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.     

Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail

One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.     

The Pauli energy grows exponentially with the electronic localisation

We investigate the Pauli energy in atoms and molecules as a measure of electron localisation. Our results indicate that the Pauli energy has an exponential dependence on the number of localised electrons. This relationship yields to a kinetic energy density expression that depends on the electron density ρ(r) and the pair density ρ₂(r, r′). The proposed equation shows certain advantages over a similar orbital-free kinetic energy functional recently proposed by Delle Site and co-workers. The methodology introduced here is a novel approach for exploring electronic quantities with a partition scheme that might be useful for research in density functional theory.     

Augmented Kierlik-Rosinberg Fundamental Measure Functional andExtension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids

From point of view of weighted density procedure, it isguessed that a Percus-Yevick (PY) compressibility excess free energydensity, appearing in the Kierlik--Rosinberg type fundamentalmeasure functional (KR-FMF) and expressed in terms of scaledparticle variables, can be substituted by a corresponding expressiondictated by a more accurate Mansoori-Carnahan-Starling-Leland(MCSL) equation of state, while retaining the original weightingfunctions; it is numerically indicated that the resultantundesirable non-self-consistency between the PY type weightingfunction and MCSL type excess free energy density had no bad effecton the performance of the resultant augmented KR-FMF which, on theone hand, preserves the exact low-density limit of the originalKR-FMF and holds a high degree of pressure self-consistency, on theother hand, improves significantly, as expected, the predictions ofdensity profile of hard sphere fluid at single hard wall contactlocation and its vicinity, and of the bulk hard sphere second orderdirect correlation function (DCF), obtained from functionaldifferentiation. The FMF is made applicable to inhomogeneousnon-hard sphere fluids by supplementing a functional perturbationexpansion approximation truncated at the lowest order with summationof higher order terms beyond the lowest term calculated by the FMFfor an effective hard sphere fluid; the resultant extended FMF onlyneeds second order DCF and pressure of the fluid considered atcoexistence state as inputs, consequently is applicable whether theconsidered temperature is above critical point or below criticalpoint. The extended MCSL-augmented KR-FMF is found to be endowedwith an excellent performance for predictions of density profile andsurface tension by comparing the present predictions of these twoquantities with available computer simulation data for inhomogeneoushard core attractive Yukawa fluid and Lennard-Jones fluid.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.     

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.     

The Explicit Density Functional and Its Connection with Entropy Maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.     

接枝聚合物对小分子的选择性吸附研究

文章应用密度泛函理论研究接枝于壁面的方阱链对二元小分子混合物的选择性吸附特性. 系统的Helmholtz剩余自由能泛函被表示为硬球排斥和方阱吸引两部分贡献之和,分别由硬球链流体状态方程和变阱宽方阱链流体状态方程的简单加权密度近似来进行计算. 用此理论方法,分别考察了接枝聚合物的结构性质,以及不同温度下接枝分子层对二元方阱流体的选择性吸附性能. 结果表明:分子刷厚度随接枝密度线性增长而随温度非线性增加,并且在高温下趋于饱和;在较低温度下,接枝聚合物刷能表现出很好的选择性吸附能力,当聚合物刷被加热到高于饱和温度时,该能力将大幅度地减弱. 关键词： 密度泛函理论 接枝聚合物 选择性吸附 方阱链     

Density Functional Approach Based on Numerically Obtained Bridge Functional

The Ornstein Zernike equation is solved with the Rogers Young approximation for bulk hard sphere fluidand Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combinedwith the test particle method is employed to determine numerically the function relationship of bridge functional as afunction of indirect correlation function. It is found that all of the calculated points from different phase space statepoints for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used tosubstitute the analytic expression of the bridge functional as a function of indirect correlation function required in themethodology [J. Chem. Phys. 112 (2000) 8079] to deterrnine the density distribution of non-uniform hard spherefluid and Lennard Jones fluid. The good agreement of theoretical predictions with the computer simulation data isobtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function intothe constructing of the density functional approximation and makes the original methodology more accurate and moreflexible for various interaction potential fluid.     

