Showing papers in "Molecular Physics in 1993"

Ab initio energy-adjusted pseudopotentials for elements of groups 13-17

Abstract: Quasi-relativistic energy-adjusted ab initio pseudopotentials for the elements of groups 13–17 up to atomic number 53 (I) are presented together with corresponding energy-optimized valence basis sets. Test calculations for atomic excitation and ionization energies show the reliability of the derived pseudopotentials and basis sets.

The Lennard-Jones equation of state revisited

Abstract: We review the existing simulation data and equations of state for the Lennard-Jones (LJ) fluid, and present new simulation results for both the cut and shifted and the full LJ potential. New parameters for the modified Benedict-Webb-Rubin (MBWR) equation of state used by Nicolas, Gubbins, Streett and Tildesley are presented. In contrast to previous equations, the new equation is accurate for calculations of vapour-liquid equilibria. The equation also accurately correlates pressures and internal energies from the triple point to about 4·5 times the critical temperature over the entire fluid range. An equation of state for the cut and shifted LJ fluid is presented and compared with the simulation data of this work, and previously published Gibbs ensemble data. The MBWR equation of state can be extended to mixtures via the van der Waals one-fluid theory mixing rules. Calculations for binary fluid mixtures are found to be accurate when compared with Gibbs ensemble simulations.

Hoover NPT dynamics for systems varying in shape and size

Abstract: In this paper we write down equations of motion (following the approach pioneered by Hoover) for an exact isothermal-isobaric molecular dynamics simulation, and we extend them to multiple thermostating rates, to a shape-varying cell and to molecular systems, coherently with the previous ‘extended system method’. An integration scheme is proposed together with a numerical illustration of the method.

Accuracy of energy-adjusted quasirelativistic ab initio pseudopotentials

Abstract: The results of valence-only self-consistent field calculations on Hg n+ (n = 0, 1, 2) and HgH n+ (n = 0, 1) using nonrelativistic and quasirelativistic energy-adjusted ab initio pseudopotentials for Hg are compared with corresponding all-electron values from nonrelativistic (Hartree-Fock) and relativistic (Dirac-Fock) atomic as well as from nonrelativistic (Hartree-Fock) and quasirelativistic (Hartree-Fock with no-pair Hamiltonian) molecular calculations. The accuracy of the energy-adjusted ab initio pseudopotential scheme, e.g., the reproduction of the major relativistic effects, is demonstrated both for the atom and the molecule. Correlation effects are included in the quasirelativistic pseudopotential studies by means of large-scale configuration interaction calculations. The quasirelativistic pseudopotential results obtained in the intermediate coupling scheme are in excellent agreement with available experimental data.

Quadrature schemes for integrals of density functional theory

Abstract: The evaluation of integrals which arise in density functional theory, as applied to molecules, as discussed. Becke's scheme for reducing them to a sum of integrals over atom based polyhedra is used...

Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation

Abstract: A method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation. Given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line. In each simulation, the pressure is adjusted to satisfy chemical potential equality according to the Gibbs-Duhem equation. Each coexistence point is determined by just one simulation, and particle insertions are never performed or attempted. Vapourliquid coexistence for the Lennard-Jones model is evaluated, and extensions are discussed.

Enhanced dye fluorescence over silver island films: analysis of the distance dependence

Abstract: Fluorescence intensity enhancement has been studied for several coverages (10-3 to 1 monolayer) of Rhodamine 6G separated from a silver island film by quartz spacer layers of varying thickness. When the dye film is brought into the proximity of the island film support, a first enhancement maximum is observed at ≈ 60 nm spacer thickness. For smaller distances, decrease in the enhancement is followed by a second maximum at 5–10 nm interlayer thickness. The magnitude of the latter maximum exhibits a pronounced dependence on dye coverage. The far-field enhancement maximum is due to an increase in fluorescence quantum yield induced by the presence of the island film substrate, combined with a resonant excitation phenomenon due to collective action of the islands. This effect is analysed in terms of stratified medium theory, in which the island film is represented by a suitable model for the effective dielectric constant. The short distance enhancement results from competition between the strongly amplified loc...

