Feynman-Hibbs potentials and path integrals for quantum Lennard-Jones systems: Theory and Monte Carlo simulations

Advances in the Dynamics of Adsorbate Diffusion on Metal Surfaces: Focus on Hydrogen and Oxygen

Adsorbates on metal surfaces are typically formed from the dissociative chemisorption of molecules occurring at gas-solid interfaces. These adsorbed species exhibit unique diffusion behaviors on metal surfaces, which are influenced by their translational energy. They play crucial roles in various fields, including heterogeneous catalysis and corrosion. This review examines recent theoretical advancements in understanding the diffusion dynamics of adsorbates on metal surfaces, with a specific emphasis on hydrogen and oxygen atoms. The diffusion processes of adsorbates on metal surfaces involve two energy transfer mechanisms: surface phonons and electron-hole pair excitations. This review also surveys new theoretical methods, including the characterization of the electron-hole pair excitation within electronic friction models, the acceleration of quantum chemistry calculations through machine learning, and the treatment of atomic nuclear motion from both quantum mechanical and classical perspectives. Furthermore, this review offers valuable insights into how energy transfer, nuclear quantum effects, supercell sizes, and the topography of potential energy surfaces impact the diffusion behavior of hydrogen and oxygen species on metal surfaces. Lastly, some preliminary research proposals are presented.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Interfacial Tensions, Solubilities, and Transport Properties of the H2/H2O/NaCl System: A Molecular Simulation Study

Data for several key thermodynamic and transport properties needed for technologies using hydrogen (H2), such as underground H2 storage and H2O electrolysis are scarce or completely missing. Force field-based Molecular Dynamics (MD) and Continuous Fractional Component Monte Carlo (CFCMC) simulations are carried out in this work to cover this gap. Extensive new data sets are provided for (a) interfacial tensions of H2 gas in contact with aqueous NaCl solutions for temperatures of (298 to 523) K, pressures of (1 to 600) bar, and molalities of (0 to 6) mol NaCl/kg H2O, (b) self-diffusivities of infinitely diluted H2 in aqueous NaCl solutions for temperatures of (298 to 723) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O, and (c) solubilities of H2 in aqueous NaCl solutions for temperatures of (298 to 363) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O. The force fields used are the TIP4P/2005 for H2O, the Madrid-2019 and the Madrid-Transport for NaCl, and the Vrabec and Marx for H2. Excellent agreement between the simulation results and available experimental data is found with average deviations lower than 10%.

Calculating Thermodynamic Factors for Diffusion Using the Continuous Fractional Component Monte Carlo Method

Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom's Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

A squarate-pillared titanium oxide quantum sieve towards practical hydrogen isotope separation

Separating deuterium from hydrogen isotope mixtures is of vital importance to develop nuclear energy industry, as well as other isotope-related advanced technologies. As one of the most promising alternatives to conventional techniques for deuterium purification, kinetic quantum sieving using porous materials has shown a great potential to address this challenging objective. From the knowledge gained in this field; it becomes clear that a quantum sieve encompassing a wide range of practical features in addition to its separation performance is highly demanded to approach the industrial level. Here, the rational design of an ultra-microporous squarate pillared titanium oxide hybrid framework has been achieved, of which we report the comprehensive assessment towards practical deuterium separation. The material not only displays a good performance combining high selectivity and volumetric uptake, reversible adsorption-desorption cycles, and facile regeneration in adsorptive sieving of deuterium, but also features a cost-effective green scalable synthesis using chemical feedstock, and a good stability (thermal, chemical, mechanical and radiolytic) under various working conditions. Our findings provide an overall assessment of the material for hydrogen isotope purification and the results represent a step forward towards next generation practical materials for quantum sieving of important gas isotopes.

