Solid hydrogen and deuterium. I. Ground-state energy calculated by a lowest order constrained-variation method

The ground-state energy of solid hydrogen and deuterium is calculated by means of a modified variational lowest order constrained-variation (LOCV) method. Both fcc and hcp H₂ and D₂ are considered, and the calculations are done for five different two-body potentials. For solid H₂ we obtain theoretical results for the ground-state binding energy per particle from –74.9 K at an equilibrium particle density of 0.700 ^–3 or a molar volume of 22.3 cm³/mole to –91.3 K at a particle density of 0.725 ^–3 or a molar volume of 21.5 cm³/mole, where =2.958 Å. The corresponding experimental result is –92.3 K at a particle density of 0.688 ^–3 or a molar volume of 22.7 cm³/mole. For solid D₂ we obtain theoretical results for the ground-state binding energy per particle from –125.7 K at an equilibrium particle density of 0.830 ^–3 or a molar volume of 18.8 cm³/mole to –140.1 K at a particle density of 0.843 ^–3 or a molar volume of 18.5 cm³/mole. The corresponding experimental result is –137.9 K at a particle density of 0.797 ^–3 or a molar volume of 19.6 cm³/mole.     

Solid hydrogen: Ground-state energy,pressure, and compressibility

The ground-state energy, the pressure, and the compressibility of solid molecular hydrogen is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or an effective interaction in coordinate space; the ground-state energies for normal hydrogen and deuterium are calculated. Also, the pressure and the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both hcp and fcc structures are considered. Theoretical results for the ground-state energy per particle are –82 K for solid hydrogen at a molar volume of 22 cm³/mole and –135 K for solid deuterium at a molar volume of 19 cm³/mole. The corresponding experimental results are –92 and –138 K, respectively. We obtain zero pressure for solid hydrogen at a molar volume of 22.45 cm³/mole and for solid deuterium at a molar volume of 19.2 cm³/mole. The corresponding experimental results are 22.65 and 19.56 cm³/mole, respectively. Theoretical results for the compressibility at zero pressure are 5.3×10^–4 atm^–1 for solid hydrogen and 2.6×10^–4 atm^–1 for solid deuterium. The corresponding experimental results are 4.9×10^–4 and 3.0×10^–4 atm^–1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.     

Solid helium. I. Ground-state energy and compressibility

The ground-state energy and the compressibility of solid helium is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or the effective interaction in coordinate space, and the ground-state energy for the two helium isotopes³He and⁴He is calculated. Also, the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both bcc and hcp structures are considered. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. Theoretical results for the ground-state energy per particle are 0.2 to 2.6 K for solid³He at a molar volume of 24 cm³/mole, and –2.4 to –5.9 K for solid⁴He at a molar volume of 20 cm³/mole. The corresponding experimental results are –1.0 and –5.6 K, respectively. Theoretical results for the compressibility are 0.0031–0.0042 atm^–1 for solid³He at a molar volume of 22 cm³/mole, and 0.0014–0.0022 atm^–1 for solid⁴He at a molar volume of 18 cm³/mole. The corresponding experimental results are 0.0032 and 0.0014 atm^–1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.     

Specific heats of solid hydrogen,solid deuterium,and solid mixtures of hydrogen and deuterium

Measurements have been made in the temperature range 0.5–5 K of the specific heats of pure solid H₂, pure solid D₂, and four solid mixtures of H₂ and D₂ with D₂ fractions between 15 and 95%, all of which systems had low concentrationc of molecules in the rotational stateJ=1. For the H₂,c=0.0023, and for the D₂,c=0.030. It was found that the observed specific heats could be described as the sum of three terms as follows. (1) A lattice specific heat. This was found to follow aT ³ function with _D =122 K for solid H₂ and _D=113.8 K for solid D₂. For the solid mixtures the lattice specifi heats have in first approximation values given by a weighted mean of the lattice specific heats of the pure components. (2) A Schottky term with a maximum at about 1.3 K for solid H₂ and 1.4 K for solid D₂, which can quantitatively be described in terms of electric quadrupole-quadrupole (EQQ) interactions in nearest-neighbor pairs and triples of molecules in the rotational stateJ=1. This term led to evaluation of , the EQQ interaction energy, giving /k=0.9 ± 0.1 K for solid H₂ and 0.93 ± 0.05 K for solid D₂. It was found, moreover, that in solid H₂ there was an appreciable enhancement with time of the number of clusters of molecules in the rotational stateJ=1 at the expense of the number of isolated singles of similar molecules, due to rotation diffusion. On the other hand no rotation diffusion was observed in solid D₂ or in the solid mixtures of H₂ and D₂, except possibly in those mixtures containing 85% H₂. (3) A second anomalous term occurring at temperatures below about 0.8 K and, by extrapolation, having its maximum below 0.5 K (the lowest temperature of our measurements). This anomaly was observed only in those samples containing D₂ and is, as yet, unexplained in detail. A further major conclusion from our results in the temperature range 0.5–5 K is that there was no evidence in the form of a sharp anomalous jump in the specific heat of any of the mixtures which could be interpreted as indicating the occurrence of isotopic phase separation. This absence of phase separation is noted, in spite of the fact that thermodynamically it is energetically favorable in the temperature range of observation.Work partially supported by a grant from the National Science Foundation and by contracts with the Office of Naval Research and DOD (Themis Program).     