A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses

Abstract: We develop and test a new elementary Monte Carlo move for use in the efficient simulation of polymer systems. The move consists of a concerted rotation around up to seven adjacent skeletal bonds that leaves the rest of the chain unaffected. No assumption is made concerning the backbone geometry other than that bond lengths and bond angles are held constant during the elementary move. Special sampling techniques are needed because the new move involves a correlated change in seven degrees of freedom along the chain backbone. We use the new move in conjunction with reptation in an isothermal-isobaric Monte Carlo simulation of a bulk tetracosane melt system and find that it improves computational efficiency relative to a purely reptation-based Monte Carlo scheme. Comparisons are also made between a concerted rotation-based Monte Carlo simulation and a molecular dynamics simulation of an oligomer of atactic polypropylene.

Asymptotic decay of liquid structure: oscillatory liquid-vapour density profiles and the Fisher-Widom line

Abstract: Recent work has highlighted the existence of a unified theory for the asymptotic decay of the density profile ρ(r) of an inhomogeneous fluid and of the bulk radial distribution function g(r). For a given short-ranged interatomic potential ρ(r) decays into bulk in the same fashion as g(r), i.e. with the same exponential decay length (α0/-1) and, for sufficiently high bulk density (ρb) and/or temperature (T), oscillatory wavelength (2π/α1). The quantities α0 and α1 are determined by a linear stability analysis of the bulk fluid; they depend on only the bulk direct correlation function. In this paper we reintroduce the concept of the Fisher-Widom (FW) line. This line was originally introduced, in say the (ρb, T plane, as that which separates pure exponential from exponentially damped oscillatory decay of g(r). We explore the relevance of the FW line for the form of the density profile at a liquid-vapour interface. Using a weighted density approximation (WDA) density functional theory we locate the FW line fo...

On the molecular mechanism of thermal diffusion in liquids

Abstract: A recently developed non-equilibrium molecular dynamics algorithm for heat conduction is used to compute the thermal conductivity, thermal diffusion factor, and heat of transfer in binary Lennard-Jones mixtures. An internal energy flux is established with local source and sink terms for kinetic energy. Simulations of isotope mixtures covering a range of densities and mass ratios show that the lighter component prefers the hot side of the system at stationary state. This implies a positive thermal diffusion factor in the definition we have adopted here. The molecular basis for the Soret effect is studied by analysing the energy flux through the system. In all cases we found that there is a difference in the relative contributions when we compare the hot and cold sides of the system. The contribution from the lighter component is predominantly flux of kinetic energy, and this contribution increases from the cold to the hot side. The contribution from the heavier component is predominantly energy transfer th...

Coexistence in small inert gas clusters

Abstract: The coexistence of solid-like and liquid-like forms of a finite atomic cluster is examined analytically and numerically using model densities of states and partition functions. Within the harmonic normal mode approximation we can calculate the caloric curve, heat capacity and total energy probability distribution of a finite atomic cluster from a single molecular dynamics trajectory. The method requires data from a high energy simulation in the microcanonical ensemble, along with systematic quenching, to provide statistics about local minima. The results provide new insight into the coexistence of solid-like and liquid-like forms of such clusters, with a clear S-bend in the microcanonical caloric curve and a bimodal distribution of the total energy around the transition temperature for a 55 atom system.

A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid

Abstract: Despite the fact that the surface tension for a Lennard-Jones fluid has been simulated many times in the past, there is some considerable disagreement between the results. This paper calculates the surface tension and density profiles for the liquid-vapour interface of a Lennard-Jones fluid using molecular dynamics (MD) simulation techniques for a variety of system sizes, film thicknesses, interfacial areas, interatomic potential cut-offs, and temperatures. The results are compared with previous work in order to resolve some of the discrepancies of the past work. Combining this work with some reliable results from the past, the minimum system size, film thickness, and equilibration time necessary for the accurate description of the surface tension was determined. Using simulation results calculated for computationally-economic values of the potential cut-off, the surface tension was extrapolated to the full potential value using a tail correction and the results compared to simulations performed with long...

