Differential virial theorem in relation to a sum rule for the exchange-correlation force in density-functional theory

Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.     

Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.     

Connection between the observable and centroid structural properties of a quantum fluid: application to liquid para-hydrogen

It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.     

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

We use the shear viscosity expression from the Enskog theory of dense gases in a perturbative scheme for the Lennard-Jones (LJ) fluid. This perturbative scheme is formulated by combining the analytic rational function approximation method of Bravo Yuste and Santos [Phys. Rev. A 43, 5418 (1991)] for the radial distribution function of hard-sphere fluids and the well known Mansoori-Canfield/Rasaiah-Stell perturbation theory to determine an effective diameter for the LJ fluid. The scheme is reliable on a wide range of temperatures and densities, and is very accurate around the critical point. Using this information, we build an accurate empirical formula for the shear viscosity in the liquid phase, which fits the recent data [K. Meier et al., J. Chem. Phys. 121, 3671 (2004)] in the whole simulation range.     

Theoretical direct correlation function for two-dimensional fluids of monodisperse hard spheres

The direct correlation function plays an important role in describing the effects of the structure of particle systems with respect to light diffraction, x-ray diffraction as well as transmission and transmission fluctuations of radiation through a dense suspension. In this paper, the direct correlation function for a monolayer of monodisperse hard spheres or disks is derived theoretically. Based on the approximation of Baus and Colot [Phys. Rev. A 36, 3912 (1987)] and the equation of state for a fluid of hard disks by Santos et al. [J. Chem. Phys. 103, 4622 (1995)], we propose a new direct correlation function, which compares well to the approximate analytical expressions and gives a good prediction of the structure factor in a wide range of monolayer density or suspension concentration. The resulting radial distribution function also agrees well with Monte Carlo computer simulation data. The corresponding contact values of the radial distribution function compare well with the results of analytic approximations, numerical solutions, and computer simulations. Our proposed direct correlation function is applied to the transmission fluctuation spectrometric study. Experimental results show good agreement with the theory.     

B80 and B101-103 clusters: remarkable stability of the core-shell structures established by validated density functionals

Prompted by the very recent claim that the volleyball-shaped B(80) fullerene [X. Wang, Phys. Rev. B 82, 153409 (2010)] is lower in energy than the B(80) buckyball [N. G. Szwacki, A. Sadrzadeh, and B. I. Yakobson, Phys. Rev. Lett. 98, 166804 (2007)] and core-shell structure [J. Zhao, L. Wang, F. Li, and Z. Chen, J. Phys. Chem. A 114, 9969 (2010)], and inspired by the most recent finding of another core-shell isomer as the lowest energy B(80) isomer [S. De, A. Willand, M. Amsler, P. Pochet, L. Genovese, and S. Goedecher, Phys. Rev. Lett. 106, 225502 (2011)], we carefully evaluated the performance of the density functional methods in the energetics of boron clusters and confirmed that the core-shell construction (stuffed fullerene) is thermodynamically the most favorable structural pattern for B(80). Our global minimum search showed that both B(101) and B(103) also prefer a core-shell structure and that B(103) can reach the complete core-shell configuration. We called for great attention to the theoretical community when using density functionals to investigate boron-related nanomaterials.     

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.     

The role of exchange-correlation functionals in the potential energy surface and dynamics of N(2) dissociation on W surfaces

We study the dissociative adsorption of N(2) on W(100) and W(110) by means of density functional theory and classical dynamics. Working with a full six-dimensional adiabatic potential energy surface (PES), we find that the theoretical results of the dynamical problem strongly depend on the choice of approximate exchange-correlation functional for the determination of the PES. We consider the Perdew-Wang-91 [Perdew et al., Phys. Rev. B 46, 6671 (1992)] and Perdew-Burke-Ernzerhof (RPBE) [Hammer et al., Phys. Rev. B 59, 7413 (1999)] functionals and carry out a systematic comparison between the dynamics determined by the respective PESs. Even though it has been shown in earlier works that the RPBE may provide better values for the chemisorption energies, our study brings evidence that it gives rise to a PES with excessive repulsion far from the surface.     