Learning the Quantum Centroid Force Correction in Molecular Systems: A Localized Approach

Molecular mechanics (MM) is a powerful tool to study the properties of molecular systems in the fields of biology and materials science. With the development of ab initio force field and the application of ab initio potential energy surface, the nuclear quantum effect (NQE) is becoming increasingly important for the robustness of the simulation. However, the state-of-the-art path-integral molecular dynamics simulation, which incorporates NQE in MM, is still too expensive to conduct for most biological and material systems. In this work, we analyze the locality of NQE, using both analytical and numerical approaches, and conclude that NQE is an extremely localized phenomenon in nonreactive molecular systems. Therefore, we can use localized machine learning (ML) models to predict quantum force corrections both accurately and efficiently. Using liquid water as example, we show that the ML facilitated centroid MD can reproduce the NQEs in both the thermodynamical and the dynamical properties, with a minimal increase in computational time compared to classical molecular dynamics. This simple approach thus largely decreases the computational cost of quantum simulations, making it really accessible to the studies of large-scale molecular systems.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor-liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Isotope-selective pore opening in a flexible metal-organic framework

Flexible metal-organic frameworks that show reversible guest-induced phase transitions between closed and open pore phases have enormous potential for highly selective, energy-efficient gas separations. Here, we present the gate-opening process of DUT-8(Ni) that selectively responds to D₂, whereas no response is observed for H₂ and HD. In situ neutron diffraction directly reveals this pressure-dependent phase transition. Low-temperature thermal desorption spectroscopy measurements indicate an outstanding D₂-over-H₂ selectivity of 11.6 at 23.3 K, with high D₂ uptake. First-principles calculations coupled with statistical thermodynamics predict the isotope-selective gate opening, rationalized by pronounced nuclear quantum effects. Simulations suggest DUT-8(Ni) to remain closed in the presence of HT, while it also opens for DT and T₂, demonstrating gate opening as a highly effective approach for isotopolog separation.

Interatomic Interactions Responsible for the Solid-Liquid and Vapor-Liquid Phase Equilibria of Neon

The role of interatomic interactions on the solid-liquid and vapor-liquid equilibria of neon is investigated via molecular simulation using a combination of two-body ab initio, three-body, and quantum potentials. A new molecular simulation approach for determining phase equilibria is also reported and a comparison is made with the available experimental data. The combination of two-body plus quantum influences has the greatest overall impact on the accuracy of the prediction of solid-liquid equilibria. However, the combination of two-body + three-body + quantum interactions is required to approach an experimental accuracy for solid-liquid equilibria, which extends to pressures of tens of GPa. These interactions also combine to predict vapor-liquid equilibria to a very high degree of accuracy, including a very good estimate of the critical properties.

New force field for GCMC simulations of D2/H2 quantum sieving in pure silica zeolites

We report a study on adsorption and coadsorption of H₂ and D₂ in FAU, MFI and CHA pure silica zeolites having different pore sizes and shapes. Adsorption capacities, selectivities, enthalpies and entropies are determined by combining experiments and GCMC simulations. We show that the force fields available in the literature cannot predict the adsorption equilibria below 77 K with sufficient accuracy. Here we propose a new force field adjusted by using our experimental data obtained for the pure silica MFI zeolite at 65 K and 77 K. With this new force field, it is possible to predict the adsorption and coadsorption equilibria on the three zeolite structures in a temperature range between 47 and 77 K with satisfactory precision. We corroborate that the step appearing on the single adsorption isotherms in CHA is the result of a molecular rearrangement of the adsorbed phase due to the apparition of a new adsorption site characterized by weaker interactions of H₂ with the adsorbent. We conclude that the quantum sieving of H₂ and D₂ not only depends on the pore size but also on the pore shape, in particular, at high loading when the confinement effects become important.

Enhanced quantum sieving of hydrogen isotopes via molecular rearrangement of the adsorbed phase in chabazite

Coadsorption experiments reveal an unexpected increase of the D2/H2 selectivity with loading in pure silica chabazite at 47 K. This effect is correlated with the appearance of a step in the adsorption isotherms of H2 and D2. Grand canonical Monte Carlo simulations show that this phenomenon is related to a molecular rearrangement of the adsorbed phase induced by its strong confinement. In the case of a H2 and D2 mixture, this rearrangement favors the adsorption of D2 having a smaller size due to quantum effects.

Barely porous organic cages for hydrogen isotope separation

The separation of hydrogen isotopes for applications such as nuclear fusion is a major challenge. Current technologies are energy intensive and inefficient. Nanoporous materials have the potential to separate hydrogen isotopes by kinetic quantum sieving, but high separation selectivity tends to correlate with low adsorption capacity, which can prohibit process scale-up. In this study, we use organic synthesis to modify the internal cavities of cage molecules to produce hybrid materials that are excellent quantum sieves. By combining small-pore and large-pore cages together in a single solid, we produce a material with optimal separation performance that combines an excellent deuterium/hydrogen selectivity (8.0) with a high deuterium uptake (4.7 millimoles per gram).

