Transitions Of H2 Research Articles

Probing secular changes in the gravitational constant with white dwarf spectra

Exploring variations in fundamental physics constants across cosmological space-time is of substantial importance in both theoretical and experimental physics. A crucial means of investigating such variations involves comparing laboratory measurements with astrophysical observations. In the present study, we employ a combination of laboratory data and observed Lyman transitions of H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_2$$\\end{document} identified in the white dwarf star GD133. Through this examination, we find the temporal variation of the gravitational constant, G˙/G=(0.016±0.098)×10-15year-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\dot{G}}}/{G} = (0.016 \\pm 0.098) \ imes 10^{-15}~\ ext {year}^{-1}$$\\end{document} with a gravitational potential ϕ≈104,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\approx 10^4,$$\\end{document} and an average total redshift of H2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_2,$$\\end{document}zabs=0.0001820(10).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{abs} =0.0001820(10).$$\\end{document} This newly determined constraint on the time variation of G serves as an important tool for advancing discussions within unified theories.

МОЛЕКУЛЯРНЫЙ ИОН ВОДОРОДА𝑯𝟐+. МАГНИТНЫЕ M1 ПЕРЕХОДЫ

The magnetic dipole transitions in the homonuclear molecular ion 𝐻2+are obtained for a range ofand L, vibrational and total orbital momentum quantum numbers, respectively. Calculations are performed in the nonrelativistic approximation. The effects of the ion spin structure on M1 transitions are also considered. Numerical calculations were carried out on the basis of “exponential” variational expansion. One of the simplest and most fully developed areas of application of quantum mechanics is the theory of atoms with one or two electrons. For hydrogen and hydrogen-like ions, calculations can be performed strictly in both Schrödinger's non-relativistic wave mechanics and Dirac's relativistic electron theory. The exact calculations are rigorous for an electron at a fixed Coulomb potential. Therefore, the hydrogen-like atom provides an excellent material for testing the validity of quantum mechanics. For such an atom, the correction terms that take into account the motion and structure of the atomic nucleus, as well as quantum electrodynamic effects, are small and can be calculated with great accuracy. Since the energy levels of hydrogen and hydrogen-like atoms can be experimentally studied with anamazing degree of accuracy, it turns out that it is possible to test the correctness of quantum electrodynamics to some extent accurately.

VUV lasing in diffuse discharges formed by runaway electrons

The parameters of stimulated emission in diffuse discharges formed in a sharply inhomogeneous electric field by runaway electrons in mixtures of rare gases with the addition of H2 and F2 at pressures up to 10 atm are studied. Efficient VUV lasing was obtained at wavelengths from 148 to 193 nm on the transitions of H2, F2 and exciplex ArF* molecules. It was shown that the addition of He buffer gas increases the pulse duration, while Ne addition improves the output energy of the VUV laser on the H2 Lyman band. A laser pulse duration over 10 ns and an output of 0.12 mJ were obtained. The diffuse discharge in mixtures of He with F2 was found to form as a result of successive ionization waves. It was shown that the laser pulse at 157 nm has three peaks, which correspond to the maxima of the diffuse discharge current. Therewith, the first or second peak of the laser radiation has the maximum intensity, depending on the amplitude of the conduction current in the primary ionization wave. A maximal F2* laser electrical efficiency of η 0 = 0.18% and an output of Q 157 = 3.8 mJ were obtained in a He–F2 gas mixture at pressure of 10 atm, which exceeds the efficiency of lasers of this type pumped by transverse volume discharges with UV preionization. Long-pulse operation of the ArF* laser was achieved in a He–Ne–Ar–F2 gas mixture. Lasing at 193 nm continued during two periods of the diffuse discharge current. The total duration of the laser pulse was as long as 40 ns, and the radiation energy at 193 nm was as high as 2 mJ from an active volume of 20 cm3.