Study of thermal properties of the metastable supersaturated vapor with the integral equation method

Pressure, excess chemical potential, and excess free energy data for different densities of the supersaturated argon vapor at reduced temperatures from 0.7 to 1.2 are obtained by solving the integral equation with perturbation correction to the radial distribution function [F. Lado, Phys. Rev. 135, A1013 (1964)]. For those state points where there is no solution, the integral equation is solved with the interaction between argon atoms modeled by Lennard-Jones potential plus a repulsive potential with one controlling parameter, alpha exp(-rsigma) and in the end, all the thermal properties are mapped back to the alpha=0 case. Our pressure data and the spinodal obtained from the current method are compared with a molecular dynamics simulation study [A. Linhart et al., J. Chem. Phys. 122, 144506 (2005)] of the same system.     

Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: an orthogonal formulation

Linear scaling density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is extended to basis-set-dependent quantum response calculations for a nonorthogonal basis set representation. The generalization is achieved by a perturbation-dependent congruence transform, derived from the factorization of the inverse overlap matrix, which transforms the generalized eigenvalue problem to an orthogonal, standard form. With this orthogonalization transform the basis-set-dependent perturbation in the overlap matrix is included in the orthogonalized Hamiltonian, which is expanded in orders of the perturbation. In this way density matrix perturbation theory developed for an orthogonal representation can be applied also to basis-set-dependent response calculations. The method offers an alternative to the previous solution of the basis-set-dependent response problem, based on a nonorthogonal generalization of the density matrix perturbation theory, where the calculations are performed within a purely nonorthogonal setting [A. M. N. Niklasson et al., J. Chem. Phys. 123, 44107 (2005)].     

Density functional theory of fluids in nanopores: analysis of the fundamental measures theory in extreme dimensional-crossover situations

Two density functional theories, the fundamental measures theory of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] and a subsequent approximation by Tarazona [Phys. Rev. Lett. 84, 694 (2000)] are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions.     

Alternative fundamental measure theory for additive hard sphere mixtures

The purpose of this short paper is to present an alternative fundamental measure theory (FMT) for hard sphere mixtures. Keeping the main features of the original Rosenfeld's FMT [Phys. Rev. Lett. 63, 980 (1989)] and using the dimensional and the low-density limit conditions a new functional is derived incorporating Boublik's multicomponent extension [Mol. Phys. 59, 371 (1986)] of highly accurate Kolafa's equation of state for pure hard spheres. We test the theory for pure hard spheres and hard sphere mixtures near a planar hard wall and compare the results with the original Rosenfeld's FMT and one of its modifications and with new very accurate simulation data. The test reveals an excellent agreement between the results based on the alternative FMT and simulation data for density profile near a contact and some improvement over the original Rosenfeld's FMT and its modification at the contact region.     

Ionic microgels as model systems for colloids with an ultrasoft electrosteric repulsion: structure and thermodynamics

We present a theoretical analysis of the structural properties and phase behavior of spherical, loosely cross-linked ionic microgels that possess a low monomer concentration. The analysis is based on the recently derived effective interaction potential between such particles [A. R. Denton, Phys. Rev. E 67, 011804 (2003)]. By employing standard tools from the theory of the liquid state, we quantitatively analyze the pair correlations in the fluid and find anomalous behavior above the overlap concentration, similar to the cases of star-branched neutral and charged polymers. We also employ an evolutionary algorithm in order to predict the crystalline phases of the system without any a priori assumptions regarding their symmetry class. A very rich phase diagram is obtained, featuring two reentrant melting transitions and a number of unusual crystal structures. At high densities, both the Hansen-Verlet freezing criterion [J.-P. Hansen and L. Verlet, Phys. Rev. 184, 151 (1969)] and the Lindemann melting criterion [F. A. Lindemann, Phys. Z. 11, 609 (1910)] lose their validity. The topology of the phase diagram is altered when the steric interactions between the polymer segments become strong enough, in which case the lower-density reentrant melting disappears and the region of stability of the fluid is split into two disconnected domains, separated by intervening fcc and bcc regions.     

Cluster pair correlation function of simple fluids: energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.     

