Ground State Of H2 Research Articles

Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field

In this work, the position-dependent mass Schrödinger equation is solved with the Pöschl-Teller-like potential in the presence of magnetic and Aharonov–Bohm (AB) flux fields. The BenDaniel-Duke ambiguity parameter ordering is used to formulate the Hamiltonian operator for the system. An approximate analytical equation of the bound-state energy spectrum is obtained using the parametric Nikiforov-Uvarov solution technique along with a Pekeris-like approximation scheme. With the aid of the obtained equation for the energy levels, analytical formulas of magnetization and magnetic susceptibility at zero-temperature are derived and subsequently used to predict the physical properties of diatomic substances including the ground state H2, HCl, CO and LiH molecules. The expression for the bound-state-energy spectrum is used to generate numerical data for the molecules. The computed energy eigenvalues agree with the literature on diatomic molecules. The study revealed that in the absence of the external fields, the energy eigenvalues and magnetic susceptibility of the system are degenerate. However, with only a low intensity AB field, the degeneracy is completely eliminated from the energy states of the molecules.

Implementation of measurement reduction for the variational quantum eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.

Electron-impact double ionization of He (1s2s 3 S)

A time-dependent close-coupling method for three-electron atomic systems is used to calculate the electron-impact double ionization of the He (1s2s 3 S) excited state. Partial cross sections are calculated for total angular momenta from . An exponential fitting expression is used to extend the calculated partial cross sections to . The total cross sections at three different incident energies are compared with recent crossed-beams measurements and are found to lie within the experimental error bars. The magnitude of the double ionization cross section is found to be similar to that of the double ionization cross section from the ground state of He.

Investigating István Mayer's “improved” definitions of bond orders and free valence for correlated singlet‐state wave functions

AbstractChosen from István Mayer's very impressive canon of important work on bond orders and related quantities, we explore a paper from 2012 which introduced a “pseudo spin density matrix” for correlated singlet‐state wave functions, leading to “improved” definitions of bond orders and free valence. Examining such “improved” bond orders for the singlet ground states of H2, N2 and CH+ we find that all of them exhibit sensible geometry dependences. Mayer's free valence index works well for H2 and N2; the asymptotic behavior for CH+ turns out to be slightly more complicated but can easily be explained. Using B2H6 to examine three‐center bonding, a simple generalization of Mayer's approach produces numerical results close to those based on the “pseudo spin density matrix.” As expected, the various “correction” terms remain small, albeit some of them are larger for the multicenter indices of ground and excited singlet states of benzene, S2N2 and square (D4h) cyclobutadiene.

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14).

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

Spectrum of Field-Ionized Triplet Gerade Rydberg States of H2 and Comparison to Multichannel Quantum-Defect Theory.

A spectrum of field-ionized triplet Rydberg states of gerade symmetry H2 has been measured, excited from the υ″ = 0, N″ = 1-3 rovibrational levels of the metastable c3Πu-2pπ state in a 6 keV fast molecular beam. The field-ionized spectrum is kinetic energy labeled in order to separate it from the well-studied υ+ ≥ 1 autoionization spectrum. The spectrum consists of both ns and nd Rydberg series with n between 10 and 28 converging to the υ+ = 0, N+ = 1-3 levels of the X+ 2Σg+ ground state of H2+. Transitions with changes in vibration and/or rotation are also identified. The spectral positions of 59 transitions in the field ionization spectrum are identified and assigned quantum numbers using the predictions of multichannel quantum-defect theory (MQDT). The transition energies and subsequent effective quantum defects are compared between the experiment and theory. Most of the observed transitions, within the experimental uncertainty of 0.2 cm-1, agree with the energies predicted by MQDT.

H2 photochemistry in interstellar ices:The formation of HCO in UV irradiated CO:H2 ice mixtures

AbstractThe role of H2 in forming interstellar complex organics is still not clear due to the high activation energies required for “non-energetic” association reactions. In this work, we investigated the potential contribution of H2 to the hydrogenated species (HnNCO) formation on dust grains when the “energetic” processing is involved. The goal is to test whether an additional hydrogenation pathway is possible upon UV irradiation of a CO:H2 ice mixture. It is proposed that the electronically excited carbon monoxide (CO*) induced by UV-photons can react with a ground-state H2 to form HCO, ultimately enhancing the production of COMs in ice mantle.

