Stable Solid Molecular Hydrogen above 900 K from a Machine-Learned Potential Trained with Diffusion Quantum Monte Carlo.

We survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with quantum Monte Carlo forces and energies. Besides the HCP and C2/c-24 phases, we find two new stable phases both with molecular centers in the Fmmm-4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm-4 phase has a reentrant melting line with a maximum at higher temperature (1450 K at 150 GPa) than previously estimated and crosses the liquid-liquid transition line around 1200 K and 200 GPa.

Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory.

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon-lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer.

The 2021 room-temperature superconductivity roadmap.

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation.

We develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born-Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron-ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born-Oppenheimer approximation. Based on the Kubo-Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure.

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion Monte Carlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2 eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330-380 GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.

Filament flexibility enhances power transduction of F-actin bundles.

The dynamic behavior of bundles of actin filaments growing against a loaded obstacle is investigated through a generalized version of the standard multifilament Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semiflexible discrete wormlike chains with a realistic value of the persistence length. By stochastic dynamic simulations, we study the relaxation of a bundle of Nf filaments with a staggered seed arrangement against a harmonic trap load in supercritical conditions. Thanks to the time scale separation between the wall motion and the filament size relaxation, mimicking realistic conditions, this setup allows us to extract a full load-velocity curve from a single experiment over the trap force/size range explored. We observe a systematic evolution of steady nonequilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L < Λ), characterized by the usual rigid filament load-velocity relationship V(F), and the flexible dynamic regime (L > Λ), where the velocity V(F, L) is an increasing function of the bundle length L at a fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore in the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to perfect load sharing.

Optical properties of high-pressure fluid hydrogen across molecular dissociation.

Optical properties of compressed fluid hydrogen in the region where dissociation and metallization is observed are computed by ab initio methods and compared with recent experimental results. We confirm that at T > 3,000 K, both processes are continuous, while at T < 1,500 K, the first-order phase transition is accompanied by a discontinuity of the dc conductivity and the thermal conductivity, while both the reflectivity and absorption coefficient vary rapidly but continuously. Our results support the recent analysis of National Ignition Facility (NIF) experiments [Celliers PM, et al. (2018) Science 361:677-682], which assigned the inception of metallization to pressures where the reflectivity is ∼0.3. Our results also support the conclusion that the temperature plateau seen in laser-heated diamond-anvil cell (DAC) experiments at temperatures higher than 1,500 K corresponds to the onset of optical absorption, not to the phase transition.

Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals.

We performed simulations for solid molecular hydrogen at high pressures (250 GPa ≤ P ≤ 500 GPa) along two isotherms at T = 200 K (phase III) and at T = 414 K (phase IV). At T = 200 K, we considered likely candidates for phase III, the C2c and Cmca12 structures, while at T = 414 K in phase IV, we studied the Pc48 structure. We employed both Coupled Electron-Ion Monte Carlo (CEIMC) and Path Integral Molecular Dynamics (PIMD). The latter is based on Density Functional Theory (DFT) with the van der Waals approximation (vdW-DF). The comparison between the two methods allows us to address the question of the accuracy of the exchange-correlation approximation of DFT for thermal and quantum protons without recurring to perturbation theories. In general, we find that atomic and molecular fluctuations in PIMD are larger than in CEIMC which suggests that the potential energy surface from vdW-DF is less structured than the one from quantum Monte Carlo. We find qualitatively different behaviors for systems prepared in the C2c structure for increasing pressure. Within PIMD, the C2c structure is dynamically partially stable for P ≤ 250 GPa only: it retains the symmetry of the molecular centers but not the molecular orientation; at intermediate pressures, it develops layered structures like Pbcn or Ibam and transforms to the metallic Cmca-4 structure at P ≥ 450 GPa. Instead, within CEIMC, the C2c structure is found to be dynamically stable at least up to 450 GPa; at increasing pressure, the molecular bond length increases and the nuclear correlation decreases. For the other two structures, the two methods are in qualitative agreement although quantitative differences remain. We discuss various structural properties and the electrical conductivity. We find that these structures become conducting around 350 GPa but the metallic Drude-like behavior is reached only at around 500 GPa, consistent with recent experimental claims.

On the properties of a bundle of flexible actin filaments in an optical trap.

