The compressibility theorem for quantum simple fluids at equilibrium

An extension of the compressibility theorem for quantum simple fluids within the pathintegral approach is presented. First, it is demonstrated that in the absence of quantum exchange, the isothermal compressibility can be formulated in an exact manner with the use of the pair radial correlation function of the path-integral centroids corresponding to the particles of the fluid. This adds up to the two known formulations based on the pair correlations between true quantum particles, namely the instantaneous and the pair linear response correlations. To complement this extension, an exact Ornstein-Zernike equation for pair centroid correlations is derived, which permits accurate estimates for the isothermal compressibility to be obtained. Several fluids are studied, new numerical results for the latter quantity are reported to support the theoretical points, and some difficulties present in this sort of calculation are discussed. The systems studied are the following: the quantum hard sphere fluid with and without attractive Yukawa interaction, liquid helium-4 and liquid para-hydrogen. Finally, the possibilities of extending the theorem to deal with quantum exchange are considered, and it is shown that the extension and its computational Ornstein-Zernike scheme also hold for a Bose fluid.     

Structural and response functions at equilibrium in path-integral quantum simple fluids

A discussion on the physical meaning of the r-space structures that can be defined in path-integral quantum simple fluids far from exchange is presented by making the connection with their associated experimentally measurable properties in k-space (response functions). The role played in this issue by weak external fields acting on the fluid is examined by considering both the standard quantum treatment of neutron scattering and the path-integral functional analysis approach. For the sake of completeness, the same discussion is presented for the approximate Gaussian Feynman-Hibbs effective potential picture that can be derived from the path-integral, and also the structural interrelations between both formalisms are stated. To illustrate the points addressed in this paper results for liquid helium-4 at 4.2 K (SVP), obtained with the use of the Aziz-Slaman and the ab initio SAPT2 pair potentials, are reported.     

Effect of short- and long-range forces on the properties of fluids. III. Dipolar and quadrupolar fluids

Using realistic pair potential models for acetone and carbon dioxide, both the spatial and orientational structure of these two typical multipolar (i.e. dipolar and quadrupolar, respectively) fluids is investigated in detail by computing the complete set of the site-site correlation functions, multipole-multipole correlation functions, and selected 2D correlation functions. The effect of the range of interactions on both the structural and thermodynamic properties of these fluids is studied by decomposing the potential into short- and long-range parts in the same manner as for water [Kolafa, J. and Nezbeda, I., 2000, Molec. Phys., 98, 1505; Nezbeda, I. and Lísal, M., 2001, Molec. Phys., 99, 291]. It is found that the spatial arrangement of the molecules is only marginally affected by the long-range forces. The effect of the electrostatic interactions is significant at short separations and cannot be neglected but nevertheless the overall structure of the short-range and full systems is similar as well as their dielectric constants. These findings are also reflected in the dependence of the thermodynamic properties on the potential range with the short-range models providing a very good approximation to those of the full system.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

Control of electron correlations in a spherical quantum dot

Spherical quantum dots containing several electrons are considered for different values of the total spin. Numerical calculations are carried out using the quantum path-integral Monte Carlo method. The dependence of the electron correlations on the dimensionless control quantum parameter q associated with the steepness of the confinement potential is studied. The quantum transition from a Wigner crystal-like state (i.e., from the regime of strongly correlated electrons) to a Fermi-liquid state (“cold” melting) driven by the parameter q is studied in detail. The behavior of the radial and pair correlation functions, which characterize quantum delocalization of the electrons, is considered.     

The equilibrium geometry of the SC3H radical: an ab initio study

The SC₃H radical is known by experiment to have a linear equilibrium structure, but even rather high-level ab initio computations give a bent equilibrium geometry. A theoretical study of the SCCCH radical has been carried out in order to analyse the influence of several factors in the computed equilibrium structure. Quadratic configuration interaction QCISD(T) and restricted coupled cluster RCCSD(T) computations have been performed in combination with large basis sets. Spin-orbit effects have been taken into account through the Breit-Pauli Hamiltonian using multi-configuration SCF and configuration interaction wavefunctions. Our final results indicate that the equilibrium structure must be linear, in agreement with the experimental studies [McCarthy, M. C., Vrtilek, J. M., Gottlieb, C. A., Wang, W., and Thaddeus, P., 1994, Astrophys. J., 431, L127; Hirahara, Y., Ohshima, Y, and Endo, Y, 1994, J. chem. Phys., 101, 7342]. Both spin-orbit and electron correlation effects appear to be of comparable importance, but an adequate computation of the correlation energy has been much more difficult and has ultimately required basis set extrapolations.     

