Showing papers in "Molecular Physics in 1979"
TL;DR: In this article, a modified Benedict-Webb-Rubin equation has been used to derive an equation of state for the Lennard-Jones fluid that is valid over a wide range of temperatures and densities.
Abstract: Molecular dynamics calculations of the pressure and configurational energy of a Lennard-Jones fluid are reported for 108 state conditions in the density range 0·35 ≦ ρ* ≦ 1·20 and temperature range 0·5 ≦ T* ≦ 6 (where ρ* = ρσ3, T* = kT/e). Particular attention is paid to the dense fluid region (ρ* ≧ 0·9), including state conditions in the subcooled liquid region. These new simulation results for P and U are combined with those of previous workers, together with low density values calculated from the virial series and values of the second virial coefficients themselves, to derive an equation of state for the Lennard-Jones fluid that is valid over a wide range of temperatures and densities. The equation of state used is a modified Benedict-Webb-Rubin equation having 33 constants. It fits the data well over the density range 0 ≦ ρ* ≦ 1·2 and for T* values ranging from 0·5 to 6·0 (the exact temperature range depending to some extent on the density considered). We also calculate for the same range of state con...
720 citations
TL;DR: In this article, the anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species 12CH4, 13 CH4, 12 CH4.
Abstract: The anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species 12CH4, 13CH4, 12CH4, 12CH3D, 12CHD3 and 12CH2D2. Six of the thirteen cubic force constants have been determined experimentally, the remaining cubic constants being fixed at values derived from ab initio calculations. The quartic force field is very crude, in that only frrrr has been refined. It is concluded however that the cubic and quartic force fields, even though they are subject to limitations, provide a considerable improvement in the experimental determination of the r e structure and the quadratic force field. The equilibrium bond length is found to be r e(CH) = 1·0858 ± 0·001 A.
400 citations
TL;DR: In this article, a computational approach to the direct configuration interaction method is described using the calculus of the generators of the unitary group and the simple structure of the generator matrices within the harmonic excitation level scheme is exploited to give a computational method that is competitive with traditional approaches.
Abstract: A computational approach to the direct configuration interaction method is described The method is formulated using the calculus of the generators of the unitary group The simple structure of the generator matrices within the harmonic excitation level scheme is exploited to give a computational method that is competitive with traditional approaches A new scheme for basis set truncation in the case of partial configuration interaction is devised employing orbital populations It is also shown that the block structure of the generator matrices leads to the definition of a new order parameter for perturbation methods which is both effective and convenient
391 citations
316 citations
TL;DR: In this paper, a hybrid of the traditional iterative scheme and the Newton-Raphson technique is proposed to obtain numerical solutions to the Percus-Yevick and hypernetted chain equations for liquid structure.
Abstract: We present a new method of obtaining numerical solutions to the Percus-Yevick and hypernetted chain equations for liquid structure. The method, which is rapidly convergent and very stable, is a hybrid of the traditional iterative scheme and the Newton-Raphson technique. We show by numerical tests for typical potentials that the method gives well-converged solutions in 20 or 30 iterations even for very high densities. The number of iterations needed is insensitive to the choice of initial estimate, even if this is extremely inaccurate.
304 citations
TL;DR: In this article, the longitudinal and transverse coherence transfer functions are evaluated and discussed in terms of transfer efficiency, oscillation frequencies, phase anomalies and multiplet effects, and the general formalism and applications to simple spin systems are presented.
Abstract: Coherence transfer between heteronuclear spin species in the rotating frame is analysed in view of application to heteronuclear two-dimensional cross-correlation spectroscopy in liquids. The general formalism and applications to simple spin systems are presented. In particular, the longitudinal and transverse coherence transfer functions are evaluated and discussed in terms of transfer efficiency, oscillation frequencies, phase anomalies and multiplet effects.
273 citations
Abstract: A general symmetry-adapted double-perturbation procedure for treating intramolecular or intra-atomic correlation in the theory of intermolecular forces is developed The method was applied to the interaction of two helium atoms The calculations were made employing the Moller-Plesset partition of atomic hamiltonians and using a large basis set of explicitly correlated gaussian wave functions At the van der Waals minimum the total intra-atomic correlation contribution to the interaction energy amounts to -2·9 K and is mainly due to the change of the dispersion energy The total interaction energy is equal to -10·3 K being in agreement with the latest experimental result of Burgmans, Farrar and Lee
218 citations
TL;DR: In this paper, a series of simulations has been made for 108 dipoles interacting through the Stockmayer potential with μ* = 1·0, ρ* = 0·8, and a variety of summation methods has been used; all lead to similar thermodynamic properties and diffusion coefficients but the autocorrelation function of the dipole moment of a spherical region varies considerably according to the summation method used.
