_{u}$$ , $$\nu ''=0$$ band and compared with published results for the Q-branch of the Fulcher- $$\alpha $$ diagonal band $$\hbox {d}^{\mathrm {3}}\Pi ^{\mathrm {-}}_{\mathrm {u}}$$ , $$\nu ' \rightarrow $$ $$\hbox {a}^{\mathrm {3}}\Sigma ^{\mathrm {+}}_{\mathrm {g}}$$ , $$\nu '' (\nu '=\nu ''=0$$ ). The population of excited energy levels, determined from the relative line intensities, was used to derive the rotational temperature of the ground state of hydrogen molecule. The boundary between the cathode sheath and negative glow region is determined using Stark polarization spectroscopy of the hydrogen Balmer alpha line. The thickness of the cathode sheath is estimated by fitting the experimentally determined distribution of electric field strength to a suitable model function. Temperature distributions along the axis of the cathode sheath are also reported and discussed. The distributions of temperature show that both bands give consistent and reasonable values for the rotational temperature and they both mutually agree within the estimated experimental uncertainties of 15%. The reported results contribute to the development of the spectroscopic method for gas temperature measurement in pure molecular hydrogen and in the gas mixture with argon.

On the use of two hydrogen bands for spectroscopic temperature measurement in a low-pressure gas discharge

Abstract We report the results of the optical emission spectroscopy measurements of rotational Trot and translational temperature Ttr of hydrogen molecules. The light source was hollow cathode glow discharge with titanium cathode operated in hydrogen at low pressure. The rotational temperature of excited electronic states of H2 was determined either from the relative line intensities of R branch of the GK → B band or from the P, Q and R-branches of the Fulcher-α diagonal band. The population of excited energy levels, determined from the relative line intensities was used to derive rotational temperature of the ground state of hydrogen molecule.

Spectroscopic study of hydrogen rotational, vibrational and translational temperatures in a hollow cathode glow discharge

The optical emission spectroscopy is used for determination of hydrogen molecule rotational Trot, vibrational Tvib, and translational temperature Ttr. The experiment was carried out using copper or titanium hollow cathode discharges operated in pure hydrogen. The rotational temperature of excited electron energy levels is determined from Fulcher-a diagonal bands (d3Πu →a3σ+gelectronic transition, P, Q and R branches), which were later used to derive rovibronic temperature of the hydrogen molecule ground state, which is assumed equal to Ttr. The vibrational temperature Tvib is determined for the same electronic transition (d3Π-u→a3σ+g, with v' = 2,3;δv = 0). For all temperatures the radial temperature distribution is reported.

Rotational and vibrational temperatures of molecular hydrogen in a hollow cathode glow discharge

Optical emission spectroscopy is used for the determination of hydrogen molecule rotational Trot and vibrational Tvib and translational temperature Ttr. The experiment was carried out using copper or titanium hollow cathode discharges operated in pure hydrogen. The rotational temperature of excited electron energy levels is determined from Fulcher-α diagonal bands ( electronic transition, P-, Q- and R-branches), which were later used to derive the rovibronic temperature of the hydrogen molecule ground state, which is assumed equal to Ttr. The vibrational temperature Tvib is determined for the same electronic transition (Q-branch with ν′ = 2,3; Δν = 0). For all temperatures the radial temperature distribution is reported.

Perturbation Treatment of the Ground State of the Hydrogen Molecule

Perturbation theory is used to obtain approximate energies and wavefunctions for the hydrogen molecule ground state. A function of simple form is chosen as zero-order function, the zero-order Hamiltonian is constructed, and the variational equation for the first-order wavefunction is solved approximately by expansion in James—Coolidge basis functions, yielding the second- and third-order energies. All integrals are calculated numerically. The binding energy and equilibrium internuclear distance are fair, but not as good as what one obtains from a comparable variational calculation.

Atomic Z Expansions and Electronic Structure of Molecules: Second-Order One-Center Calculation of the Hydrogen-Molecule Ground State

Double-perturbation theory is applied to calculate the ground state of the hydrogen molecule. In this treatment the unperturbed system is formed by the two noninteracting electrons moving in the field of a virtual nucleus of charge Z located halfway between the two hydrogen nuclei. The rest of the molecular Hamiltonian—electronic repulsion and the part of the electron—nuclear attraction—is treated as a perturbation. We determine the virtual charge Z from the variational principle for the total energy through first order. With this approach the total molecular energy of H2 can be built up from the energy Z expansion of (1s)2 1S, twice the exact electronic energy of 1sσ H2+, and correction terms of second and higher orders. Using the published results for (1s)2 1S and 1sσ H2+ we calculate the second-order corrections to get the equilibrium distance within 4% of the very accurate result obtained by Kol/os and Roothaan; our dissociation energy is 4.207 eV, 11% smaller than their value 4.747 eV.

Electronic Energy of the Hydrogen Molecule Ground State by the Local-Energy Method

The least-squares local-energy method is applied to the hydrogen molecule in greater detail. Equations are given for the Hamiltonian operator and local energy for diatomic molecules in the mixed interelectronic-confocal elliptic coordinate system. Wavefunctions with up to 22 terms and larger numbers of points are considered and it is shown that both lead to values for the dissociation energy that are within ±0.0001 hartrees of the exact value, 0.1744 hartrees.

Natural Expansion of Exact Wavefunctions. II. The Hydrogen-Molecule Ground State

The Kolos and Roothaan wavefunction for H2 has been analyzed into natural orbitals. It was found that the first natural orbital is nearly the SCF function. The first four natural orbitals provide a good description of the molecule and give a total energy of —1.169884 hartrees. Beyond the first four terms, the natural expansion becomes more slowly convergent.

Electric and Magnetic Properties of the Hydrogen Molecule

The hydrogen molecule ground state has been studied for a long time by valence theorists. Comparison with experiment has been limited to the energy, bond distance, vibration frequency, and the electric and magnetic polarizabilities. Recent radio-frequency experiments on hydrogen have yielded new quantities, the nuclear magnetic shielding constant, the spin-spin coupling constant, and the electric field gradient at the nucleus. In this paper, variation methods are described for the calculation of the new types of polarizability. These methods can be applied to more complex molecules and appear to open new possibilities for the semiquantitative interpretation of the results of high-resolution nuclear magnetic resonance. An extensive comparison is made between the experimental quantities and theoretical values using various wave functions. The most important factor affecting the accuracy of the charge density is the use of an effective nuclear charge.

Natural Spin Orbital Analysis of Hydrogen Molecule Wave Functions

Approximate wave functions for the hydrogen molecule ground state previously available in the literature are analyzed quantitatively into approximate natural spin orbital functions with particular attention to the corresponding occupation numbers. The analysis demonstrates the very great similarity of all such trial wave functions, and especially the largely molecular orbital nature of the wave function. In addition it shows a close relationship between the molecular orbital and valence bond functions, and the importance for allowing for angular correlation of the electrons by including terms dependent upon the azimuthal coordinate. The analysis particularly demonstrates that approximate natural spin orbital occupation numbers are nearly invariant under a wide variety of choices of basis functions, and therefore are particularly suitable for comparison of different approximate functions and for discussion of their respective properties.