Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations.

Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both 4He and 3He. For the third density virial coefficient C(T), uncertainties have been reduced by a factor of 4-5 compared to the previous state of the art; the accuracy of first-principles C(T) now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5 K. For the third acoustic virial coefficient γa(T), we applied the Schlessinger point method, which can calculate γa and its uncertainty based on the C(T) data, overcoming some limitations of direct path-integral calculation. The resulting γa are calculated at temperatures down to 0.5 K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.

Comprehensive quantum calculation of the first dielectric virial coefficient of water.

We present a complete calculation, fully accounting for quantum effects and for molecular flexibility, of the first dielectric virial coefficient of water and its isotopologues. The contribution of the electronic polarizability is computed from a state-of-the-art intramolecular potential and polarizability surface from the literature, and its small temperature dependence is quantified. The dipolar polarizability is calculated in a similar manner with an accurate literature dipole-moment surface; it differs from the classical result both due to the different molecular geometries sampled at different temperatures and due to the quantization of rotation. We calculate the dipolar contribution independently from spectroscopic information in the HITRAN2020 database and find that the two methods yield consistent results. The resulting first dielectric virial coefficient provides a complete description of the dielectric constant at low density that can be used in humidity metrology and as a boundary condition for new formulations for the static dielectric constant of water and heavy water.

Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium.

The four-body nonadditive contribution to the energy of four helium atoms is calculated and fitted for all geometries for which the internuclear distances exceed a small minimum value. The interpolation uses an active learning approach based on Gaussian processes. Asymptotic functions are used to calculate the nonadditive energy when the four helium atoms form distinct subclusters. The resulting four-body potential is used to compute the fourth virial coefficient D(T) for helium, at temperatures from 10 to 2000 K, with a path-integral approach that fully accounts for quantum effects. The results are in reasonable agreement with the limited and scattered experimental data for D(T), but our calculated results have much smaller uncertainties.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

Understanding anharmonic effects on hydrogen desorption characteristics of MgnH2n nanoclusters by ab initio trained deep neural network.

Magnesium hydride (MgH2) has been widely studied for effective hydrogen storage. However, its bulk desorption temperature (553 K) is deemed too high for practical applications. Besides doping, a strategy to decrease such reaction energy for releasing hydrogen is the use of MgH2-based nanoparticles (NPs). Here, we investigate first the thermodynamic properties of MgnH2n NPs (n < 10) from first-principles, in particular by assessing the anharmonic effects on the enthalpy, entropy and thermal expansion by means of the stochastic self consistent harmonic approximation (SSCHA). This method goes beyond previous approaches, typically based on molecular mechanics and the quasi-harmonic approximation, allowing the ab initio calculation of the fully-anharmonic free energy. We find an almost linear dependence on temperature of the interatomic bond lengths - with a relative variation of few percent over 300 K - alongside with a bond distance decrease of the Mg-H bonds. In order to increase the size of MgnH2n NPs toward experiments of hydrogen desorption we devise a computationally effective machine learning model trained to accurately determine the forces and total energies (i.e. the potential energy surfaces), integrating the latter with the SSCHA model to fully include the anharmonic effects. We find a significative decrease of the H-desorption temperature for sub-nanometric clusters MgnH2n with n ≤ 10, with a non-negligible, although little effect due to anharmonicities (up to 10%).

Path-integral calculation of the third dielectric virial coefficient of noble gases.

We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient Cɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

Path-integral calculation of the fourth virial coefficient of helium isotopes.

We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients D(T) of 4He and 3He as functions of temperature from 2.6 K to 2000 K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for 4He at the temperatures considered, but for 3He, they are necessary for quantitative accuracy below about 4 K. Our results are consistent with previous theoretical work (also with some of the limited and scattered experimental data) for 4He; for 3He, there are no experimental values, and this work provides the first values of D(T) calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures, the uncertainties related to the three-body potential and omitted higher-order contributions become dominant.

Adsorption separation of heavier isotope gases in subnanometer carbon pores.

Isotopes of heavier gases including carbon (13C/14C), nitrogen (13N), and oxygen (18O) are highly important because they can be substituted for naturally occurring atoms without significantly perturbing the biochemical properties of the radiolabelled parent molecules. These labelled molecules are employed in clinical radiopharmaceuticals, in studies of brain disease and as imaging probes for advanced medical imaging techniques such as positron-emission tomography (PET). Established distillation-based isotope gas separation methods have a separation factor (S) below 1.05 and incur very high operating costs due to high energy consumption and long processing times, highlighting the need for new separation technologies. Here, we show a rapid and highly selective adsorption-based separation of 18O2 from 16O2 with S above 60 using nanoporous adsorbents operating near the boiling point of methane (112 K), which is accessible through cryogenic liquefied-natural-gas technology. A collective-nuclear-quantum effect difference between the ordered 18O2 and 16O2 molecular assemblies confined in subnanometer pores can explain the observed equilibrium separation and is applicable to other isotopic gases.