Theoretical study of intramolecular effects and rotational spectra for H2–AgCl complex: A corrected intermolecular potential energy surface

An efficient model was developed by optimizing the terms of intermolecular potential and monomer rotations in the Hamiltonian, and then was applied to determine the global structures and rotational transitions of H2–AgCl complex. Based on this model, a detailed study of intramolecular effects were examined for intermolecuar vibrational modes, rotational transition frequencies, and spectroscopic parameters relative to those of rigid-rotor-approximation model. Firstly, the full-dimensional equilibrium geometry is determined to be (Re, r1e, r2e, θ1e, θ2e, φe) = (2.370 Å, 0.7785 Å, 2.2579 Å, 90.0°, 180.0°, 0.0°), and the averaged structure is determined to be (Rν, r1ν, r2ν, θ1ν, θ2ν, φν) = (2.436 Å, 0.7905 Å, 2.2604 Å, 76.4°, 172.8°, 0.0°), which are in excellent agree with the available data of experimental observations. In addition, the available transitions were accurately predicted with the maximal percentage error of 0.05%. Based on the determined spectroscopic parameters, two perpendicular bands were predicted and will be helpful to guide the further investigations in the far infrared spectral region experimentally.

Accurate absolute frequency measurement of the S(2) transition in the fundamental band of H2 near 2.03 μm.

A series of spectra of the quadrupolar electric S(2) transition of H2 in the 1-0 band near 4917 cm-1 has been recorded at seven pressure values between 2 and 100 Torr. The comb-referenced cavity ring down spectroscopy (CR-CRDS) technique was used for the recording of this very weak transition. The accuracy of the spectrum frequency axis is achieved by linking the CRDS setup to an optical frequency comb referenced to a GPS-referenced 10 MHz rubidium clock. Applying a multi-spectrum fit procedure to the seven averaged spectra with a quadratic speed dependence Nelkin-Ghatak profile, the transition frequency is determined (ν0 = 147 408 142 357 kHz) with an uncertainty of 150 kHz (∼1 × 10-9 in relative). This represents the smallest uncertainty achieved so far for a transition in the fundamental band of H2. The experimental frequency reported in this work is 1.53 MHz higher than the best-to-date theoretical value. This difference represents 1.5 times the 1σ-uncertainty (about 1 MHz) of the calculated frequency. The measurements also allow for the determination of the absolute intensity value of the S(2) line which shows an agreement with the ab initio value at the per mil level. In addition, the cross section of the collision induced absorption (CIA) underlying the S(2) line is accurately retrieved from the quadratic pressure dependence of the baseline level of the recorded spectra.

The ortho-para transition, confinement and self-diffusion of H2 in three distinct carbide-derived carbons by quasi- and inelastic neutron scattering

Microporous carbon materials are promising for hydrogen storage due to their structural variety, high specific surface area, large pore volume and relatively low cost. Carbide-derived carbons are highly valued as model materials because their porous structure is fine-tuned through the choice of the precursor carbide and the synthesis route. This study investigates H2 adsorption in three carbide derived carbons with well-defined pores and pore size distributions with quasi- and inelastic neutron scattering methods. Concerning previous studies, a wider neutron energy transfer window is investigated, and a detailed quantitative evaluation of the graphitic structure is presented. The graphitic structure of the carbon is shown to influence the speed of the ortho-to-para transition of H2. Namely, the ortho-para transition was the slowest in carbon derived from TiC, which also had the smallest average stacking size of graphene layers. The possibility to inhibit the ortho-para transition in cryo-adsorption devices is sought after to mitigate the evaporation of H2 during storage. In addition, the self-diffusion of H2 in different timescales is detected in carbon derived from Mo2C, demonstrating the usefulness of obtaining data in a wide energy window.