Measurement of C2 and CH temperatures in argon‐acetylene low‐pressure microwave‐induced plasma

The emission spectra of C2(d3Πg–a3Πu), CH(A2Δ–X2Π), and CH(B2Σ–X2Π) bands are analysed to measure rotational Trot, vibrational Tvib, and gas temperature Tg from Ar/C2H2 (5–20% C2H2) microwave‐induced plasma (MIP). In case when helium and hydrogen are used in the gas mixture instead of argon, no significant change in Trot is noticed. Both studied temperatures are insensitive in terms of the C2H2 percentage. From CH(0–0, A2Δ–X2Π) band R2 branch lines, two Trot (Trot ∼ 520–580 K for J′ = 3–9 and Trot ∼ 1,700–1,800 K for J′ = 10–17) are determined. The lower Trot equals the Tg (500–700 K) measured from C2 bands in this study. The H2 Fulcher‐α diagonal bands are recorded as well in the H2/C2H2 mixtures and Trot∼750–900 K of the H2 ground state measured. Tvib ∼ 6,000 K in Ar/C2H2 MIP is calculated from the integral intensity ratio of C2(2,1) and C2(3,2) bands.

Transferability of the Specific Reaction Parameter Density Functional for H2 + Pt(111) to H2 + Pt(211).

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD3 + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H2 + Pt(111) with chemical accuracy is also capable of accurately describing H2 + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H2 + Pt(111). Our calculations used the Born–Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H2. The theoretical results for sticking of H2 and D2 on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron–hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron–hole pair excitation on sticking are found.

Double resonance rotational spectroscopy of He-HCO.

The ground state of He-HCO+ is investigated using a recently developed double resonance technique, consisting of a rotational transition followed by a vibrational transition into a dissociative state. In order to derive precise predictions for the rotational states, the high resolution infrared predissociation spectroscopy of the v1 C-H stretching mode is revisited. Eleven pure rotational transitions are measured via the double resonance method. A least squares fit of these transitions to a standard linear rotor Hamiltonian reveals that the semirigid rotor model cannot fully describe the loosely bound He-HCO+ complex. The novel double resonance technique is compared with other action spectroscopic schemes, and some potential future applications are presented.

Elastic anomaly of helium films at a quantum phase transition

Helium films show various quantum phases that undergo quantum phase transitions by changing coverage n. We found anomalous elastic phenomena in bosonic 4He and fermionic 3He films adsorbed on a glass substrate. The films stiffen under AC strain at low temperature with an excess dissipation. The onset temperature of the stiffening decreases to 0 K as n approaches a critical coverage nc. The elastic anomaly is explained by thermal activation of helium atoms from the localized to extended states with a distributed energy gap. We determine for the first time the energy band structure of helium films from elasticity. The ground states of 4He and 3He at n < n_c are identically gapped and compressible, which are possibly a sort of Mott insulator or Mott glass.

On the Choice of the Wavefunction of the Ground State of He for Precision Calculations of Autoionization State Parameters above the Excited Ion Formation Threshold

The necessity of choosing multiparametric wavefunctions for describing the ground state of an atom in the problems of ionization of atoms by photons and electrons has been substantiated for the He atom as an example. Comparative analysis of application of different ground-state wavefunctions for this atom has been performed. The energies, widths, and partial widths of the lower autoionization state 1P of the He atom above the excited ion formation threshold has been performed. It is shown that in contrast to total widths of quasi-stationary states, which differ insignificantly for different wavefunctions of the ground state, the partial widths are substantially different.

Total, state-selective and differential cross sections for single electron capture in He+–He collisions

The total, state-selective and angular-differential cross sections for single electron capture in He+–He collisions are investigated by using the two-center atomic orbital close-coupling method in the energy range 0.2–650 keV/u. The angular-differential cross sections for electron capture to the ground state of He are calculated at collision energies of 0.625, 1.25, 7.5, 25, 60, and 150 keV/u within the eikonal approximation for the scattering amplitude. Both total and differential cross sections are compared with the available experimental and theoretical data. The calculated differential cross sections exhibit oscillatory structures with exponentially decreasing amplitude and frequency decreasing with increasing the collision energy. They show good agreement with the experimental data for scattering angles where decreases with increasing the collision energy ( for E = 0.625 keV/u, for E = 150 keV/u). We found out that for a given collision energy, the oscillatory structure of angular-differential cross section is strongly correlated with the oscillatory structure of the impact parameter dependence of electron capture probability.

