Feynman Hibbs Approach Research Articles

Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular Potentials.

The second to eighth virial coefficients of methane were determined for temperatures up to 1200 K using an existing ab initio-based and empirically fine-tuned two-body potential combined with a new empirical nonadditive three-body potential. Nuclear quantum effects were accounted for by the semiclassical Feynman-Hibbs approach. The numerical evaluation of the high-dimensional integrals through which the virial coefficients are expressed was performed employing the Mayer-sampling Monte Carlo technique. By fitting suitable mathematical functions to the calculated virial coefficients, an analytical eighth-order virial equation of state (VEOS8) was obtained. Pressures p computed as a function of temperature T and density ρ using VEOS8 agree highly satisfactorily with p(ρ, T) values obtained with the experimentally based reference equation of state for methane of Setzmann and Wagner (SWEOS) at state points at which VEOS8 is sufficiently converged. It is shown that it is essential to account for nonadditive three-body interactions in the calculations in order to achieve good agreement with the SWEOS.

Adsorption of hydrogen isotopes in the zeolite NaX: Experiments and simulations

Among the different methods to separate hydrogen isotopes one is based on the physisorption at low temperature (below 100 K) where quantum effects induce a particular behavior. In the present work, we study the adsorption of single H2 and D2 on the zeolite NaX by combining experiments (manometry) from 30 to 150 K and molecular dynamics simulations at 40 and 77 K. Simulations also include the adsorption analysis for T2. Adsorption on NaX membranes is simulated and quantum corrections are introduced by using the well-known Feynman–Hibbs approach into the interaction potentials. Experimental adsorption isotherms are reproduced by using the Toth equation and it is shown that the adsorption capacity increases with the molecular weight of the isotopes. Isosteric enthalpies evidence a heterogeneous adsorption process with two type of hydrogen isotopes differently linked to the zeolitic structure. The calculated pair distribution functions at high loadings exhibit a liquid-like structuration in the supercages of NaX, which may explain the different adsorption capacities for H2, D2 and T2 and the heterogeneity of the adsorption process.

Examination of the Feynman-Hibbs Approach in the Study of NeN-Coronene Clusters at Low Temperatures.

Feynman-Hibbs (FH) effective potentials constitute an appealing approach for investigations of many-body systems at thermal equilibrium since they allow us to easily include quantum corrections within standard classical simulations. In this work we apply the FH formulation to the study of NeN-coronene clusters (N = 1-4, 14) in the 2-14 K temperature range. Quadratic (FH2) and quartic (FH4) contributions to the effective potentials are built upon Ne-Ne and Ne-coronene analytical potentials. In particular, a new corrected expression for the FH4 effective potential is reported. FH2 and FH4 cluster energies and structures-obtained from energy optimization through a basin-hopping algorithm as well as classical Monte Carlo simulations-are reported and compared with reference path integral Monte Carlo calculations. For temperatures T > 4 K, both FH2 and FH4 potentials are able to correct the purely classical calculations in a consistent way. However, the FH approach fails at lower temperatures, especially the quartic correction. It is thus crucial to assess the range of applicability of this formulation and, in particular, to apply the FH4 potentials with great caution. A simple model of N isotropic harmonic oscillators allows us to propose a means of estimating the cutoff temperature for the validity of the method, which is found to increase with the number of atoms adsorbed on the coronene molecule.

Some thermodynamics and transport properties and new equation of state for fluid hydrogen using a new intermolecular potential

A new pair-potential energy function of hydrogen molecule has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, and thermal conductivity of hydrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed molecular dynamics simulation to obtain some thermodynamics and transport properties of fluid hydrogen at different temperatures and densities using our calculated pair-potential supplemented by quantum corrections following the Feynman–Hibbs approach. To take higher-body forces into account, the simple three-body potentials of Hauschild and Prausnitz (1993) and Wang and Sadus (2006) used with the calculated two-body potential to improve the prediction of the properties of fluid hydrogen without requiring an expensive three-body calculation. The molecular dynamics simulation has been also used to determine a new equation of state for hydrogen. Our results are in a good agreement with experiment and literature values.

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid neon using a new intermolecular potential from molecular dynamics simulation

A new pair potential energy function of neon has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. The pair potential reproduces the second virial coefficient, viscosity, thermal conductivity, and self-diffusion coefficient of neon in a good accordance with experimental data over wide ranges of temperature and density. We have also performed molecular dynamics simulation to obtain some thermodynamics, transport, and structural properties of fluid neon at different temperatures and densities using our calculated pair potential supplemented by quantum corrections following the Feynman–Hibbs approach. The significance of this work is that the three-body expression of Wang and Sadus (J Chem Phys 125:144509–1, 2006) can be used to improve the prediction of the pressures of neon without requiring an expensive three-body calculation. The molecular dynamics simulation of neon has been also used to determine a new equation of state for neon. Our results are in a good agreement with experiment and literature values.

