Showing papers in "Molecular Physics in 1988"

Phase equilibria by simulation in the Gibbs ensemble

Abstract: The Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos [1] is generalized and applied to mixture and membrane equilibria. An alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented. The method is then generalized for the calculation of phase equilibria of mixtures by simulation in a constantpressure Gibbs ensemble and the calculation of equilibria across semipermeable membranes with an imposed osmotic pressure difference. The method is used to calculate phase equilibria for binary mixtures of Lennard-Jones molecules. Good agreement is found with published results obtained using other simulation techniques. The computer time required for the Gibbs method is only a small fraction of the corresponding requirement for previously available simulation techniques. Calculations for simple osmotic systems are performed for the first time by simulation, ...

An analysis of the accuracy of Langevin and molecular dynamics algorithms

Abstract: Analytic expressions for mean squared positions and velocities of a harmonic oscillator are derived for Langevin dynamics algorithms valid in the high and low friction limits, and for the Verlet algorithm. For typical values of the parameters, errors in the positions are small. However, if the velocity is defined by the usual Verlet form, kinetic energies (and therefore calculated temperatures) can be in error by several per cent for the Langevin algorithms. If the Bunger-Brooks-Karplus algorithm is used to calculate positions, a simple redefinition of the velocity results greatly in improved kinetic energies. In addition, due to cancellation of errors in the velocities and the positions, the correct virial is obtained. The effect of including the force derivative in diffusive algorithms is examined. Positional and velocity averages are calculated for the Verlet algorithm for arbitrary initial conditions, and errors in the total energy and virial are analysed. Connection is made with the Langevin algorith...

Phase equilibria of associating fluids : spherical molecules with multiple bonding sites

Abstract: The effect of molecular associations on the phase coexistence properties of fluids with one or two directional, attractive centres is investigated. The individual molecules are represented by hard-sphere repulsive cores with off-centre, square-well attractive sites. Such a system’s thermodynamic properties can be calculated by using expressions based on a theory recently proposed by Wertheim. Isothermal-isobaric Monte Carlo simulations of hard-sphere fluids with one or two attractive sites are shown to be in good agreement with the results of the theory. In order to study the system’s phase equilibria using the theory, a simple van der Waals mean-field term is added to account for the dispersion forces. The critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site. Furthermore, results are presented for the degree of association in the gas and liquid phases along the vapour pressure curve. The theory can treat fluids with strong hydrogen-bonding associations such as those found in the carboxylic acids, the aliphatic alcohols, hydrogen fluoride, water etc.

High resolution solid-state N.M.R.

Abstract: By means of rotations around two axes inclined at zeros (magic angles) of the l = 2 and l = 4 Legendre polynomials, first-order and second-order N.M.R. broadening can be averaged away. Experiments with a double-rotor on the central (1/2 ↔ - 1/2) transition of sodium-23 in polycrystalline sodium oxalate illustrate the elimination of broadening due to second-order quadrupolar effects leading to a thirtyfold increase in resolution compared to magic-angle spinning.

Pseudopotentials for main group elements (IIIa through VIIa)

Abstract: Semiempirical pseudopotentials including core-polarization potentials have been generated for main group elements IIIa through VIIa, with main quantum numbers n ⩽ 5. Test calculations with these pseudopotentials have been performed for atomic ionization energies.

An analysis of the hydrogen bond in BASE-HF complexes using the theory of atoms in molecules

Abstract: The nature, energetics and mechanism of BASE-HF hydrogen bonding (where BASE = OC, SC, N2, HCN, H3N, O3, SCO, CO2, N2O, SO2, H2CO, H2O, HF, H3P, H2S and HCl) are examined using the theory of atoms in molecules. The results are obtained from RHF/6-311 + +G**//6-31 G** calculations. A quantitative description of the electron redistribution and changes in atomic properties, including populations, energies, volumes and moments upon hydrogen bond formation are given by the theory, information which in turn provides a qualitative understanding of the hydrogen bond. A hydrogen bond results from the interaction of two closed-shell systems and the theory quantifies the concept of the mutual penetration of the van der Waals envelopes of the acid and base molecules. It is found that the extent of this penetration and the factors which govern it are of paramount importance in determining the strength of the interaction.