Erratum: Improved First-Principles Calculation of the Third Virial Coeffcient of Helium.

[This corrects the article on p. 729 in vol. 116.].

Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials.

Path-Integral Monte Carlo methods were applied to calculate the second, B(T), and the third, C(T), virial coefficients for water. A fully quantum approach and state-of-the-art flexible-monomer pair and three-body potentials were used. Flexible-monomer potentials allow calculations for any isotopologue; we performed calculations for both H2O and D2O. For B(T) of H2O, the quantum effect contributes 25% of the value at 300 K and is not entirely negligible even at 1000 K, in accordance with recent literature findings. The effect of monomer flexibility, while not as large as some claims in the literature, is significant compared to the experimental uncertainty. It is of opposite sign to the quantum effect, smaller in magnitude than the latter below 500 K, and varies from 2% at 300 K to 10% at 700 K. When monomer flexibility is accounted for, results from the CCpol-8sf pair potential are in excellent agreement with the available experimental data and provide reliable B(T) values at temperatures outside the range of experimental data. The flexible-monomer MB-pol pair potential yields B(T) values that are slightly too high compared to experiment. For C(T), our calculations confirm earlier findings that the use of three-body potential is necessary for meaningful predictions. However, due to various uncertainties of the potentials used, especially the three-body ones, we were not able to establish benchmark values of C(T), although our results are in qualitative agreement with available experimental data. The quantum effect, never before included for water, reduces the magnitude of the classical value for H2O by a factor of 2.5 at 300 K and is not entirely negligible even at 1000 K.

A novel combined experimental and multiscale theoretical approach to unravel the structure of SiC/SiOx core/shell nanowires for their optimal design.

In this work we propose a realistic model of nanometer-thick SiC/SiOx core/shell nanowires (NWs) using a combined first-principles and experimental approach. SiC/SiOx core/shell NWs were first synthesised by a low-cost carbothermal method and their chemical-physical experimental analysis was accomplished by recording X-ray absorption near-edge spectra. In particular, the K-edge absorption lineshapes of C, O, and Si are used to validate our computational model of the SiC/SiOx core/shell NW architectures, obtained by a multiscale approach, including molecular dynamics, tight-binding and density functional simulations. Moreover, we present ab initio calculations of the electronic structure of hydrogenated SiC and SiC/SiOx core/shell NWs, studying the modification induced by several different substitutional defects and impurities into both the surface and the interfacial region between the SiC core and the SiOx shell. We find that on the one hand the electron quantum confinement results in a broadening of the band gap, while hydroxyl surface terminations decrease it. This computational investigation shows that our model of SiC/SiOx core/shell NWs is capable to deliver an accurate interpretation of the recorded X-ray absorption near-edge spectra and proves to be a valuable tool towards the optimal design and application of these nanosystems in actual devices.

Time correlation functions of simple liquids: A new insight on the underlying dynamical processes.

Extensive molecular dynamics simulations of liquid sodium have been carried out to evaluate correlation functions of several dynamical quantities. We report the results of a novel analysis of the longitudinal and transverse correlation functions obtained by evaluating directly their self- and distinct contributions at different wavevectors k. It is easily recognized that the self-contribution remains close to its k → 0 limit, which turns out to be exactly the autocorrelation function of the single particle velocity. The wavevector dependence of the longitudinal and transverse spectra and their self- and distinct parts is also presented. By making use of the decomposition of the velocity autocorrelation spectrum in terms of longitudinal and transverse parts, our analysis is able to recognize the effect of different dynamical processes in different frequency ranges.

All-dimensional H2-CO potential: Validation with fully quantum second virial coefficients.

We use a new high-accuracy all-dimensional potential to compute the cross second virial coefficient B12(T) between molecular hydrogen and carbon monoxide. The path-integral method is used to fully account for quantum effects. Values are calculated from 10 K to 2000 K and the uncertainty of the potential is propagated into uncertainties of B12. Our calculated B12(T) are in excellent agreement with most of the limited experimental data available, but cover a much wider range of temperatures and have lower uncertainties. Similar to recently reported findings from scattering calculations, we find that the reduced-dimensionality potential obtained by averaging over the rovibrational motion of the monomers gives results that are a good approximation to those obtained when flexibility is fully taken into account. Also, the four-dimensional approximation with monomers taken at their vibrationally averaged bond lengths works well. This finding is important, since full-dimensional potentials are difficult to develop even for triatomic monomers and are not currently possible to obtain for larger molecules. Likewise, most types of accurate quantum mechanical calculations, e.g., spectral or scattering, are severely limited in the number of dimensions that can be handled.

