Rational Regulation of Optimal Oxygen Vacancy Concentrations on VO2 for Superior Aqueous Zinc-Ion Battery Cathodes.

VO2 with its special tunnel structure and high theoretical capacity is an ideal candidate for cathode materials for aqueous zinc-ion batteries (ZIBs). However, the slow kinetics and structural instability due to the strong electrostatic interactions between the host structure of VO2 and Zn2+ hinder its application. Defect engineering is a well-recognized strategy for improving the intrinsic ion-electron dynamics and structural stability of this material. However, the preparation of oxygen vacancies poses significant difficulties, and it is challenging to control their concentration effectively. Excessive or insufficient vacancy concentration can have a negative effect on the cathode material. Herein, we propose electrode materials with controlled oxygen vacancies prepared in situ on carbon nanofibers (CNF) by a simple, one-step hydrothermal process (Ov-VO2@CNF). This method can balance the adsorption energy and migration energy barrier easily, and we maximized the adsorption energy of Zn2+ while minimizing the adsorption energy barrier. Notably, the Ov2-VO2@CNF electrode delivered a high specific capacity (over 450 mAh g-1 at 0.1 A g-1) and excellent cycle stability (318 mAh g-1 at 5 A g-1 capacity after 2000 cycles with a capacity retention of 85%). This rational design of precisely regulated defect engineering provides a way to obtain advanced electrode materials with excellent comprehensive properties.

Synthesis and Mechanism of 1D ZnO Based on Alkaline Dissolution-Conversion Strategy of High Stable and Soluble ɛ-Zn(OH)2.

A high soluble and stable ɛ-Zn(OH)2 precursor is synthesized at below room temperature to efficiently prepare ZnO whiskers. The experimental results indicate that the formation of ZnO whiskers is carried out mainly via two steps: the formation of ZnO seeds from ɛ-Zn(OH)2 via the in situ solid conversion, and the following growth of whiskers via dissolution-precipitation route. The decrease of temperature from 25 to 5 °C promotes the formation of ɛ-Zn(OH)2 with higher solubility and stability, which balances the conversion and dissolution rates of precursor. The Rietveld refinement, DFT calculations and MD simulations reveal that the primary reason for these characteristics is the expansion of ɛ-Zn(OH)2 lattice due to temperature, causing difficulties in the dehydration of adjacent ─OH. Simultaneously, the larger specific surface area favors the dissolution of ɛ-Zn(OH)2. Based on this precursor, well-dispersed ZnO whiskers with 9.82 µm in length, 242.38 nm in diameter, and an average aspect ratio of 41 are successfully synthesized through a SDSN-assisted hydrothermal process at 80 °C. The process has an extremely high solid content of 2.5% (mass ratio of ZnO to solution) and an overall yield of 92%, which offers a new approach for the scaled synthesis of high aspect ratio ZnO whiskers by liquid-phase method.

Theoretical insights into surface-phase transition and ion competition during alkali ion intercalation on the Cu4Se4 nanosheet.

The development of stable and efficient electrode materials is imperative and also indispensable for further commercialization of sodium/potassium-ion batteries (SIBs/PIBs) and new detrimental issues such as proton intercalation arise when utilizing aqueous electrolytes. Herein the electrochemical performance of the Cu4Se4 nanosheet was determined for both organic and aqueous SIBs and PIBs. By means of density functional theory calculation, Na+, K+ and H+ intercalations onto both sides of the Cu4Se4 nanosheet were revealed. The Cu4Se4 nanosheet well maintains its metallic electronic conductivity and the changes in lateral lattice parameters are within 4.66% during the whole Na+/K+ intercalation process for both SIBS and PIBs. The theoretical maximum Na/K storage capacity of 188.07 mA h g-1 can be achieved by stabilized second-layer adsorption of Na+/K+. The migration barriers of Na and K atoms on the Cu4Se4 nanosheet are 0.270 and 0.173 eV, respectively. It was discovered that Na/K- intercalation in the first layer is accompanied by a first-order surface phase transition, resulting in an intercalation voltage plateau of 0.659/0.756 V, respectively. The region of the two-surface phase coexistence for PIBs, is shifted toward a lower coverage when compared with that for SIBs. The partially protonated Cu4Se4 nanosheet (HxCu4Se4, x ≤ 10/9) was revealed to be structurally and thermodynamically stable. While the partially protonated Cu4Se4 nanosheet is favorable in acidic electrolytes (pH = 0) when protons and Na/K ions compete, we showed that Na+/K+ intercalated products may be preferred over H+ at low coverages in alkali electrolyte (pH = 14). However, the proton intercalation substantially decreases the battery capacity in aqueous SIBs and PIBs. Our work not only identifies the promising performance of Cu4Se4 nanosheets as an electrode material of SIBs and PIBs, but also provides a computational method for aqueous metal-ion batteries.

