2,327 research outputs found

### 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

### Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems

### 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

### Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas

We use variational quantum Monte Carlo to calculate the density-functional
exchange-correlation hole n_{xc}, the exchange-correlation energy density
e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron
gas systems in which strong density inhomogeneities are induced by a
cosine-wave potential. We compare our results with the local density
approximation and the generalized gradient approximation. It is found that the
nonlocal contributions to e_{xc} contain an energetically significant
component, the magnitude, shape, and sign of which are controlled by the
Laplacian of the electron density.Comment: 4 pages, 3 figure

### 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

### 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 account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kweeâ€“Zhangâ€“Krakauer functional in density functional theory. To study the closure of the band gap with increasing pressure, we perform 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 in the quasi-harmonic approximation, 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 (2012 Phys. Rev. Lett. 108, 146402) 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 P63/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 (2010 Phys. Rev. B 82 060101), which also reported a hexagonal-close-packed arrangement of hydrogen molecules

### {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit

We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm
dense uniform electron gas in the thermodynamic limit. By combining QMC data
with linear response theory we are able to remove finite-size errors from the
potential energy over the entire warm dense regime, overcoming the deficiencies
of the existing finite-size corrections by Brown \emph{et al.}~[PRL
\textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$
electrons enable us to compute the potential energy $V$ and the
exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with
an unprecedented accuracy of $|\Delta V|/|V|, |\Delta F_{xc}|/|F|_{xc} \sim
10^{-3}$. A comparison of our new data to the recent parametrization of
$F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals
significant deviations to the latter

### Nature of the metallization transition in solid hydrogen

We present an accurate study of the static-nucleus electronic energy band gap of solid molecular hydrogen at high pressure. The excitonic and quasiparticle gaps of the C 2 / c , P c , P b c n , and P 6 3 / m structures at pressures of 250, 300, and 350 GPa are calculated using the fixed-node diffusion quantum Monte Carlo (DMC) method. The difference between the mean-field and many-body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean-field gap of an infinite system to obtain an estimate of the many-body gap in the thermodynamic limit. By comparing our static-nucleus DMC energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen

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