Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

The plasmon–exciton interaction in layered nanostructures with two-dimensional J-aggregates

The transformation of the electronic excitation energy in a plane-layered nanostructure with two-dimensional J-aggregates of a cyanine dye has been studied theoretically. The dependences of the plasmon–exciton interaction energy on the system parameters have been determined. In the case of small values of the Rabi frequency, the rates of nonradiative energy transfer from surface plasmon–polaritons of the metal substrate to molecular excitons of J-aggregates have been calculated in terms of the perturbation theory. The dispersion laws for hybrid plasmon–exciton states have been determined, and it has been shown that the Rabi splitting can range up to 100 meV.     

Hydrogen chemisorption on Al,Mg and Na surfaces — calculation of adsorption sites and binding energies

Chemisorption properties for H on Al, Mg and Na surfaces have been computed. Starting with the results from a self-consistent, Kohn-Sham calculation for a H-jellium system, the effects of the substrate pseudopotential lattice have been included by first order perturbation theory. An improved method, namely inclusion of part of the pseudopotentials in a self-consistent way and only the remainder in perturbation theory, has also been used. Binding energies, bond lengths, vibrational frequencies and activation energies have been calculated. It is found that the three substrates behave qualitatively different, as Al is a segregator, Na is an absorber and Mg is in between. Calculated bond lengths agree in general well with the ones for the corresponding molecules. The binding energy is predicted to be below or close to the dissociation energy of H₂ for Al and Na, while it is slightly larger for Mg.     

Effects of disorder on the correlation energy of rings of hydrogen atoms

The correlation energy of disordered systems has been calculated by means of second-order Rayleigh-Schrödinger perturbation theory in the M?ller-Plesset partitioning. Rings of hydrogen atoms have been chosen as model systems and the degree of disorder has been varied from complete delocalization to complete localization of the one-particle states. The correlation energy was found to have an extremum at an intermediate degree of disorder, corresponding to incomplete localization.     

Direct determination of free energies of colloidal dispersions

Helmholtz free energies of electrostatically-stabilized colloidal dispersions of monodispersed spherical particles have been obtained using computer experiments. Boltzmann sampling has been shown to be sufficient for determining free energy differences between two dispersions whose pair-potentials are close to each other. Non-Boltzmann sampling has been used when the pair-potentials differ substantially. These results have been compared with the results based on perturbation theory. The techniques used, thus, offer a direct method to test the latter.     

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.     

Equation of state of metallic helium

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.     

腔内像散扰动对正支共焦腔模式影响的数值分析

 针对激光器出光过程中腔内像差扰动带来的输出光束质量和光束能量下降问题,分析了腔内像差扰动对非稳腔模式的影响,并采用数值迭代法计算了理想情形和腔内像散扰动对无源正支共焦腔输出模式强度和相位分布的影响,进一步采用Zernike模式法对光束相位进行了像差拟合,得到了前35阶Zernike像差系数、点扩散函数(PSF)分布和环围能量曲线,计算了腔内像散扰动量与远场Strehl比的关系。结果表明：对小菲涅耳数正支共焦腔,腔内像散扰动对输出光束强度和相位分布均有明显影响,相位分布中一些高阶Zernike像差也有所增大。因此在进行腔内像差校正时,应优先考虑此类像差的校正。     

On the use of MP2 theory for electron molecules correlation in atoms and molecules

The use of Moeller-Plesset perturbation theory, frequently designated MPn, in describing electron correlation in atomic and molecular systems is critically examined. Some recently published studies have examined the higher terms in the Moeller-Plesset perturbation expansion and the convergence behaviour of the perturbation series. From these investigations conclusions about the applicability of the low order theory have been drawn which, in view of the widespread use of MP2, demand more thorough analysis. Combining the Rayleigh-Schrödinger and the Brillouin-Wigner perturbation expansions avoids an infinite order expansion and yields a closed expression which consists of the MP2 energy components together with a remainder term. The applicablity of MP2 theory then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms in the perturbation series.     