Possibilities of Controlling the Quantum States of Hole Qubits in an Ultrathin Germanium Layer Using a Magnetic Substrate: Results from ab Initio Calculations.

Using density functional theory in the noncollinear approximation, the behavior of quantum states of hole qubits in a Ge/Co:ZnO system was studied in this work. A detailed analysis of the electronic structure and the distribution of total charge density and hole states was carried out. It was shown that in the presence of holes, the energetically more favorable quantum state is the state |0˃, in contrast to the state |1˃ when there is no hole in the system. The favorability of hole states was found to be dependent on the polarity of the applied electric field.

A theoretical descriptor for screening efficient NO reduction electrocatalysts from transition-metal atoms on N-doped BP monolayer.

An electrochemical nitric oxide (NO) reduction reaction (NORR) is proposed as an attractive method for simultaneous realization of NO removal and ammonia (NH3) synthesis. Here, the potentials of 29 transition-metal atoms anchored on the nitrogen-doped BP monolayer (MN3/BP) as efficient NORR catalysts are systematically examined using first-principles calculations. Combining the adsorption Gibbs free energies of the N and OH species, a simple descriptor is constructed and a volcano plot of the NORR limiting potentials on the single atom catalysts (SACs) is established. Consequently, the MoN3/BP and IrN3/BP SACs are picked out as promising NORR electrocatalysts for NH3 synthesis with the limiting potentials of -0.10 V and -0.06 V, respectively. Their corresponding rate constants are significantly larger than or close to that of the excellent Pt(111) surface. The electronic analysis shows that the Mo-4d or Ir-5d orbitals can be well hybridized with the NO-2p orbitals, sufficiently activating the adsorbed NO species. Particularly, the MoN3/BP and IrN3/BP SACs possess high thermal stabilities and can be easily synthesized by using MoCl3 and IrCl3 as precursors, respectively. This work not only offers a simple descriptor to efficiently design NORR electrocatalysts but also provides a comprehensive atomic understanding on the mechanism of NO-to-NH3 conversion.

Enhanced catalytic performance of pillared δ-MnO2 with enlarged layer spaces for lithium- and sodium-oxygen batteries: a theoretical investigation.

Facing the challenge of increasingly severe environmental issues, many researchers are committed to seeking "post lithium-ion batteries" that can replace fossil fuels, one of which is alkali-metal-oxygen batteries. Nevertheless, the main bottleneck restricting the development of these batteries is the need for suitable catalysts to facilitate the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). In this study, we attempt to modify the catalytic performance of δ-MnO2 for lithium- and sodium-oxygen batteries (LOBs and SOBs) by constructing 1,4-benzenedisulfonic acid, 2-chloro-1,4-benzenedisulfonic acid, and 2-fluoro-1,4-benzenedisulfonic acid pillared structures (H-, Cl-, and F-MnO2). Their dynamic stability and catalytic mechanism have been explored by employing density functional theory (DFT). H-MnO2 possesses a theoretical discharge voltage of 2.645 V for LOBs, which is 0.293 V larger than that of Cl-MnO2. The discharge voltage of Cl-MnO2 for SOBs is 3.152 V; however, H-MnO2 impedes the formation of sodium superoxide and can hardly promote the ORR in SOBs. Both H- and Cl-MnO2 can prevent the parasitic disproportionation reaction in LOBs and SOBs that produce active singlet oxygen through different reaction mechanisms. We believe that the constructed pillared structures are efficient ORR/OER catalysts for alkali-metal-oxygen batteries. Our research provides a theoretical basis for the micro-level mechanism of LOBs and SOBs catalyzed by the pillared δ-MnO2 and sheds light on ameliorating the properties of the catalyst by constructing pillared structures.

How Do Oxygen Vacancies Influence the Catalytic Performance of Two-Dimensional Nb2 O5 in Lithium- and Sodium-Oxygen Batteries?