On the connection between the supermolecular Møller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces

Abstract: This paper presents the first rigorous analysis of the MP2 and MP3 supermolecular treatments in terms of the perturbation theory of intermolecular forces. In order to connect the two formalisms the MP energies are first expanded in terms of an auxiliary double-perturbation theory in spirit similar to the one proposed by Sadlej (1980, Molec. Phys., 39, 1249). In the next step, each term of this expansion is related to the perturbation theory of intermolecular interactions in the formulation of Szalewicz and Jeziorski (1979, Molec. Phys., 38, 191). Although the formal analysis neglects intermolecular exchange effects, a generalization of the final results is proposed so as to accommodate exchange effects. The supermolecular MP2 interaction energy contains the second-order intrasystem correlation correction to the Coulomb energy, in addition to the UCHF dispersion. The supermolecular MP3 term additionally involves the following: first-order intrasystem (apparent) correlation correction to the second-order UC...

Prediction of the structures of hydrogen-bonded complexes using the laplacian of the charge density

Abstract: The laplacian of the charge density is used to predict the structures and geometries of hydrogen-bonded gas-phase complexes of the type BASE-HF. The bases used are N2, OC, SC, OCO, SCO, HCN, N2O, HCP, H2O, H2S, H3N, H3P, O3, OSO, H2CO, HF, HCl, N2S and H2CS. Many of the weaker complexes have not been characterized experimentally, and so, results of full 6–31 G** geometry optimizations are presented. The laplacian of the charge density, ∇2ρ, determines where charge is locally concentrated and depleted. The point where ∇2ρ attains its maximum magnitude in a region of charge concentration in the base defines the site of electrophilic attack by the acidic H of HF. The angle of electrophilic attack predicted in this manner is compared with the ab initio equilibrium angle that the hydrogen of HF makes with the base. In general, the angles predicted using the laplacian are in good agreement with the ab initio and experimental results. The present results are also compared with those obtained from electrostatic m...

Monte Carlo simulation of multicomponent equilibria in a semigrand canonical ensemble

Abstract: A general formalism and methodology are presented for the Monte Carlo simulation of equilibria in multicomponent systems, and are applied to the study of phase equilibrium in a model binary mixture, and to phase and chemical equilibrium in the ternary mixture Br2−Cl2−BrCl. Very good agreement with available experimental data is obtained. The formalism is based upon an ensemble in which the ratios of all fugacities to a reference fugacity are imposed. Simulations of mixtures performed in this ensemble fluctuate in composition while keeping constant the total number of particles. The reference fugacity is computed by integration of simulation averages of the composition for varying values of the fugacity ratios. Several features of the approach are: (1) it can be readily applied to mixtures of any number of components, even to polydisperse systems, with little additional computational effort; (2) the chemical potential of only one species at one state need be evaluated by conventional techniques, regardless...

An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles

Abstract: Current supercomputers and the impending availability of large scale parallel machines makes possible the study by molecular dynamics of a number of fundamental problems in condensed matter science hitherto beyond our scope because of the enormous computing time involved. This is because a realistic model of such systems contains one or two orders of magnitude more particles than the systems studied to date. Moreover, the intermolecular forces between these particles will usually include contributions from distributions of permanent electric charges, so that the usual assumption of short-ranged forces cannot be made. We give a list of typical problems in this class and attack the problem of improving the performance of molecular dynamics algorithms to take advantage of these new architectures. We use the Jacobi theta function transformation to derive rapidly computable forms for the energy of and forces between large assemblies of N particles interacting in periodic boundary conditions as the sum of real ...

