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.     

Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures

An enhanced KR-fundamental measure functional (FMF) is elaborated andemployed to investigate binary and ternary hard sphere fluids near a planarhard wall or confined within two planar hard walls separated by certaininterval. The present enhanced KR-FMF incorporates respectively, for aim ofcomparison, a recent 3rd-order expansion equation of state (EOS) and aBoublik's extension of Kolafa's EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory (SPT) relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictionsand corresponding density profiles produced in different periods indicatesthe excellent performance of the present enhanced KR-FMF-3rd-order EOS incomparison with other available density functional approximations (DFAs).There are two anomalous situations from whose density profiles all DFAsstudied deviate significantly; however, subsequent new computer simulationresults for state conditions similar to the two anomalous situations are invery excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that (i) the validity of the ``naive' substitutionelaborated in the present paper and peculiar to the original KR-FMF is stillin operation even if inhomogeneous mixtures are being dealt with; (ii) thehigh accuracy and self-consistency of the third order EOS seem to allow forapplication of the KR-FMF-third order EOS to more severe state conditions;and (iii) the ``naive' substitution enables very easy the combination of theoriginal KR-FMF with future's more accurate but potentially more complicatedEOS of hard sphere mixtures.     

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 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.     

Electronic Excitations in Pyrrole: A Test Case for Determination of Chromophores in the Chromogenic Effects of Neurotoxic Hydrocarbons by Time-Dependent Density Functional Theory and Single-Excitation Configuration Interaction Methods

Time-dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) calculations on the electronic excitations in pyrrole have been performed to examine the reliability of these first-principles electronic structure methods in predicting electronic excitation spectraof pyrrole-containing compounds. Both the TD-DFT and CIS calculations led to satisfactory results when compared to available experimental data, particularly for low-lying excited states. The TD-DFT and CIS calculations provide lower and upper limits of the excitation energies, respectively, for low-lying singlet excited states. These results suggest that these methods can be used for the prediction of the excitation spectra, particularly the excitation energies for low-lying excited states, of chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons, which are believed to be substituted pyrroles and their adducts with proteins. As an example of a practical application, the spectrum of the widely used 2,5-dimethylpyrrole has been calculated. It is shown that the 2,5-dimethylpyrrole molecule does not have an absorption in the region of the visible spectrum (400-700 nm), suggesting that the absorption observed at 530 nm and the color of 2,5-dimethylpyrrole is due to another species, probably a product of possible 2,5-dimethylpyrrole autoxidation. This suggests that the conclusions from previously reported experimental studies of biochemical reactions of neurotoxic γ-diketones need to be reexamined in terms of the relationship of chromogenicity to neurotoxicity.     

Contact values of highly asymmetric hard sphere mixtures from Fundamental Measure Density Functional Theory

The White Bear version of Fundamental Measure Theory (FMT-WB) has been tested in binary mixtures of hard spheres in the vicinity of the colloidal limit, where the size ratio of the two species is exceedingly large and the large sphere mole fraction is infinitely low. Contact values of large–large sphere radial distribution functions have been calculated and compared with molecular dynamics simulations and previously proposed theoretical formulas. In contrast to the failure of BMCSL (Boublik, Mansoori, Carnahan, Starling, Leland equation of state) predictions, FMT-WB gives good agreement with simulation for a range of species size ratios and mole fractions. The performance of BMCSL is qualitatively related to one of its model parameters, which could indicate the reliability of the BMCSL result. Our results confirm the accuracy of FMT-WB in the colloidal limit for the first time and suggest that BMCSL contact values must be applied carefully to account for chain connectivity when studying certain cases with classical Density Functional Theories.     

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.     

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.     

Mean Spherical Approximation-Based Partitioned Density Functional Theory

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.     

Density Functional Study of Cationic and Anionic Ag_mCu_n (m + n ≤ 5) Clusters

The structural and energetic properties of bimetallic Ag m Cu n clusters (m + n ≤ 5) in the cationic and anionic charged states have been investigated by density functional theory with relativistic effective core potentails.The stable cationic pentamers have three-dimensional structures in contrast to anionic clusters assume planar structures.For the given cluster size the electron affinities decrease as the Cu content increases,while no clear trend can be found in adiabatic ionization potentials.The binding energy per atom also increases with the increasing Cu content and follows the order anion cation.The most probable dissociation channels of the clusters considered are also discussed.     

