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.     

Thermodynamic study of fluid in terms of equation of state containing physical parameters

We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster.Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy.The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied.Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity(radial distribution function).From the thermodynamic profile of the fluid,the model results are discussed in terms of the cavity due to the closed surface along with suitable energy.The present calculation is based upon the sample thermodynamic data for n-hexanol,such as the ultrasonic wave,density,volume expansion coefficient,and ratio of specific heat in the liquid state,and it is consistent with the thermodynamic relations containing physical parameters such as size and energy.Since the data is restricted to n-hexanol,we avoid giving the physical meaning of f,which is the key parameter studied in the present work.     

A Calculation Approach to Elastic Constants of Crystallines at High Pressure and Finite Temperature

Elastic constants of Na and Li metals are calculated successfully for temperatures up to 350K and pressures up to 30GPa using a scheme without involving any adjustable parameter.Elastic constants are assumed to depend only on an effective pair potential that is only determined by the average interatomic distance.Temperature has an effect on elastic constants by way of charging the equilibrium.The elastic constants can be obtained by fitting the relationship between total energy and strain tensor using the new set of lattice parameters obtained by calculating displacement of atoms at the finite temperature and at a fixed pressure.The relationship between the effective pair potential and the interatiomic distance is fitted by using a series of data of cohesive energy corresponding to lattice parameters.     

Molecular dynamics simulation of self-diffusion coefficients for liquid metals

The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.     

Modified Eyring viscosity equation and calculation of activation energy based on the liquid quasi-lattice model

Viscosity is an important physical parameter of fluid,and the Eyring viscosity equation is a popular viscosity theory.Based on the Eyring reaction rate equation and Boltzmann statistical theory,and including the probabilities of creating a hole in liquid and the transition to the neighboring hole,a modified Eyring viscosity equation was proposed.According to the structural characteristics of short-range order,liquid is treated as a quasi-lattice structure in a small region.The activation energy,which is the minimum energy needed for the molecule to jump to its neighboring hole because of the restriction of other molecules around it,was analytically calculated from an intermolecular Lennard-Jones potential function and a Stockmayer potential function.The viscosity values of 37 kinds of typical liquids at 25°C and the dependence of viscosity of three kinds of liquids on temperatures were calculated with this modified viscosity equation,and the calculated results agree with the experimental values to some extent.This work not only enriches the understanding of the mechanism of liquid viscosity,but also could provide some theoretical guides for the relevant studies and applications.     

Density Profile of a Hard Disk Liquid System under Gravity

The free energy and the density profile of a hard disk liquid system under gravity axe calculated by using the dimensional crossover of Rosenfeld hard sphere （3D） functional as well as the functional constructed from the scaled-particle theory which is considered to be very accurate. The two methods give the consistent results for a wide range of packing fractions.     

A New Method for Characterizing Single Parametric Model Potential

A novel approach of characterizing single parametric model potential is proposed by equating total pair wise force to zero. Our well-established single parametric model potential is characterized using the proposed idea and compared the obtained parameter with parameters computed by previously used approaches. Thus characterized pseudopotential is then tested to compute total energy of alkali metals. The results establish the reliability of proposed idea of making total pair wise force to zero in determining the parameter of the pseudopotential.     

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B1∏ of 7LiH

The reasonable dissociation limit of the second excited singlet state B¹∏ of ⁷LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B¹\Pi state are calculated using a symmetry-adapted-cluster configuration--interaction method in full active space. The whole potential energy curve for the B¹∏ state is obtained over the internuclear distance ranging from about 0.10nm to 0.54nm, and has a least-square fit to the analytic Murrell--Sorbie function form. The vertical excitation energy is calculated from the ground state to the B¹∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B¹∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.     

