The re-entrant transition from the molecular to atomic phases of dense fluids: The case of hydrogen.

A simple phenomenological thermodynamic model is developed to describe the chemical bonding and unbonding in homonuclear diatomic systems. This model describes the entire phase diagram of dimer-forming systems and shows a transition from monomers to dimers, with monomers favored at both very low and very high pressures, as well as at high temperatures. In the context of hydrogen, the former region corresponds to hydrogen present in most interstellar gas clouds, while the latter is associated with the long sought-after fluid metallic phase. The model predicts a molecular to atomic fluid transition in dense deuterium, which is in agreement with recently reported experimental measurements.

H2 Chemical Bond in a High-Pressure Crystalline Environment.

We show that the hydrogen in metal superhydride compounds can adopt two distinct states-atomic and molecular. At low pressures, the maximum number of atomic hydrogens is typically equal to the valency of the cation; additional hydrogens pair to form molecules with electronic states far below the Fermi energy causing low-symmetry structures with large unit cells. At high pressures, molecules become unstable, and all hydrogens become atomic. This study uses density functional theory, adopting BaH4 as a reference compound, which is compared with other stoichiometries and other cations. Increased temperature and zero-point motion also favor high-symmetry atomic states, and picosecond-timescale breaking and remaking of the bond permutations via intermediate H3- units.

From Atoms to Colloids: Does the Frenkel Line Exist in Discontinuous Potentials?

The Frenkel line has been proposed as a crossover in the fluid region of phase diagrams between a "nonrigid" and a "rigid" fluid. It is generally described as a crossover in the dynamical properties of a material and as such has been described theoretically using a very different set of markers from those with which is it investigated experimentally. In this study, we have performed extensive calculations using two simple yet fundamentally different model systems: hard spheres and square-well potentials. The former has only hardcore repulsion, while the latter also includes a simple model of attraction. We computed and analyzed a series of physical properties used previously in simulations and experimental measurements and discuss critically their correlations and validity as to being able to uniquely and coherently locate the Frenkel line in discontinuous potentials.

Chemically Assisted Precompression of Hydrogen Molecules in Alkaline-Earth Tetrahydrides.

Through a series of high pressure diamond anvil experiments, we report the synthesis of alkaline earth (Ca, Sr, Ba) tetrahydrides, and investigate their properties through Raman spectroscopy, X-ray diffraction, and density functional theory calculations. The tetrahydrides incorporate both atomic and quasi-molecular hydrogen, and we find that the frequency of the intramolecular stretching mode of the H2δ- units downshifts from Ca to Sr and to Ba upon compression. The experimental results indicate that the larger the host cation, the longer the H2δ- bond. Analysis of the electron localization function (ELF) demonstrates that the lengthening of the H-H bond is caused by the charge transfer from the metal to H2δ- and by the steric effect of the metal host on the H-H bond. This effect is most prominent for BaH4, where the precompression of H2δ- units at 50 GPa results in bond lengths comparable to that of pure H2 above 275 GPa.

Krypton and the Fundamental Flaw of the Lennard-Jones Potential.

We have performed a series of neutron scattering experiments on supercritical krypton. Our data and analysis allow us to characterize the Frenkel line crossover in this model monatomic fluid. The data from our measurements was analyzed using Empirical Potential Structure Refinement to determine the short- and medium-range structure of the fluids. We find evidence for several shells of neighbors which form approximately concentric rings of density about each atom. The ratio of second to first shell radius is significantly larger than in any crystal structure. Modeling krypton using a Lennard-Jones potential is shown to give significant errors, notably that the liquid is overstructured. The true potential appears to be longer ranged and with a softer core than the 6-12 powerlaws permit.

Fitting the reproduction number from UK coronavirus case data and why it is close to 1.

We present a method for rapid calculation of coronavirus growth rates and [Formula: see text]-numbers tailored to publicly available UK data. We assume that the case data comprise a smooth, underlying trend which is differentiable, plus systematic errors and a non-differentiable noise term, and use bespoke data processing to remove systematic errors and noise. The approach is designed to prioritize up-to-date estimates. Our method is validated against published consensus [Formula: see text]-numbers from the UK government and is shown to produce comparable results two weeks earlier. The case-driven approach is combined with weight-shift-scale methods to monitor trends in the epidemic and for medium-term predictions. Using case-fatality ratios, we create a narrative for trends in the UK epidemic: increased infectiousness of the B1.117 (Alpha) variant, and the effectiveness of vaccination in reducing severity of infection. For longer-term future scenarios, we base future [Formula: see text] on insight from localized spread models, which show [Formula: see text] going asymptotically to 1 after a transient, regardless of how large the [Formula: see text] transient is. This accords with short-lived peaks observed in case data. These cannot be explained by a well-mixed model and are suggestive of spread on a localized network. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

How to determine solubility in binary mixtures from neutron scattering data: The case of methane and water.