Lattice heat capacities of solid argon

An anharmonic rigid-atom model has been used to study the heat capacities of solid argon. The model derives the interatomic forces by BuckinghamCorner potential and takes account of all neighbour interaction. The contribution of the cubic and quartic terms of the potential energy expansion to the heat capacities have been accounted for through Helmholtz-free energy by perturbation theory. It is concluded that the model is most suitable among the ones designed for the class of solids to which argon belongs.     

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.     

Zum Drei- und Vierkörperproblem der Kernphysik

The independent pair model has been applied to the nuclear three- and four-body problem. The equations of the model have been solved by a perturbation approach in the case of spin- and charge-independent central two-body forces with hard-core. In lowest order of perturbation theory the nuclear average potential has been approximated by an oscillator potential including an effective mass, the parameters of which were so chosen as to give as nearly a self-consistent potential as possible. For a sqare well two-body interaction the lowest order equations have been solved exactly, the corrections are shown to be small. Some tests for the internal consistency of the approach have been developped and are shown to be well fulfilled by our solutions. According to a proposal byLipkin we succeeded in separating off the energy of the center of mass motion. The results for the binding energy of He⁴(27,9 MeV), the binding energy of H³ (7,1 MeV), the energy difference between H³ and He³ (0,735 MeV) and the RMS-radius of He⁴ (1,75f) are in rather good agreement with experimental results.     

Energy fluxes in helical magnetohydrodynamics and dynamo action

Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is of firstorder in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 10⁸ years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.     

（CX3）2Y型分子的内旋转势能函数

研究有Ｍ（≥２）个等价的Ｎ（≥３）重对称内旋转陀螺的分子，将内旋运动方程解耦，应用无波函数微扰理论，导出内旋转能谱解析式，应用所得结果及扭转频率的光谱数据，确定了（ＣＨ３）２Ｏ与（ＣＦ３）２ＣＯ分子的内旋转势能函数。     

Modified Perturbation Theory of an Anharmonic Oscillator

A modification of the perturbation theory of a symmetrical anharmonic oscillator is suggested. A more complex zero-order approximation of perturbation theory that considers to a certain degree anharmonicities is chosen rather than a harmonic oscillator model. This approximation is an analog of the self-consistent field model well known in the theory of many-particle systems. A comparison of modified and conventional perturbation theories demonstrates that the modified perturbation theory has much wider applicability range. It can be used for larger values of the parameters at which the conventional perturbation theory becomes inapplicable, namely, for strong anharmonicity and upper energy levels.     

High-order perturbed corrections with scaling transformation

The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.     

Thermodynamics of simple models of associating fluids: primitive models of ammonia,methanol, ethanol and water

Thermodynamic P-V-T properties of primitive models that descend directly from realistic Hamiltonians and reproduce the structure of real fluids have been studied both by means of theory and computer simulations. Analytic expressions for the Helmholtz free energy of four typical associating fluids, ammonia, methanol, ethanol and water, have been derived using the thermodynamic perturbation theory. Whereas for the models which allow only single bonding of each site the first-order theory is sufficient, for models in which some sites may form simultaneously up to two bonds the theory has to be extended to the second order. Comparison with simulation data shows that the theory is very accurate and has therefore also been used to determine vapour–liquid equilibria. We have found fundamental differences in the behaviour of different models; these differences are linked to the properties of the hydrogen-bond network that are discussed in detail.     

Hall Conductivity in a Quasi—Two—Dimensional disordered Electron System

By making use of the diagrammatic techniques in perturbation theory,we have investigated the Hall effect in a quasi-two dimensional disordered electron system.In the weakly localized regime,the analytical expression for quantum correction to Hall conductivity has been obtained using the kubo formalism and quasiclassical approximation.The relevant dimensional crossover behavior from three dimensions to two dimensions with decreasing the interlayer hopping energy is discussed.The quantum interference effect is shown to have a vanishing correction to the Hall coefficient.     

H2S2分子的阻碍内旋转势能函数

应用无波函烽微扰理论导出了分子障碍内旋转能谱的解析式，基于扭转频率光谱数据，确定了Ｈ２Ｓ２分子的阻碍内旋转势能函数。     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)