Analysis of the first infrared spectrum of quasi-bound H2 line emission in Herbig-Haro 7

Context. Highly excited molecular hydrogen (H2) has been observed in many regions of shocked molecular gas. A recently published K-band spectrum of Herbig-Haro 7 (HH7) contains several vibration-rotation lines of H2 from highly excited energy levels that have not been detected elsewhere, including a line at 2.179 μm identified as arising from the v = 2, J = 29 level, which lies above the dissociation limit of H2. One emission line at 2.104 μm in this spectrum was unidentified. Aims. We aim to complete the analysis of the spectrum of HH7 by including previously missing molecular data that have been recently computed. Methods. We re-analysed the K-band spectrum, emphasising the physics of quasi-bound upper levels that can produce infrared emission lines in the K band. Results. We confirm the identification of the 2 − 1 S(27) line at 2.1785 μm and identify the line at 2.1042 μm as due to the 1−0 S(29) transition of H2, whose upper level energy is also higher than the dissociation limit. This latter identification, its column density, and the energy of its upper level further substantiate the existence of a hot thermal component at 5000 K in the HH7 environment. Conclusions. The presence of the newly identified 1 − 0 S(29) line, whose quasi-bound upper level (v = 1, J = 31) has a significant spontaneous dissociation probability, shows that dissociation of H2 is occurring. The mechanism by which virtually all of the H2 in levels with energies from 20 000 K to 53 000 K is maintained in local thermodynamic equilibrium at a single temperature of ∼5000 K remains to be understood.

Exciton Nature of Plasma Phase Transition in Warm Dense Fluid Hydrogen: ROKS Simulation.

The transition of warm dense fluid hydrogen from an insulator to a conducting state at pressures of about 20-400 GPa and temperatures of 500-5000 K has been the subject of active scientific research over the past few decades. However, various experimental and theoretical methods do not provide consistent results. In this work, we have applied the restricted open-shell Kohn-Sham (ROKS) method for first principles molecular dynamics of dense hydrogen after thermal excitation to the first singlet excited state. The Wannier localization method has allowed us to analyze the exciton dynamics in this system. The model shows that a key mechanism of the transition is associated with the dissociation of electron-hole pairs, which allows explaining several stages of the transition of fluid H2 from molecular state to plasma. This mechanism is able to give a quantitative description of several experimental results as well as to resolve the discrepancies between experimental studies.

The obscured nucleus and shocked environment of VV 114E revealed by JWST/MIRI spectroscopy

ABSTRACT Compact Obscured Nuclei (CONs) potentially hide extreme supermassive black hole (SMBH) growth behind large column densities of gas/dust. We present a spectroscopic analysis of the heavily obscured nucleus and the surrounding environment of the eastern region of the nearby (z = 0.02007) interacting galaxy VV 114 with the JWST Mid-InfraRed Instrument (MIRI). We model the spectrum from 4.9 to 28 μm to extract polycyclic aromatic hydrocarbon (PAH) emission and the underlying obscured continuum. We find that the NE nucleus (A) is highly obscured where the low PAH equivalent width (EW) ratio, EW(12.7)/EW(11.3), reveals a dust enshrouded continuum source. This is confirmed by decomposing the continuum into nuclear and star-forming where the nuclear component is found to be typical of CONs. The 11.3/6.2 PAH flux ratio is consistent with originating in star-forming regions rather than typical AGN. The second nucleus (B) is much less obscured, with PAH flux ratios also typical of star-forming regions. We do not detect any high ionization lines such as [Ne v] or [Ne vi] which suggests that if an AGN is present it must be highly obscured. Additionally, we detect a shock front south of the secondary nucleus (B) in the [Fe ii] (5.34 μm) line and in warm molecular hydrogen. The 6.2 PAH emission does not spatially coincide with the low-J transitions of H2 but rather appears strong at the shock front which may suggest destruction of the ionized PAHs in the post-shock gas behind the shock front.

