An efficient method for accurate evaluation of the site–site direct correlation functions of molecular fluids

The direct correlation function (DCF) plays an important role in liquid integral-equation theories and non-mean-field applications of the classical density functional theory (DFT). While for a simple fluid the DCF can easily be calculated from the radial distribution function via the Fourier transform and/or, for special cases, can be derived from analytical solutions of the Ornstein–Zernike equation, computation of the site–site DCFs of a molecular fluid is more challenging because of numerical issues associated with solving the matrix integral equations. This paper describes a new theoretical method for accurate evaluation of the site–site DCFs of molecular fluids by combination of molecular simulation and analytical asymptotic analysis. The computational procedure entails four steps: (1) molecular simulation is used to calculate the site–site total correlation functions (TCFs) in real space; (2) the reference-interaction-site model (RISM) is used to calculate the site–site DCFs in Fourier space at large wavenumbers; (3) asymptotic expressions are derived for the TCFs and DCFs in the limit of small wavenumbers; and (4) site–site DCFs over the entire range are obtained by interpolation of the asymptotic results. The numerical procedure has been illustrated by application to bulk SPC/E water. Accurate evaluation of the site–site DCFs for water lays a foundation for future applications of the DFT to aqueous systems with atomic details.     

Chandler—Silbey—Ladanyi integral equation theory for semiflexible molecules

Extension of Chandler—Silbey—Ladanyi (CSL) integral equation theory for the fluid of semi-flexible site—site molecules is proposed. The Percus—Yevick type of the closure is used to describe the structural properties of the fluid consisting of semiflexible linear chain triatomic molecules. Results for the site—site intramolecular and intermolecular radial distribution functions (RDFs) are compared with the corresponding computer simulation results and results of self-consistent reference interaction site model (RISM) theory. In general both theories give reasonably good agreement with corresponding Monte Carlo simulation data. The exception is the RDF between the terminal sites, for which none of the theories is satisfactory. The present version of CSL theory appears to be slightly more accurate than the self-consistent RISM approach.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.     

Liquids in equilibrium: Beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T_c is predicted from the structure route. This T_c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.     

Structure and equation of state of interaction site models for disc-shaped lamellar colloids

We apply RISM (reference interaction site model) and PRISM (polymer-RISM) theories to calculate the site–site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness Dσ. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number n of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic–nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios Dσ nearly collapse on a single master curve.     

Model of silica glass from combined classical and ab initio molecular-dynamics simulations

A Car-Parrinello (CP) molecular dynamics simulation of vitreous silica, combined with classical molecular dynamics, is presented. The equilibration of the liquid, quench and relaxation of the glass are performed classically using the van Beest, Kramer and van Santen (BKS) potential [12] and the resulting configuration (coordinates and velocities) is used as input for the CP simulation. A remarkable stability of the CP dynamics is observed justifying this procedure and validating the BKS potential. Several structural and electronic properties are calculated and compared with experiments. Received 23 March 1999 and Received in final form 15 July 1999     

Density functional theory of liquids, some extensions and applications

The density functional theory(DFT) of nonuniform liquids plays an important role in classical many-body theory because of its (mathematical)simplicity and (physical)clarity. Some extensions and applications of DFT, including a new proposal for an m-body hypernetted-chain(HNC) equation for the static structure of liquids are presented.     

Quantum-mechanical calculations based on density functional theory

The basic concepts of density functional theory (DFT) together with the local density approximation (LDA) and the recent improvement in form of the generalized gradient approximations (GGA) are discussed. Band structure calculations using the full-potential linearized augmented plane wave (FP-LAPW) method are presented in relation to pseudopotential schemes both corresponding to T=0. For finite temperatures the most advanced technique is the Car-Parrinello (CP) molecular dynamics (MD) approach, e.g. in its projector augmented wave (PAW) implementation. In CP-MD simulations nuclear motion and the electronic degrees of freedom are treated within one formalism. Such DFT calculations are illustrated for selected examples, including the breathing mode of BaBiO₃. the phase transition in SrTiO₃ and VO₂ and the Li diffusion in the superionic conductor Li₃N studied by conventional and CP molecular dynamics.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Density functional theory approach to the freezing transition in two-dimensional colloid system

The freezing transition of two-dimensional colloid system is studied by the density functional theory (DFT). The liquid direct-pair correlation function (DPCF) is simulated by molecular dynamics simulations. With the DPCF, the freezing transition is determined using DFT with the Fourier components of the density ρ _K as the order parameters. The DFT results are consistent with the simulation results if ρ _Ks of the lowest three shells of reciprocal lattice vector (RLV) are used in the DFT calculation. The first order freezing transition takes place at DPCF ρ₀ C(k_a) = 0.788 on the first RLV shell. The laser induced freezing of colloid system is also studied using the DFT.     

氮气在MCM-41中毛细凝聚的模拟和理论研究

采用巨正则系综 Monte Carlo 方法(GCMC)以及基于扩展基本度量理论和 MBWR 状态方程的密度泛函理论,研究了 77.4 K 时氮气在不同孔径的 MCM-41 分子筛中吸附的密度分布和吸附等温线.提出的平均场权重密度泛函理论,克服了平均场近似预测主体相热力学性质时的偏差,获得的密度分布和吸附等温线与 GCMC 分子模拟结果有着很好的一致性.     