Ab initio calculations on accurate dissociation energy, equilibrium geometry, and analytic potential energy function for the 6~3Π state of ~7LiH molecule

The accurate dissociation energy and equilibrium geometry of the 63Π state of 7LiH molecule is calculated using a symmetry-adapted-cluster configuration-interaction method in full active space. And the calculated results are 0.2580 eV and 0.1958 nm for the dissociation energy and equilibrium geometry, respectively. The whole potential energy curve for the 63Π state is also calculated over the internuclear separation range from about 0.10 to 0.54 nm. The results are fitted by the Murrell-Sorbie function. It is found that the Murrell-Sorbie function form, which is mainly used to fit the ground-state potential energy function, is well suitable for the excited triplet b3Π state. The vertical excitation energy from the ground state to the 63Π state is calculated to be 4.233 eV. Based on the analytic potential energy function, the harmonic frequency of 610.88 cm-1 about this state is firstly estimated. Compared with other theoretical results, this work is the most complete effort to deal with the analytic potential energy function and the harmonic frequency of this state.     

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.     

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.     

Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases, the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Opactiy of Hot and Dense Plasmas of a Mixture using an Average—Atom Approach

An average-atom model is propsed to calculate the opacities of hot and dense plasmas of a mixture.A selfconsistent scheme is used to reach the requirements of the same temperature and chemical potential for all kinds of atoms in the mixtures,the same electron density at the boundaries between the atoms,and the electrical neutrality within each atomic sphere.The orbital energies and wavefunctions for the bound electrons are calculated with the Dirac-Slater equations.The occupation numbers at each orbital of each kind of atom are determined by the Fermi-Dirac distribution with the same chemical potential for all kinds of atoms.As an example,the opacity of the mixture of Au and Cd is calculated at a few temperatures and densities.     

Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases,the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Finite—Amplitude Vibration of a Bubble

The Rayleigh-Plesset equation for bubble vibration is modified.The numerical solution of new equation is obtained by means of the symbolic computation programme.The acceleration of the liquid on the surface of the bubble,or pressure in the bubble,displays much intenseδ-impulse with a very short duration from ns to ps.SUggestions for developing the measurements of sonoluminescence and cavitation fusion(if any) are presented.     

Deformed Potential Energy of Super Heavy Element Z = 120 in a Generalized Liquid Drop Model

The macroscopic deformed potential energy for super-heavy elements Z=120 is determined within a generalized liquid drop model (GLDM). The shell correction is calculated with the Strutinsky method and the microscopic single particle energies are derived from the shell model in an axially deformed Woods-Saxon potential with the same quasi-molecular shape. The total potential energy of a nucleus is calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is adopted to describe the deformed potential energies in a set of cold reactions. The neck in the quasi-molecular shape is responsible to the deep valley of the fusion barrier due to shell corrections. In the cold fusion path, the double-hump fusion barrier is predicted by the shell correction and complete fusion events may occur. The results show that some of projectile-target combinations in the entrance channel, such as ^50Ca ^252Fm→120 and 58Fe 244 pu→^302 120 , favour the fusion reaction, which can be considered as candidates for the synthesis of super heavy nuclei Z=120 and the former might be the best cold fusion reaction to produce the nucleus ^302 120among them.     

Drop Size Dependence of the Contact Angle of Nanodroplets

The contact angle of nanosized non-polarized argon sessile droplets on a solid substrate is studied by using molecular dynamics simulations. It is found that the drop size dependence of the contact angle is sensitive to the interaction between the liquid molecules and solid molecules. The contact angle decreases with the decreasing drop size for larger interaction between the liquid molecules and the solid substrate, and vice versa. This observation is consistent with most of the previous theoretical and experimental results.     

Monte Carlo Simulation on Energy Deposition of Low-Energy Electrons in Liquid Water

A Monte Carlo approach to simulate the transport and energy deposition of low energy electrons (E0≤10keV) in liquid water is presented. The elastic scattering of electrons is described by Mott cross section, which is derived from the relativistic wave equation of Dirac. The inelastic scattering model of electrons is based on the dielectric response theory with exchange effect included. A new method of sampling various inelastic scattering events is proposed in the simulation. Using the approach stated, the spatial distribution of inelastic scattering events and energy deposition of electrons in liquid water are computed and the results are compared with other theoretical studies.