Computation of some thermodynamic properties of helium–neon and helium–krypton fluid mixtures using molecular dynamics simulation

We have performed molecular dynamics simulations to obtain internal energy and pressure of helium–neon and helium–krypton mixtures at different densities using accurate recently two-body ab initio potentials supplemented by quantum corrections following the Feynman–Hibbs approach. The significance of this work is that the three-body expression of Wang and Sadus [22] was used to improve prediction of the pressures and internal energies of helium + krypton and helium + neon mixtures without requiring an expensive three-body calculation. Our results show a good agreement with the corresponding experimental data.

Numerical estimation of hydrogen storage limits in carbon-based nanospaces

Theoretical limits of the hydrogen adsorption in carbon nanospaces are modeled using Monte Carlo simulations. A detailed analysis of storage capacity of slit pores has been performed as a function of the pore size, gas pressure (up to 100 bars) and temperature of adsorption (77 and 298 K). The H 2–slit wall interaction has been modeled assuming energies of adsorption ranging from 4.5 kJ/mol (pure graphene surface) to 15 kJ/mol (hypothetical chemically modified graphene). The quantum nature of H 2 has been incorporated in the calculations using the Feynman–Hibbs approach. It has been shown that in a hypothetical chemically modified porous carbon, with energy of adsorption of 15 kJ/mol or higher and pore size between 0.8 and 1.1 nm, the gravimetric and volumetric storage capacity can achieve targets required for practical applications. The relation between the energy of adsorption and the effective delivery has been discussed.

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.

Quantum computation of the properties of helium using two-body and three-body intermolecular potentials: a molecular dynamics study

We have performed the molecular dynamics simulation to obtain energy, pressure, and self-diffusion coefficient of helium at different temperatures and densities using Lennard–Jones (LJ), Hartree–Fock dispersion-Individual damping (HFD-ID) potential, and the HFD-like potential which has been obtained with an inversion of viscosity data at zero pressure supplemented by quantum corrections following the Feynman–Hibbs approach. The contribution of three-body interactions using an accurate simple relationship reported by Wang and Sadus between two-body and three-body interactions has been also involved for non-effective potentials (HFD-ID and HFD-like) in simulation. Our results show a good agreement with corresponding experimental data. A comparison of our simulated results with other molecular simulations using different potentials is also included.

Quantum Effect Induced Reverse Kinetic Molecular Sieving in Microporous Materials

We report kinetic molecular sieving of hydrogen and deuterium in zeolite rho at low temperatures, using atomistic molecular dynamics simulations incorporating quantum effects via the Feynman-Hibbs approach. We find that diffusivities of confined molecules decrease when quantum effects are considered, in contrast with bulk fluids which show an increase. Indeed, at low temperatures, a reverse kinetic sieving effect is demonstrated in which the heavier isotope, deuterium, diffuses faster than hydrogen. At 65 K, the flux selectivity is as high as 46, indicating a good potential for isotope separation.

Quantum computation of the thermodynamics, structural and transport properties of Lennard–Jones liquid systems: The Feynman–Hibbs approach

The properties of liquid helium, liquid methane and liquid neon are calculated over a large range of temperature from classical molecular dynamics simulations. The molecular interactions are represented by Lennard–Jones pair potentials supplemented by quantum corrections following the Feynman–Hibbs approach. Results include thermodynamics, structural and transport properties for the quantum and the classical Lennard–Jones models. By increasing the number of iterations, we observe a decrease in the uncertainties in the stress autocorrelation function. The data reported in the paper are also compared, where possible, with previous path-integral simulation results and with available experimental information.

Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach.

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections.

Hydrogen-bonding in light and heavy water under normal and extreme conditions

Our purpose is to report results of molecular dynamics (MD) simulation on light and heavy water modelled by a central force potential related to those proposed in the 1970s by Lemberg, Rahman and Stillinger. Quantum effects are taken into account by implementing in the MD code the Feynman–Hibbs quantum approximation. The evolution of the energetics, the structure and the diffusivity of the two isotopic species is investigated between ambient and supercritical conditions and compared with experimental data and with classical simulations as well. The accuracy of the results and the very low cost in computer time make the Feynman–Hibbs approach a possible alternative to the path integral simulation methods used in the literature.

Quantum effects in simulated water by the Feynman–Hibbs approach

Quantum effects in water are investigated by implementing the Feynman–Hibbs effective potential in a molecular-dynamics code. The reference potential chosen for water is a new central force model related to the one proposed in the 1970s by Lemberg and Stillinger [J. Chem. Phys. 62, 1677 (1975)]. The evolution of the thermodynamics, the structure, the diffusivity, and the dynamics in light and heavy water is investigated over a large range of temperature and is compared with experimental data and with classical simulations as well. It is found that quantum effects are significant near ambient conditions and vanish with increasing temperature less drastically than generally assumed. The most affected quantity is the self-diffusion coefficient for which is predicted a marked increase of the isotopic ratio (DH2O/DD2O) in going into the supercooled region. The accuracy of the results and the very low cost in computer time make the Feynman–Hibbs approach a valuable procedure to rapidly estimate the order of magnitude of the quantum contributions to intermolecular properties of water.