Dynamics of geometric discord and measurement-induced nonlocality at finite temperature

By using geometric measure of discord (GMOD) [B. Dakić, V. Vedral, Č. Brukner, Phys. Rev. Lett. 105, 109502 (2010)] and measurement-induced nonlocality (MIN) [S. Luo, S. Fu, Phys. Rev. Lett. 106, 120401 (2011)], we investigate quantum correlation of a pair of two-level systems, each of which is interacting with a reservoir at finite temperature T. We show that, for a broad class of states of the system, GMOD and MIN can endure sudden death, and there is no asymptotic decay for MIN while asymptotic decay exists for GMOD. We also give the dynamics of GMOD and MIN with respect to the temperature and illustrate their different characteristics.     

Perturbation theory for the square-well dimer fluid

An analytical equation of state is presented for the square-well dimer fluid of variable well width (1 ≤ λ ≥ 2) based on Barker-Henderson perturbation theory using the recently developed analytical expression for radial distribution function of hard dimers. The integral in the first- and the second-order perturbation terms utilizes the Tang, Y and Lu, B. C.-Y., 1994, J. chem. Phys., 100, 6665 formula for the Hilbert transform. To test the equation of state, NVT and Gibbs ensemble Monte Carlo simulations for square-well dimer fluids are performed for three different well widths (λ = 1.3, 1.5 and 1.8). The prediction of the perturbation theory is also compared with that of thermodynamic perturbation theory in which the equation of state for the square-well dimer is written in terms of that of square-well monomers and the contact value of the radial distribution function.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.     

The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

In the classical limit no work is needed to couple a system to a bath with sufficiently weak coupling strength (or with arbitrarily finite coupling strength for a linear system) at the same temperature. In the quantum domain this may be expected to change due to system-bath entanglement. Here we show analytically that the work needed to couple a single linear oscillator with finite strength to a bath cannot be less than the work obtainable from the oscillator when it decouples from the bath. Therefore, the quantum second law holds for an arbitrary temperature. This is a generalization of the previous results for zero temperature [Ford and O'Connell, Phys. Rev. Lett. 96, 020402 (2006); Kim and Mahler, Eur. Phys. J. B 54, 405 (2006)]; in the high temperature limit we recover the classical behavior.     

Decay of correlations and related sum rules in a layered classical plasma

Summary The asymptotic behaviours of particle correlation functions and the related sum rules are discussed for a layered classical plasma withe ²/r interactions in the fluid state, in dependence on the number of layers. These properties derive from consistency conditions imposed by screening on the hierarchical equations, as already treated by A. Alastuey and P. A. Martin (J. Stat. Phys.,39, 405 (1985)) for various Coulomb fluids. The main results concern i) the type of clustering of correlations needed for the validity of multipolar sum rules at various orders, ii) the proof that the pair correlation function in a finite multilayer may carry an electric dipole moment and the calculation of its partioning among the layers, and iii) the dimensionality crossover in an infinitely extended or periodically repeated multiplayer with varying interlayer spacing and wave vector.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

A computer simulation study of racemic mixtures

A simple model for a chiral molecule is proposed. The model consists of a central atom bonded to four different atoms in tetrahedral coordination. Two different potentials were used to describe the pair potentials between atoms: the hard sphere potential and the Lennard-Jones potential. For both the hard sphere and the Lennard-Jones chiral models, computer simulations have been performed for the pure enantiomers and also for the racemic mixture. The racemic mixture consisted of an equimolar mixture of the two optically active enantiomers. It is found that the equations of state are the same, within statistical uncertainty, for the pure enantiomer fluid and for the racemic mixture. Only at high pressures does the racemic mixture seem to have a higher density, for a given pressure, than the pure enantiomer. Concering the structure, no difference is found in the site-site correlation functions between like and unlike molecules in the racemic mixture either at low or at high densities. However, small differences are found for the site-site correlations of the pure enantiomer and those of the racemic mixtures. In the Lennard-Jones model, similar conclusions are drawn. The extension of Wertheim's first-order perturbation theory, denoted bonded hard sphere theory (ARCHER, A. L., and JACKSON, G., 1991, Molec. Phys., 73, 881; AMOS, M. D., and JACKSON, G., 1992, J. chem. Phys., 96, 4604), successfully reproduces the simulation results for the hard chiral model. Virial coefficients of the hard chiral model up to the fourth have also been evaluated. Again, no differences are found between virial coefficients of the pure fluid and of the racemic mixture. All the results of this work illustrate the quasi-ideal behaviour of racemic mixtures in the fluid phase.     

