Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.     

Equilibrium properties of a semiclassical fluid with square-well plus hard core potential

A cluster expansion theory, in which the quantum hard sphere system is taken as a reference system and the attractive interactions as a perturbation, is applied to calculate the equilibrium properties of the square-well fluid in the semiclassical limit. The radial distribution function and direct correlation function are obtained using the exponential approximation. The isothermal compressibility is also evaluated.     

非迭代冻结密度近似方法在计算氢键相互作用的合理性研究

为计算相互作用较弱的分子碎片之间的耦合能,Harris从密度泛函理论出发,提出了一种简化方法,即冻结密度近似(FDA)方法.对该方法在描述分子间氢键作用的合理性进行了验证.对水分子间的HO┉H氢键、甲酰胺与水分子间的NH┉O氢键、二氟甲烷和水分子间的OH┉F氢键,以及DNA中的碱基(AT,GC)之间的N—H┉O,N—H┉N等类型的氢键的计算表明:若电子交换关联采用非定域自旋密度近似,FDA的计算结果同其他abinitio方法的计算结果以及实验结果都符合得很好.FDA在计算过程中既不需要求解泊松方程,也不需要进行反复的自洽迭代,所以运算速度较快,在研究生物大分子体系中的氢键相互作用方面具有一定的使用价值 关键词： 冻结密度近似 氢键 密度泛函     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

A New Uniform Phase Bridge Functional: Test and Its Application to Non-uniform Phase Fluid

A new bridge functional as a function of indirect correlation function was proposed, which was basedon analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whoserenormalization resulted in an adjustable parameter determined by the thermodynamics consistency condition. Theproposed bridge functional was tested by applying it to bulk hard sphere and hard core Yukawa fluid for the predictionof structure and thermodynamics properties based on the OZ equation. As an application, the present bridge functionalwas employed for non-uniform fluid of the above two kinds by means of the density functional theory methodology, theresulting density distribution profiles were in good agreement with the available computer simulation data.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

The generating functional for the probability density functions of Navier-Stokes turbulence

A generating functional for the equal-time spatial probability density functions which represent the ensemble of turbulent incompressible Navier-Stokes fluids is introduced. By formally solving the linear evolution equation satisfied by this functional, the probability densities are represented as functional integrals. It is shown that the generating functional can be regarded as the space characteristic functional of a generalized random field defined on the phase space spanned by the material position and velocity fields of a fluid particle. The interpretation of this random field, which satisfies a dynamical equation similar to Vlasov's, is clarified through the formal analogies between the statistics of molecules and fluid particles at the functional level. A class of statistically realizable and solvable models is also considered within the context of the present formalism.     

Shielded distribution approximation for a wall-bounded classical fluid

We investigate lower order distribution functions in classical fluids in the presence of large-scale inhomogeneities, in particular those imposed by wall contacts. The consequences of the effective shielding of a wall by the nearest particle of the set being considered are determined in the context of two distribution function hierarchies, kinematic and dynamic in origin. The effects of both flat and spherical, hard and soft walls are considered, as well as those of curved and double walls. A few correction sequences to the basic shielding approximation are discussed.Supported in part by the Department of Energy under contract DE-AC02-76 ERO 3077.     

Time-dependent density functional theory for quantum transport

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reducedsingle electron density matrix based hierarchical equation of motion, which can be derived from Liouville–von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.     

Solvation force in hard ellipsoid fluids with HNW interaction

In present work, using density functional theory and extended restricted orientation model, the one particle density of hard Gaussian overlap fluid near the colloid walls is calculated. The hard needle–wall interaction between molecules and colloids are considered. Using non-linear equation, proposed by Grimson–Rickyazen, the solvation force of hard ellipsoidal molecular fluid with hard Gaussian overlap interaction is calculated. We could not find the exact or simulation results for comparison. The results in the case k = 2.0 are compared with the solvation force of one-dimensional hard rod fluids. The results are corresponded, qualitatively.     

A new real-space algorithm for realistic density functional calculations

We present the implementation of a fast real-space algorithm for density functional calculations for atomic nanoclusters. The numerical method is based on a fourth-order operator splitting technique for the solution of the Kohn-Sham equation [1]. The convergence of the procedure is about one order of magnitude better than that of previously used second-order operator factorizations. The method has now been extended to deal with non-local pseudopotentials of the Kleinman-Bylander [2] type, permitting calculations for realistic systems, without significantly degrading the convergence rate. We demonstrate the convergence of the method for the examples C and C₆₀ and present examples of structure calculations of Na and Mg clusters.     

两相湍流统一色噪声法概率密度函数模型

统一色噪声近似方法对简单一维色噪声问题研究较为充分, 本文将统一色噪声法应用到高度复杂的多维气固两相湍流系统之中.首先从颗粒运动Langevin方程出发, 利用统一色噪声法获得两相湍流Fokker-Planck方程, 然后以此为基础建立颗粒轨道两阶矩模型.文中建立的新模型成功应用于后台阶两相湍流流场的数值模拟, 预报合理正确.研究表明, 对于多维两相湍流系统, 统一色噪声法仍然行之有效.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

Density functional theory for molecular orientation of hard rod fluids in hard slits

A density functional theory (DFT) is used to investigate molecular orientation of hard rod fluids in a hard slit. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect with the first order thermodynamics perturbation theory for chain connectivity. In the DFT approach, the intra-molecular bonding orientation function is introduced. We consider the effects of molecular length (i.e. aspect ratio of rod) and packing fraction on the orientations of hard rod fluids and flexible chains. For the flexible chains, the chain length has no significant effect while the packing fraction shows slight effect on the molecular orientation distribution. In contrast, for the hard rod fluids, the chain length determines the molecular orientation distribution, while the packing fraction has no significant effect on the molecular orientation distribution. By making a comparison between molecular orientations of the flexible chain and the hard rod fluid, we find that the molecular stiffness distinctly affects the molecular orientation. In addition, partitioning coefficient indicates that the longer rodlike molecule is more difficult to enter the confined phase, especially at low bulk packing fractions.     

扩展桥密度泛函近似于非匀一非硬球流体

为了将非匀一硬球流体的桥密度泛函近似扩展到非匀一非硬球流体,提出了一个理论方案．所得的LJ流体的密度泛函近似计算简单,精确．特别是密度泛函近似仅仅需要共存体相流体的二阶直接相关函数作为输入,因而可以应用于超临界与亚临界温度．所提出的理论方案可以认为是热力学理论的非匀一对应物．     

Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory

We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.     

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus–Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus–Yevick theory for this system and a reasonable compromise between accuracy and simplicity.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

硅团簇自旋电子器件的理论研究

利用过渡金属掺杂的硅基团簇, 构建了一种自旋分子结; 并利用第一性原理方法, 对其电子自旋极化输运性质进行了研究. 计算表明, 通过过渡金属掺杂可以有效地产生自旋极化电流, 磁性金属Fe和非磁性金属Cr和Mn掺杂的体系呈现出较明显的自旋极化透射现象, 但分子结的自旋极化输运能力与团簇孤立状态下的磁矩无一致性.从Sc到Ni的掺杂, 体系的自旋极化透射能力先增大后迅速减小, 在Fe掺杂的Si₁₂团簇中出现最大值. 关键词： 硅团簇 自旋极化输运 密度泛函理论 非平衡格林函数