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Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

Drummond ND, Monserrat B, Lloyd-Williams JH, López Ríos P, Pickard CJ, Needs RJ - Nat Commun (2015)

Bottom Line: By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase.Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment.This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Lancaster University, Lancaster LA1 4YB, UK.

ABSTRACT
Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

No MeSH data available.


Atomic structures of the five H phases considered in this work.(a) P21/c-24, (b) C2/c-24, (c) Cmca-12, (d) Pc-48 and (e) Cmca-4. The blue dumbbells indicate short bonds between atoms (<0.8 Å). The white dumbbells indicate long bonds between atoms (< 0.9 Å). The red lines indicate close contacts between atoms (<1.2 Å) in the layered structures. P21/c-24 consists of molecules arranged on a distorted hexagonal close-packed lattice. C2/c-24, Cmca-12 and Cmca-4 consist of layers of molecules whose bonds lie within the planes of the layers, forming distorted hexagonal patterns, and we show top–down views of single layers. Pc-48 consists of alternate layers of isolated strongly bonded molecules and weakly bonded graphene-like sheets, and we show a top–down view of four layers. The structures are shown at a common DFT–PBE pressure (250 GPa).
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f1: Atomic structures of the five H phases considered in this work.(a) P21/c-24, (b) C2/c-24, (c) Cmca-12, (d) Pc-48 and (e) Cmca-4. The blue dumbbells indicate short bonds between atoms (<0.8 Å). The white dumbbells indicate long bonds between atoms (< 0.9 Å). The red lines indicate close contacts between atoms (<1.2 Å) in the layered structures. P21/c-24 consists of molecules arranged on a distorted hexagonal close-packed lattice. C2/c-24, Cmca-12 and Cmca-4 consist of layers of molecules whose bonds lie within the planes of the layers, forming distorted hexagonal patterns, and we show top–down views of single layers. Pc-48 consists of alternate layers of isolated strongly bonded molecules and weakly bonded graphene-like sheets, and we show a top–down view of four layers. The structures are shown at a common DFT–PBE pressure (250 GPa).

Mentions: Candidate structures for phases II, III and IV have been suggested by structure searches based on density functional theory (DFT)26272829303132, although it should be emphasized that none of these structures has been identified as being unambiguously correct. The candidate structures for phase II consist of packings of molecules with bond lengths almost identical to the zero-pressure value2627. We have modelled phase II using a molecular structure of P21/c symmetry with 24 atoms in the primitive unit cell, which we refer to as P21/c-24; see Fig. 1a. (We adopt the convention of labelling structures by their symmetry followed by the number of atoms per primitive cell.) P21/c-24 is the most stable structure found to date in static-lattice DFT within the pressure range appropriate for phase II, and its vibrational characteristics are also compatible with those of phase II. We model phase III using a C2/c-24 structure consisting of layers of molecules whose bonds lie within the planes of the layers, forming a distorted hexagonal pattern26; see Fig. 1b. This very stable structure can account for the high IR activity of phase III26. We also consider a molecular Cmca-12 structure26, which is similar to C2/c-24, but slightly denser; see Fig. 1c. We model phase IV by a Pc-48 structure2829, shown in Fig. 1d, which consists of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. This type of structure was predicted by Pickard and Needs26. Pc-48 can account for the occurrence of stiff and soft vibronic modes in phase IV, and its stabilization by temperature. Finally, we consider the Cmca-4 structure33, which has weaker molecular bonds than C2/c-24 and Cmca-12, and is shown in Fig. 1e. The main goals of our present work are to obtain accurate theoretical results for the relative stabilities of the P21/c-24, C2/c-24, Cmca-12, Pc-48 and Cmca-4 structures of H at pressures of 100–400 GPa and temperatures of 0–500 K, and to use these data to construct a temperature–pressure phase diagram of H. We have not considered phase I in our calculations, which is stable at low pressures, because an accurate description of this phase would require a full quantum treatment of the proton spin. Instead we focus our attention on the phase behaviour at higher pressures, where the candidate structures are such that the nuclei are highly localized and hence the motion of the protons is likely to be well-described by collective bosonic vibrational modes.


Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

Drummond ND, Monserrat B, Lloyd-Williams JH, López Ríos P, Pickard CJ, Needs RJ - Nat Commun (2015)

Atomic structures of the five H phases considered in this work.(a) P21/c-24, (b) C2/c-24, (c) Cmca-12, (d) Pc-48 and (e) Cmca-4. The blue dumbbells indicate short bonds between atoms (<0.8 Å). The white dumbbells indicate long bonds between atoms (< 0.9 Å). The red lines indicate close contacts between atoms (<1.2 Å) in the layered structures. P21/c-24 consists of molecules arranged on a distorted hexagonal close-packed lattice. C2/c-24, Cmca-12 and Cmca-4 consist of layers of molecules whose bonds lie within the planes of the layers, forming distorted hexagonal patterns, and we show top–down views of single layers. Pc-48 consists of alternate layers of isolated strongly bonded molecules and weakly bonded graphene-like sheets, and we show a top–down view of four layers. The structures are shown at a common DFT–PBE pressure (250 GPa).
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Related In: Results  -  Collection

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f1: Atomic structures of the five H phases considered in this work.(a) P21/c-24, (b) C2/c-24, (c) Cmca-12, (d) Pc-48 and (e) Cmca-4. The blue dumbbells indicate short bonds between atoms (<0.8 Å). The white dumbbells indicate long bonds between atoms (< 0.9 Å). The red lines indicate close contacts between atoms (<1.2 Å) in the layered structures. P21/c-24 consists of molecules arranged on a distorted hexagonal close-packed lattice. C2/c-24, Cmca-12 and Cmca-4 consist of layers of molecules whose bonds lie within the planes of the layers, forming distorted hexagonal patterns, and we show top–down views of single layers. Pc-48 consists of alternate layers of isolated strongly bonded molecules and weakly bonded graphene-like sheets, and we show a top–down view of four layers. The structures are shown at a common DFT–PBE pressure (250 GPa).
Mentions: Candidate structures for phases II, III and IV have been suggested by structure searches based on density functional theory (DFT)26272829303132, although it should be emphasized that none of these structures has been identified as being unambiguously correct. The candidate structures for phase II consist of packings of molecules with bond lengths almost identical to the zero-pressure value2627. We have modelled phase II using a molecular structure of P21/c symmetry with 24 atoms in the primitive unit cell, which we refer to as P21/c-24; see Fig. 1a. (We adopt the convention of labelling structures by their symmetry followed by the number of atoms per primitive cell.) P21/c-24 is the most stable structure found to date in static-lattice DFT within the pressure range appropriate for phase II, and its vibrational characteristics are also compatible with those of phase II. We model phase III using a C2/c-24 structure consisting of layers of molecules whose bonds lie within the planes of the layers, forming a distorted hexagonal pattern26; see Fig. 1b. This very stable structure can account for the high IR activity of phase III26. We also consider a molecular Cmca-12 structure26, which is similar to C2/c-24, but slightly denser; see Fig. 1c. We model phase IV by a Pc-48 structure2829, shown in Fig. 1d, which consists of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. This type of structure was predicted by Pickard and Needs26. Pc-48 can account for the occurrence of stiff and soft vibronic modes in phase IV, and its stabilization by temperature. Finally, we consider the Cmca-4 structure33, which has weaker molecular bonds than C2/c-24 and Cmca-12, and is shown in Fig. 1e. The main goals of our present work are to obtain accurate theoretical results for the relative stabilities of the P21/c-24, C2/c-24, Cmca-12, Pc-48 and Cmca-4 structures of H at pressures of 100–400 GPa and temperatures of 0–500 K, and to use these data to construct a temperature–pressure phase diagram of H. We have not considered phase I in our calculations, which is stable at low pressures, because an accurate description of this phase would require a full quantum treatment of the proton spin. Instead we focus our attention on the phase behaviour at higher pressures, where the candidate structures are such that the nuclei are highly localized and hence the motion of the protons is likely to be well-described by collective bosonic vibrational modes.

Bottom Line: By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase.Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment.This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Lancaster University, Lancaster LA1 4YB, UK.

ABSTRACT
Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

No MeSH data available.