Effective Spherical Potentials Research Articles

Interaction potential and gaseous ion mobility of CO+ ions in He

An effective spherical interaction potential for HeCO+ and values for the momentum-transfer collision integral are obtained from experimental ion mobility data by using the direct inversion method. The potential is fitted to a Morse–Spline–van der Waals (MSV) model potential. Consistency is checked by calculating collision integrals and the mobilities of CO+ ions in He gas from the MSV potential and showing that they agree with the experimental data. The separation- and angle-dependent interaction potential energy surface is calculated from the spin-unrestricted, fourth-order Moller–Ploesset theory with single, double, triple and quadruple excitations, using a 6-311++G(3df,3pd) basis set while correcting for basis set superposition error. Full and partial versions of the ab initio potentials are used to determine the transport cross-sections for the collisions of CO+ with He as a function of the collision energy at fixed angles between the C–O bond axis and the internuclear axis. Finally, the transport coefficients of CO+ ions moving through He are calculated accurately, over a wide range of reduced electric field and gas temperature, using an extension of the Monchick–Mason approximation.

Determination of and interaction potentials from gaseous ion mobility data

Effective spherical interaction potentials for and are calculated from experimental gaseous ion mobility data by using the direct inversion method. The potentials obtained are used to obtain best-fit parameters of the Morse-Morse-Spline-Van der Waals (MMSV) potential model. The MMSV potentials were then employed to compute the mobility of ion in argon and krypton gases at 300 K. Results show that the MMSV potentials reproduce the experimental ion mobilities within their experimental accuracy.

Viscosity and thermal conductivity from non-conformal potentials. I Theory and application to noble gases

The approximate non-conformal (ANC) theory provides effective spherical potentials for more than 40 pure real gases and predicts many of their binary mixtures in the case of the second volumetric virial coefficients B(T). Each substance is characterized by only three parameters; besides the usual minimum energy ε and its corresponding position r m, a softness parameter s is proposed to take account of the form of a particular potential. In this work the ANC theory is extended to take account of viscosity η(T) and thermal conductivity λ(T) coefficients in dilute gases. Very simple expressions are derived to calculate the appropriate collision integral Ω as a function of temperature and in terms of the parameters ε, r m and s, using a reference collision integral Ω0(T). The theory is successfully applied to the noble gases Ne, Ar, Kr and Xe, with deviations from experiment for η(T) and λ(T) within experimental uncertainties. In the case of Ne, the ANC potential obtained here reproduces simultaneously η(T) and λ(T) as well as B(T) within experimental uncertainty, using a single set of parameters. A prediction for the radon gas is proposed.

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ε and distance rm-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ε, rm, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H2, N2, O2 and CI2) and a dozen small polyatomics. It is found that the ANC model η (T, ε, rm, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.

Consistent anisotropic repulsions for simple molecules

We extract atom-atom potentials from the effective spherical potentials that successfully model Hugoniot experiments on molecular fluids, e.g., ${\mathrm{O}}_{2}$ and ${\mathrm{N}}_{2}.$ In the case of ${\mathrm{O}}_{2}$ the resulting potentials compare very well with the atom-atom potentials used in studies of solid-state properties, while for ${\mathrm{N}}_{2}$ they are considerably softer at short distances. Ground-state $(T=0 \mathrm{K})$ and room-temperature calculations performed with the N-N potential resolve the previous discrepancy between experimental and theoretical results.

The influence of image interactions on the structure of water and electrolytes in front of a metal surface

The structure of liquid water in contact with a metallic planar wall is calculated for the central force water model which is a stoichiometric mixture of partially charged hydrogen and oxygen atoms interacting via effective spherical pair potentials. The density profiles near the wall are obtained from the Wertheim–Lovett–Mou–Buff equation where the bulk information enters through the direct correlation functions. In this approach image interactions which are characteristic for a metallic boundary, and which cannot be treated as a simple particle–wall interaction are considered within a mean-field ansatz. We discuss the structural properties of the interface layer for both cases, the charged and the uncharged wall, and compare the results to those for an unpolarizable boundary where the image forces have been switched off. The differential capacitance as function of the wall charge is seen to show a characteristic “hump” which can be related to the transition between two possible icelike water structures in front of the wall.

The structure of water at a planar wall: An integral equation approach with the central force model

The structure of liquid water in contact with a planar wall is calculated for the central force model by which water is modeled as a stoichiometric mixture of partially charged hydrogen and oxygen atoms interacting via effective spherical pair potentials. The density profiles near the wall are obtained from the Wertheim–Lovett–Mou–Buff equation extended to mixtures with coulombic interactions. The correlations in the bulk liquid are calculated by adding bridge functions of appropriate reference hard sphere systems to the hypernetted chain equation. We have obtained structural (stoichiometry, hydrogen bonds) and thermodynamic properties in good agreement with computer simulations. We also expose the water to electric fields due to a surface charge on the wall.

