Thermodynamically self-consistent liquid state theories for systems with bounded potentials

The mean spherical approximation (MSA) can be solved semianalytically for the Gaussian core model (GCM) and yields exactly the same expressions for the energy and the virial equations. Taking advantage of this semianalytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the energy or virial route. Utilizing standard thermodynamic relations this leads to two differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integrodifferential-equation-based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.     

Self-consistent Ornstein-Zernike approximation for the Sogami-Ise fluid

We generalize the self-consistent Ornstein-Zernike approximation (SCOZA) to a fluid of particles with a pair potential consisting of a hard-core repulsion and a linear combination of Sogami-Ise tails, w(r)=-epsilonsigma summation operator (nu)(K(nu)/r+L(nu)z(nu))e(-z(nu)(r-sigma)). The formulation and implementation of the SCOZA takes advantage of the availability of semianalytic results for such systems within the mean-spherical approximation. The predictions for the thermodynamics, the phase behavior and the critical point are compared with optimized random phase approximation results; further, the effect of thermodynamic consistency is investigated.     

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.     

A self-consistent Ornstein-Zernike approximation for a fluid with a screened power series interaction

We present a thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) for a fluid of spherical particles with a pair potential given by a hard-core repulsion and screened power series (SPS) tails. We take advantage of the known analytic properties of the solution of the Ornstein-Zernike equation for the case in which the direct correlation function outside the repulsive core is given by the SPS tails [M. Yasutomi, J. Phys.: Condens. Matter 13, L255 (2001)]: c(r)=∑(n=1) (N)exp(-z(n)r)∑(τ=-1) (L(n) )K((n,τ))z(n) (τ+1)r(τ) r>1. The analytic properties are rewritten so as to be optimally suited to the numerical computations. The SCOZA is known to provide very good overall thermodynamics, remarkably accurate critical point, and coexistence curve. In this paper, we present some numerical results for parameters in c(r) which are chosen to fit the Lennard-Jones potential. We show that both the energy and the compressibility paths lead to the same thermodynamics with high accuracy due to the thermodynamic consistency condition that has been enforced. The present method will be applicable to fluids with a large variety of smooth, realistic isotropic potentials where the pair potentials can be fitted by the SPS tails. The fitting procedure is superior to that by multi-Yukawa tails which is the only method presented so far.     

Vapor-liquid equilibrium and critical behavior of the square-well fluid of variable range: a theoretical study

The vapor-liquid phase behavior and the critical behavior of the square-well (SW) fluid are investigated as a function of the interaction range, lambdain [1.25, 3], by means of the self-consistent Ornstein-Zernike approximation (SCOZA) and analytical equations of state based on a perturbation theory [A. L. Benavides and F. del Rio, Mol. Phys. 68, 983 (1989); A. Gil-Villegas, F. del Rio, and A. L. Benavides, Fluid Phase Equilib. 119, 97 (1996)]. For this purpose the SCOZA, which has been restricted up to now to a few model systems, has been generalized to hard-core systems with arbitrary interaction potentials requiring a fully numerical solution of an integro-partial differential equation. Both approaches, in general, describe well the liquid-vapor phase diagram of the square-well fluid when compared with simulation data. SCOZA yields very precise predictions for the coexistence curves in the case of long ranged SW interaction (lambda>1.5), and the perturbation theory is able to predict the binodal curves and the saturated pressures, for all interaction ranges considered if one stays away from the critical region. In all cases, the SCOZA gives very good predictions for the critical temperatures and the critical pressures, while the perturbation theory approach tends to slightly overestimate these quantities. Furthermore, we propose analytical expressions for the critical temperatures and pressures as a function of the square-well range.     

Hybrid integral equation/simulation model for enhancing free energy computations

Integral equation theory is used for extrapolating free energy data from molecular simulations of a reference state with respect to a modification of the interaction potential. The methodology is applied to the correction of artefacts arising from potential shifting and truncation. Corrective contributions for the hydration free energy with respect to the full potential are analysed for the case that both the solute-solvent as well as the solvent-solvent potentials are truncated and modified by a shifted-force term, reaching beyond the range of the dielectric continuum approximation and simple long-range correction expressions. The model systems argon in water and pure water are used as examples for apolar and polar solutes, revealing significant correction contributions even for the short-ranged dispersive interactions and the magnitude of solute-solvent and solvent-solvent components. In comparison with simulation-based extrapolation techniques the integral equation method is shown to be capable of quantitatively predicting truncation artefacts at negligible computational overhead.     