Alkali metal-oxygen batteries possess a higher specific capacity than alkali-ion batteries and stand out as the most competitive next-generation energy source. The core reaction mechanism of the battery is mainly the formation of alkali metal oxide during the discharge process and the decomposition of these oxides during the charge process. A large number of researchers have devoted themselves to seeking promising catalysts for the reaction. Two-dimensional Nb2 O5 was discovered to be a highly potential catalyst that can promote the reaction of alkali-metal-oxygen batteries, but few studies focus on it. In this study, the catalytic performance of both pristine Nb2 O5 and oxygen-deficiency modified Nb2 O5 was investigated. Furthermore, the effect of oxygen defects on catalytic performance was analyzed from multiple angles, namely, the reaction mechanism, d-band center theory, and the diffusion behavior of alkali metals. The exploration revealed the microscopic mechanism of oxygen deficiency affecting the alkali-metal battery reaction and provided a theoretical basis for quantitatively changing the d-band center of the catalyst through oxygen deficiency to ultimately change the performance of the catalyst.

Theoretical Exploration of Electrochemical Nitrate Reduction Reaction Activities on Transition-Metal-Doped h-BP.

Electrocatalytic conversion of nitrate (NO3-) into ammonia can not only eliminate harmful pollutant but also provide a green method for a low-temperature ammonia synthesis. The electrochemical NO3- reduction reactions (NO3RRs) of a series of transition-metal-doped hexagonal boron phosphide (h-BP) monolayers were comprehensively evaluated using density functional theory. The V-doped h-BP monolayer was found to stand near the top of the volcano plot with the limiting potential of -0.22 V versus a reversible hydrogen electrode, exhibiting the lowest overpotential among the investigated systems in this work. Besides, the competing hydrogen evolution reaction is significantly suppressed due to the weak adsorption of the H atom. Importantly, the structure of the V-doped h-BP monolayer can be retained very well until 900 K, illustrating the initial indication of high thermal stability and great promise for synthesis. This study not only offers an eligible NO3RR electrocatalyst but also provides an atomic understanding of the behind mechanisms of the NO3RR process.

Single Nb or W Atom-Embedded BP Monolayers as Highly Selective and Stable Electrocatalysts for Nitrogen Fixation with Low-Onset Potentials.

Conversion of dinitrogen (N2) molecules into ammonia through electrochemical methods is a promising alternative to the traditional Haber-Bosch process. However, searching for an eligible electrocatalyst with high stability, low-onset potential, and superior selectivity is still one of the most challenging and attractive topics for the electrochemical N2 reduction reaction (NRR). Here, by means of first-principles calculations and the conductor-like screening model, four comprehensive criteria were proposed to screen out eligible NRR electrocatalysts from 29 atomic transition metals embedded on the defective boron phosphide (BP) monolayer with B-monovacancy (M/BP single-atom catalysts, SAC, M = Sc-Zn, Y-Cd, and Hf-Hg). Consequently, the Nb/BP and W/BP SACs are identified as the promising candidates, on which the N2 molecule can only be activated through the enzymatic pathway with the onset potentials of -0.25 and -0.19 V, and selectivities of 90.5 and 100%, respectively. It is worth noting that the W/BP SAC has the lowest overpotential among the 29 systems investigated. The electronic properties were also calculated in detail to analyze the activity origin. Importantly, the Nb/BP and W/BP SACs possess high thermal stabilities due to that their structures can be retained very well up to 1000 and 700 K, respectively. This work not only provides an efficient and reliable method to screen eligible NRR electrocatalysts but also paves a new way for advancing sustainable ammonia synthesis.

A Theoretical Analysis on the Oxidation and Water Dissociation Resistance on Group-IV Phosphide Monolayers.

Group-IV phosphide monolayers (MP, M=C, Si, Ge and Sn) provide a versatile platform for photocatalysts, as well as optoelectronic and nanoelectronic devices. Herein, comprehensive first-principles calculations and ab initio molecular dynamics (AIMD) simulations were performed to explore their stabilities in the air. We identified that the MP monolayers have excellent mechanical properties and their carrier mobilities are higher than that of phosphorene. The MP monolayers were predicted to possess superior oxidation resistance than the boron phosphide (BP) monolayer based on the proposed donation-backdonation theory. It was observed that the dissociation and chemisorption of a water molecule on the monolayers are kinetically difficult both in the water and in oxygen-water environments involving energy barriers of 1.28-3.48 eV. We also performed AIMD simulations at 300, 1000, 1200 and 1500 K. It is noteworthy that only the carbon phosphide (CP) monolayer can retain an intact structure at 1500 K, while the other three monolayers can just sustain to 1200 K. These results provide a guidance for their practical application and experimental fabrication.

