Fate of density functional theory in high-pressure solid hydrogen

This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point energy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semi-local Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular P$6_3$/m, C2/c, Cmca-12, and Cmca structures in the pressure range from $100<P<500$ GPa over which phases I, II and III are observed experimentally. At the static level of theory, in which proton zero-point energy is ignored, the LDA, PBE and BLYP functionals give very different structural transition and metallization pressures, with the BLYP phase diagram in better agreement with experiment. Nevertheless, all three functionals provide qualitatively the same information about the band gaps of the four structures and the phase transitions between them. Going beyond the static level, we find that the frequencies of the vibron modes observed above 3000 cm$^{-1}$ depend strongly on the choice of exchange-correlation functional, although the low-frequency part of the phonon spectrum is little affected. The largest and smallest values of the proton zero-point energy, obtained using the BLYP and LDA functionals, respectively, differ by more than 10 meV/proton. Including the proton zero-point energy calculated from the phonon spectrum within the harmonic approximation improves the agreement of the BLYP and PBE phase diagrams with experiment. Taken as a whole, our results demonstrate the inadequacy of mean-field-like density functional calculations of solid molecular hydrogen in phases I, II and III and emphasize the need for more sophisticated methods.Comment: Accepted for publicatio

Quantum Monte Carlo Study of High Pressure Solid Molecular Hydrogen

We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {\bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {\bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules

Dissociation of high-pressure solid molecular hydrogen: Quantum Monte Carlo and anharmonic vibrational study

A theoretical study is reported of the molecular-to-atomic transition in solid hydrogen at high pressure. We use the diffusion quantum Monte Carlo method to calculate the static lattice energies of the competing phases and a density-functional-theory-based vibrational self-consistent field method to calculate anharmonic vibrational properties. We find a small but significant contribution to the vibrational energy from anharmonicity. A transition from the molecular Cmca-12 direct to the atomic I4_1/amd phase is found at 374 GPa. The vibrational contribution lowers the transition pressure by 91 GPa. The dissociation pressure is not very sensitive to the isotopic composition. Our results suggest that quantum melting occurs at finite temperature.Comment: Accepted for publication by Phys. Rev. Let

Direct Dry Carbonation of Mining and Industrial Wastes in a Fluidized Bed for Offsetting Carbon Emissions

The direct dry mineral carbonation of selected mining and industrial wastes, using carbon dioxide derived from combustion flue gas, was evaluated. Specifically, coal fly ash from two Australian brown coal-fired power plants, red mud from the refinement of bauxite into alumina, and diamond tailings were considered, due to their relevant residual alkali content. These materials were tested in a laboratory-scale fluidized bed reactor at different temperatures (300–450° C), in a reactive environment that simulated the typical CO2 concentration in a combustion flue gas. The experimental results showed a low, but still appreciable, CO2 capture capacity for three of the tested materials, which appears to be more favorable in the lower temperature range and with relatively fast kinetics, indicating the practical relevance of the process. One of the fly ashes exhibited a different behavior; starting at 350° C, the sorbent began to release CO2, rather than absorb it. This suggested that the sorbent was already extensively carbonated by weathering before the tests. This study provides some evidence for the possible viability of recycling mining waste and for the circular economy in offsetting carbon emissions in the mining industry

Using Bayesian Model Averaging (BMA) to calibrate probabilistic surface temperature forecasts over Iran

Using Bayesian Model Averaging (BMA), an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM), with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and for HRM the initial and boundary conditions come from analysis of Global Model Europe (GME) of the German Weather Service. The resulting ensemble of seven members was run for a period of 6 months (from December 2008 to May 2009) over Iran. The 48-h raw ensemble outputs were calibrated using BMA technique for 120 days using a 40 days training sample of forecasts and relative verification data. <br><br> The calibrated probabilistic forecasts were assessed using rank histogram and attribute diagrams. Results showed that application of BMA improved the reliability of the raw ensemble. Using the weighted ensemble mean forecast as a deterministic forecast it was found that the deterministic-style BMA forecasts performed usually better than the best member's deterministic forecast

Large-scale study of the effect of wellbore geometry on integrated reservoir-wellbore flow

Extraction of coal seam gas (CSG) prior to mining is crucial for reducing the potential risks of gas outburst and explosions during underground coal mining as well as gas production purposes. Many numerical and experimental studies have been carried out to identify the factors affecting the gas productivity. These factors include coal properties, gas content and wellbore geometries. Two different flow conditions determine the gas production efficiency: The gas flow inside the wellbore injected from wall, and the flow through porous coal medium. The full understanding of simultaneous flow of fluids through reservoir and wellbore is critical for analysing the reservoir behaviour. However, previous studies examined the flow of these fluids separately. In this research, a large scale three-dimensional model for simulation of integrated reservoir-wellbore flow is developed to study the effect of wellbore geometry on flow characteristics and wellbore productivity. Four different wellbore diameters of 0.075, 0.10, 0.125 and 0.15 m as well as three different lengths of 50, 100, and 150 m were chosen to accomplish the parametric study of wellbore geometry. It is assumed that the wellbores were in a steady-state condition for two different single phase scenarios of water and methane gas flow. The simulation results were validated against the pressure drop models for internal single phase gas and water flow reported in the literature. The obtained results revealed that increasing the wellbore diameter led to reduction of fluid pressure in the coal seam. Regarding the effect of wellbore length, it was observed that at a specific distance from wellbore outlet, the pressure distribution is independent of the wellbore length and upstream effects. It is also shown that wellbore production could be enhanced by increasing the diameter and the length of wellbore for both gas and liquid flow. The developed integrated framework can be used further for study of any enhanced gas recovery method by changing the boundary conditions based on the physical model

Resonating Valence Bond wave function with molecular orbitals: application to first-row molecules

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant non-dynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be2, B2, C2, N2, O2, and F2) and heteronuclear (LiF, and CN) dimers for which strong non-dynamical correlations and/or weak van der Waals interactions are present