A new approach for efficient simulation of Coulomb interactions in ionic fluids

We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cutoff distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma-->0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.     

A Molecular Theory of the Hydration Force in an Electrolyte Solution

A model, consisting of a pair of large macroions in a dipolar hard sphere-point ion electrolyte, is considered in order to evaluate the hydration force (solvent-mediated) contribution to the force between colloidal particles, which is missing in the DLVO theory. Using the mean spherical approximation (MSA), an explicit expression for this force is obtained. It is shown that the force consists of the hard-core exclusion term that was proposed recently by Henderson and Lozada-Cassou (HLC) [J. Colloid Interface Sci.121, 486 (1988)], and a dipole alignment contribution that originates from the orientational ordering of the solvent molecules near the colloidal particles. The long-range asymptotic form of the total force is given by a Coulomb contribution and is described by the Poisson–Boltzmann or Derjaguin–Landau–Verwey–Overbeek (DLVO) result. The hydration force is short-ranged and extends about ten solvent layers and is responsible for the oscillations of the total force. The total force that we obtain is similar to the semiempirical result of HLC. The comparison with the experimental results for a 10⁻³M KCl electrolyte solution is discussed.     

Thermodiffusion of interacting colloids. II. A microscopic approach

A microscopic approach is presented to describe the contribution to the thermal diffusion coefficient of colloids due to intercolloidal particle interactions. An exact expression for the leading-order virial coefficient of the thermal diffusion coefficient of interacting colloidal spheres is derived in terms of the intercolloidal pair-interaction potential and hydrodynamic interaction functions. This general expression is explicitly evaluated for hard-core interactions and for spheres with a short-ranged attractive potential. The derivation is based on a Smoluchowski equation that is generalized to include temperature gradients. For short-ranged attractive potentials, a negative Soret coefficient is predicted under certain conditions, when the depth of the attraction increases with increasing temperature.     

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

Soft core thermodynamics from self-consistent hard core fluids

In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA)-an accurate liquid state theory that has been restricted so far to hard core systems-to arbitrary soft core systems we study a combination of SCOZA with a recently developed perturbation theory. The latter was constructed by Ben-Amotz and Stell [J. Phys. Chem. B 108, 6877 (2004)] as a reformulation of the Weeks-Chandler-Andersen [J. Chem. Phys. 54, 5237 (1971)] perturbation theory directly in terms of an arbitrary hard sphere reference system. We investigate the accuracy of the combined approach for the Lennard-Jones fluid in comparison with simulation data and pure perturbation theory predictions and determine the dependence of the thermodynamic properties and the phase behavior on the choice of the effective hard core diameter of the reference system.     

Potential functions for alkali halide molecules

Repulsion and dispersion parameters for alkali–metal halide diatomic molecules were computed by ionic Rittner and truncated Rittner models with radial dependent repulsion terms. Experimental data on the bond energies, the equilibrium interionic distances, and the spectroscopic frequencies were employed for the purpose. The polarizabilities used were also computed from the experimental dipole moments of alkali–metal halides. The potential parameters obtained were compared with parameters from other sources and checked for consistency. The computed potential parameters of alkali–metal halide monomer molecules were used to predict the energetics and geometries for alkali–metal halide dimer molecules. The predicted values are in good agreement with experiment and other calculations indicating the consistency and reliability of the potential employed. Although the magnitude of repulsive and dispersive energy terms varies with potential functions employed, the difference between the two for a molecule is constant. The repulsive term is more sensitive than the attractive term. The uncertainty in the exponential repulsion results in an inaccurate representation of the attractive contribution. Introduction of the radial-dependent repulsion term changes the relative magnitudes of repulsive and dispersive parameters and hence the relative contribution to the total potential with monomers. But this has no significant effect on the energetics and geometries of the dimers.     

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.     

Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching

A novel least-squares fitting approach is presented to obtain classical force fields from trajectory and force databases produced by ab initio (e.g., Car-Parrinello) molecular dynamics (MD) simulations. The method was applied to derive effective nonpolarizable three-site force fields for liquid water at ambient conditions from Car-Parrinello MD simulations in the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure includes a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The various parameterizations of the water force field differ by an enforced smooth cut-off applied to the short-ranged interaction term. These were obtained by fitting to the trajectory and force data produced by Car-Parrinello MD simulations of systems of 32 and 64 H(2)O molecules. The new water force fields were developed assuming both flexible or rigid molecular geometry. The simulated structural and self-diffusion properties of liquid water using the fitted force fields are in close agreement with those observed in the underlying Car-Parrinello MD simulations. The resulting empirical models compare to experiment much better than many conventional simple point charge (SPC) models. The fitted potential is also shown to combine well with more sophisticated intramolecular potentials. Importantly, the computational cost of the new models is comparable to that for SPC-like potentials.     

Liquid—gas transition for hard spheres with attractive Yukawa tail interactions

We describe the liquid-gas transition in the hard sphere system with Yukawa tail interactions in the mean spherical approximation. The dependence of critical temperature and density on the range of the interaction is shown and the spinodal curve for a short-ranged potential and a long—ranged potential is presented. The compressibility, energy and virial pressures are presented for a long-ranged potential. Liquid phase pressures are calculated by integrating round the coexistence region, rather than through it.     

Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations

Approximations to the Breit-Pauli form of the spin-orbit coupling (SOC) operator are examined. The focus is on approximations that lead to an effective quasi-one-electron operator which leads to efficient property evaluations. In particular, the accurate spin-orbit mean-field (SOMF) method developed by Hess, Marian, Wahlgren, and Gropen is examined in detail. It is compared in detail with the "effective potential" spin-orbit operator commonly used in density functional theory (DFT) and which has been criticized for not including the spin-other orbit (SOO) contribution. Both operators contain identical one-electron and Coulomb terms since the SOO contribution to the Coulomb term vanishes exactly in the SOMF treatment. Since the DFT correlation functional only contributes negligibly to the SOC the only difference between the two operators is in the exchange part. In the SOMF approximation, the SOO part is equal to two times the spin-same orbit contribution. The DFT exchange contribution is of the wrong sign and numerically shown to be in error by a factor of 2-2.5 in magnitude. The simplest possible improvement in the DFT-SOC treatment [Veff(-2X)-SOC] is to multiply the exchange contribution to the Veff operator by -2. This is verified numerically in calculations of molecular g-tensors and one-electron SOC constants of atoms and ions. Four different ways of handling the computationally critical Coulomb part of the SOMF and Veff operators are discussed and implemented. The resolution of the identity approximation is virtually exact for the SOC with standard auxiliary basis sets which need to be slightly augmented by steep s functions for heavier elements. An almost as efficient seminumerical approximation is equally accurate. The effective nuclear charge model gives results within approximately 10% (on average) of the SOMF treatment. The one-center approximation to the Coulomb and one-electron SOC terms leads to errors on the order of approximately 5%. Small absolute errors are obtained for the one-center approximation to the exchange term which is consequently the method of choice [SOMF(1X)] for large molecules.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.     

Calculations of the indirect nuclear spin–spin coupling constants of PbH4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH₄ using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation. Received: 16 November 1998 / Accepted: 30 March 1999 / Published online: 14 July 1999     

Phase behavior of ionic fluids in slitlike pores: a density functional approach for the restricted primitive model

We present a density functional theory of nonuniform ionic fluids. This theory is based on the application of the electrostatic contribution to the free energy functional arising from mean spherical approximation for a bulk restricted primitive model and from the energy route bulk equation of state. In order to employ this functional we define a reference fluid and additional averaged densities, according to the approach introduced by Gillespie, Nonner and Eisenberg [J. Phys.: Condens. Matter 14, 12129 (2002)]. In the case of bulk systems the proposed theory reduces to the mean spherical approximation equation of state, arising from the energy route and thus it predicts the first-order phase transition. We use this theory to investigate the effects of confinement on the liquid-vapor equilibria. Two cases are considered, namely an electrolyte confined to the pore with uncharged walls and with charged walls. The dependence of the capillary evaporation diagrams on the pore width and on the electrostatic potential is determined.