Monte Carlo simulations of liquid acetonitrile with a three-site model

Abstract: A simple intermolecular potential function has been devised to yield good thermodynamic and structural results for liquid acetonitrile The function was tested in Monte Carlo statistical mechanics simulations for the liquid at temperatures of 25°C and 70°C at 1 atm. The average errors in the computed densities and heats of vaporization are 1–2 per cent. The structural results are presented by means of radial distribution functions and dipole-dipole correlation functions, and compared with prior findings. In addition, the importance of the electrostatic interactions in determining the liquid's structure is illustrated by the results of a simulation at 25°C with the partial charges set to zero.

Extended gaussian-type valence basis sets for calculations involving non-empirical core pseudopotentials

Abstract: Revised values of core pseudopotential parameters are presented together with optimized PS-31 G valence basis sets for atoms from Li to Ca and from Ga to Kr. Studies with more than thirty test molecules indicate a very good agreement with 6–31 G results for atomization energies, geometries, dipole moments and force constants.

Simulation of the adhesive-hard-sphere model

Abstract: Monte Carlo simulations of the three-dimensional sticky-hard-sphere system are presented. A new modified Monte Carlo algorithm has been developed which makes it possible to explore the phase diagram for a large region of both the packing fraction and the stickiness parameter τ. The phase diagram is calculated, as well as pair distribution functions and structure factors. Cluster percolation has been studied and its relation to the phase diagram. The simulation results are compared with predictions, obtained from the Percus-Yevick approximation, which can be solved analytically for this model. The potential relevance of the present simulation results for experiments on clustering in neutral colloids is discussed.

A polarizable water model for calculation of hydration energies

Abstract: A molecular model for electronic polarization of water is defined, consisting of interacting point dipole polarizabilities in an electric field generated by atomic point charges, which represent the gasphase dipole moment of water molecules. The induced dipole equations are solved self consistently. The model has been implemented in a Monte Carlo hydration simulation program, and its computational performance is discussed. Results of calculations of hydration and protonation energies of amines (including glycine) are presented and discussed, together with results for the water dimer and for liquid water. Solvent induction appears significant to describe quantitatively solvent screening of interactions between charges on the solute. In combination with solvent polarization a quantum chemical charge model is found superior to an empirical set of charges. Inadequacies of the Lennard-Jones type modelling of non-electrostatic interactions between water molecules are demonstrated.

A realistic double many-body expansion (DMBE) potential energy surface for ground-state O3 from a multiproperty fit to ab initio calculations, and to experimental spectroscopic, inelastic scattering, and kinetic isotope thermal rate data

Abstract: A new single-valued potential energy surface is reported for the ground electronic state of ozone from the double many-body expansion (DMBE) method. The parameters appearing in the DMBE formalism are determined from a multiproperty analysis using ab initio energies, and experimental data from spectroscopic, incomplete total scattering cross section, and kinetic thermal rate measurements. Based on this new surface, thermal rate coefficients for the 18O + 16O2 → 18O16O + 16O isotope exchange reaction are also reported over the temperature range 300 < T < 2000 K from the quasi-classical trajectory method.

The solution of the reference hypernetted-chain approximation for water-like models

Abstract: In this paper we examine the dielectric and structural properties of hard polarizable multipolar models for liquid water. The theoretical results were obtained by solving the self-consistent mean field (SCMF) approximation together with the reference hypernetted-chain (RHNC) theory. The dielectric constants are in good agreement with experiment over a large range of temperatures and pressures. The rather poor agreement between the radial distribution functions determined for our water-like fluids at 25°C and those measured for liquid water is discussed.

Widom's method for uniform and non-uniform electrolyte solutions

Abstract: We develop and apply test particle methods to calculate chemical potentials in uniform and non-uniform electrolytes using computer simulations. Our techniques are based on the well-known Widom method, but account for non-electroneutral particle fluctuations, implicitly suppressed in a usual Canonical Ensemble Monte Carlo simulation. These fluctuations are shown to contribute greatly to the Widom average for a single ionic species. We compare our results with similar Grand Canonical Monte Carlo simulations for 1:1, 2:1 and 2:2 uniform electrolytes, and 1:1 electrolytes at a charged planar interface. In general, we find good agreement between the methods, all within the statistical fluctuations. The advantages of using the test particle approaches are discussed.