Low-temperature hydrogen-graphite system revisited: Experimental study and Monte Carlo simulation

Hydrogen adsorption by microporous carbon materials attracts much attention for the past few decades, which has been stimulated by growing interest in hydrogen storage. Numerous studies of this topic based on molecular simulation technique have been reported. However, in many cases, the reliability of the results obtained with numerical methods is insufficient, which is a consequence of poor reference data used for fitting parameters of the fluid-fluid and fluid-solid potentials. This study is devoted to a detailed experimental investigation of the hydrogen-graphite system and its modeling with a kinetic Monte Carlo method at temperatures from 20 to 77 K and the bulk pressure from 0.1 Pa to 100 kPa. We found that the best fit of the bulk hydrogen equation of state corresponds to the 10-6 Lennard-Jones potential with the temperature dependent parameters to account for the quantum effects. The experimental hydrogen adsorption isotherms on the graphite surface were fitted with a high accuracy, which constitutes a firm basis of subsequent simulation of hydrogen adsorption in various nanoporous carbons and their pore size distribution analysis using a kernel generated with the developed approach.

Molecular Sieves for the Separation of Hydrogen Isotopes

Stable molecular hydrogen isotopes, D₂ and T₂, are both scarce and essential in several energy, industrial, and large-scale fundamental research applications. Due to the chemical similarity of these isotopes, their extraction and purification from hydrogen has relied for decades on expensive and energy-demanding processes. However, factoring in the phenomenon of quantum sieving could provide a new route for these separations. In this work, we have explored how to separate hydrogen isotopes by adsorption taking these quantum effects into account. To this end, we have conducted adsorption measurements to test our deuterium model and performed a widespread computational screening over 210 pure-silica zeolites for D₂/H₂ and T₂/H₂ separations. Based on low-coverage adsorption properties, a reduced set of zeolites have been singled out and their performance in terms of adsorption capacity, selectivity, and dynamic behavior have been assessed. Overall, the BCT-type zeolite clearly stands out for highly selective separations of both D₂ and T₂ over H₂, achieving the highest reported selectivities at cryogenic temperatures. We also identified other interesting zeolites for the separation of hydrogen isotopes that offer an alternative way to tackle similar isotopic separations by an aimed selection or design of porous materials.

Functional materials discovery using energy-structure-function maps

Molecular crystals cannot be designed in the same manner as macroscopic objects, because they do not assemble according to simple, intuitive rules. Their structures result from the balance of many weak interactions, rather than from the strong and predictable bonding patterns found in metal-organic frameworks and covalent organic frameworks. Hence, design strategies that assume a topology or other structural blueprint will often fail. Here we combine computational crystal structure prediction and property prediction to build energy-structure-function maps that describe the possible structures and properties that are available to a candidate molecule. Using these maps, we identify a highly porous solid, which has the lowest density reported for a molecular crystal so far. Both the structure of the crystal and its physical properties, such as methane storage capacity and guest-molecule selectivity, are predicted using the molecular structure as the only input. More generally, energy-structure-function maps could be used to guide the experimental discovery of materials with any target function that can be calculated from predicted crystal structures, such as electronic structure or mechanical properties.

Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line

Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.

Computer simulation of liquid-vapor coexistence of confined quantum fluids

The liquid-vapor coexistence (LV) of bulk and confined quantum fluids has been studied by Monte Carlo computer simulation for particles interacting via a semiclassical effective pair potential Veff(r) = VLJ + VQ, where VLJ is the Lennard-Jones 12-6 potential (LJ) and VQ is the first-order Wigner-Kirkwood (WK-1) quantum potential, that depends on β = 1∕kT and de Boer's quantumness parameter Λ=h/σ√mε, where k and h are the Boltzmann's and Planck's constants, respectively, m is the particle's mass, T is the temperature of the system, and σ and ε are the LJ potential parameters. The non-conformal properties of the system of particles interacting via the effective pair potential Veff(r) are due to Λ, since the LV phase diagram is modified by varying Λ. We found that the WK-1 system gives an accurate description of the LV coexistence for bulk phases of several quantum fluids, obtained by the Gibbs Ensemble Monte Carlo method (GEMC). Confinement effects were introduced using the Canonical Ensemble (NVT) to simulate quantum fluids contained within parallel hard walls separated by a distance Lp, within the range 2σ ≤ Lp ≤ 6σ. The critical temperature of the system is reduced by decreasing Lp and increasing Λ, and the liquid-vapor transition is not longer observed for Lp∕σ < 2, in contrast to what has been observed for the classical system.