A three-component model on the structure of colloidal solution with size-asymmetric electrolytes

ABSTRACT

A three-component model on the structure of colloidal solution with size asymmetric electrolytes is attempted here using density functional theory and Monte Carlo simulation. The solvent is represented as an individual component along with that as a dielectric continuum. The theory uses a weighted density approximation for the hard-sphere contribution to the free energy, whereas the ionic contribution is evaluated through a perturbation expansion around the bulk density. The theory is found to reproduce the simulation data quite well for a wide range of parametric conditions. The present study reflects the importance of the presence of the solvent in determining the structural behaviour of spherical double layers.     

Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules

An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the manybody electronic problem here resembles the Kohn–Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg–Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg–Kohn theorems do also hold for a density model of this type. We then present a proof-of-concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.     

Exact orbital-free kinetic energy functional for general many-electron systems

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.     

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．     

Detailed investigation of thermodynamic properties of hexagonal osmium using the ab-initio technique

The finite-temperature density functional theory and the quasiharmonic approximation are adopted to investigate thermodynamics properties of hexagonal osmium. By varying lattice volume, the anharmonic effect is part considered in present work. Phonon frequencies calculations are performed from density functional perturbation theory (DFPT). By fitting the total free energy (including both electronic and vibrational parts) to equation of states at different temperatures, some classical thermodynamic quantities and their pressure and temperature dependences are investigated systematically. The results are in good agreement with the available experimental and theoretical data.     

高压下氧化镉弹性性质、电子结构和光学性质的第一性原理研究

 运用基于密度泛函理论的平面波赝势方法（PWP）,计算研究了氧化镉NaCl结构（B1结构）和CsCl结构（B2结构）在不同压力条件下的几何结构、弹性性质、电子结构和光学性质。交换关联能分别采用广义梯度近似（GGA）和局域密度近似（LDA）。通过比较计算和实验得到的晶格常数和体模量不难发现,LDA的计算结果更符合实验值。在高压的作用下,两种结构的导带能级有向高能级移动的趋势,而价带能级有向低能级移动的趋势,因此直接带隙变大。同时,对照态密度分布图及高压下能级的移动情况,分析了CdO两种结构在高压作用下的光学性质。     

An effective tridental molecular clip for fullerenes

By means of density functional calculations, we studied the performance of 2 fullerene receptors that contain 3 corannulene or triphenylene pincers. For the first time, we found a receptor that has a small tendency to form intramolecular stacks between the 3 corannulene pincers. After comparing their ability to trap fullerenes, with that of buckycatcher, buckycatcher‐II, and the Venus flytrap, we conclude that a record‐breaking association constant is expected for the receptor with 3 corannulene pincers. Although triphenylene is less effective than the corannulene units in forming inclusion complexes with C₆₀, the triphenylene‐based host is also expected to have a high association constant. Finally, we discuss the theoretical problems found in reproducing the experimental free energy changes in solution for buckycatcher, buckycatcher‐II, and the Venus flytrap.     

Advances and challenges in DFT-based energy materials design

The growing worldwide energy needs call for developing novel materials for energy applications. Ab initio density functional theory (DFT) calculations allow the understanding and prediction of material properties at the atomic scale, thus, play an important role in energy materials design. Due to the fast progress of computer power and development of calculation methodologies, DFT-based calculations have greatly improved their predictive power, and are now leading to a paradigm shift towards theory-driven materials design. The aim of this perspective is to introduce the advances in DFT calculations which accelerate energy materials design. We first present state-of-the-art DFT methods for accurate simulation of various key properties of energy materials. Then we show examples of how these advances lead to the discovery of new energy materials for photovoltaic, photocatalytic, thermoelectric, and battery applications. The challenges and future research directions in computational design of energy materials are highlighted at the end.