Analytic solution of the RISM equation for symmetric diatomics with Yukawa closure

We present the site-site direct correlation function c(r) for a fluid of hard diatomic symmetric molecules obtained from Monte Carlo simulation data via the RISM integral equation. This c(r) ensures that the site-site correlation function given by the RISM equation is exact, and thus provides a basis for critically examining the usual closure for the RISM equation. As an example of an improved closure we present the analytic solution of the RISM integral equation with a Yukawa closure for c(r).     

Wave packet molecular dynamics–density functional theory method for non‐ideal plasma and warm dense matter simulations

A new wave packet molecular dynamics–density functional theory (WPMD‐DFT) method is proposed for atomistic simulations of non‐ideal plasma and warm dense matter. The method is based on the WPMD approach, where the electronic exchange and correlation effects are treated using an additional energy term taken from DFT. This term is calculated by integration over the mesh values of the wave packet density. The local density approximation is implemented so far. WPMD‐DFT is meant as a replacement for the anti‐symmetrized WPMD (AWPMD) method which is more time consuming and lacks electron correlation. In this paper, we compare the results obtained by WPMD‐DFT, WPMD, AWPMD, classical molecular dynamics, and path integral Monte Carlo methods for the internal energy of the hydrogen plasma in the temperature range 10–50 kK and electron number density from 10²⁰ to 10²⁴ cm^?3. We also demonstrate the ability to handle the simultaneous dynamics of electrons and ions by calculating the electron–ion temperature relaxation. The scalability of the WPMD‐DFT method with the number of electrons is shown for implementations in central processing unit and graphical processing unit.     

The mean spherical model for asymmetric electrolytes: thermodynamics and the pair correlation function

It is shown that the RISM theory of molecular liquids provides an accurate prediction of the measured neutron scattering structure factor of deuterated liquid chloroform.     

Correlation functions for diatomic symmetric molecules from the RISM equation

Using the solution of the RISM equation for diatomic symmetric molecules outlined in a previous paper, the site-site radial distribution function (RDF) is calculated and compared with the Monte Carlo results and the numerical RDF of Lowden and Chandler. The RDF calculated here and the numerical RDF of Lowden and Chandler agree well at intermediate and high densities. At low density, however, both have systematic errors. The agreement between the RDF calculated here and the Monte Carlo results suggests that a simplified formulation of the RISM solution may serve well as a reference system in a perturbation theory for diatomic fluids.     

The structure of liquid bromine

The atom-atom correlation function for liquid bromine, derived from the X-ray diffraction studies reported in the preceding paper, is compared with the results of Monte Carlo computer simulations and reference site interaction model (RISM) calculations for various bromine-like model molecules. The models used included the two-centre Lennard-Jones interaction model, both by itself and with idealized point quadrupole and quadrupole-induced dipole interaction terms in the computer simulations, and two and three-centre hard-sphere models in RISM. None of these models lead to atom-atom correlation functions which are in good agreement with that obtained from experiment. This suggests that additional information about the interactions between bromine molecules will be needed before the structure of liquid bromine can be completely understood. Finally, by comparing the results of our computer simulations with RISM results for analogous models, we obtain some insight into the accuracy of the reference site interaction model.     

Structural properties of effective potential model by liquid state theories

This paper investigates the structural properties of a model fluid dictated by an effective inter-particle oscillatory potential by grand canonical ensemble Monte Carlo (GCEMC) simulation and classical liquid state theories.The chosen oscillatory potential incorporates basic interaction terms used in modeling of various complex fluids which is composed of mesoscopic particles dispersed in a solvent bath,the studied structural properties include radial distribution function in bulk and inhomogeneous density distribution profile due to influence of several external fields.The GCEMC results are employed to test the validity of two recently proposed theoretical approaches in the field of atomic fluids.One is an Ornstein-Zernike integral equation theory approach;the other is a third order + second order perturbation density functional theory.Satisfactory agreement between the GCEMC simulation and the pure theories fully indicates the ready adaptability of the atomic fluid theories to effective model potentials in complex fluids,and classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids under the single component macro-fluid approximation.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

金属铜的晶格结构与热力学性质的第一性原理计算

基于第一性原理,利用密度泛函理论(DFT)和密度泛函的微扰理论(DFPT),以及广义梯度近似(GGA),研究了过渡金属Cu的晶体结构、能量、电子能带和态密度、声子的能带结构和态密度,以及其在298.15K下的热容,体积模量,格林艾森参数和体胀系数等热力学函数并与实验值作了对比.通过分析Cu的晶格几何与能量之间的关系,讨论了金属Cu的固-液相变与晶格声子振动能量之间可能的内在联系,首次提出直接得到Cu熔化温度Tm的静力学方法,研究了熔化温度与压强的关系.计算结果与实验值符合较好,明显优于分子动力学模拟的结果.     

Exchange-correlation and layer-thickness effects in quasi-two dimensional electron liquids

We demonstrate a replacement of the non-uniform sub-band density of quasi-2D electron layers by an effective uniform-slab density. Exchange, correlation and Fermi-liquid properties are determined via a mapping of the electron liquid to a classical fluid, using the hyper-netted-chain equation inclusive of bridge corrections, (i.e. the CHNC), as a function of the density, spin-polarization, layer width and the temperature. Our parameters-free theory is in good accord with quantum simulations, with effective-mass and spin-susceptibility results for 2D layers found in GaAs/AlGaAs structures.