Hypothetical high-surface-area carbons with exceptional hydrogen storage capacities: open carbon frameworks

A class of high-surface-area carbon hypothetical structures has been investigated that goes beyond the traditional model of parallel graphene sheets hosting layers of physisorbed hydrogen in slit-shaped pores of variable width. The investigation focuses on structures with locally planar units (unbounded or bounded fragments of graphene sheets), and variable ratios of in-plane to edge atoms. Adsorption of molecular hydrogen on these structures was studied by performing grand canonical Monte Carlo simulations with appropriately chosen adsorbent-adsorbate interaction potentials. The interaction models were tested by comparing simulated adsorption isotherms with experimental isotherms on a high-performance activated carbon with well-defined pore structure (approximately bimodal pore-size distribution), and remarkable agreement between computed and experimental isotherms was obtained, both for gravimetric excess adsorption and for gravimetric storage capacity. From this analysis and the simulations performed on the new structures, a rich spectrum of relationships between structural characteristics of carbons and ensuing hydrogen adsorption (structure-function relationships) emerges: (i) Storage capacities higher than in slit-shaped pores can be obtained by fragmentation/truncation of graphene sheets, which creates surface areas exceeding of 2600 m(2)/g, the maximum surface area for infinite graphene sheets, carried mainly by edge sites; we call the resulting structures open carbon frameworks (OCF). (ii) For OCFs with a ratio of in-plane to edge sites ≈1 and surface areas 3800-6500 m(2)/g, we found record maximum excess adsorption of 75-85 g of H(2)/kg of C at 77 K and record storage capacity of 100-260 g of H(2)/kg of C at 77 K and 100 bar. (iii) The adsorption in structures having large specific surface area built from small polycyclic aromatic hydrocarbons cannot be further increased because their energy of adsorption is low. (iv) Additional increase of hydrogen uptake could potentially be achieved by chemical substitution and/or intercalation of OCF structures, in order to increase the energy of adsorption. We conclude that OCF structures, if synthesized, will give hydrogen uptake at the level required for mobile applications. The conclusions define the physical limits of hydrogen adsorption in carbon-based porous structures.

Selective D2 adsorption enhanced by the quantum sieving effect on entangled single-wall carbon nanotubes

The quantum sieving effect of D(2) over H(2) is examined at 40 and 77 K by means of experiments and GCMC simulations, for two types of single-wall carbon nanotubes that are distinguishable by their unique entangled structures; (1) a well-bundled SWCNT and (2) loosely-assembled SWCNT produced by the super growth method (SG-SWCNT). Oxidized SWCNT samples of which the so-called internal sites are accessible for H(2) and D(2), are also studied. Experimental H(2) and D(2) adsorption properties on the well-bundled SWCNTs are compared with the simulated ones, revealing that pore-blocking and restricted diffusion of the molecules suppress the high selectivity of D(2) over H(2). The non-oxidized SG-SWCNT assembly shows the highest selectivity among the SWCNT samples, both at 40 and 77 K. The high selectivity of the SG-SWCNT assembly, which is pronounced even at 77 K, is ascribed to their unique assembly structure.

On the strength of the hydrogen-carbon interaction as deduced from physisorption

We deduce a new value for the potential well depth for the C-H2 interaction on the basis of experimental validations of isotherms of H2 and D2 predicted using independently characterized microstructural parameters. We use two carbons, one an activated carbon fiber whose structure has been recently characterized by us (Nguyen, T. X.; cohaut, N.; Bae, J.-S.; Bhatia, S. K. Langmuir 2008, 24, 7912) using hybrid reverse Monte Carlo simulation (HRMC) and the other the commercial Takeda 3A carbon molecular sieve whose pore size distribution is determined here from the 273 K CO2 adsorption isotherm. The conventional grand canonical Monte Carlo simulation technique incorporating a semiclassical Feynman and Hibbs (FH) potential approximation (FHGCMC) as well as path integral Monte Carlo calculations is employed to determine theoretical adsorption isotherms. It is found that curvature enhances the well depth for the LJ C-H2 interaction by a factor of 1.134 over that for a flat graphite surface, consistent with our recent study (Nguyen, T. X.; cohaut, N.; Bae, J.-S.; Bhatia, S. K. Langmuir 2008, 24, 7912). A value of the C-C well depth of 37.26 K, used for estimating the C-H2 well depth in conjunction with the Berthelot rules, with the Steele C-C well depth used for interaction with heavier gases (Ar, CO2 and CH4), leads to excellent agreement with experimental isotherms in all cases.