Stabilities of group-III phosphide (MP, M = B, Al, Ga and In) monolayers in oxygen and water environments.

Group-III phosphide (MP, M = B, Al, Ga and In) monolayers have promising applications in photocatalysis, nanoelectronics and optoelectronics. Their stabilities in oxygen and water environments are crucial to their practical applications. In order to investigate the stabilities of the MP monolayers, density functional theory calculations combined with ab initio molecular dynamics (AIMD) simulations were performed to illustrate their interactions with oxygen and water molecules. It was found that an oxygen molecule spontaneously dissociates on the AlP, GaP and InP monolayers. In the meantime, the corresponding monolayer structures are severely distorted after annealing. In contrast, BP monolayer is stable in the oxygen environment due to a high dissociative barrier of 0.89 eV. We found that a water molecule dissociates on AlP monolayer with a dissociative energy barrier of 0.42 eV, but it can be stably adsorbed on the BP, GaP and InP monolayers without the breakage of O-H bonds. Nevertheless, with the increase of the number of water molecules, the formed intermolecular H-bonding can promote interactions between water molecules and the monolayers, leading to structural distortion in the GaP and InP monolayers. When putting a water molecule near the oxygen molecule, the oxidation barrier of the BP monolayer is reduced to 0.75 eV, which is still high enough to maintain its stable state. This investigation theoretically provides environmental conditions for the experimental fabrication and practical application of semiconductor monolayers.

Quantum capacitance, electrostatic potential, electronic and structural data for bare and functionalized niobium carbide MXenes.

The data reported in this article are structural and physicochemical properties for bare and F, O, OH and CH3O-functionalized Nb n+1C n (n = 1, 2, 3 and 4) MXenes. The structural properties are presented as top views and side views from the X direction of the optimal structures of studied MXenes. The physicochemical properties include quantum capacitances, electrostatic potentials and electronic properties such as the projected density of states (PDOS) and band structures. Further interpretation and discussion of these data can be obtained from the article entitled "Possibility of bare and functionalized niobium carbide MXenes for electrode materials of supercapacitors and field emitters" (Xin and Yu, 2017) [1].

Efficient and Reversible Electron Doping of Semiconductor-Enriched Single-Walled Carbon Nanotubes by Using Decamethylcobaltocene.

Single-walled carbon nanotubes (SWCNTs) offer great potential for field-effect transistors and integrated circuit applications due to their extraordinary electrical properties. To date, as-made SWCNT transistors are usually p-type in air, and it still remains challenging for realizing n-type devices. Herein, we present efficient and reversible electron doping of semiconductor-enriched single-walled carbon nanotubes (s-SWCNTs) by firstly utilizing decamethylcobaltocene (DMC) deposited by a simple spin-coating process at room temperature as an electron donor. A n-type transistor behavior with high on current, large I on /I off ratio and excellent uniformity is obtained by surface charge transfer from the electron donor DMC to acceptor s-SWCNTs, which is further corroborated by the Raman spectra and the ab initio simulation results. The DMC dopant molecules could be reversibly removed by immersion in N, N-Dimethylformamide solvent, indicating its reversibility and providing another way to control the carrier concentration effectively as well as selective removal of surface dopants on demand. Furthermore, the n-type behaviors including threshold voltage, on current, field-effect mobility, contact resistances, etc. are well controllable by adjusting the surface doping concentration. This work paves the way to explore and obtain high-performance n-type nanotubes for future complementary CMOS circuit and system applications.

Binding energy and work function of organic electrode materials phenanthraquinone, pyromellitic dianhydride and their derivatives adsorbed on graphene.