Multiple gas phases in supernova remnant IC 443: mapping shocked H2 with VLT/KMOS

ABSTRACT Supernovae and their remnants provide energetic feedback to the ambient interstellar medium (ISM), which is often distributed in multiple gas phases. Among them, warm molecular hydrogen (H2) often dominates the cooling of the shocked molecular ISM, which has been observed with the H2 emission lines at near-infrared wavelengths. Such studies, however, were either limited in narrow filter imaging or sparsely sampled mid-infrared spectroscopic observations with relatively poor angular resolutions. Here we present near-infrared (H and K bands) spectroscopic mosaic observations towards the A, B, C, and G regions of the supernova remnant (SNR) IC 443, with the K-band Multi-Object Spectrograph (KMOS) onboard the Very Large Telescope (VLT). We detected 20 rotational–vibrational transitions of H2, one H line (Brγ), and two [Fe ii] lines, which dominate broad-band images at both H and K bands. The spatial distribution of H2 lines at all regions is clumpy on scales from ∼0.1 down to ∼0.008 pc. The fitted excitation temperature of H2 is between 1500 and 2500 K, indicating warm shocked gas in these regions. The multigas phase comparison shows stratified shock structures in all regions, which explains the coexistence of multiple types of shocks in the same regions. Lastly, we verify the candidates of young stellar objects previously identified in these regions with our spectroscopic data, and find none of them are associated with young stars. This sets challenges to the previously proposed scenario of triggered star formation by SNR shocks in IC 443.

On the accuracy of H i observations in molecular clouds – More cold H i than thought?

ABSTRACT We present a study of the cold atomic hydrogen (H i) content of molecular clouds simulated within the SILCC-Zoom project for solar neighbourhood conditions. We produce synthetic observations of H i at 21 cm, including H i self-absorption (HISA) and observational effects. We find that H i column densities, $N_{\rm H\, \small {\rm I}}$, of ≳1022 cm−2 are frequently reached in molecular clouds with H i temperatures as low as ∼10 K. Hence, HISA observations assuming a fixed H i temperature tend to underestimate the amount of cold H i in molecular clouds by a factor of 3–10 and produce an artificial upper limit of $N_{\rm H\, \small {\rm I}}$ around 1021 cm−2. We thus argue that the cold H i mass in molecular clouds could be a factor of a few higher than previously estimated. Also, $N_{\rm H\, \small {\rm I}}$ PDFs obtained from HISA observations might be subject to observational biases and should be considered with caution. The underestimation of cold H i in HISA observations is due to both the large H i temperature variations and the effect of noise in regions of high optical depth. We find optical depths of cold H i around 1–10, making optical depth corrections essential. We show that the high H i column densities (≳1022 cm−2) can in parts be attributed to the occurrence of up to 10 individual H i–H2 transitions along the line of sight. This is also reflected in the spectra, necessitating Gaussian decomposition algorithms for their in-depth analysis. However, also for a single H i–H2 transition, $N_{\rm H\, \small {\rm I}}$ frequently exceeds 1021 cm−2, challenging one-dimensional, semi-analytical models. This is due to non-equilibrium chemistry effects and the fact that H i–H2 transition regions usually do not possess a one-dimensional geometry. Finally, we show that the H i gas is moderately supersonic with Mach numbers of a few. The corresponding non-thermal velocity dispersion can be determined via HISA observations within a factor of ∼2.