On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate.

A study of the pair and triplet structures of the quantum hard-sphere Yukawa fluid

The pair and triplet structures of the quantum hard-sphere Yukawa fluid, evaluated for equilateral and isosceles correlations in both the r and the k spaces for a range of conditions and with a particular focus on a region where the onset of increasing number fluctuations takes place (for densities 0.4<or=rho(N) ( *)<or=0.5, along the isotherm lambda(B) ( *)=0.6), are computed via path-integral Monte Carlo simulations in the canonical ensemble and an appropriate Ornstein-Zernike framework. For a given type of correlation (instantaneous, continuous linear response, and centroids), the structural results in r space display how the correlation functions approach each other with decreasing densities as a result of the increasing fluctuations. An attempt at obtaining improved isothermal compressibilities by using a simplified grand-canonical correction to the canonical pair radial functions is also discussed in detail. The results for triplets in k space are based on triplet direct correlation function calculations and are restricted to the higher-density region of the interval studied. Complementary results report an assessment of the performances of the Kirkwood superposition and the Jackson-Feenberg convolution. Comparisons with results also obtained in this work for the bare quantum and the classical hard-sphere fluids are made, allowing one to draw conclusions on the interplay between the inclusion of Yukawa attractions and the quantum diffraction effects in hard-sphere fluids.

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. II. Structural features

The structural features of the quantum hard-sphere system in the region of the fluid-face-centered-cubic-solid transition, for reduced number densities 0.45<rhoN*<or=0.9 (reduced de Broglie wavelengths lambdaB*<or=0.8), are presented. The parameters obtained with path-integral Monte Carlo simulations for the fluid, amorphous, and solid phases are related to the distinct sorts of pair correlations that can be defined in a path-integral quantum fluid (instantaneous, continuous linear response and centroids). These parameters cover the pair radial correlation functions, the configurational structure factors, the order parameters Q4 and Q6, and the radii of gyration of the path-integral necklaces. Also, the fluid static structure factors have been computed by solving appropriate Ornstein-Zernike equations. A number of significant regularities in the above parameters involving both sides of the crystallization line are reported, and a comparison with results for Lennard-Jones quantum systems that can be found in the literature is made. On the other hand, the main amplitudes of the quantum fluid structure factors follow a complex behavior along the crystallization line, which points to difficulties in identifying a neat rule, similar to that of Hansen-Verlet for classical fluids, for these quantum amplitudes. To complete this study a further analysis of the instantaneous and centroid triplet correlations in the vicinities of the fluid-face-centered-cubic-solid phase transition of hard spheres has been performed, and some interesting differences between the classical and quantum melting-freezing transition are observed.

Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.

Hydrogen storage in nanoporous carbon materials: myth and facts

We used Grand canonical Monte Carlo simulation to model the hydrogen storage in the primitive, gyroid, diamond, and quasi-periodic icosahedral nanoporous carbon materials and in carbon nanotubes. We found that none of the investigated nanoporous carbon materials satisfy the US Department of Energy goal of volumetric density and mass storage for automotive application (6 wt% and 45 kg H(2) m(-3)) at considered storage condition. Our calculations indicate that quasi-periodic icosahedral nanoporous carbon material can reach the 6 wt% at 3.8 MPa and 77 K, but the volumetric density does not exceed 24 kg H(2) m(-3). The bundle of single-walled carbon nanotubes can store only up to 4.5 wt%, but with high volumetric density of 42 kg H(2) m(-3). All investigated nanoporous carbon materials are not effective against compression above 20 MPa at 77 K because the adsorbed density approaches the density of the bulk fluid. It follows from this work that geometry of carbon surfaces can enhance the storage capacity only to a limited extent. Only a combination of the most effective structure with appropriate additives (metals) can provide an efficient storage medium for hydrogen in the quest for a source of "clean" energy.