Negative charges in liquid hydrogen and deuterium

The temperature and pressure dependence of the mobilities of negative charges injected into liquid hydrogen and deuterium have been measured. We propose the existence of two types of charge carriers in liquid parahydrogen. One is a bubble with an electron inside while the other has higher mobility. Relaxation of the current through liquid hydrogen was observed. It is suggested that in liquid and solid hydrogen under -irradiation neutral complexes are created which can trap the negative charges and have a lifetime of about 10 hours.     

Determination of compressibility and virial co-efficients by the burnett method

An analytical method of determining the compressibility and virial coefficients from the experimental results by the Burnett method is described.     

Elastic constants of solid hexagonal close-packed hydrogen and deuterium

Zero-pressure elastic constants for hcpp-H₂ ando-D₂ atT=0 K are calculated within the framework of the self-consistent phonon approximation with cubic anharmonicities. A pairwise additive model potential of the Barker-Pompe form, which reproduces the equation of state in the solid over a wide range of pressures, is used for the calculations. Debye temperatures and Grüneisen constants are also presented and the results are compared with recent experiments on the velocity of sound, inelastic neutron scattering, and specific heat.     

Probing protein ligand interactions by automated hydrogen/deuterium exchange mass spectrometry

Amide hydrogen/deuterium exchange is a powerful biophysical technique for probing changes in protein dynamics induced by ligand interaction. The inherent low throughput of the technology has limited its impact on drug screening and lead optimization. Automation increases the throughput of H/D exchange to make it compatible with drug discovery efforts. Here we describe the first fully automated H/D exchange system that provides highly reproducible H/D exchange kinetics from 130 ms to 24 h. Throughput is maximized by parallel sample processing, and the system can run H/D exchange assays in triplicate without user intervention. We demonstrate the utility of this system to differentiate structural perturbations in the ligand-binding domain (LBD) of the nuclear receptor PPARgamma induced upon binding a full agonist and a partial agonist. PPARgamma is the target of glitazones, drugs used for treatment of insulin resistance associated with type II diabetes. Recently it has been shown that partial agonists of PPARgamma have insulin sensitization properties while lacking several adverse effects associated with full agonist drugs. To further examine the mechanism of partial agonist activation of PPARgamma, we extended our studies to the analysis of ligand interactions with the heterodimeric complex of PPARgamma/RXRalpha LBDs. To facilitate analysis of H/D exchange of large protein complexes, we performed the experiment with a 14.5-T Fourier transform ion cyclotron resonance mass spectrometer capable of measuring mass with accuracy in the ppb range.     

Comparison of electronic structures of doped ZnS and ZnO calculated by a first-principle pseudopotential method

Electronic band calculations of doped and undoped ZnO and ZnS have been done using density functional theory under the local density approximation so as to clarify the reason of the difference in behaviors of doped ZnO and ZnS. The reason why the electrical conductivity of ZnS is difficult to be increased by doping was discussed. In the case of doped ZnS, an impurity level was generated at deep position below the bottom of the conduction band of the host ZnS lattice and Fermi level was located at this impurity level. On the contrary, the shape of the density of states curve and the band structures of doped and undoped ZnO are alike with each other and the donor band is hybridized with the conduction band of the ZnO host material. This seems to result in contribution of doped electrons to electrical current in the case of doped ZnO.     

ERD facility for analysis of hydrogen and deuterium in solids

Hydrogen is the lightest element in nature, and so, its detection and quantitative analysis is difficult by the conventional methods utilized for other elements. In the recent years the technique of elastic recoil detection analysis (ERD) using 1–2 MeV He⁺ beam has been developed to quantitatively and simultaneously analyze hydrogen and its isotopes in solids. Such a facility has been set up using the 2 MeV Van-de-Graaff accelerator at IIT Kanpur. It facilitates H and D analysis in a material up to a depth of ∼ 1μm with a detection sensitivity of 0·1 at.% and depth resolution of about 300 ?. The application potential of this setup is illustrated by presenting the results of measurements performed on Al:H:D systems prepared by plasma source ion implantation and highT _c YBCO pellets exposed to humid atmosphere.     

Reference wavelengths for strong lines of atomic hydrogen and deuterium

Wavelengths of the individual fine-structure components of the n = 1-2 (Ly(alpha)), n = 1-3 (Ly(beta)), n = 1-4 (Ly(gamma)), n = 1-5 (Ly(delta)), n = 1-6 (Ly(epsilon)), n = 1-7 (Ly(zeta)), n = 2-3 (H(alpha)), n = 2-4 (H(beta)), n = 2-5 (H(gamma)), n = 2-6 (H(delta)), and n = 2-7 (H(epsilon)) transitions of H and D are determined from theoretical values for the binding energies. Theoretical line strengths are used to obtain recommended values for the peaks of unresolved blends of these components as likely to be observed with discharge light sources and spectrometers with low to moderate resolution.     