Electroactive organic compounds are a novel group of green cathode materials for rechargeable metal-ion batteries. However, the organic battery life is short because the organic compounds can be dissolved by nonaqueous electrolytes. Here a comparative investigation of phenanthraquinone (PQ), pyromellitic dianhydride (PMDA) and their derivatives, i.e., benzo[1,2-b:4,3-b']difuran-4,5-dione (BDFD), benzo[1,2-b:4,3-b']dithiophene-4,5-quinone (BDTQ), 3,8-phenanthroline-5,6-dione (PAD), pyromellitic dithioanhydride (PMDT), pyromellitic diimide (PMDI) and 1,4,5,8-anthracenetetrone (ATO), adsorbed on graphene is performed using a density functional theory (DFT) with a van der Waals (vdW) dispersion-correction. The computed results show a strong physisorption with the binding energies between 1.10 and 1.56 eV. A sequence of the calculated binding energies from weak to strong is found to be BDFD < BDTQ < PMDA ≤ PMDI < PMDT < PQ < PAD < ATO. The formation of stable organic molecule-graphene nanocomposites can prevent the dissolution of the eight organic compounds in nonaqueous electrolyte and hence improve cycling performance of batteries. In addition, the work functions for the nanocomposites are found to be strongly affected by the work function of each organic compound. To understand the DFT results, a novel simple expression is proposed to predict the work function of the nanocomposites from the interfacial dipole and the work functions of the isolated graphene nanosheet and organic molecules. The predicted work functions for the nanocomposites from the new equation agree quite well with the values calculated from the vdW dispersion-corrected DFT.

DFT study on the atomic-scale nucleation path of graphene growth on the Cu(111) surface.

The nucleation path of graphene growth on the Cu(111) surface is investigated by importing carbon atoms step-by-step using density functional theory (DFT) calculations. An overall path of graphene nucleation has been proposed based on configuration and energy analysis. At the very first stage, linear chains will be formed and dominate the copper surface. Then, Y-type (furcate) carbon species will be shaped when new carbon atoms are absorbed aside the linear chains. Finally, ring-containing carbon species and graphene islands will be formed stepwise, with energetic preference. We find that the Y-type and ring-containing carbon species are not likely formed directly at the initial stage of graphene nucleation, but should be formed starting from linear chains. The nucleation limiting step is the formation of the Y-type species, which must pass an energy barrier of about 0.25 eV. These underlying observations are instructive to stimulate future experimental efforts on graphene synthesis.

Can all nitrogen-doped defects improve the performance of graphene anode materials for lithium-ion batteries?

The electronic and adsorption properties of graphene can be changed significantly through substitutional doping with nitrogen and nitrogen decoration of vacancies. Here ab initio density functional theory with a dispersion correction was used to investigate the stability, magnetic and adsorption properties of nine defects in graphene, including both nitrogen substitutional doping and nitrogen decoration of vacancies. The results indicate that only pyridinic N2V2 defect in graphene shows a ferromagnetic spin structure with high magnetic moment and magnetic stabilization energy. Not all nitrogen-doped defects can improve the capacity of the lithium-ion batteries. The adsorption energies of a lithium atom on nitrogen-substituted graphenes are more positive, indicating that they are meta-stable and no better than the pristine graphene as anode materials of lithium-ion batteries. Nitrogen-decorated single and double vacancy defects, especially for the pyridinic N2V2 defect in graphene, can greatly improve the reversible capacity of the battery in comparison with the pristine graphene. The theoretical prediction of the reversible capacity of the battery is 1039 mA h g(-1) for the nitrogen-doped graphene material synthesized by Wu et al., which is in good agreement with the experimental data (1043 mA h g(-1)). The theoretical computations suggest that nitrogen-decorated single and double vacancy defects in graphene are the promising candidate for anode materials of lithium-ion batteries. Each nitrogen atom in the decoration can improve the reversible capacity of the battery by 63.3-124.5 mA h g(-1) in a 4 × 4 supercell of graphene. The present work provides crucial information for the development of N-doped graphene-based anode materials of lithium-ion batteries.

Interaction of human synovial phospholipase A2 with mixed lipid bilayers: a coarse-grain and all-atom molecular dynamics simulation study.

Human secreted phospholipase A2s have been shown to promote inflammation in mammals by catalyzing the first step of the arachidonic acid pathway by breaking down phospholipids, producing fatty acids, including arachidonic acid. They bind to the membrane water interface to access their phospholipid substrates from the membrane. Their binding modes on membrane surfaces are regulated by diverse factors, including membrane charge, fluidity, and heterogeneity. The influence of these factors on the binding modes of the enzymes is not well understood. Here we have studied several human synovial phospholipase A2 (hs-PLA2)/mixed bilayer systems through a combined coarse-grain and all-atom molecular dynamics simulation. It was found that hydrophobic residues Leu2, Val3, Ala18, Leu19, Phe23, Gly30, and Phe63 that form the edge of the entrance of the hydrophobic binding pocket in hs-PLA2 tend to penetrate into the hydrophobic area of lipid bilayers, and more than half of the total amino acid residues make contact with the lipid headgroups. Each enzyme molecule forms 19-38 hydrogen bonds with the bilayer to which it binds, most of which are with the phosphate groups. Analysis of the root-mean-square deviation (rmsd) shows that residues Val30-Thr40, Tyr66-Gln80, and Lys107-Arg118 have relatively large rmsds during all-atom molecular dynamics simulations, in accordance with the observation of an enlarged entrance region of the hydrophobic binding pocket. The amino acid sequences forming the entrance of the binding pocket prefer to interact with lipid molecules that are more fluid or negatively charged, and the opening of the binding pocket would be larger when the lipid components are more fluid.