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects.

We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.

Three-body nonadditive potential for argon with estimated uncertainties and third virial coefficient.

The three-body nonadditive interaction energy between argon atoms was calculated at 300 geometries using coupled cluster methods up to single, double, triple, and noniterative quadruple excitations [CCSDT(Q)], and including the core correlation and relativistic effects. The uncertainty of the calculated energy was estimated at each geometry. The analytic function fitted to the energies is currently the most accurate three-body argon potential. Values of the third virial coefficient C(T) with full account of quantum effects were computed from 80 to 10000 K by a path-integral Monte Carlo method. The calculation made use of an existing high-quality pair potential [Patkowski, K.; Szalewicz, K. J. Chem. Phys. 2010, 133, 094304] and of the three-body potential derived in the present work. Uncertainties in the potential were propagated to estimate uncertainties in C(T). The results were compared with available experimental data, including some values of C(T) newly derived in this work from previously published high-accuracy density measurements. Our results are generally consistent with the available experimental data in the limited range of temperatures where data exist, but at many conditions, especially at higher temperatures, the uncertainties of our calculated values are smaller than the uncertainties of the experimental values.

Non-adiabatic ab initio molecular dynamics of supersonic beam epitaxy of silicon carbide at room temperature.

In this work, we investigate the processes leading to the room-temperature growth of silicon carbide thin films by supersonic molecular beam epitaxy technique. We present experimental data showing that the collision of fullerene on a silicon surface induces strong chemical-physical perturbations and, for sufficient velocity, disruption of molecular bonds, and cage breaking with formation of nanostructures with different stoichiometric character. We show that in these out-of-equilibrium conditions, it is necessary to go beyond the standard implementations of density functional theory, as ab initio methods based on the Born-Oppenheimer approximation fail to capture the excited-state dynamics. In particular, we analyse the Si-C(60) collision within the non-adiabatic nuclear dynamics framework, where stochastic hops occur between adiabatic surfaces calculated with time-dependent density functional theory. This theoretical description of the C(60) impact on the Si surface is in good agreement with our experimental findings.

Second virial coefficients of H2 and its isotopologues from a six-dimensional potential.

We employ path-integral Monte Carlo techniques to compute the second virial coefficient as a function of temperature for molecular hydrogen (H(2)), deuterium (D(2)), and tritium (T(2)), along with the mixed isotopologues HD, HT, and DT. The calculations utilize a new six-dimensional (6D) potential, which is derived by combining our previous high-quality ground-state 4D potential for the H(2) dimer with the 6D potential of Hinde. This new 6D potential is reduced to a set of 4D potentials by fixing the intramolecular coordinates at their expectation values for each temperature and isotopic combination. The results for H(2) are in good agreement with experimental data; the effect of the temperature dependence of the average bond length is only significant above approximately 1000 K. For D(2) and HD, the available experimental data are much more limited; our results agree with the data and provide reliable values at temperatures where no experimental data exist. For the species containing tritium, our results provide the only data available.

OBGMX: a web-based generator of GROMACS topologies for molecular and periodic systems using the universal force field.

OBGMX is a web service providing topologies for the GROMACS molecular dynamics software package according to the Universal Force Field, as implemented in the Open Babel package. OBGMX can deal with molecular and periodic systems. The geometrical parameters appearing in the potential energy functions for the bonded interactions can be set to those measured in the input configuration. The performance of OBGMX in reproducing the structure of periodic systems is analyzed by calculating the root mean-squared displacements of optimized configurations of a large set of metal-organic frameworks. OBGMX is available at http://software-lisc.fbk.eu/obgmx/.

Collective dynamics of supercooled water close to the liquid-liquid coexistence lines.

We report molecular dynamics simulation results for the collective dynamical properties of supercooled bulk water at 180 K at three different densities, corresponding to different phases whose coexistence has recently been discovered in the supercooled regime. In this study, we focus on the behaviour of the longitudinal and transverse current correlation functions and their relative spectra, which we analyze in detail to understand the dynamical processes responsible for the main features observed. Despite the considerable differences in the structure and densities of the three thermodynamic states considered, the obtained current correlation functions show rather similar behaviour in every case. We show that the longitudinal spectra can only be described in terms of three Lorentzian lines, while the accurate reproduction of the transverse spectra requires at least four separate spectral lines. In fact, the behaviour of the peak frequency of the modes necessary to reproduce the spectra as a function of the wavevector indicates in a clear way the nature of the dynamical process. We demonstrate the presence of collective modes associated with the propagation of both longitudinal and transverse sound along with the important contribution of "optical-like" modes, which point out the relevance of localized motions for a right interpretation of the spectral line shape. The wavevector dependence of the relative contributions of the various modes to the total spectral area is also discussed.