Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

We have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

Phase diagram of two-dimensional binary Yukawa mixtures

We have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.     

Salt-induced effective interactions and phase separation of an ultrasoft model of polyelectrolytes

We use a semi-grand canonical version of mean-field density functional theory to determine the total effective interaction energy of a solution of penetrable polyions characterised by a Gaussian charge distribution, in the presence of added salt. We then apply this effective representation of semi-flexible polyelectrolyte chains to investigate the possibility of a phase separation similar to that predicted earlier for charge-stabilised hard-sphere colloids. Apart from the absence of a hard-core repulsion, the effective pair potential is similar to the familiar Derjaguin-Landau-Verwey-Overbeek (DLVO) potential between charged-stabilised colloids, i.e. of the screened-Coulomb (Yukawa) form, but the effective valence of the polyions differs significantly from that of the DLVO pair potential, especially at high salt concentration. The existence of a well-defined closed-loop spinodal curve predicted by our mean-field calculation points to a phase separation between solutions with high and low polyion concentrations under reasonable physical conditions. The salt concentration at the upper critical point is typically two orders of magnitude larger than in the case of hard-core polyions, indicating that polyion penetrability appears to enhance the tendency towards phase separation.     

First-principles study on the geometric and electronic structures and phase transition of PbZr1-xTixO3 solid solutions

With first-principles virtual-crystal approximation calculations, we systematically investigate the geometric and elec- tronic structures as well as the phase transition of lead zirconate titanate (PbZr1-xTixO3 or PZT) as a function of Ti content for the whole range of 0 ≤ x Ti ≤ 1. It can be found that, with the increase of the Ti content, the PbZr1-xTixO3 solid solu- tions undergo a rhombohedral-to-tetragonal phase transition, which is consistent with the experimental results. In addition, we also show the evolution in geometric and electronic structures of rhombohedral and tetragonal PbZr1-x TixO3 with the increasing content of Ti.     

Quantum phase transitions in two-dimensional strongly correlated fermion systems

In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal−insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a combination of the cellular dynamical mean-field theory (CDMFT) and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.     

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT _s (>T _c), not at critical temperatureT _c. This occurs due to the anisotropy of such 2D systems.     

单层二硫化钼多相性质及相变的第一性原理研究

本文基于密度泛函的第一性原理,并引入范德瓦耳斯力修正,研究了单层二硫化钼2H,1T,ZT三种相的电学性质及相变原理.首先通过结构弛豫确定了三种相的几何结构,能带和态密度计算证实1T相具有金属性质,ZT相具有半导体性质,带隙为0.01 eV.然后结合变形势理论计算了2H和ZT相的迁移率,ZT相的迁移率高达104cm~2·V~(-1)·s~(-1),进一步拓展了单层二硫化钼的应用范围.最后通过对比三种相吸附锂原子结合能,计算2H-1T相变能量曲线,解释了引起二硫化钼相变的原因.本文的研究结果将对单层二硫化钼实验制备表征以及相关光电器件性能分析提供重要参考.     

二维声子晶体中简单旋转操作导致的拓扑相变

构建了一种简单的二维声子晶体:由两个横截面为三角形的钢柱所组成的复式元胞按三角点阵的形式排列在空气中,等效地形成了一个蜂巢点阵结构.当三角形钢柱的取向与三角点阵的高对称方向一致时,整个体系具有C_(6v)对称性.研究发现:在保持钢柱填充率不变的条件下,只需要将所有三角柱绕着自己的中心旋转180°,就可实现二重简并的p态和d态在布里渊区中心Γ点处的频率反转,且该能带反转过程实质上是一个拓扑相变过程.通过利用Γ点的P态和d态的空间旋转对称性,构造了一个赝时反演对称性,并在声学系统中实现了类似于电子系统中量子自旋霍尔效应的赝自旋态.随后通过k·p微扰法导出了Γ点附近的有效哈密顿量,并分别计算了拓扑平庸和非平庸系统的自旋陈数,揭示了能带反转和拓扑相变的内在联系.最后通过数值模拟演示了受到拓扑不变量保护的声波边界态的单向传输行为和对缺陷的背向散射抑制.文中所研究的声波体系,尽管材料普通常见,但其拓扑带隙的相对宽度超过21%,比已报道的类似体系的带隙都要宽,且工作原理涵盖从次声波到超声波的很大频率范围,从而在实际应用上具有较大的优势和潜力.     

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.     