A grand canonical Monte Carlo study of Lennard-Jones mixtures in slit shaped pores

Abstract: The grand-canonical Monte Carlo (GCMC) technique has been used for simulating the adsorption of mixtures in slit pores with graphite properties. Spherical Lennard-Jones models were used to model methane and ethane at super critical temperatures. A GCMC algorithm for mixtures which included attempts to change identities of particles was found to be more effective than conventional GCMC. Results were compared with density functional theory (DFT) calculations of Tan and Gubbins (1992; J. phys. Chem., 96, 845) and with ideal adsorbed solution theory (IAST) isotherms derived from single component data. Our simulation results were found to agree qualitatively rather than quantitatively with the DFT mixture results, the IAST was found to work well for the system studied. Adsorption selectivity was found to depend on packing considerations as well as the relative potential well depths of the adsorbate wall interactions.

Computer simulation studies of anisotropic systems: XXI. Parametrization of the Gay-Berne potential for model mesogens

Abstract: The Gay-Berne potential is proving to be of considerable value in computer simulation studies of liquid crystals. However, the parameters employed in the potential were chosen by comparison with that for a line of four Lennard-Jones centres; they may not, therefore, be appropriate for mesogenic molecules. To see if this is the case we have estimated the parameters in the Gay-Berne potential by comparison with the site-site potential constructed for p-terphenyl, which has a molecular structure typical of many mesogens. Unlike the Gay-Berne potential the site-site potential is biaxial, and a method for projecting out this biaxiality is proposed. The resultant uniaxial model has then been used to obtain values for the parameters occurring in the Gay-Berne potential. These are found to differ significantly from those proposed originally; they are, we believe, more appropriate for investigations of the behaviour of liquid crystals. Our own molecular dynamics simulations, based on the new parametrization, revea...

Computer simulation study of liquid crystal formation in a semi-flexible system of linked hard spheres

Abstract: Results are reported for a molecular dynamics simulation study of a flexible model mesogen composed of seven tangential spheres. We follow the ‘rattling spheres’ method by which bonded atoms are constrained to lie within narrow potential wells. The dynamics of the system is that of a hard sphere fluid with added constraints. The phase diagram of our model system is calculated as a function of density and shows the presence of three fluid phases. These are assigned to be isotropic, nematic and smectic-A phases. Results are reported for the orientational order, radial distribution functions, structure factors and single-particle structural data within these phases. A small but significant change in shape is measured as the nematic phase is entered from the isotropic liquid. This is interpreted in terms of a quenching of allowed conformations parallel to the director.

Theory and simulation for associating fluids with four bonding sites

Abstract: In this paper we present new results from molecular simulation and theory for associating hard spheres and Lennard-Jones (LJ) spheres with four association or hydrogen-bonding sites. The association interaction is modelled with a highly anisotropic square well. Results from the first-order perturbation form of Wertheim's theory are compared with simulation results. The agreement between simulation and theory for compressibility factor, configurational energy, fraction of monomers, and bonding distribution is good. We also obtained the cluster size distribution and the average cluster size from simulation. An expression based on the assumptions of the theory and statistical arguments was developed for the average cluster size. The agreement between simulation and this equation for average cluster size is good for small and moderate strengths of the association potential. Finally the vapour-liquid coexistence curves for associating LJ fluids were obtained from theory.