We establish the statistical mechanics framework for a bundle of Nf living and uncrosslinked actin filaments in a supercritical solution of free monomers pressing against a mobile wall. The filaments are anchored normally to a fixed planar surface at one of their ends and, because of their limited flexibility, they grow almost parallel to each other. Their growing ends hit a moving obstacle, depicted as a second planar wall, parallel to the previous one and subjected to a harmonic compressive force. The force constant is denoted as the trap strength while the distance between the two walls as the trap length to make contact with the experimental optical trap apparatus. For an ideal solution of reactive filaments and free monomers at fixed free monomer chemical potential µ1, we obtain the general expression for the grand potential from which we derive averages and distributions of relevant physical quantities, namely, the obstacle position, the bundle polymerization force, and the number of filaments in direct contact with the wall. The grafted living filaments are modeled as discrete Wormlike chains, with F-actin persistence length ℓp, subject to discrete contour length variations ±d (the monomer size) to model single monomer (de)polymerization steps. Rigid filaments (ℓp = ∞), either isolated or in bundles, all provide average values of the stalling force in agreement with Hill's predictions Fs (H)=NfkBTln(ρ1/ρ1c)/d, independent of the average trap length. Here ρ1 is the density of free monomers in the solution and ρ1c its critical value at which the filament does not grow nor shrink in the absence of external forces. Flexible filaments (ℓp < ∞) instead, for values of the trap strength suitable to prevent their lateral escape, provide an average bundle force and an average trap length slightly larger than the corresponding rigid cases (few percents). Still the stalling force remains nearly independent on the average trap length, but results from the product of two strongly L-dependent contributions: the fraction of touching filaments ∝〈L〉(O.T.) (2) and the single filament buckling force ∝〈L〉(O.T.) (-2).

Liquid-liquid phase transition in hydrogen by coupled electron-ion Monte Carlo simulations.

The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron-ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25-30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.

Probabilistic Derivation of Spatiotemporal Correlation Functions in the Hydrodynamic Limit.

In this paper, we use probability theory to prove in suitable conditions the equivalence of equilibrium time correlation functions of microscopic density fields with the time correlation functions of local macroscopic density fields evolved by hydrodynamics in (approximate) phenomenological continuum theories of matter. We further discuss a useful and rigorous numerical algorithm, derived from this framework, to compute macroscopic space- and time-dependent behaviors (such as the hydrodynamical one) via molecular dynamics simulations.

Particle-Based Modeling of Living Actin Filaments in an Optical Trap.

We report a coarse-grained molecular dynamics simulation study of a bundle of parallel actin filaments under supercritical conditions pressing against a loaded mobile wall using a particle-based approach where each particle represents an actin unit. The filaments are grafted to a fixed wall at one end and are reactive at the other end, where they can perform single monomer (de)polymerization steps and push on a mobile obstacle. We simulate a reactive grand canonical ensemble in a box of fixed transverse area A, with a fixed number of grafted filaments N f , at temperature T and monomer chemical potential µ 1 . For a single filament case ( N f = 1 ) and for a bundle of N f = 8 filaments, we analyze the structural and dynamical properties at equilibrium where the external load compensates the average force exerted by the bundle. The dynamics of the bundle-moving-wall unit are characteristic of an over-damped Brownian oscillator in agreement with recent in vitro experiments by an optical trap setup. We analyze the influence of the pressing wall on the kinetic rates of (de)polymerization events for the filaments. Both static and dynamic results compare reasonably well with recent theoretical treatments of the same system. Thus, we consider the proposed model as a good tool to investigate the properties of a bundle of living filaments.

A semi-flexible model prediction for the polymerization force exerted by a living F-actin filament on a fixed wall.

We consider a single living semi-flexible filament with persistence length ℓp in chemical equilibrium with a solution of free monomers at fixed monomer chemical potential µ1 and fixed temperature T. While one end of the filament is chemically active with single monomer (de)polymerization steps, the other end is grafted normally to a rigid wall to mimic a rigid network from which the filament under consideration emerges. A second rigid wall, parallel to the grafting wall, is fixed at distance L < < ℓp from the filament seed. In supercritical conditions where monomer density ρ1 is higher than the critical density ρ1c, the filament tends to polymerize and impinges onto the second surface which, in suitable conditions (non-escaping filament regime), stops the filament growth. We first establish the grand-potential Ω(µ1, T, L) of this system treated as an ideal reactive mixture, and derive some general properties, in particular the filament size distribution and the force exerted by the living filament on the obstacle wall. We apply this formalism to the semi-flexible, living, discrete Wormlike chain model with step size d and persistence length ℓp, hitting a hard wall. Explicit properties require the computation of the mean force f̄i(L) exerted by the wall at L and associated potential f̄i(L)=-dWi(L)/dL on a filament of fixed size i. By original Monte-Carlo calculations for few filament lengths in a wide range of compression, we justify the use of the weak bending universal expressions of Gholami et al. [Phys. Rev. E 74, 041803 (2006)] over the whole non-escaping filament regime. For a filament of size i with contour length Lc = (i - 1) d, this universal form is rapidly growing from zero (non-compression state) to the buckling value fb(Lc,ℓp)=π(2)kBTℓp4Lc (2) over a compression range much narrower than the size d of a monomer. Employing this universal form for living filaments, we find that the average force exerted by a living filament on a wall at distance L is in practice L independent and very close to the value of the stalling force Fs (H)=(kBT/d)ln(ρˆ1) predicted by Hill, this expression being strictly valid in the rigid filament limit. The average filament force results from the product of the cumulative size fraction x=x(L,ℓp,ρˆ1), where the filament is in contact with the wall, times the buckling force on a filament of size Lc ≈ L, namely, Fs (H)=xfb(L;ℓp). The observed L independence of Fs (H) implies that x ∝ L(-2) for given (ℓp,ρˆ1) and x∝lnρˆ1 for given (ℓp, L). At fixed (L,ρˆ1), one also has x∝ℓp (-1) which indicates that the rigid filament limit ℓp → ∞ is a singular limit in which an infinite force has zero weight. Finally, we derive the physically relevant threshold for filament escaping in the case of actin filaments.