利用密度泛函理论研究六种多环芳烃的分子结构以及拉曼光谱

利用DFT理论B3LYP/6-31+G(d, p)方法对六种PAHs分子进行理论计算, 可以得到六种多环芳烃分子的分子构型信息, 其中包括具体的键长、键角以及整个分子的长宽信息, 从而为我们能够更加深入地理解稠环芳烃的大小与环糊精内腔的尺寸匹配效应对SERS增强效果的影响提供了理论依据; 还利用Gaussview对这些分子的拉曼光谱给出具体的峰位, 并对计算出的六种多环芳烃的拉曼光谱进行主要峰位的指认。通过与实验测得拉曼光谱的对应关系, 从而对实验所得的拉曼光谱在理论上进行了有力的补充。     

On the Derivation of a Density Functional Theory for Microphase Separation of Diblock Copolymers

We consider here the problem of phase separation in copolymer melts. The Ohta–Kawasaki density functional theory gives rise to a nonlocal Cahn–Hilliard-like functional, promoting the use of ansatz-free mathematical tools for the investigation of minimizers. In this article we re-derive this functional as an offspring of the self-consistent mean field theory, connecting all parameters to the fundamental material parameters and clearly identifying all the approximations used. As a simple example of an ansatz-free investigation, we calculate the surface tension in the strong segregation limit, independent of any phase geometry.     

CdS掺Mg和Ni电子结构和光学性质的密度泛函理论研究

采用基于密度泛函理论的第一性原理赝势平面波方法,对闪锌矿结构CdS和CdS∶M(M=Mg,Ni)几何结构、能带结构、电子态密度和光学性质进行了系统的研究。几何结构研究对掺杂后体系晶格常量进行了优化计算,结果表明Mg和Ni原子掺入CdS后晶格常量均减小,晶格发生局部畸变。进一步研究了掺杂对体系电子结构的影响,能带结构和电子态密度分析表明由于Ni 3d电子的引入使CdS∶Ni成为半金属铁磁半导体,而Mg 3s电子的引入CdS∶Mg带隙变宽。另外,体系掺杂后,吸收系数分析表明掺杂导致吸收峰在可见光波长区域变化显著,且掺Ni导致吸收峰进一步向长波方向移动。     

Universality principle and the development of classical density functional theory

The universality principle of the free energy density functional and the ‘test particle' trick by Percus are combined to construct the approximate free energy density functional or its functional derivative. Information about the bulk fluid radial distribution function is integrated into the density functional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum density functional theory.     

Structures and Stability of Metal Amidoboranes （MAB）： Density Functional Calculations

Molecule geometry structures, frequencies, and energetic stabilities of ammonia borane （AB, NH3BH3 ） and metal amidoboranes （MAB, MNH2BH3）, formed by substituting H atom in AB with one of main group metal atoms, have been investigated by density-functional theory and optimized at the B3LYP levels with 6-311G＋＋ （3dr, 3pd） basic set. Their structural parameters and infrared spectrum characteristic peaks have been predicted, which should be the criterion of a successfully synthesized material. Several parameters such as binding energies, vibrational frequencies, and the energy gaps between the HOMO and the LUMO have been adopted to characterize and evaluate their structure stabilities. It is also found that the binding energies and HOMO-LUMO energy gaps of the MAB obviously change with the substitution of the atoms. MgAB has the lowest binding energy and is easier to decompose than any other substitutional structures under same conditions, while CaAB has the highest chemical activity.     

Mean Spherical Approximation-Based Partitioned Density Functional Theory

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0^(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ^3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.     

杀草强分子的拉曼光谱的密度泛函理论研究

本文采用密度泛函理论(density functional theory,DFT),在B3LYP杂化泛函,6-31++g(d,p)(C,H,N)和LanL2DZ(Ag)基组下对杀草强分子及其Ag复合物的结构进行了优化;通过频率计算,获得了杀草强分子及其Ag复合物的拉曼光谱,并利用势能函数分布(PED)对拉曼光谱进行了指认,结合SERS光谱推测了杀草强和增强基底之间的吸附方式;采用含时密度泛函理论(time dependent density functional theory,TDDFT)对杀草强分子和杀草强分子-Ag复合物进行了激发态的分析计算。     

FeS2(pyrite)电子结构与光学性质的密度泛函计算

采用局域密度近似的自洽密度泛函理论计算了FeS2的电子结构与光学性质。费米能级附近区域的能带与态密度计算表明价带极大值在X（100）点和导带极小值在G（000）点,直接带隙和音接带隙分别为0.74eV、0.6eV。并用电子结构信息精确计算了介质极化矩阵元,从而给出了FeS2的介电函数虚部及相关光学参量,理论结果与实验符合甚佳。     

吩噻嗪表面增强拉曼光谱的密度泛函理论研究

吩噻嗪是含有N、S的杂环化合物,具有大的离域π键。用Gaussian 09程序,在B3LYP方法下,Ag原子使用LANL2DZ赝式基组,C、H、N、S等原子使用6-31++G(d,p)基组,优化并计算了吩噻嗪和吩噻嗪银配合物(PTH-Ag)的拉曼光谱,并利用GaussianView对PTH分子进行归属,为食品和产品中吩噻嗪残留的定性、定量测定提供理论依据。计算结果说明连接Ag原子越多,增强效果越明显。     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.