The anisotropic potential energy surfaces of H2, N2, and Ar with C2H2 from total differential scattering experiments

The total differential scattering cross sections for H2, N2, and Ar with C2H2 were measured on an in-plane crossed molecular beam apparatus at collision energies of 1051, 1056, and 929 K, respectively. Well resolved rainbow oscillations for N2 and Ar, and diffraction oscillations for H2, showed two interference effects. Effective spherical and anisotropic potentials were obtained from analysis using single channel and infinite-order-sudden (IOS) methods, based on the semiclassical Jeffreys–Wentzel–Kramers–Brillouin (JWKB) approximation. The damping of oscillations showed the importance of anisotropy in the pair potentials. Total differential scattering cross sections calculated using the IOS method were in excellent agreement with the experimental data.

ChemInform Abstract: Effective Spherical Potentials for Liquid Propane.

Effective spherical potentials for molecular liquids, in particular the RAM, the median and the virial potentials, have been evaluated for a model of propane due to Lusting (R. Lusting, Mol. Phys., 1986, 59, 173). The thermodynamic and structural predictions of the sphericalized potentials have been tested, and are compared with each other, with experimental results for propane, and with simulation results, perturbation theory and RISM calculations to be satisfactory for modelling liquid propane. The use of non-spherical reference fluids is briefly discussed. An effective Lennard-Jones plus quadrupole potential used in the framework of the Twu–Gubbins perturbation theory is found to give a good account of the thermodynamic behaviour of propane.

Effective spherical potentials for liquid propane

Effective spherical potentials for molecular liquids, in particular the RAM, the median and the virial potentials, have been evaluated for a model of propane due to Lusting (R. Lusting, Mol. Phys., 1986, 59, 173). The thermodynamic and structural predictions of the sphericalized potentials have been tested, and are compared with each other, with experimental results for propane, and with simulation results, perturbation theory and RISM calculations to be satisfactory for modelling liquid propane. The use of non-spherical reference fluids is briefly discussed. An effective Lennard-Jones plus quadrupole potential used in the framework of the Twu–Gubbins perturbation theory is found to give a good account of the thermodynamic behaviour of propane.

Anisotropic intermolecular potentials for HeC2H2, HeC2H4, and HeC2H6, and an effective spherical potential for HeCHF3 from multiproperty fits

Differential cross section (DCS) measurements are reported for scattering of a He atomic beam by crossed beams of C2H2, C2H4, C2H6, and CHF3. In addition, interaction virial measurements and accurate limiting diffusion measurements are presented for these systems. Damping of the DCS diffraction oscillations is used to extract anisotropic intermolecular potentials, which are constrained in multiproperty fits to accurately reproduce the dilute gas data. The radial anisotropies determined are in the sequence C2H6>C2H4∼C2H2>CHF3, as sampled by the He probe.

Vibrational frequency shifts in dense molecular fluids

A theory is presented for calculating the bond length and vibrational frequency shifts in dense molecular fluids. We combine equation-of-state calculations based on the effective spherical potentials of Shaw, Johnson, and co-workers with a simple model for the interactions of a molecule with the surrounding fluid. The repulsive interactions are approximated with the hard-sphere model of Schweizer and Chandler. We extend their model by including an improved treatment of the long-range attractive interactions and the centrifugal forces. We apply this model to fluid nitrogen and compare with static and shock wave experimental frequency shifts, as well as computer simulation data, over a wide range of pressures and temperatures. We find that while the results using this simple model are reasonably close to experiment in the region appropriate to shock conditions, agreement with data taken under static high-pressure conditions (at lower temperatures) is not as good. Inadequacies of the model and possible improvements are discussed.

Limitations on the usefulness of the angular median and related potentials

The use of the angular median and related effective spherical potentials to predict thermodynamic properties of nonpolar homonuclear diatomic liquids has recently been shown to be efficient and accurate. Here we compare the results obtained from median-like methods for some other molecular liquids with simulation data. We find impressive agreement for linear triatomic molecules but results for tetrahedral molecules and for the overlap potential are very poor. The characteristic shape of potential energy frequency distributions at fixed separations is suggested as a criterion for the success or otherwise of the median potential.

An approximate variational method for improved thermodynamics of molecular fluids

For a certain class of thermodynamic perturbation theories, a generalization of the Gibbs–Bogoliubov inequality holds through second order of perturbation theory and for a subset of terms the inequality is true to infinite order. Using this approximate variational principle, a perturbation theory is chosen for which the Helmholtz free energy of the reference system is minimized under the constraint that the first order term is identically zero. We apply these ideas to the determination of effective spherical potentials that accurately reproduce the thermodynamics of nonspherical molecular potentials. For a diatomic-Lennard-Jones (DLJ) potential with l/σ=0.793, the resulting spherical reference potential is identical to the median average over angles for the repulsive part of the potential, but differs in the attractive well. The variational effective spherical potential leads to more accurate thermodynamics than the median, however, particularly in the triple point region.

