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.     

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 perturbation density functional theory for hydrogen bonding cyclic molecules

Using the framework of Wertheim's thermodynamic perturbation theory, a new polyatomic density functional theory is developed to account for the intermolecular association of cyclic molecules in interfacial systems. To test the theory, Monte Carlo simulations in the canonical ensemble were performed for the specific case of an associating triatomic ring with one association site next to a hard wall. The theory and simulation results were found to be in good agreement.     

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.     

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.     

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     

The critical supersaturations predicted by nucleation theory

A general set of equations is derived for calculating the supersaturation required to obtain a given rate of nucleation. This set is general enough to encompass all the present theories, the classical theory, the Lothe-Pound theory, the Reiss-Katz-Cohen theory, a recent theory by H. Reiss, and any other theory which includes a size-dependent correction to the classical theory. Comparison of these predictions is made for various substances.     

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.     

水分子链受限于单壁碳纳米管结构的密度泛函理论研究

本文采用第一性原理的密度泛函理论,主要以(6,6)Armchair型,(11,0)Zigzag型单壁碳纳米管为研究对象,研究了水分子链在碳纳米管内部吸附的稳定结构,以及结合能随其结构的变化.结果表明:当水分子链受限于碳纳米管内部时,引起碳纳米管直径收缩,这主要是由于水分子链与碳纳米管之间的氢键作用以及范德华弱相互作用所引起的.随着碳纳米管半径的增加,两种单体之间的结合能逐渐减小,但当碳纳米管半径增加至6.78时,其结合能又有所增加,这是由于在优化过程中,水分子链单体之间的氢键作用大于水分子链与碳纳米管之 关键词： 水分子链/单壁碳纳米管 密度泛函理论 结构稳定性     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide (GaP) from zinc-blende (ZB) to a rocksalt (RS) structure is investigated by the plane-wave pseudopotential density functional theory (DFT). Lattice constant a₀, elastic constants c_ij, bulk modulus B₀ and the pressure derivative of bulk modulus B₀' are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/V₀, the Debye temperature θ, the heat capacity C_v and the thermal expansion coefficient α are also discussed in a pressure range from 0 GPa to 40 GPa and a temperature range from 0 K to 1500 K.     

Elastic properties of Nb-based alloys by using the density functional theory

A first-principles density functional approach is used to study the electronic and the elastic properties of Nb₁₅X(X = Ti, Zr, Hf, V, Ta, Cr, Mo, and W) alloys. The elastic constants c₁₁ and c₁₂, the shear modulus C', and the elastic modulus E_〈100〉 are found to exhibit similar tendencies, each as a function of valence electron number per atom (EPA), while c₄₄ seems unclear. Both c₁₁ and c₁₂ of Nb₁₅X alloys increase monotonically with the increase of EPA. The C' and E_〈100〉 also show similar tendencies. The elastic constants (except c₄₄) increase slightly when alloying with neighbours of a higher d-transition series. Our results are supported by the bonding density distribution. When solute atoms change from Ti(Zr, Hf) to V(Ta) then to Cr(Mo, W), the bonding electron density between the central solute atom and its first neighbouring Nb atoms is increased and becomes more anisotropic, which indicates the strong interaction and thus enhances the elastic properties of Nb-Cr(Mo, W) alloys. Under uniaxial 〈100〉 tensile loading, alloyed elements with less (more) valence electrons decrease (increase) the ideal tensile strength.     

氧化镁纳米管团簇电子结构的密度泛函研究

用密度泛函理论（DFT）的杂化密度泛函B3LYP方法在6-31G（d）基组水平上对MgO纳米管团簇的二元环双管、三元环、三元环双管三种构型共21个团簇进行优化,对各构型的平均结合能、能隙、平均原子电荷以及总电荷密度进行了理论研究. 结果表明,平均结合能和配位数呈线性关系;随着纳米管的生长,团簇的稳定性增加,其中以三元环纳米管最为稳定;生长过程中发生原子间的电荷转移现象,预测出至无限长时的平均原子电荷分别为1298,1270,1306;混合离子共价键始终存在于MgO纳米管团簇之中. 关键词： 氧化镁 纳米管团簇 密度泛函理论 电子结构     

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.     

特丁基对苯二酚的光谱及密度泛函研究

特丁基对苯二酚是重要的食品抗氧化剂.理论上,基于密度泛函理论,采用B3LYP泛函及6-311G(d,p)基组在气相环境下优化分子的结构并进行频率计算.在此基础上,基于含时密度泛函理论,选用SMD(solvation model based on density)溶剂模型,利用B3LYP泛函并结合def2-TZVP基组计...     

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.     

质子与羟基碰撞的含时密度泛函理论研究

采用将含时密度泛函理论和分子动力学非绝热耦合的方法,研究了不同入射速度下质子与羟基碰撞的反应动力学.计算了碰撞前后质子动能和羟基动能的变化及羟基电子和质子的运动.计算结果表明,质子沿垂直羟基分子轴方向入射时,质子与羟基碰撞后,质子被反弹且动能损失并俘获了羟基中氧的一部分电子,而丢失部分电子的羟基则获得动能以伸缩振动的形式向计算边界平动.随着入射质子的初动能增加,质子从羟基中俘获的电子增多,碰撞后羟基的键长变长,羟基振动变强而伸缩振动频率降低.此外,还发现质子的入射方向对碰撞过程的激发动力学有很大的影响.质子从不同的方向入射时,质子的入射初动能越大,其损失的动能越多且损失的动能与入射初动能呈线性关系,而入射方向对质子动能损失的影响很小.在质子入射初动能较低(小于25 eV)的情况下,羟基获得的动能与质子入射初动能呈线性关系且与入射方向无关;在质子入射初动能较高(大于25 eV)时,当质子沿羟基分子轴方向入射时,羟基动能的增量远大于质子沿垂直于羟基分子轴方向入射时羟基动能的增量.     

原子核结构的相对论第一性原理研究

过去几十年中,原子核物理的相对论密度泛函理论得到很大发展,可以成功地描述各种原子核现象。文章阐述在相对论框架下研究原子核多体问题的必要性,介绍原子核物理中相对论密度泛函理论的基本概念,回顾相对论密度泛函理论在描述原子核基态、手征转动和动力学过程等方面的应用,讨论基于原子核物理的相对论第一性原理研究,即完全自洽的相对论Brueckner—Hartree—Fock理论,构建微观普适的密度泛函的基本思想。     

Vibrational analysis of L-serine using the density functional theory

In this paper, we present a computational study of L-serine using ab initio molecular dynamics simulation based on density functional theory (DFT) within the ultrasoft pseudopotentials and generalized-gradient approximation. Taking into account the intermolecular interactions, we can indeed simulate the features of the experimental results very well for L-serine zwitterions in its solid state. The vibrational spectrum of L-serine performed by DFT was in excellent agreement with our previous inelastic incoherent neutron scattering spectra measured at 20K for L-serine in the 10--200meV region on HET spectrometers at ISIS, Rutherford Appleton Laboratory.