It has recently been discovered that, when subjected to moderate amounts of pressure, methane dissolves in water to form binary mixtures of up to 40% molar methane. No significant solubility of water in methane is known. In these mixtures, the water hydrogen-bond network is largely complete and surrounds the methane molecules. The discovery of this dense mixture has once again highlighted the technical difficulties involved in accurately describing and sampling mixing phenomena both computationally and experimentally. Here, we present a systematic and critical study of the methods employed to characterize binary mixtures and their robustness. This study highlights the requirements needed to develop a quantitative understanding, and it proposes new and more accessible measures of miscibility to investigators, particularly for in silico analysis.

Frenkel Line in Nitrogen Terminates at the Triple Point.

Recent studies on supercritical nitrogen revealed clear changes in structural markers and dynamical properties when the coordination number approaches its maximum value. The line in P and T space where these changes occur is referred to as the Frenkel line. Here, we qualitatively reproduce such changes in the supercritical regime using the popular "optimized potential for liquid simulation" (OPLS) classical force field for molecular dynamics. Unfortunately, at 160 K, OPLS nitrogen predicts sublimation rather than producing a liquid phase; therefore, we developed our own force field to achieve quantitative agreement with experimental data. We confirm the asymptotic behavior of the coordination number on crossing the Frenkel line and note an associated change in the diffusion constant, consistent with the non-rigid to rigid liquid-like character of the "transition". The simulations allow us to track the Frenkel line to subcritical temperatures and demonstrate that it terminates at the triple point. This establishes the experimentally measurable changes, which could unequivocally determine the Frenkel line in other systems.

Isotope Quantum Effects in the Metallization Transition in Liquid Hydrogen.

Quantum effects in condensed matter normally only occur at low temperatures. Here we show a large quantum effect in high-pressure liquid hydrogen at thousands of Kelvins. We show that the metallization transition in hydrogen is subject to a very large isotope effect, occurring hundreds of degrees lower than the equivalent transition in deuterium. We examined this using path integral molecular dynamics simulations which identify a liquid-liquid transition involving atomization, metallization, and changes in viscosity, specific heat, and compressibility. The difference between H_{2} and D_{2} is a quantum mechanical effect that can be associated with the larger zero-point energy in H_{2} weakening the covalent bond. Our results mean that experimental results on deuterium must be corrected before they are relevant to understanding hydrogen at planetary conditions.

Pressure-Induced Synthesis and Properties of an H2S-H2Se-H2 Molecular Alloy.

The chalcogens are known to react with one another to form interchalcogens, which exhibit a diverse range of bonding and conductive behavior due to the difference in electronegativity between the group members. Through a series of high-pressure diamond anvil experiments combined with density functional theory calculations, we report the synthesis of an S-Se hydride. At pressures above 4 GPa we observe the formation of a single solid composed of both H2Se and H2S molecular units. Further compression in a hydrogen medium leads to the formation of an alloyed compound (H2SxSe1-x)2H2, after which there is a sequence of pressure-induced phase transitions associated with the arrested rotation of molecules. At pressures above 50 GPa, there is a symmetrization of hydrogen bonds concomitantly with a closing band gap and increased reflectivity of the compound, indicative of a transition to a metallic state.

High pressure hydrogen and the Potts model on a triangular lattice.

We present Monte Carlo studies and analysis of the frustrated antiferromagnetic Potts model of a triangular lattice. This Potts model shows a remarkably rich range of structures, and striking similarities to the high pressure phases of hydrogen which are typified by hexagonal close packed layered structures [1]. There are four known H2molecular phases, all of which are isostructural to within the resolution of x-ray diffraction. Experimentally, the phase lines have been mapped by spectroscopy, which cannot reveal the structure. Study by density functional theory (DFT) has suggested a large number of candidate structures, based on the hexagonal-close packing of H2molecules. The Potts model exhibits structures similar to DFT candidate hydrogen phases I, II and III: the range of different Potts model structures suggests that the hydrogen system in the 'phase II' region, may exhibit more than a single phase. It also suggests reorientational excitations which may be detectable in spectroscopy.

Synthesis of Weaire-Phelan Barium Polyhydride.