Free energy of particle insertion

Abstract: In free energy simulations involving the creation of a new particle in a condensed medium, there is a well-known ‘origin singularity’ when the particle is first introduced, unless the coupling of the particle with its surroundings is increased very slowly. This singularity is analysed theoretically for a liquid that interacts with the new particle through a soft-sphere or a Lennard-Jones potential, using a virial expansion of the free energy derivative. For a soft-sphere potential u(r) = λα Ar-n (where λ is a coupling constant), we show rigorously that the derivative of the free energy with respect to λ is infinite at the origin if and only if α < n/3. This confirms a previous, approximate, prediction based on scaled particle theory. For a Lennard-Jones potential u(r) = λα Ar -12 + λβ Br -6, such that α ˇ- 2β, the derivative of the free energy is again infinite if and only if α < n/3. If the volume of the solute is proportional to the coupling constant, there is no singularity.

On the effects of association in fluids with spherically symmetric interactions

Abstract: The multidensity formalism proposed recently by Wertheim is reformulated in order to describe the effects of association in fluids with spherically symmetric interactions. The basic idea is to separate the total potential into nonassociative and associative parts and make different approximations for each part of the potential. The idea is realized by assuming that the maximum number of particles which can be associated simultaneously with a particular particle is limited and equal to n s. This property of steric saturation is introduced explicitly into the theory via the resummation of diagrams in the activity expansion of the logarithm of the grand partition function. The diagrams appearing in the activity expansion of the one-point density are classified in terms of the number of associative bonds incident upon the labelled white circle. The topological reduction of the diagrams carried out on the basis of this classification leads to an expansion in terms of n s + 1 densities. A generalized version of...

Calculations for the vibration-rotation levels of H+ 2 in its ground and first excited electronic states

Abstract: Non-adiabatic dissociation energies are calculated for 462 vibration-rotation levels of the ground electronic state of H+ 2, together with the three vibration-rotation levels of the first excited electronic state, using a transformed Hamiltoonian and an artificial-channels scattering method. Coupling of rotational and electronic angular momenta is accounted for, so that ground state levels with the highest N are included. Relativistic and radiative corrections are made to give dissociation energies, that of the 0,0 level of the ground electronic state agreeing with experiment. In particular, calculated energy separations are in excellent agreement with the few available experimental values.

The stability of the AB13 crystal in a binary hard sphere system

Abstract: A numerical study of the stability of the AB13 crystal structure in a mixture of dissimilar hard spheres is reported. This crystal structure has recently been observed by Bartlett and coworkers in experiments on suspensions of colloidal hard-sphere mixtures. We find that, over a range of densities and diameter ratios, the AB13 phase is thermodynamically stable both with respect to the fluid mixture and the crystal structures of pure A and pure B. A tentative phase diagram is presented.

Layering, freezing transitions, capillary condensation and diffusion of methane in slit carbon pores

Abstract: Grand canonical Monte Carlo and molecular dynamics simulation methods have been used to study layering transitions, freezing transitions, capillary condensation and adsorption hysteresis for a simple model of methane confined in slit carbon micropores at temperatures between 60 K and 135 K and for pore widths from 19 A to 76 A. The grand potentials of the systems were calculated and the thermodynamic phase transitions between the two branches of the isotherms were found. The mobility of molecules perpendicular to the pore walls and the diffusion coefficient parallel to the pore walls were calculated for layers near the wall.

Adsorption of CO2 over univalent cation-exchanged ZSM-5 zeolites

Abstract: Isotherms and IR spectra were measured for CO2-MZSM-5 (M = Li+, Na+, K+, Rb+, Cs+) adsorption systems. The observed adsorption characteristics were well approximated by a physical adsorption where the van der Waals force and an electrostatic interaction force are operating: the degree of irreversible adsorption (chemisorption) was less than 10% of the total adsorption. Although the adsorbed CO2 molecule interacts with both the cation and the pore wall, only the CO2-cation interaction can convert the IR inactive ν1 vibration into an IR active state. The adsorption model proposed enables us to calculate the initial heat of adsorption as well as the molecular orientation angle of CO2 against the cation site.