高压下BeP2N4结构相变和电子结构的第一性原理计算

 基于密度泛函理论的第一性原理方法,计算了硅铍石型和尖晶石型结构BeP₂N₄的总能量随体积的变化关系。利用Brich-Murnaghan状态方程,通过能量和体积拟合,得到了2种结构的体变模量及其对压强的一阶导数。在压力作用下,BeP₂N₄的相变是从硅铍石型结构（空间群R-3,No.148）转变到尖晶石型结构（空间群Fd-3m,No.227）,计算出的相变点与其它理论值符合得非常好。同时计算了BeP₂N₄的相对晶格常数a/a₀和相对体积V/V₀的压缩率,在低压下发现,尖晶石结构BeP₂N₄的压缩率接近金刚石,进一步计算了不同压力下的体弹模量B_H、剪切模量G_H、B_H/G_H和杨氏模量E。此外,对两种结构的BeP₂N₄的电子态密度和带隙随压强的变化关系进行了计算和分析。结果表明：在压力作用下,上价带顶向费米能级移动,并有一定的展宽。Be—N、P—N键缩短,电子转移增加,导致电荷发生重新分布。     

密度泛函交换关联势与过渡金属化合物光学非线性的计算研究

在优化几何构型的基础上，对一系列强关联过渡金属化合物，采用密度泛函理论方法中各种 交换关联势计算了电子偶极矩、一阶光学极化率和一阶光学超极化率.考虑基组和频率影响 ，对比从头算MP2，HF方法及实验值，评价了各种交换关联势的计算表现.在此基础上，讨论 新的混合密度泛函交换关联势，以提高密度泛函理论方法计算含有过渡金属体系非线性光学 性质的精度. 关键词： 密度泛函方法 过渡金属化合物 非线性光学     

Thermodynamics and structure of a two-dimensional asymmetric electrolyte by integral equation theory

Integral equation theories and Monte–Carlo simulations were used to determine the thermodynamic and structural properties of a two-dimensional asymmetric Coulomb system. We check correctness of different closures in integral equations and their ability to reproduce Kosterlitz–Thouless and vapour–liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared with Monte–Carlo data. Among selected closures, hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz–Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.     

Phase transitions in hadronic systems and thermodynamics of a system with an exponential spectrum

Both nuclear matter and hadronic matter at high excitations can be described by a liquid-vapor phase transition. For the hadronic systems, a system with an exponential mass spectrum (Hagedorn-like or bag-like) leads to a thermodynamics which is identical to that of a two phase coexistence at a fixed temperature.     

高压下SiO_2的第一性原理计算

基于密度泛函理论(DFT)的第一性原理,采用Hartree-Fork(HF)方法,分别计算了Si O2的α-石英结构、金红石结构以及氯化钙结构的总能量随体积的变化关系。利用Murnaghan状态方程,通过能量和体积拟合,得到了3种结构的体变模量及其对压强的一阶导数。计算结果表明,随着压强的增加,Si O2会从α-石英结构转变为金红石结构,与实验结果和其它理论结果一致;金红石结构与氯化钙结构之间不存在相变,可以共存。此外,对具有α-石英结构的Si O2的晶格常数、电子态密度和带隙随压强的变化关系进行了计算和分析,结果表明:加压作用下,能带向高能方向移动,Si─O键缩短,电子数转移增加,带隙展宽,电荷发生重新分布。     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. II.T>T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects aboveT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

Spin-spin correlation function in the two-dimensional Ising model with linear defects. I.T<T c

The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects belowT _c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.     

CUO分子结构与势能函数

用密度泛函理论的B3LYP方法,对铀原子采用14个价电子的准相对论有效原子实势及(6s5p2d4f)[3s3p2d2f]收缩价基集合,碳、氧原子采用6311G全电子基集合,应用Gaussian98程序对一氧化碳气体与铀表面相互作用的可能分子结构CUO(角形Cs和线形C∞v构型)分子进行几何优化计算,得到了稳定结构的几何构形、能量、谐振频率、力学性质和电性质,并用微观可逆性原理分析了其可能的离解极限.结果表明,势能函数等值势能面图能清晰地再现CUO分子的结构特征和离解能;铀原子与一氧化碳的反应是势垒较低、容易进行的反应 关键词： CUO 密度泛函理论 分子结构 势能函数     

Mg2C高压性质的从头计算法研究

运用基于密度泛函理论的平面波赝势方法,结合广义梯度近似,系统地研究了Mg2C在高压下的结构相变、电子结构和光学性质。计算结果表明Mg2C在高压下将发生两次相变,一次是从反萤石到反氯化铅结构的一阶相变在30.09 GPa,另一次是从反氯化铅结构到Ni2In型结构的二阶相变在260 GPa。此外,对压力下电子结构和光学性质的分析表明,Mg2C的带隙宽度随着压力增加而增加,与Mg2Si在压力下表现出金属性有很大不同。