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

From point of view of weighted density procedure, it is guessed that a Percus-Yevick （PY） compressibility excess free energy density, appearing in the Kierlik Rosinberg type fundamental measure functional （KR-FMF） and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori Carnahan-Starling Leland （MCSL） equation of state, while retaining the original weighting functions; it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting function and MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-ffMF which, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressure self-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard sphere fluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlation function （DCF）, obtained from functional differentiation. The FMF is made applicable to inhomogeneous non-hard sphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order with summation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid; the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state as inputs, consequently is applicable whether the considered temperature is above critical point or below critical point. The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions of density profile and surface tension by comparing the present predictions of these two quantities with available computer simulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard-3ones 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.     

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．     

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.     

三碘甲状腺素团簇结构与光谱性质的密度泛函理论研究

我们利用密度泛函理论(DFT),在B3LYP/Lan12mb基组水平上,得到了三碘甲状腺素团簇的几何和电子结构.在此基础上,利用含时密度泛函理论(TDDFT),使用相同的基组和采用极化连续介质模型(PCM),对其溶剂效应下的吸收光谱进行研究．研究结果表明,优化所得三碘甲状腺素团簇的对称性为C₁;在基态稳定结构基础上,研究了该分子的红外和拉曼分子振动谱特性,同时研究了其输运性质,即三碘甲状腺素团簇为p型输运材料;通过含时密度泛函理论,在优化好的基态结构基础上,又计算了它的溶剂效应,进一步得出该分子在水溶剂中的吸收光谱特性.     

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.     

密度泛函理论研究吲哚并咔唑同分异构体结构,芳香性和光谱性质

在B3LPY/6-31G(d, p)基组水平上,利用密度泛函理论(DFT)优化了吲哚并咔唑五种同分异构体的几何和电子结构.基于这五种同分异构体的几何结构下,其吸收和发射光谱的研究使用相同的基组水平并采用极化连续介质模型(PCM)下用含时密度泛函理论(TD-DFT)计算.由于三种近似线性分子(吲哚并[2,3-a]咔唑、吲哚并[2,3-b]咔唑和吲哚并[3,2-b]咔唑)的电荷转移跃迁的振荡强度较大,这些异构体的发射光谱存在明显差异;基于吲哚并[2,3-c]咔唑和吲哚并[3,2-a]咔唑的构型特征,这两种同分异构体的发射谱具有高能量.比较计算结果表明,吲哚并[2,3-b]咔唑在这些分子中的振荡强度最大.这是因为当吲哚并咔唑的五种同分异构体的结构从基态变为激发态时,这些分子的分子轨道(MO)能级不同.由计算结果还得出,这五个分子适用于P型传输材料,并且每个分子的三个苯环均具有共轭效应.     

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.     

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.     

钯催化亚烷基环丙基酮开环反应机制的理论研究

在BHandHLYP/6-31G(d,p)（Pd用LANL2DZ基组）计算水平上对钯催化的亚烷基环丙酮开环反应机制进行了理论研究,使用极化连续介质模型（PCM）考虑了溶剂（二氯甲烷）的影响。优势路径计算表明,在反应循环的第一步中,Pd通过与羰基O原子及双键配位形成前驱物1a。随后,由于Pd与碳碳双键和羰基氧原子的配位作用提高了碳碳双键的亲电性,从而使得它很容易和相邻的羰基通过[2＋2]进行环加成反应。此过程涉及一个从“临界中间体”2a到“临界过渡态”tsa2的“临界转化区域”。进一步,C4上的H原子发生迁移形成中间体4a和HPdCl,HPdCl进攻C1-C4键生成中间体5a,最后,通过无能垒的过程,生成产物6a,并释放出Pd催化剂R2。     

钯催化亚烷基环丙基酮开环反应机制的理论研究

在BHandHLYP/6-31G(d,p)（Pd用LANL2DZ基组）计算水平上对钯催化的亚烷基环丙酮开环反应机制进行了理论研究,使用极化连续介质模型（PCM）考虑了溶剂（二氯甲烷）的影响。优势路径计算表明,在反应循环的第一步中,Pd通过与羰基O原子及双键配位形成前驱物1a。随后,由于Pd与碳碳双键和羰基氧原子的配位作用提高了碳碳双键的亲电性,从而使得它很容易和相邻的羰基通过[2＋2]进行环加成反应。此过程涉及一个从“临界中间体”2a到“临界过渡态”tsa2的“临界转化区域”。进一步,C4上的H原子发生迁移形成中间体4a和HPdCl,HPdCl进攻C1-C4键生成中间体5a,最后,通过无能垒的过程,生成产物6a,并释放出Pd催化剂R2。     