Structural and kinetic properties of alpha-tocopherol in phospholipid bilayers, a molecular dynamics simulation study.

Structural and kinetic properties of vitamin E in biomembranes provide the key to understanding the biological functions of this lipophilic vitamin. We report a series of molecular dynamics simulations of two alpha-tocopherol/phosphatidylcholine systems and two alpha-tocopherol/phosphatidylethanolamine systems in water at 280, 310, and 350 K. The preferential position, hydrogen bonding, orientation, and dynamic properties of the alpha-tocopherol molecule in the bilayers have been examined. In all the four systems simulated, the vitamin remains in one leaflet of lipid bilayer at 280 and 310 K but flips over from one side to the other at 350 K within 200 ns of the simulation. The hydroxyl oxygen in the headgroup of alpha-tocopherol preferred a location between the third and the fifth carbon atom in the sn-2 acyl chains of the lipids. Hydrogen bonding analysis shows that the hydrogen bonds are mainly with the oxygens of the fatty acid esters rather than with the phosphate oxygens of the lipid molecule, and those with the amino groups are trivial in the case of phosphatidylethanolamines, at all three temperatures. The hydrogen bonds with phosphatidylethanolamines are more stable than those with phosphatidylcholines at low temperatures. The orientation of alpha-tocopherol in the bilayers is relatively flexible: the chromanol ring takes various tilt angles with respect to the bilayer normal, and the isoprenyl chain is mobile and able to adopt many different conformers. Calculation of lateral diffusion coefficients of alpha-tocopherol and phospholipid molecules shows that alpha-tocopherol has a comparable diffusion rate with phospholipid molecules at the gel phase but diffuses more rapidly than lipid molecules at the liquid-crystal phase.

Ion distributions, exclusion coefficients, and separation factors of electrolytes in a charged cylindrical nanopore: a partially perturbative density functional theory study.

The structural and thermodynamic properties for charge symmetric and asymmetric electrolytes as well as mixed electrolyte system inside a charged cylindrical nanopore are investigated using a partially perturbative density functional theory. The electrolytes are treated in the restricted primitive model and the internal surface of the cylindrical nanopore is considered to have a uniform charge density. The proposed theory is directly applicable to the arbitrary mixed electrolyte solution containing ions with the equal diameter and different valences. Large amount of simulation data for ion density distributions, separation factors, and exclusion coefficients are used to determine the range of validity of the partially perturbative density functional theory for monovalent and multivalent counterion systems. The proposed theory is found to be in good agreement with the simulations for both mono- and multivalent counterion systems. In contrast, the classical Poisson-Boltzmann equation only provides reasonable descriptions of monovalent counterion system at low bulk density, and is qualitatively and quantitatively wrong in the prediction for the multivalent counterion systems due to its neglect of the strong interionic correlations in these systems. The proposed density functional theory has also been applied to an electrolyte absorbed into a pore that is a model of the filter of a physiological calcium channel.

High-order virial coefficients and equation of state for hard sphere and hard disk systems.

A very simple and accurate approach is proposed to predict the high-order virial coefficients of hard spheres and hard disks. In the approach, the nth virial coefficient B(n) is expressed as the sum of n(D-1) and a remainder, where D is the spatial dimension of the system. When n > or = 3, the remainders of the virials can be accurately expressed with Padé-type functions of n. The maximum deviations of predicted B(5)-B(10) for the two systems are only 0.0209%-0.0044% and 0.0390%-0.0525%, respectively, which are much better than the numerous existing approaches. The virial equation based on the predicted virials diverges when packing fraction eta = 1. With the predicted virials, the compressibility factors of hard sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to eta = 0.545. The compressibility factors of hard disk fluid can be predicted very accurately up to eta = 0.63. The simulated B(7) and B(10) for hard spheres are found to be inconsistent with the other known virials and therefore they are modified as 53.2467 and 105.042, respectively.