Theoretical studies on tunneling ionizations of helium atom in intense laser fields

Our generalized Keldysh theory is applied to the simplest many-electron atom, helium atom. For the single ionization (He-->He(+)+e) we derive a compact rate formula, which does not contain any series summation or integral and thus is as simple as the Ammosov-Delone-Krainov ionization rates. In addition to its simplicity, our formula can explicitly show the wavelength dependence. Furthermore a simple form of the angular distribution of the photoelectron is available. Our compact formula agrees well with both the exact numerical calculations [A. Scrinzi et al., Phys. Rev. Lett. 83, 706 (1999)] and experimental data [B. Walker et al., Phys. Rev. Lett. 73, 1227 (1994)] in the intensity range of I<5x10(15) Wcm(2). In higher intensity regions, we suggest to utilize another simple formula which is valid in the tunneling limit.     

Effective electrostatic interactions in solutions of polyelectrolyte stars with rigid rodlike arms

In solutions of star-branched polyelectrolytes, electrostatic interactions between charged arms on neighboring stars can compete with intrastar interactions and rotational entropy to induce anisotropy in the orientational distribution of arms. We explore the influence of arm orientational anisotropy on effective star-star interactions for model stars comprising rigid rodlike arms with evenly spaced charged monomers interacting via an effective screened-Coulomb (Yukawa) potential. Monte Carlo simulation and density-functional theory are used to compute the arm orientational distributions and effective pair potentials between weakly charged stars. For comparison, a torque balance analysis is performed to obtain the configuration and energy of the ground state, in which the torque vanishes on each arm of the two-star system. The degree of anisotropy is found to increase with the strength of electrostatic interactions and proximity of the stars. As two stars begin to overlap, the forward arms are pushed back by interstar arm-arm repulsion, but partially interdigitate due to rotational entropy. At center-center separations approaching complete overlap, the arms relax to an isotropic distribution. For nonoverlapping stars, anisotropy-induced changes in the intra- and interstar arm-arm interactions largely cancel and the effective pair interactions are then well approximated by a simple Yukawa potential, as predicted by linear-response theory for a continuum model of isotropic stars [A. R. Denton, Phys. Rev. E 67, 11804 (2003)]. For overlapping stars, the effective pair interactions in the simple rigid-arm-Yukawa model agree closely with simulations of a molecular model that includes flexible arms and explicit counterions [A. Jusufi et al., Phys. Rev. Lett. 88, 018301 (2002); J. Chem. Phys. 116, 11011 (2002)].     

Fundamental measure theory in cylindrical geometry

Density functional theory as proposed by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] is used to study hard sphere mixture exposed by cylindrically symmetric external field. Exploiting the symmetry of the system, explicit formulas for the weighted densities are derived. The resulting density profiles are compared with new grand canonical Monte Carlo simulations. The comparison reveals very good agreement between the predicted and simulated results even at high densities and very narrow pores. Finally, simple algorithms for computing complete elliptic functions of the first and second kinds that occur in the derived formulae are presented to make the paper self-contained.     

On correlated electron-nuclear dynamics using time-dependent density functional theory

We discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surface-hopping framework using time-dependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surface-hopping method proposed by Craig et al. [Phys. Rev. Lett. 95, 163001 (2005)] that is based on Kohn-Sham potential energy surfaces. Limitations of this approach arise due to the Kohn-Sham surfaces generally having different gradients than the true TDDFT-corrected ones. Two mechanisms of the linear response procedure cause this effect: we illustrate these with examples.     

The decay of pair correlations in quantum hard-sphere fluids

A study of the asymptotic decay of the pair radial correlations in the bare quantum hard-sphere (QHS) fluid and in the quantum hard-sphere Yukawa (QHSY) fluid is presented. The conditions explored are far from quantum exchange and are contained within the region (0.1相似文献   

Variationally stable calculations for molecular systems: polarizabilities and two-photon ionization cross section for the hydrogen molecule

The variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] has been applied for the first time to the study of multiphoton processes in molecular systems. The generalization in theory is presented, as well as the calculation of properties such as the static and dynamic polarizabilities of the hydrogen molecule and the generalized two-photon ionization cross section. The Schwinger variational iterative method [R. R. Lucchese and V. McKoy, Phys. Rev. A 21, 112 (1980)] has been applied in the achievement of the photoelectron wave function, while a Hartree-Fock representation has been used for the target. This research has been motivated by the scarceness of ab initio calculations of molecular multiphoton ionization cross sections in the literature.