Mg-Al-N三元团簇的密度泛函理论研究

运用杂化密度泛函方法B3LYP在6-311+G^*计算水平上研究Mg_xAl_yN(x,y=1-5)团簇的结构.对Mg_xAl_yN团簇最低能量结构的稳定性和电子特性进行研究.结果表明,Mg_xAl_yN(x+y≤4)团簇的构型主要是平面结构.Mg_xAl_yN团簇的最低能量结构主要是由Al_nN或Mg_x-1Al_y+1N的构型演变而来.Mg_xAl_yN团簇离解成原子或者较小团簇是相对稳定的.和相邻团簇相比,MgAl₃N和Mg₃Al₃N拥有较高的稳定性.随着团簇尺寸的增加,Mg_xAl_yN团簇同时表现出共价键,离子键和金属键的特点.另外,随着团簇尺寸的增加,团簇的垂直电离势和电子亲合能呈现小的震荡,但并没发现整体的变化规律.     

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.     

基于密度泛函理论的高精度有机分子化学位移在线计算系统平台

近年来,随着计算化学理论的不断突破,以及计算硬件性能的大幅提高,基于第一性原理针对有机分子开展¹H和¹³C核磁共振化学位移的精确计算技术也取得了很大进展,部分方法已经逐步用于较大分子及较复杂分子体系的准确预测．本文建立了一个基于密度泛函理论的高精度有机分子化学位移在线计算系统平台,能够在线交互式完成分子量小于800的分子的化学位移计算服务．该系统平台工具能加快构建分子结构与核磁共振谱图的映射关系过程,为有机分子核磁共振谱图的高效指认,以及结构精确解析提供一个新的有力支撑．     

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.     

CuSi6团簇几何结构和性质的密度泛函理论研究

利用密度泛函理论(DFT)的B3LYP方法,采用全电子基组6-311+G(d)研究了CuSi6团簇的几何构型和电子结构性质,计算表明CuSi6团簇存在多个能量相近的稳定异构体,且结构中存在多个Cu-Si键,多个低能异构体共存解释了实验中观察到的CuSi6团簇较强的现象。对于CuSi6团簇,计算得到的三个最稳定异构体的垂直电离能,电子亲和能和HOMO-LUMO能隙均相对较大,也表明这三个异构体较为稳定。     

Cd团簇的第一性原理研究

基于密度泛函理论（DFT）中的广义梯度近似（GGA）对Cdn(2≤n≤13)团簇进行了结构优化。其基态结构由较为松散平面结构向紧凑型堆积,主要以三角或四角双锥结构为基本单元,通过边戴帽或面戴帽形成较为稳定的Cdn团簇。随着原子数目增加,Cdn(2≤n≤13)团簇的稳定性在增强,结合该团簇的HOMO- LUMO能隙分布,发现n=4,10是铬团簇的幻数。通过电荷转移和垂直电离势（VIPs）计算发现n=6是Cdn团簇原子间相互作用力由范德瓦尔斯力向共价键结合方式转变的转折点。     

非传统超导PuCoGa5晶体结构和电子性质的密度泛函理论研究

基于密度泛函理论的全势能线性缀加平面波方法（FLAPW）,采用局域自旋密度近似（LSDA）及LSDA+U方法报道了Pu基超导体系PuCoGa₅的晶格参数,原子占位和电子性质.LSDA+U方法不仅考虑Pu-5f而且考虑了Co-3d的库伦排斥作用U和Hund交换相关作用J.结果表明LSDA+U在同时考虑Pu和Co的强关联作用时晶格参数和原子占位与相关理论和实验数据吻合较好,特别是PuCoGa₅中Pu-5f的强定域特征尤其是自旋向下的电子.此外,Pu-5f与Co-3d电子的轨道杂化明显强于Ga-4p电子.