Thermodynamics using effective spherical potentials for CO2 anisotropies

We examine the fluid thermodynamics of a model homonuclear diatomic system with anisotropies characteristic of CO2. The density (CO2 densities) and temperature regime is 1.6 g/cm3≲ρ≲2.6 g/cm3 and 1000 K≲T≲7000 K. Extensive molecular dynamics data for the model equation of state are presented. Comparisons are then made to the thermodynamics from three effective spherical potentials; the potential median, the radial median, and an exponential-six with parameters adjusted to best fit the true thermodynamics. The two median potentials typically give 3% agreement for the higher temperature fluid with a 5%–10% comparison nearer the freezing line for both pressure and internal energy while the fit is good to 3% or better. Thus there exists an effective spherical potential that very accurately models the thermodynamics of dense fluid CO2, a system whose potential energy in the repulsive region varies by three to four orders of magnitude as a function of angles with fixed center of mass separation. The median averages give an excellent representation of this effective spherical potential.

Shocked states from initially liquid oxygen–nitrogen systems

Sets of pressures and their corresponding specific volumes and internal energies are derived from measurements on steadily propagating, planar shock waves propelled by explosively driven metal assemblies into a 1:1 atomic mixture of the elements nitrogen and oxygen in each of two liquid initial states. One of these is the equimolar solution of O2 and N2, at T≂85 K, v0≂1.06 cm3/g; the other is the pure explosive compound NO, at T≂122 K, v0≂0.79 cm3/g. Results for this system are calculated with effective spherical potentials and presented graphically for comparison with the measurements. Single- and reflected-shock states are reported, as are incidental new results on pure liquid N2 at 85 K. The method of measurement is described, with reference to its previous applications to liquid O2 and Ar. First-shock pressures from both initial forms lie between 10 and 30 GPa, and the Hugoniots intersect at a common state, near 21 GPa, where a single reflected-shock Hugoniot is centered. Concordant measured state variables at this intersection provide novel confirmation of the expectation, inherently incorporated into theory, that unique equilibrium states are reached. Accounting for densities of these states by theory indicates a significant amount of oxidized nitrogen, in reversible equilibrium with major, but not exclusive, N2 and O2 components. This is treated as residual NO only, although the uncertainty in the potentials for other oxides does not assure their absence.

Effective spherical potentials for the thermodynamics of homonuclear diatomic Lennard-Jones liquids

The predictions of several effective spherical potentials for thermodynamic properties of symmetric diatomic Lennard-Jones molecules are examined. The effective potentials are obtained by splitting the molecular potential in various ways followed by adding the separate angular medians of the two parts. Luckily, the best results are obtained when each site–site interaction is divided into its individual power law terms. It is therefore possible to obtain quite accurate thermodynamic properties over a continuous range of elongations using linear combinations of just two spherical potentials for which accurate analytic fitting functions are provided.

Effective spherical potentials for molecular fluids

A method is described by which second virial coefficient data from an anisotropic potential can be used to define an effective spherical potential. Equilibrium liquid state properties are calculated using this effective spherical potential and found to agree closely with those obtained from the original anisotropic potential.

Electron correlation effects on the N2–N2 interaction

A b initio self-consistent field, configuration interaction, and many-body perturbation theory methods are used to calculate the intermolecular potential between two nitrogen molecules. The emphasis is placed on the repulsive region important at the temperatures and pressures encountered in detonations. In addition, electron gas calculations are employed to fit and extend the ab initio data. We also generate effective spherical potentials which fit dilute gas virial, viscosity, and differential scattering data while being constrained by Hugoniot or ab initio data in the repulsive region. Finally, we discuss the roles of electron correlation and of many-body effects on the N2–N2 interaction. Comparisons are also made to the Ar2 potential where similar ab initio calculations are compared to an accurate empirical potential.

The thermodynamics of dense fluid nitrogen by molecular dynamics

We present an extensive set of molecular dynamics results for the thermodynamics of dense fluid N2. The density and temperature regime is 1.3 g/cm3≲ρ≲2.3 g/cm3 and 500 K≲T≲12 000 K. These data are then analyzed to study the effects of internal degrees of freedom on the N2 equation of state. Most importantly, we demonstrate the existence of an effective spherical potential that models very accurately (to 1.5% or better in pressure and energy) the true equation of state for the anisotropic N2 potential. We discuss the relation of this effective potential to the median average over angles and other averaging methods, including the arithmetic mean.