Density Functional Approach Based on Numerically Obtained Bridge Functional

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

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.     

All-electron study of ultra-incompressible superhard material ReB2: structural and electronic properties

This paper investigates the structural and electronic properties of rhenium diboride by first-principles calculation based on density functional theory. The obtained results show that the calculated equilibrium structural parameters of ReB2 are in excellent agreement with experimental values. The calculated bulk modulus is 361 GPa in comparison with that of the experiment. The compressibility of ReB2 is lower than that of well-known OsB2. The anisotropy of the bulk modulus is confirmed by c/a ratio as a function of pressure curve and the bulk modulus along different axes along with the electron density distribution. The high bulk modulus is attributed to the strong covalent bond between Re-d and B-p orbitals and the wider pseudogap near the Fermi level, which could be deduced from both electron charge density distribution and density of states. The band structure and density of states of ReB2 exhibit that this material presents metallic behavior. The good metallicity and ultra-incompressibility of ReB2 might suggest its potential application as pressure-proof conductors.     

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.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

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.     

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.     

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.     

Nucleation for Lennard-Jones Fluid by Density Functional Theory

A non-mean field density functional theory is employed to investigate the vapour-liquid nucleation. The excess Helmholtz free energy functional is formulated in terms of a local density approximation for short ranged repulsion and a density-gradient expansion for long-ranged attractions. An analytical expression for the direct correlation function of a Lennard-Jones fluid is utilized to take into account the effect of long-ranged attractions on intermolecular correlations. With the predicted bulk properties and surface tension as input, the nucleation properties including density profile, work of formation and number of particles at the reduced temperatures T^* = 0.694 and 0.741 are investigated. The obtained number of particles in the critical nucleus agrees well with the simulation data.     

Thin-Thick Film Transitions on a Planar Solid Surface： A Density Functional Study

A weighted density functional theory is proposed to predict the surface tension and thin-thick film transition of a Lennard-Jones fluid on a planar solid surface. The underlying density functional theory for the Lennard-Jones fluid at low temperature is based on a modified fundamental measure theory for the hard-core repulsion, a Taylor expansion around zero-bulk-density for attraction, and a correlation term evaluated by the weighted density approximation with a weight function of the Heaviside step function. The predicted surface tension and thin-thick film transition agree well with the results from the Monte Carlo simulations, better than those from alternative approaches. For the Ar/CO2 system, the prewetting line has been calculated. The predicted reduced surface critical temperature is about 0.97, and the calculated wetting temperature is below the triple-point temperature. This is in agreement with the experimental observation.     

The improved output performance of a broad-area vertical-cavity surface-emitting laser with an optimized electrode diameter

The output performance of a 980-nm broad-area vertical-cavity surface-emitting laser(VCSEL) is improved by optimizing the p-electrode diameter in this study.Based on a three-dimensional finite-element method,the current density distribution within the active region of the VCSEL is optimized through the appropriate adjustment of the p-electrode diameter,and uniform current-density distribution is achieved.Then,the effects of this optimization are studied experimentally.The L-I-V characteristics under different temperatures of the VCSELs with different p-electrode diameters are investigated,and better temperature stability is demonstrated in the VCSEL with an optimized p-electrode diameter.The far-field measurements show that with an injected current of 2 A,the far-field divergence angle of the VCSEL with an optimized p-electrode diameter is 9°,which is much lower than the far-field angle of the VCSEL without this optimization.Also the VCSEL with an optimized p-electrode diameter shows a better near-field distribution.     

Ab-initio density functional theory study of a WO3 NHa-sensing mechanism

WO3 bulk and various surfaces are studied by an ab-initio density functional theory technique. The band structures and electronic density states of WO3 bulk are investigated. The surface energies of different WO3 surfaces are compared and then the （002） surface with minimum energy is computed for its NH3 sensing mechanism which explains the results in the experiments. Three adsorption sites are considered. According to the comparisons of the energy and the charge change between before and after adsorption in the optimal adsorption site Olc, the NH3 sensing mechanism is obtained.     

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.     

Supermode analysis of seven-core photonic quasi-crystal fibers

We design custom-shaped modes for a sixfold symmetric photonic quasi-crystal fiber （PQF）, an optical fiber with a sixfold symmetric quasi-periodic array of air holes in the cladding region. The supermodes of the PQF are calculated by the finite element method, and the coupling of an in-phase supermode for the quasi-periodic optical fiber is numerically optimized to obtain identical values. The optimization is guaranteed by the selection of appropriate PQF design parameters. The eigenvalue equation associated with a seven-core PQF is derived from a coupled mode equation. We realize mode shaping and provide the far-field distribution mode of PQFs. The results are beneficial for the structural design and uniform distribution of the in-phase supermodes of PQFs.     

Probability of Field-Aligned Currents Observed by the Satellite Cluster in the Magnetotail

Field-aligned current （FAC） density distribution at the plasma sheet boundary layers is statistically studied. The FAC is calculated by the so-called curlometer technique with the data from FGM onboard the four Cluster spacecraft in 2001. By calculation we obtain a large number of FAC samples. In the samples, most of calculated FAC densities were very small and around zero caused by some errors or noise. In order to get the real FAC density distribution in the magnetotail, we use a three-Gaussian distribution to fit the errors, then subtract the estimated error contribution from the full distribution and obtain the FAC density distribution. The result shows that the FAC occurrence versus its density has a distribution consisting of a Gauss/an distribution with an additional decreasing exponential distribution. The most probable value of the FAC density is 3.45 pT/km.     

Thermodynamic Properties of Hard-Sphere Fluid under Confined Condition Based on Bridge Density Function

Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first-order direct correlation function to a non-uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non-uniform first-order direct correlation function.     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

Ab-initio density functional theory study of a WO3 NH3-sensing mechanism

WO 3 bulk and various surfaces are studied by an ab-initio density functional theory technique.The band structures and electronic density states of WO 3 bulk are investigated.The surface energies of different WO 3 surfaces are compared and then the (002) surface with minimum energy is computed for its NH 3 sensing mechanism which explains the results in the experiments.Three adsorption sites are considered.According to the comparisons of the energy and the charge change between before and after adsorption in the optimal adsorption site O 1c,the NH 3 sensing mechanism is obtained.     

First-principles study of the electronic structure and optical properties of cubic Perovskite NaMgF_3

The structural, electronic, and optical properties of cubic perovskite NaMgF3 are calculated by plane-wave pseudopo- tential density functional theory. The calculated lattice constant a0, bulk modulus B0, and the derivative of bulk modulus B~ are 3.872/~, 78.2 GPa, and 3.97, respectively. The results are in good agreement with the available experimental and theo- retical values. The electronic structure shows that cubic NaMgF3 is an indirect insulator with a wide forbidden band gap of Eg = 5.90 eV. The contribution of the different bands is analyzed by total and partial density of states curves. Population analysis of NaMgF3 indicates that there is strong ionic bonding in the MgF2 unit, and a mixture of ionic and weak covalent bonding in the NaF unit. Calculations of dielectric function, absorption coefficient, refractive index, electronic energy loss spectroscopy, optical reflectivity, and conductivity are also performed in the energy range 0 to 70 eV.