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations.

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to θ solvent.

We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the θ point and the good-solvent regime. We use the generalized free-volume theory, which takes into account the polymer-concentration dependence of the depletion thickness and of the polymer compressibility. This approach turns out to be quite accurate as long as q = Rg/Rc ≲ 1 (Rg is the radius of gyration of the polymer and Rc is the colloid radius). We find that, close to the θ point, the phase diagram is not very sensitive to solvent quality, while, close to the good-solvent region, changes of the solvent quality modify significantly the position of the critical point and of the binodals. We also analyze the phase behavior of aqueous solutions of charged colloids and polymers, using the approach proposed by Fortini et al. [J. Phys.: Condens. Matter 17, 7783 (2005)].

Accurate coarse-grained models for mixtures of colloids and linear polymers under good-solvent conditions.

A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach, groups of monomers are mapped onto a single pseudoatom (a blob) and the effective blob-blob interactions are obtained by requiring the model to reproduce some large-scale structural properties in the zero-density limit. We show that an accurate parametrization of the polymer-colloid interactions is obtained by simply introducing pair potentials between blobs and colloids. For the coarse-grained (CG) model in which polymers are modelled as four-blob chains (tetramers), the pair potentials are determined by means of the iterative Boltzmann inversion scheme, taking full-monomer (FM) pair correlation functions at zero-density as targets. For a larger number n of blobs, pair potentials are determined by using a simple transferability assumption based on the polymer self-similarity. We validate the model by comparing its predictions with full-monomer results for the interfacial properties of polymer solutions in the presence of a single colloid and for thermodynamic and structural properties in the homogeneous phase at finite polymer and colloid density. The tetramer model is quite accurate for q ≲ 1 (q=Rg/Rc, where Rg is the zero-density polymer radius of gyration and Rc is the colloid radius) and reasonably good also for q = 2. For q = 2, an accurate coarse-grained description is obtained by using the n = 10 blob model. We also compare our results with those obtained by using single-blob models with state-dependent potentials.

Consistent coarse-graining strategy for polymer solutions in the thermal crossover from good to θ solvent.

We extend our previously developed coarse-graining strategy for linear polymers with a tunable number n of effective atoms (blobs) per chain [G. D'Adamo et al., J. Chem. Phys. 137, 024901 (2012)] to polymer systems in thermal crossover between the good-solvent and the θ regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e., not too close to the θ point, for a wide range of chain volume fractions Φ = c∕c* (c* is the overlap concentration), up to Φ ≈ 30. Scaling crossover functions for global properties of the solution are obtained by Monte Carlo simulations of the Domb-Joyce model with suitably rescaled on-site repulsion. They provide the input data to develop a minimal coarse-grained model with four blobs per chain (tetramer model). As in the good-solvent case, the coarse-grained model potentials are derived at zero density, thus avoiding the inconsistencies related to the use of state-dependent potentials. We find that the coarse-grained model reproduces the properties of the underlying, full-monomer system up to some reduced density Φ which increases when lowering the temperature towards the θ state. Close to the lower-temperature crossover boundary, the tetramer model is accurate at least up to Φ ~/= 10, while near the good-solvent regime reasonably accurate results are obtained up to Φ ~/= 2. The density region in which the coarse-grained model is predictive can be enlarged by developing coarse-grained models with more blobs per chain. We extend the strategy used in the good-solvent case to the crossover regime. This requires a proper treatment of the length rescalings as before, but also a proper temperature redefinition as the number of blobs is increased. The case n = 10 is investigated in detail. We obtain the potentials for such finer-grained model starting from the tetramer ones. Comparison with full-monomer results shows that the density region in which accurate predictions can be obtained is significantly wider than that corresponding to the tetramer case.

Predicting the thermodynamics by using state-dependent interactions.

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distribution functions of the original system as accurately as possible. We consider standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the low-density regime and polymer solutions under good-solvent conditions. Moreover, we show that the state-dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.

Nuclear quantum effects and nonlocal exchange-correlation functionals applied to liquid hydrogen at high pressure.

Using first-principles molecular dynamics, we study the influence of nuclear quantum effects (NQEs) and nonlocal exchange-correlation density functionals (DFs) near molecular dissociation in liquid hydrogen. NQEs strongly influence intramolecular properties, such as bond stability, and are thus an essential part of the dissociation process. Moreover, by including DFs that account for either the self-interaction error or dispersion interactions, we find a much better description of molecular dissociation and metallization than previous studies based on classical protons and/or local or semilocal DFs. We obtain excellent agreement with experimentally measured optical properties along Hugoniot curves for precompressed states, and while we still find a first-order liquid-liquid transition at low temperatures, transition pressures are increased by more than 100 GPa.