Cosmic rays in molecular clouds probed by H2 rovibrational lines

Context. Low-energy cosmic rays (<1 TeV) play a fundamental role in the chemical and dynamical evolution of molecular clouds, as they control the ionisation, dissociation, and excitation of H2. Their characterisation is therefore important both for the interpretation of observations and for the development of theoretical models. However, the methods used so far for estimating the cosmic-ray ionisation rate in molecular clouds have several limitations due to uncertainties in the adopted chemical networks. Aims. We refine and extend a previously proposed method to estimate the cosmic-ray ionisation rate in molecular clouds by observing rovibrational transitions of H2 at near-infrared wavelengths, which are mainly excited by secondary cosmic-ray electrons. Methods. Combining models of interstellar cosmic-ray propagation and attenuation in molecular clouds with the rigorous calculation of the expected secondary electron spectrum and updated electron-H2 excitation cross sections, we derive the intensity of the four H2 rovibrational transitions observable in cold dense gas: (1−0)O(2), (1−0)Q(2), (1−0)S(0), and (1−0)O(4). Results. The proposed method allows the estimation of the cosmic-ray ionisation rate for a given observed line intensity and H2 column density. We are also able to deduce the shape of the low-energy cosmic-ray proton spectrum impinging upon the molecular cloud. In addition, we present a look-up plot and a web-based application that can be used to constrain the low-energy spectral slope of the interstellar cosmic-ray proton spectrum. We finally comment on the capability of the James Webb Space Telescope to detect these near-infrared H2 lines, which will make it possible to derive, for the first time, spatial variation in the cosmic-ray ionisation rate in dense gas. Besides the implications for the interpretation of the chemical-dynamic evolution of a molecular cloud, it will finally be possible to test competing models of cosmic-ray propagation and attenuation in the interstellar medium, as well as compare cosmic-ray spectra in different Galactic regions.

Observations and Analysis of CH+ Vibrational Emissions from the Young, Carbon-rich Planetary Nebula NGC 7027: A Textbook Example of Chemical Pumping

Abstract We discuss the detection of 14 rovibrational lines of CH+, obtained toward the planetary nebula NGC 7027 with the iSHELL spectrograph on NASA’s Infrared Telescope Facility (IRTF) on Maunakea. Our observations in the 3.49–4.13 μm spectral region, obtained with a 0.″375 slit width that provided a spectral resolving power λ/Δλ ∼ 80,000, have resulted in the unequivocal detection of the R(0)−R(3) and P(1)−P(10) transitions within the v = 1−0 band of CH+. The R-branch transitions are anomalously weak relative to the P-branch transitions, a behavior that is explained accurately by rovibronic calculations of the transition dipole moment reported in a companion paper. Nine infrared transitions of H2 were also detected in these observations, comprising the S(8), S(9), S(13), and S(15) pure rotational lines; the v = 1−0 O(4)−O(7) lines; and the v = 2−1 O(5) line. We present a photodissociation model, constrained by the CH+ and H2 line fluxes that we measured, that includes a detailed treatment of the excitation of CH+ by inelastic collisions, optical pumping, and chemical (“formation”) pumping. The latter process is found to dominate the excitation of the observed rovibrational lines of CH+, and the model is remarkably successful in explaining both the absolute and relative strengths of the CH+ and H2 lines.

Stabilizing LiNi0.8 Co0.15 Mn0.05 O2 Cathode by Doping Sulfate for Lithium-Ion Batteries.

Residual sulfate (SO4 2- ) in precursor Ni0.8 Co0.15 Mn0.05 (OH)2 (pre-NCM) is commonly regarded as being harmful to Li[Ni0.8 Co0.15 Mn0.05 ]O2 (NCM) performance, leading to significant performance losses and also hampering the electrode fabrication. Therefore, manufacturers try their best to lower sulfate contents in pre-NCM. However, how the sulfate affects the cathode materials is not systematically studied. To address these issues, NCM was synthesized with different amounts of intentionally added sulfate (NH4 )2 SO4 in pre-NCM. It was demonstrated that anionic SO4 2- doped in NCM could influence the grain size in sintering process and stabilize the layer structure during the charge-discharge process at a certain doping amount. The first-principles calculations suggested that the SO4 2- doped in the transition metal layer could effectively facilitate Li+ diffusion in the lattice. SO4 2- doping could reduce the energy barrier for Li+ migration and then suppress drastic contraction of the c axis during cycling. The phase transition of H2 to H3 caused by c axis contraction was suppressed and the cycling performance was enhanced. The capacity retention could reach 80.9 (0.2 C) and 80.4 % (1 C) after 380 and 240 cycles in coin cells, respectively. These findings illustrate that a certain amount of sulfate could be beneficial to NCM cathodes.