Free energy changes on freezing and melting ductile metals

Abstract: The variation in Landau free energy while melting platinum was investigated at a number of temperatures using computer simulation with a model potential. The technique used was to apply a biasing potential in a Monte Carlo simulation with umbrella sampling. From the Landau free energy curves one can determine the difference in free energies between the solid and liquid phases easily and accurately, the thermodynamic melting point (Tm), and the limit of metastability of the crystalline phase. The latter occurs at approximately 1·2Tm. It was difficult to freeze the material, but, using a suitable order parameter, this was achieved. Unlike earlier results on a soft sphere system, there was no evidence for nucleation of a metastable body-centred-cubic phase. One possible reason is the existence of local icosahedral order in the liquid phase of the metal. The surface free energy of the solid-liquid surface was estimated from the free energy barrier to melting. Model rhodium behaved in a very similar way.

Continuum-configurational-bias Monte Carlo simulations of long-chain alkanes

Abstract: The recently introduced continuum-configurational-bias method for Monte Carlo simulations is employed for the generation of large samples of many-chain n-alkane systems with chain lengths of 11, 24 and 71 carbon atoms. The simulations are used to investigate the adequacy of representing methylene groups as united-atom Lennard-Jones interaction sites, and to test the configurational-bias approach against traditional random moves and reptation moves with respect to the computational efficiency and numerical stability of the calculated ensemble averages. The results of simulations with constant pressure, temperature, and number of molecules demonstrate that, with an appropriate mixture of different types of Monte Carlo moves, an efficient and stable strategy can be obtained. Adjustment of the Lennard-Jones parameters leads to results that are in good agreement with experimental data for the density of liquid alkanes over a large temperature interval.

Simulation of hard triatomic and tetratomic molecules. A test of associating fluid theories

Abstract: Results of isothermal-isobaric Monte Carlo simulations for hard tangent homonuclear triatomic and tetratomic molecules are presented for fixed and flexible angle models. The simulation results are compared to the prediction of Wertheim's first (TPT1) and second-order (TPT2) thermodynamic perturbation theory for associating fluids and the Zhou and Stell approach. The theories are applied for hard spheres with two association sites in the limit of complete bonding. Both TPT2 and the Zhou-Stell theories produce equations of similar structure and are able to predict the density and bond angle dependence of the simulation results. Extensions of the theories to linear and branched hard chains, fused sphere molecules and mixtures are discussed and compared to new and existing simulation results.

Van der Waals theory of curved surfaces

Abstract: Van der Waals theory of a planar liquid-vapour interface, extended with a squared Laplacian term in the expression for the free energy, is used to study curved interfaces. Expressions, closely related to previously derived expressions by Fisher, M. P. A., and Wortis, M., 1984, Phys. Rev. B, 29, 6252, and Gompper, G., and Zschocke, S., 1992, Phys. Rev. A, 46, 4836 are given for the Tolman length (or, equivalently, spontaneous curvature) and rigidity constants of bending and Gaussian curvature. It is shown that these expressions follow also from a statistical mechanical (or virial) approach in which a local, mean field approximation is made for the pair density. The density profile of the curved surface is calculated to first order in the curvature which allows the derivation of explicit expressions for the various coefficients.

Practical schemes for distributed polarizabilities

Abstract: A general formalism for distributed molecular polarizabilities has already been established [1]. It requires the matrix elements of the multipole moment operators to be partitioned between a number of regions of the molecule. In the present paper, various partitioning methods are investigated. One partitioning scheme, based on Gauss-Hermite quadrature, stands out as more stable than others which can be applied to general geometries. Symmetry requirements, however, are not automatically fulfilled when this scheme is used, so symmetrization schemes are also discussed. Calculations of the Rayleigh-Schrodinger induction energy using these distributed polarizabilities are used as a guide for judging the usefulness of the partitioning schemes. Morokuma analysis is used as a standard for comparison. The results support the view that the partitioning scheme based on Gauss-Hermite quadrature is preferred because of its greater stability.