Tracking hydrogen/deuterium exchange at glycan sites in glycoproteins by mass spectrometry

Hydrogen/deuterium exchange coupled to mass spectrometry (HDX-MS) has emerged as a technique for studying glycoproteins, which are often refractory to classical methods. Glycan chains are generally assumed to exchange protons very rapidly, making them invisible to this technique. Here, we show that under conditions commonly used for HDX-MS, acetamido groups within glycan chains retain a significant amount of deuterium. Using mono- and polysaccharide standards along with glycopeptides from a panel of glycoproteins, we demonstrate that N-acetyl hexosamines, along with modified Asn side chains, are responsible for this effect. Model compounds for sialic acid also displayed similar exchange kinetics, but terminal sialic acids in the context of an entire glycan chain did not contribute to deuterium retention. Furthermore, the presence of sialic acid appears to enhance the exchange rate of the nearby N-acetyl glucosamines. The ability to detect deuterium exchange at the glycan level opens the possibility of applying HDX-MS to monitor glycan interactions and dynamics.     

Chemical sputtering and surface damage of graphite by low-energy atomic and molecular hydrogen and deuterium projectiles

We present experimental methane production yields for H⁺, ions incident on ATJ graphite in the energy range 10–250 eV/H. Below about 60 eV/H, the molecular H species give higher methane yields/H when compared with isovelocity H⁺, similar to our earlier measurements for incident deuterium atomic and molecular ions. For both D and H atomic and molecular projectiles, the yields/atom coalesce onto a single curve below projectile energies of 60 eV/atom, when plotted as a function of maximum energy transfer, under the assumption that, below this energy, the incident molecular species are largely undissociated when undergoing C–C bond breaking collisions during their collision cascade and thus produce more damage. Raman spectroscopy of a graphite sample exposed to high fluences of D⁺ and beams at high and low energies qualitatively confirmed the assumption that more surface damage is produced by the low-energy incident molecular species than by isovelocity atomic ions. While the two high-energy beam-exposed spots showed similar damage, the low-energy molecular-beam-exposed spot showed slightly more damage than the corresponding D⁺-beam-exposed spot.     

Density dependence of the elastic constants of hcp hydrogen and deuterium

The elastic constants of hcp H₂ and D₂ are calculated for densities up to 10 cm³/mole (20 kbar at T = 4.2 K). An Isotropic pair potential is utilized in the computations and cubic anharmonic corrections are incorporated into the lattice dynamics. The results are compared with sound velocity, specific heat, and Brillouin and neutron scattering measurements.     

An improved experimental equation of state of solid hydrogen and deuterium

We have analyzed a large set of data in the literature as well as new data of our own to provide an improved equation of state of solid para-hydrogen and ortho-deuterium, with pressures ranging from 0 to 25 kbar (at the melting line). Results, including pressure, bulk modulus, and thermal expansion, are tabulated for a dense set of molar volumes as a function of temperature.Partial financial support provided by the Stichting FOM.     

Site-specific analysis of gas-phase hydrogen/deuterium exchange of peptides and proteins by electron transfer dissociation

To interpret the wealth of information contained in the hydrogen/deuterium exchange (HDX) behavior of peptides and proteins in the gas-phase, analytical tools are needed to resolve the HDX of individual exchanging sites. Here we show that ETD can be combined with fast gas-phase HDX in ND(3) gas and used to monitor the exchange of side-chain hydrogens of individual residues in both small peptide ions and larger protein ions a few milliseconds after electrospray. By employing consecutive traveling wave ion guides in a mass spectrometer, peptide and protein ions were labeled on-the-fly (0.1-10 ms) in ND(3) gas and subsequently fragmented by ETD. Fragment ions were separated using ion mobility and mass analysis enabled the determination of the gas-phase deuterium uptake of individual side-chain sites in a range of model peptides of different size and sequence as well as two proteins; cytochrome C and ubiquitin. Gas-phase HDX-ETD experiments on ubiquitin ions ionized from both denaturing and native solution conditions suggest that residue-specific HDX of side-chain hydrogens is sensitive to secondary and tertiary structural features occurring in both near-native and unfolded gas-phase conformers present shortly after electrospray. The described approach for online gas-phase HDX and ETD paves the way for making mass spectrometry techniques based on gas-phase HDX more applicable in bioanalytical research.     

Binding energy of liquid4He calculated by the hypernetted-chain method

The hypernetted-chain (HNC) method for quantum many-body calculations is investigated in some detail by means of calculations of the binding energy and the equilibrium density for liquid⁴He. The calculations are done for six different two-body potentials, and the results are compared with experimental results and other theoretical results obtained by the lowest order constrained variation (LOCV) method. Our HNC results are, in general, quite different from the results obtained by the LOCV method—the LOCV binding energies are generally reduced by 2–5 K in the HNC calculations. The results are also very dependent on the chosen potential, especially at high densities.