On Precision Measurement of the Frequency of the 11S–23S Forbidden Transition of a Helium Atom

The possibility is demonstrated of a precision frequency measurement for the 11S0−23S1 forbidden transition (at 62.6 nm) of a helium atom using the stimulated Raman scattering method. The 11S0 singlet state is the ground state of 4He, while the metastable 23S1 state has the lowest energy in the triplet part of the spectrum (4He*). The transition has a very small natural width, which allows us to consider it as a possible reference for creation of a frequency standard in the vacuum ultraviolet region.

Vibrational kinetics of electronically excited states in H2 discharges

The evolution of atmospheric pressure hydrogen plasma under the action of repetitively ns electrical pulse has been investigated using a 0D state-to-state kinetic model that self-consistently couples the master equation of heavy particles and the Boltzmann equation for free electrons. The kinetic model includes, together with atomic hydrogen states and the vibrational kinetics of H2 ground state, vibrational levels of singlet states, accounting for the collisional quenching, having a relevant role because of the high pressure. The mechanisms of excitations, radiative decay and collisional quenching involving the excited H2 states and the corresponding cross sections, integrated over the non-equilibrium electron energy distribution function (EEDF) to obtain kinetic rates, are discussed in the light of the kinetic simulation results, i.e. the time evolution during the pulse of the plasma composition, of the EEDF and of the vibrational distributions of ground and singlet excited states.

Comments on “Statistical complexity and Fisher–Shannon information measure of [formula omitted]” [Phys. Lett. A 372 (13) (2008) 2271–2273

We point out and correct the erroneous numerical results calculated by H.E. Montgomery Jr. and K.D. Sen concerning the statistical complexity and the Fisher–Shannon information measure for the ground state H2+ molecule ion as a function of internuclear distance in momentum space and as a product in position and momentum spaces. In addition we have shown that Coulson-type wave function approximation used by authors leads to notable (up to almost 20%) discrepancies between such approximated results and exact ones.

Potential energy surfaces in atomic structure: The role of Coulomb correlation in the ground state of helium

For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a conditional amplitude, which depends functionally on the interelectronic distance $r_{12}$ and parametrically on $r_1$ and $r_2$. Applying the variational principle, we derive pseudoeigenvalue equations for these two amplitudes, which cast the internal Schr\"odinger equation in a form akin to the Born-Oppenheimer separation of nuclear and electronic degrees of freedom in molecules. The marginal equation involves an effective radial Hamiltonian, which contains a nonadiabatic potential energy surface that takes into account all interparticle correlations in an averaged way, and whose unique eigenvalue is the internal energy. At each point $(r_1,r_2)$, such surface is, in turn, the unique eigenvalue in the conditional equation. Employing the ground state of He as prototype, we show that the nonadiabatic potential energy surface affords a molecularlike interpretation of the structure of the atom, and aids in the analysis of energetic and spatial aspects of the Coulomb correlation, in particular correlation-induced symmetry breaking and quantum phase transition.

Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+.

Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+} ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.

H2 Adsorption in a Porous Crystal: Accurate First-Principles Quantum Simulation.

A general method is presented for constructing, from ab initio quantum chemistry calculations, the potential energy surface (PES) for H2 absorbed in a porous crystalline material. The method is illustrated for the metal-organic framework material MOF-5. Rigid body quantum diffusion Monte Carlo simulations are used in the construction of the PES and to evaluate the quantum ground state of H2 in MOF-5, the zero-point energy, and the enthalpy of adsorption at 0 K.

Time delay anisotropy in photoelectron emission from isotropic helium

SynopsisIn contrast to expectations, we observe that the photoionization time delay from the 1s2 spherically symmetric ground state of He depend on the electron emission direction with respect to an external reference. We attribute the observed anisotropy to the interplay between different final quantum states, which become accessible once two photons are involved in the photoionization process. This is a universal effect, which needs to be taken into account for any study dealing with photoionization dynamics.