Calculations for vibration-rotation levels of HD+, in particular for high N

Abstract: Nonadiabatic dissociation energies are calculated for 619 vibration-rotation levels of the ground electronic state of HD+ using a transformed Hamiltonian and an artificial-channels scattering method. In particular, coupling of rotational and electronic angular momenta is accounted for, so that levels with high N may be studied. Relativistic and radiative corrections are added to give dissociation energies, from which calculated transition energies may be compared with the experimentally available values; the agreement is good, in most cases to within experimental error (0·001 cm-1).

Vapour-liquid equilibria of Stockmayer fluids: computer simulations and perturbation theory

Abstract: By M. E. VAN LEEUWEN, B. SMIT and E. M. HENDRIKS Koninklijke/Shell-Laboratorium, Amsterdam, P.O. Box 3003, 1003 AA Amsterdam, The Netherlands (Received 16 April 1992; accepted 1 July 1992) Gibbs ensemble simulation data for Stockmayer fluids with #.2 = 3.0 and #.2 = 4.0 in the reduced temperature range of 0-77 (resp. 0.80)-0"98 and pre- sented and compared with predictions based on the perturbation theories of Stell, G., Rasaiah, J. C., and Narang, H., 1972, Molec. Phys., 23, 393; 1974, 27, 1393. The description of the reference fluid is improved by applying the mod- ified Benedict-Webb-Rubin equation of state instead of the Verlet-Weis imple- mentation of the Weeks-Chandler-Andersen perturbation scheme. Second virial coefficients predicted by perturbation theory to order #4 agree for Stock- mayer fluids with #,2 < 4 very well with exact values. Perturbation theory is capable of describing the low-density region of Stockmayer fluids with rather strong dipole moments. For these high values of the dipole moment, the Pad6 approximation of perturbation theory deviates significantly from the simulated coexistence curves in density and pressure. Compared with perturbation theory to order #4, however, it is a far better approximation of the Stockmayer fluid coexistence curve. The behaviour of the Pad6 approximation in the critical region is not satisfactory. 1. Introduction Electrostatic interactions affect thermodynamic behaviour. For relatively simple polar model fluids several theories have been developed [1-3]. A convenient model for a polar fluid is a 'soft-core' dipolar molecule, represented by the Stockmayer potential (Lennard-Jones potential with an embedded point dipole). The two most important molecular theories for model polar fluids are integral equation theories and (Pople-Stell) perturbation theories. If the Ornstein-Zernike equation is supplemented with an approximate closure relation, an integral equation is obtained for the direct correlation function and the radial distribution function [2]. For polar fluids this involves expansions of angular- dependent functions. Starting from the well known hypernetted-chain equation Patey and others [4-6] considered linear expressions (LHNC) and quadratic expressions (QHNC), and obtained a numerically tractable scheme. Fries and Patey [7] devel- oped a general method for fluids with anisotropic interactions, the reference hypernetted-chain (RHNC) theory. Lee et al. [8] applied this approximation to Stockmayer fluids, and found that the dielectric constant predicted with the full RHNC theory agrees better with computer simulation results than those predicted with the LHNC and QHNC theories. Another approach to describe the behaviour of simple polar model fluids is the use of perturbation theories, as pioneered by Pople and further developed by Stell et al. [9-13]. In these theories, the free Helmholtz energy is expressed as the sum of a

Critical behaviour of ionic fluids

Abstract: The past 25 years have seen detailed experimental confirmation, in many fluids, of concepts from the theory of critical phenomena. It has been demonstrated that fluids belong to the universality class of the 3D Ising model, with critical exponents as given by renormalization group calculations. Nevertheless, there is an important class of fluid systems, those with ionic components, for which it is not clear that the notions of critical behaviour developed for uncharged systems apply. We will review the available experimental evidence, and assess the state of theoretical knowledge.