By combining pressures up to 50 GPa and temperatures of 1200 K, we synthesize the novel barium hydride, Ba8H46, stable down to 27 GPa. We use Raman spectroscopy, X-ray diffraction, and first-principles calculations to determine that this compound adopts a highly symmetric Pm3¯n structure with an unusual 534:1 hydrogen-to-barium ratio. This singular stoichiometry corresponds to the well-defined type-I clathrate geometry. This clathrate consists of a Weaire-Phelan hydrogen structure with the barium atoms forming a topologically close-packed phase. In particular, the structure is formed by H20 and H24 clathrate cages showing substantially weakened H-H interactions. Density functional theory (DFT) demonstrates that cubic Pm3¯n Ba8H46 requires dynamical effects to stabilize the H20 and H24 clathrate cages.

Understanding high pressure molecular hydrogen with a hierarchical machine-learned potential.

The hydrogen phase diagram has several unusual features which are well reproduced by density functional calculations. Unfortunately, these calculations do not provide good physical insights into why those features occur. Here, we present a fast interatomic potential, which reproduces the molecular hydrogen phases: orientationally disordered Phase I; broken-symmetry Phase II and reentrant melt curve. The H2 vibrational frequency drops at high pressure because of increased coupling between neighbouring molecules, not bond weakening. Liquid H2 is denser than coexisting close-packed solid at high pressure because the favored molecular orientation switches from quadrupole-energy-minimizing to steric-repulsion-minimizing. The latter allows molecules to get closer together, without the atoms getting closer, but cannot be achieved within in a close-packed layer due to frustration. A similar effect causes negative thermal expansion. At high pressure, rotation is hindered in Phase I, such that it cannot be regarded as a molecular rotor phase.

Effect of school closures on mortality from coronavirus disease 2019: old and new predictions.

OBJECTIVE: To replicate and analyse the information available to UK policymakers when the lockdown decision was taken in March 2020 in the United Kingdom. DESIGN: Independent calculations using the CovidSim code, which implements Imperial College London's individual based model, with data available in March 2020 applied to the coronavirus disease 2019 (covid-19) epidemic. SETTING: Simulations considering the spread of covid-19 in Great Britain and Northern Ireland. POPULATION: About 70 million simulated people matched as closely as possible to actual UK demographics, geography, and social behaviours. MAIN OUTCOME MEASURES: Replication of summary data on the covid-19 epidemic reported to the UK government Scientific Advisory Group for Emergencies (SAGE), and a detailed study of unpublished results, especially the effect of school closures. RESULTS: The CovidSim model would have produced a good forecast of the subsequent data if initialised with a reproduction number of about 3.5 for covid-19. The model predicted that school closures and isolation of younger people would increase the total number of deaths, albeit postponed to a second and subsequent waves. The findings of this study suggest that prompt interventions were shown to be highly effective at reducing peak demand for intensive care unit (ICU) beds but also prolong the epidemic, in some cases resulting in more deaths long term. This happens because covid-19 related mortality is highly skewed towards older age groups. In the absence of an effective vaccination programme, none of the proposed mitigation strategies in the UK would reduce the predicted total number of deaths below 200 000. CONCLUSIONS: It was predicted in March 2020 that in response to covid-19 a broad lockdown, as opposed to a focus on shielding the most vulnerable members of society, would reduce immediate demand for ICU beds at the cost of more deaths long term. The optimal strategy for saving lives in a covid-19 epidemic is different from that anticipated for an influenza epidemic with a different mortality age profile.

Composition-Gradient-Mediated Semiconductor-Metal Transition in Ternary Transition-Metal-Dichalcogenide Bilayers.

The semiconductor-metal transition (SMT) enables multiple applications of one single material, especially in modern devices. How to control it remains one of the most intriguing questions in material physics/chemistry, especially in two-dimensional layered materials. In this work, we report realization of SMT in MoS2-xOx bilayers, driven by the concentration gradient of the chalcogen atom across the van der Waals (vdW) gap of the disordered bilayers. Using the cluster expansion method, we determined that either semiconducting (stable) or metallic states (metastable) can be realized in MoS2-xOx bilayers with the same composition. Machine learning analysis revealed that the concentration gradient of the chalcogen atom across the vdW gap is the leading fingerprint of SMT, with structural distortion induced by atom mixing being a significant secondary factor. The electronic origin of the SMT is the broadening of the Mo dz2 and O pz bands, accompanied by the redistribution of the d electrons. This in-vdW-gap composition-gradient-driven SMT phenomenon also applies to MoSe2-xOx and MoTe2-xOx bilayers. The present work provides an alternative mechanism of SMT and demonstrates that the composition gradient across the vdW gap in the bilayer materials can be another degree of freedom to tune the band gaps without introducing extrinsic elements. Our findings will benefit the material design for small-scale and energy-efficient electronic devices.

Quantitative Rotational to Librational Transition in Dense H2 and D2.