On the equilibrium structure of dense fluids

Abstract: A factorization ansatz for the triplet direction correlation function c (3) is combined with the exact relation between c (3) and the derivative of the pair function c (2) with respect to density to derive a simple and tractable approximation for c (3) in dense, classical fluids. The predictions of this approximation are found to be in good agreement with the results of ‘exact’ molecular dynamics simulations for the ‘soft sphere’ model near freezing. The approximate c (3) is then used to derive an improved integral equation for the pair correlation function which is found to yield satisfactory results. In another application, the third order term in the density functional theory of freezing is systematically evaluated for the first time and is found to lead to significant improvement over the usual second order theory, particularly for soft interatomic repulsions.

Adsorption of fluids in model zeolite cavities

Abstract: The adsorption of molecules into a zeolite has been studied in two simple model systems with spherical cavities and with Lennard-Jones molecules as adsorbents. The thermodynamic and structural properties have been calculated by a virial expansion and by direct calculation of the partition functions. The results are compared with those obtained by a grand canonical Monte Carlo simulation and good agreement is found at low occupancies with the virial expansion, and up to medium occupancies with the partition functions. It is shown that the direct calculation of the partition functions can be made for systems containing up to about six molecules.

Interpretation of the Hartree-Fock interaction energy between closed-shell systems

Abstract: In the present paper a decomposition of the Hartree-Fock interaction energy of two closed-shell systems is given. The decomposition is obtained by performing the Hartree-Fock iterations for the supersystem in a way different from the traditional one. The procedure is called the Pauli blockade method since the interacting molecules are deformed in the field of their partners under the constraint that they cannot penetrate each others occupied spaces. The zeroth iteration of the above procedure gives the Heitler-London interaction energy and in the consecutive iterations the total energy of the supersystem is minimized letting the charge distribution of molecule A adapt itself to the presence of molecule B and vice versa, until self-consistency is achieved. It is also shown that unphysical charge transfer may occur in some methods if during mutual deformations the intersystem Pauli exclusion principle is not observed. This confirms earlier suggestions that the so called weak symmetry forcing in the perturba...

Electric dipole interactions in molecular crystals

Abstract: The importance of dipolar interactions is highlighted in a wide range of molecular crystal properties. Molecules respond via an effective polarizability (appropriate to the crystal phase) to a local field arising from the applied field and the fields of the surrounding induced dipoles, determined self-consistently. An exact treatment is possible for perfect crystals and crystals with localized imperfections, yielding the inverse dielectric function characterizing the crystal response. From this, results follow for the crystal linear and nonlinear dielectric response, for Coulomb exciton energies, and for the intensities of lattice vibrational spectra. A direct extension yields the polarization energy associated with the induced dipoles. This provides insight into the energetics of excess charge carriers in perfect and imperfect crystals and of charge-transfer excitons, into electronic Stark spectra, and into aspects of lattice dynamics and phase transitions.

Henry constants in non-ideal fluid mixtures

Abstract: Infinite-dilution chemical potentials (or Henry's constants) of highly non-ideal binary Lennard-Jones mixtures were calculated using Widom's test particle method in the canonical and Kirkwood's charging method in the isothermal-isobaric ensemble. For large solutes at high densities, the results were significantly different from previous values obtained using the umbrella sampling test-particle method in the canonical ensemble. The difference can be attributed to the much more severe system size dependence of the canonical ensemble for large solutes using umbrella sampling methods. Simulations were carried out at a variety of temperatures and densities for infinitely dilute mixtures with C ≡ e AB /e BB ⩽ 2 and D ≡ (σ AB /σ BB )3 ⩽ 3·5 (Here e and σ are the Lennard-Jones energy and size parameters, A and B refer to the solute and solvent respectively.) It was found that the test particle method is applicable to mixtures at reduced density ρ* ≡ ρσ3 BB ⩽ 0·5 with C ⩽ 2 and D ⩽ 3·5. For higher densities and/or...