Rate constants for the H+ + H2 reaction from 5 K to 3000 K with a statistical quantum method.

An exhaustive investigation of state-to-state H+ + H2(v, j) → H+ + H2(v', j') transitions for rovibrational levels of molecular hydrogen below 1.3 eV from the bottom of the H2 well is carried out by means of a statistical quantum method, which assumes the complex-forming nature of the process. Integral cross sections for transitions involving states H2(v = 0, j = 0-12), H2(v = 1, j = 0-8), and H2(v = 2, j = 0-3) are obtained for collision energies within a range of Emin = 10-5 eV and Emax = 2 eV. Rate constants are then calculated between T = 5 K and 3000 K, and they are compared, when possible, with previous values reported in the literature. As a first application, the cooling rate coefficient of H2 excited by protons is determined and compared with a recent estimate.

Exploring the Possibility of Identifying Hydride and Hydroxyl Cations of Noble Gas Species in the Crab Nebula Filament

Abstract The first identification of the argonium ion ( ) toward the Crab Nebula supernova remnant was proclaimed by Herschel in the submillimeter and far-infrared domains. Very recently, the discovery of the hydro-helium cation ( ) in the planetary nebula (NGC 7027) by SOFIA has been reported. The elemental abundance of neon is much higher than that of argon. However, the presence of neonium ions ( ) is yet to be confirmed in space. Though the hydroxyl radicals (−OH) are very abundant in both neutral and cationic forms, hydroxyl cations of such noble gases (i.e., ArOH+, NeOH+, and HeOH+) are yet to be identified in space. Here, we employ a spectral synthesis code to examine the chemical evolution of the hydride and hydroxyl cations of the various isotopes of Ar, Ne, and He in the Crab Nebula filament and calculate their line emissivity and intrinsic line surface brightness. We successfully explain the observed surface brightness of two transitions of ArH+ (617 and 1234 GHz), one transition of OH+ (971 GHz), and one transition of H2 (2.12 μm). We also explain the observed surface brightness ratios between various molecular and atomic transitions. We find that our model reproduces the overall observed features when a hydrogen number density of ∼(104–106) cm−3 and a cosmic-ray ionization rate per H2 of ∼(10−11–10−10) s−1 are chosen. We discuss the possibility of detecting some hydride and hydroxyl cations in the Crab and diffuse cloud environment. Some transitions of these molecules are highlighted for future astronomical detection.

Molecular Gas and Dust Heating in Active Galaxies: Growing Black Holes or Tidal Shocks?

Abstract We investigate if and how growing supermassive black holes (SMBH) known as active galactic nuclei (AGN) and gravitational interactions affect the warm molecular gas and dust of galaxies. Our analysis focuses on the morphologies and warm ISM properties of 630 galaxies at z < 0.1. We use grizy images from the Pan-STARRS survey to classify the galaxies into mergers, early mergers, and non-mergers. We use MIR spectroscopic measurements of emission from rotational H2 transitions, dust, and polycyclic aromatic hydrocarbon (PAH) features, and silicate emission or absorption lines at 9.7 μm to study how gravitational interactions impact the warm ISM in AGN and non-AGN hosts. We find that in AGN-hosts, the ISM is warmer, the ratios of H2 to PAHs are larger, the PAH emission-line ratios and silicate strengths have a wider range of values than in non-AGN hosts. We find some statistical differences between the H2 emission of mergers and non-mergers, but those differences are less statistically significant than those between AGN and non-AGN hosts. Our results do not establish a relation between the rate of BH growth and the warm ISM but point to highly statistically significant differences between AGN hosts and non-AGN hosts, differences that are not present with the same statistical significance between mergers and non-mergers. We speculate that the combination of triggering mechanisms, AGN orientations, and evolutionary stages that allow AGN to be classified as such in the MIR indicate that those AGN are energetically coupled on kiloparsec scales to their host galaxies’s warm ISM. Future optical and IR, spatially resolved spectroscopic studies are best suited to characterize this connection.