Raman spectroscopy demonstrates that the rotational spectrum of solid hydrogen, and its isotope deuterium, undergoes profound transformations upon compression while still remaining in phase I. We show that these changes are associated with a loss of quantum character in the rotational modes and that the angular momentum J gradually ceases to be a good quantum rotational number. Through isotopic comparisons of the rotational Raman contributions, we reveal that hydrogen and deuterium evolve from a quantum rotor to a harmonic oscillator. We find that the mechanics behind this transformation can be well-described by a quantum-mechanical single inhibited rotor, accurately reproducing the striking spectroscopic changes observed in phase I.

Counterintuitive effects of isotopic doping on the phase diagram of H2-HD-D2 molecular alloy.

Molecular hydrogen forms the archetypical quantum solid. Its quantum nature is revealed by behavior which is classically impossible and by very strong isotope effects. Isotope effects between [Formula: see text], [Formula: see text], and HD molecules come from mass difference and the different quantum exchange effects: fermionic [Formula: see text] molecules have antisymmetric wavefunctions, while bosonic [Formula: see text] molecules have symmetric wavefunctions, and HD molecules have no exchange symmetry. To investigate how the phase diagram depends on quantum-nuclear effects, we use high-pressure and low-temperature in situ Raman spectroscopy to map out the phase diagrams of [Formula: see text]-HD-[Formula: see text] with various isotope concentrations over a wide pressure-temperature (P-T) range. We find that mixtures of [Formula: see text], HD, and [Formula: see text] behave as an isotopic molecular alloy (ideal solution) and exhibit symmetry-breaking phase transitions between phases I and II and phase III. Surprisingly, all transitions occur at higher pressures for the alloys than either pure [Formula: see text] or [Formula: see text] This runs counter to any quantum effects based on isotope mass but can be explained by quantum trapping of high-kinetic energy states by the exchange interaction.

Phase diagram of the frustrated FCC antiferromagnet from effective-field theory.

The phase diagram of a face-centred cubic (FCC) antiferromagnet is calculated from the effective field theory (EFT) of Honmura and Kaneyoshi taking into account not only the effect of interaction with nearest neighbours, J 1, but also the effect of second neighbours, J 2. The phase diagram for the nearest neighbour case away from the triple point, which in our calculations is predicted to be at H = 4 and T = 0, is close to cluster variation method (CVM) and Monte Carlo (MC) results. Similar to MC and CVM predictions, we observe that the increasing second neighbours interaction pushes the triple point towards zero field. Our calculations also show that for α = -J 2/J 1 = 0.3, the triple point merges with the transition point of the L10 phase, one of the ground states, at H = 0 and changes the nature of phase transition from first- to second-order, in full agreement with Monte Carlo predictions. The phase diagram with the effect of second neighbours calculated for several values of α are in good agreement with available MC and CVM predictions.

On the chain-melted phase of matter.

Various single elements form incommensurate crystal structures under pressure, where a zeolite-type "host" sublattice surrounds a "guest" sublattice comprising 1D chains of atoms. On "chain melting," diffraction peaks from the guest sublattice vanish, while those from the host remain. Diffusion of the guest atoms is expected to be confined to the channels in the host sublattice, which suggests 1D melting. Here, we present atomistic simulations of potassium to investigate this phenomenon and demonstrate that the chain-melted phase has no long-ranged order either along or between the chains. This 3D disorder provides the extensive entropy necessary to make the chain melt a true thermodynamic phase of matter, yet with the unique property that diffusion remains confined to 1D only. Calculations necessitated the development of an interatomic forcefield using machine learning, which we show fully reproduces potassium's phase diagram, including the chain-melted state and 14 known phase transitions.

Stacking Characteristics of Close Packed Materials.

It is shown that the enthalpy of any close packed structure for a given element can be characterized as a linear expansion in a set of continuous variables α_{n}, which describe the stacking configuration. This enables us to represent the infinite, discrete set of stacking sequences within a finite, continuous space of the expansion parameters H_{n}. These H_{n} determine the stable structure and vary continuously in the thermodynamic space of pressure, temperature, or composition. The continuity of both spaces means that only transformations between stable structures adjacent in the H_{n} space are possible, giving the model predictive as well as descriptive ability. We calculate the H_{n} using density functional theory (DFT)and interatomic potentials for a range of materials. Some striking results are found: e.g., the Lennard-Jones potential model has 11 possible stable structures and over 50 phase transitions as a function of cutoff range. The very different phase diagrams of Sc, Tl, Y, and the lanthanides are understood within a single theory. We find that the widely reported 9R-fcc transition is not allowed in equilibrium thermodynamics, and in cases where it has been reported in experiments (Li, Na), we show that DFT theory is also unable to predict it.