Angle-average for the powers of the distance between two separated vectors

Abstract: Closed analytical formulae are derived for the angle-average of arbitrary powers of the distance between two separated vectors. It is also shown how coefficients of an expansion in spherical harmonics can be obtained in a closed analytical form.

The effects of morphology and exchange on proton N.M.R. relaxation in agarose gels

Abstract: The effects of morphology and exchange on N.M.R. relaxation times in agarose gels are interpreted within a unified theoretical framework based on the generalized Bloch equations. By acknowledging the spacial dependence of the N.M.R. parameters it is shown how the relaxation behaviour depends on the distance scale characterizing the heterogeneity of the gel. If this distance scale is sufficiently small to allow complete diffusive averaging we recover the traditional results based on the Bloch-McConnell equations describing relaxation in a homogeneous system. This is the case for fresh agarose gels which show monoexponential relaxation and has been widely interpreted in terms of the rapid exchange of protons between populations of ‘free’ and ‘bound’ water. Conversely, if the distance scale characterizing the heterogeneity is sufficiently large to prevent complete diffusive averaging our model predicts multiexponential relaxation. This is the case with the transverse magnetization in agarose gels that have b...

The intermolecular potential of chlorine

Abstract: We present an anisotropic atom-atom effective pair potential for chlorine and compare it with a wide range of experimental data. The crystal structure, lattice frequencies, liquid structure factor, and several thermodynamic properties of the liquid are all well reproduced. Reasonable agreement with experiment is also obtained for the structure factor of the gas, and for the second virial coefficient over a range of temperatures.

Self-diffusion measurements of ethanol and propanol

Abstract: Self-diffusion coefficients of ethanol and 1-propanol were measured by the N.M.R. spin-echo technique over the temperature range 285 K ⩽- T ⩽- 320 K and the pressure range 0·1 MPa ⩽- P ⩽- 400 MPa. The results are interpreted on the basis of the rough hard-sphere model. A test of the Stokes-Einstein relation is performed and a modification of it is proposed.

Infrared Fourier transform spectroscopy of XeH

Abstract: The infrared emission spectrum of the Rydberg molecule XeH was recorded with the Kitt Peak Fourier transform spectrometer. XeH was made in a hollow cathode discharge of 2·2 torr H2 and 0·1 torr Xe. The 0-0 bands of the C 2Π-B 2Σ+ and the D 2Σ+-C 2Π transitions were observed near 3250 cm−1 and 4420 cm−1, respectively. A rotational analysis provides spectroscopic constants for these states.

Observation and assignment of tunnelling-rotational transitions in the far infrared spectrum of (HF)2

Abstract: Several ΔK = +1 subbands of the tunnelling-rotational spectrum of (HF)2 were observed for the first time between 20 and 170 cm-1 at a resolution of 0·012 – 0·025 cm-1 in a thermostated long path cell at 245 K and 2 kPa. Assisted by combination differences from the v 1 fundamental, we are able to confirm and extend previous results on the ground state of (HF)2 for K values ranging from 0 to 4. Perturbations are found in some transitions involving high K-levels. Some additional results on the tunnelling splittings in vibrationally excited states (v 1 = 1) are presented and discussed in relation to dynamical and electronic effects upon excitation of the HF stretching motions.

Normal modes and local modes in H2 X: beyond the x, K relations

Abstract: The so-called ‘x, K relations’, which interrelate the normal mode and local mode descriptions of the stretching vibrations of polyatomic molecules, demand simple numerical relationships between the...

Local-mode to normal-mode hamiltonian transformation for X-H stretchings

Abstract: The relationship between the local-mode and the normal-mode treatments of X-H stretchings is analysed by expressing the hamiltonian in terms of boson operators and transforming the operators rather than the basis functions. The transformation is exact, non-perturbative, and solves in a general form the open problem of the mathematical link between the two theories.