Pure Bound Field theory and the Decay of Moun in Meso-Atoms

In the present paper we consider the electrically bound quantum particles within the framework of pure bound field theory (PBFT) (Kholmetskii, A.L., et al.: Phys. Scr. 82, 045301 (2010)), which explicitly takes into account the non-radiative nature of electromagnetic (EM) field generated by bound charges in the stationary energy states, and evokes the appropriate modifications of bound EM field, which secure the total momentum conservation law for the isolated system “electron plus nucleus” in the absence of EM radiation. Such a PBFT gives the same gross as well as fine structure of atomic energy levels, as those furnished by the common approach, but implies a scaling transformation of radial coordinates. In this paper we find out that in the classical limit this transformation reflects the dependence of time rate for the orbiting electron on the electric potential of the binding EM field in addition to relativistic dependence on its Lorentz factor. We show that this effect completely eliminates the available up to date discrepancy between calculated and experimental data on the decay rate of bound muon in meso-atoms. We emphasize that the revealed dependence of time rate of quantum electrically bound particles on the electric potential represents the specific effect of PBFT, and, in general, is not extended to the classical world.     

Dynamics of atom scattering from 4He nanoclusters

We present a microscopic theory and results of atom scattering calculations to determine the dispersion of surface modes (ripplons) of superfluid helium-4 nanodroplets, expanding previous work [J. Chem. Phys. 115, 10161 (2001)]. A quantum transport formalism is adapted to the many-body scattering problem, yielding both elastic and inelastic fluxes. We demonstrate that, in analogy to the dynamic structure function S(k,ω) obtained from neutron scattering, a dynamic structure function σ(k,ω) can be obtained from ³He scattering. The ³He dynamic structure function σ(k,ω) is sensitive to surface dynamics, whereas the neutron dynamic structure function S(k,ω) is dominated by bulk-like excitations, in particular by rotons. Unlike for neutron-scattering, the total inelastic cross section for atom-scattering on ⁴He nanodroplets is large which we believe makes experimental detection feasible. We also show that scattering identical particles, i.e. ⁴He atoms, does not provide information about the dispersion of surface modes. Instead, inelastically scattered ⁴He atoms preferably lose roughly half their energy.     

New accurate binary hard sphere mixture radial distribution functions at contact and a new equation of state

New and very accurate formulae for additive binary hard sphere (HS) mixture radial distribution functions (RDFs) at contact are proposed in a simple analytical form. Using the virial theorem, the formulae also provide a new HS mixture equation of state (EOS). The new RDF formulae are the most accurate currently available. The new EOS is of comparable accuracy with that of Malijevsky, A., and Veverka, J. (1999, Phys. Chem. chem. Phys., 1, 4267), which is the most accurate HS mixture EOS currently available. However, the new EOS proposed here is of much simpler analytical form.     

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.     

Theoretical calculation of the structure of a polarizable-ionic fluid

Much theory of the structures of fluids depends on the assumption of pair-additive forces between the particles. Simulations and experiments have shown that many molten salts, molecular fluids and other systems have structures that depend sensitively on polarization of their electron clouds, or on other internal distortions. In such cases, the forces are not pair additive and the theoretical calculation of structure, expressed as a radial distribution function, g(r), is not possible using the ordinary methods. Part of the problem is that the internal structure is quantum mechanical. A theoretical method for the calculation of the structure of a fluid of polarizable particles is presented here, in a form that may be applied to any one of many structure theories in common use. The method is inspired by work on the simulation of polarizable fluids. It is applied to a simple model of a molten salt with polarizable ions. The theory is applicable to particles carrying any combination of induced electrical multipole moments, along with charges and permanent moments.