Generalized Hartree-Fock with Nonperturbative Treatment of Strong Magnetic Fields: Application to Molecular Spin Phase Transitions.

In this work, we present a framework of an ab initio variational approach to effectively explore electronic spin phase transitions in molecular systems inside of a homogeneous magnetic field. In order to capture this phenomenon, the complex generalized Hartree-Fock ([Formula: see text]) method is used in the spinor formalism with London orbitals. Recursive algorithms for computing the one- and two-electron integrals of London orbitals are also provided. A Pauli matrix representation of the [Formula: see text] method is introduced to separate spin contributions from the scalar part of the Fock matrix. Next, spin phase transitions in two different molecular systems are investigated in the presence of a strong magnetic field. Noncollinear spin configurations are observed during the spin phase transitions in H2 and a dichromium complex, [(H3N)4Cr(OH)2Cr(NH3)4]4+, with an increase in magnetic field strength. The competing driving forces of exchange coupling and the spin Zeeman effect have been shown to govern the spin phase transition and its transition rate. Additionally, the energetic contributions of the spin Zeeman, orbital Zeeman, and diamagnetic terms to the potential energy surface are also analyzed.

Phase Transition of H2 in Subnanometer Pores Observed at 75 K.

Here we report a phase transition in H2 adsorbed in a locally graphitic Saran carbon with subnanometer pores 0.5-0.65 nm in width, in which two layers of hydrogen can just barely squeeze, provided they pack tightly. The phase transition is observed at 75 K, temperatures far higher than other systems in which an adsorbent is known to increase phase transition temperatures: for instance, H2 melts at 14 K in the bulk, but at 20 K on graphite because the solid H2 is stabilized by the surface structure. Here we observe a transition at 75 K and 77-200 bar: from a low-temperature, low-density phase to a high-temperature, higher density phase. We model the low-density phase as a monolayer commensurate solid composed mostly of para-H2 (the ground nuclear spin state, S = 0) and the high-density phase as an orientationally ordered bilayer commensurate solid composed mostly of ortho-H2 (S = 1). We attribute the increase in density with temperature to the fact that the oblong ortho-H2 can pack more densely. The transition is observed using two experiments. The high-density phase is associated with an increase in neutron backscatter by a factor of 7.0 ± 0.1. Normally, hydrogen produces no backscatter (scattering angle >90°). This backscatter appears along with a discontinuous increase in the excitation mass from 1.2 amu to 21.0 ± 2.3 amu, which we associate with collective nuclear spin excitations in the orientationally ordered phase. Film densities were measured using hydrogen adsorption. No phase transition was observed in H2 adsorbed in control activated carbon materials.

Constraint on a varying proton-to-electron mass ratio from H2and HD absorption atzabs≃ 2.34

Molecular hydrogen absorption in the damped Lyman-alpha system at z = 2.34 towards quasar Q1232+082 is analyzed in order to derive a constraint on a possible temporal variation of the proton-to-electron mass ratio, mu, over cosmological timescales. Some 106 H2 and HD transitions, covering the range 3290-3726 \AA, are analyzed with a comprehensive fitting technique, allowing for the inclusion of overlapping lines associated with hydrogen molecules, the atomic hydrogen lines in the Lyman-alpha forest as well as metal lines. The absorption model, based on the most recent and accurate rest wavelength for H2 and HD transitions, delivers a value of dmu/mu = (19 +/- 9 +/- 5)x 10^(-6). An attempt to correct the spectrum for possible long-range wavelength distortions is made and the uncertainty on the distortion correction is included in the total systematic uncertainty. The present result is an order of magnitude more stringent than a previous measurement from the analysis of this absorption system, based on a line-by-line comparison of only 12 prominent and isolated H2 absorption lines. This is consistent with other measurements of dmu/mu from 11 other absorption systems in showing a null variation of the proton-to-electron mass ratio over a look-back time of 11 Gyrs.