Abstract: Truncation of the interaction between dipoles in the computer simulation of polar fluids is responsible for an upward drift in the total energy of the system. Methods of avoiding this are discussed. A series of simulations has been made for 108 dipoles interacting through the Stockmayer potential with μ* = 1·0, ρ* = 0·8. A variety of summation methods has been used; all lead to closely similar thermodynamic properties and diffusion coefficients but the autocorrelation function of the dipole moment of a spherical region varies considerably according to the summation method used.
217 citations
TL;DR: In this paper, the intensity of X-ray scattering from three compounds has been measured photographically at a number of temperatures, and the results suggest that f d(β) is close to the true singlet distribution so that the dominant angular fluctuations are co-operative and involve several molecules.
Abstract: The intensities of X-ray scattering from three compounds has been measured photographically at a number of temperatures. The substances studied were 4,4′di-n-octyloxyazoxybenzene (OOAB) and its di-n-heptyl homologue (HOAB) in their nematic and smectic C phases and ethyl-4-(4′acetoxybenzylidene)aminocinnamate (EABAC) in its nematic and smectic A phases. In all cases except the smectic C phase of HOAB the distribution function f d(β) describing the orientation of the local director for clusters of ≳ 10 molecules relative to the average director has been determined. The form of f d(β) is close to that predicted by simple mean field theory although the magnitude of the order parameters ⟨P 2⟩ in general differ significantly. from the simple mean field values. The results suggest that f d(β) is close to the true singlet distribution so that the dominant angular fluctuations are co-operative and involve several molecules. For the smectic phases properties of the density wave f(z) which is the smectic layer distr...
194 citations
TL;DR: In this paper, an optimized version of the force bias scheme is presented for the Monte Carlo simulation of water in which the random walk of the individual molecule is biased in the direction of the forces and torque acting on the molecule.
Abstract: An optimized version of the force bias scheme is presented for the Monte Carlo simulation of water in which the random walk of the individual molecule is biased in the direction of the force and torque acting on the molecule. A new criterion is developed to judge the efficiency of sampling the configuration space by studying the translational and rotational diffusion of individual molecules during the random walk. The force bias method is compared with the uniform sampling method using ST2 water as an example, and with molecular dynamics. Similarities and differences between molecular dynamics and Monte Carlo are discussed with respect to pair correlations and energy distributions.
157 citations
TL;DR: In this article, expressions for the generated antiStokes spectral density in coherent anti-Stokes Raman spectroscopy (CARS) are obtained, which take into account the finite linewidths of laser sources and which may be used to analyse observed spectra.
Abstract: Expressions for the generated antiStokes spectral density in coherent antiStokes Raman spectroscopy (CARS) are obtained, which take into account the finite linewidths of laser sources and which may be used to analyse observed spectra. Lorentzian and gaussian laser lineshapes are taken as special cases, which enable further analytic results for single and multiline CARS spectra to be derived. Emphasis is placed on scanning and broadband (multiplex) CARS techniques, and the choice of laser sources discussed from the spectral point of view. As examples of multiline spectra an analytical account of a periodic spectrum is presented and temperature measurement from Q-branch spectra is treated.
TL;DR: In this article, the second and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule were calculated by the finite-field RSMP and single + double excitation CI (SDCI) methods for the same basis set.
Abstract: Ordinary Rayleigh-Schrodinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. [2/1] Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced 1s1p2d/1p polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable ...
TL;DR: In this article, the authors used SCF and CI wavefunctions of the properties of methane to calculate octopole and hexa-decapole moments, the polarizability, hyperpolarizability and dipole-quadrupole polarizer, diamagnetic contributions to the nuclear magnetic shielding constants, and magnetizability.
Abstract: Accurate calculations are made using SCF and CI wavefunctions of the properties of methane The properties considered are the octopole and hexa-decapole moments, the polarizability, hyperpolarizability and dipole-quadrupole polarizability, the diamagnetic contributions to the nuclear magnetic shielding constants, and to the magnetizability, and the electric field gradient at the hydrogen nucleus Where accurate experimental values are known these are found to be in excellent agreement with the ab initio values The accuracy of determining multipole moments and polarizabilities from collision induced spectra is discussed
TL;DR: In this article, a statistical mechanical theory of the Frank elastic constants is formulated and a free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients.
Abstract: A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K 1, K 2 and K 3 are calculated. The results of these calculations are similar to those given by Priest and by Straley.
TL;DR: In this paper, general expressions for the various independent fluoresence intensities in a uniaxial mesophase in terms of reorientational correlation functions are derived for the case of a fluorescent probe with effective cylindrical symmetry.
Abstract: The study of time dependent fluorescence polarization can give information on static and dynamic properties in liquid crystals. Here general expressions are derived for the various independent fluoresence intensities in a uniaxial mesophase in terms of reorientational correlation functions. The case of a fluorescent probe with effective cylindrical symmetry is treated in detail and the effect of varying the orientation of the absorption and emission dipole moment in the molecular frame is discussed. Explicit expressions for the time dependent intensities are obtained assuming a diffusional and a strong collision model for reorientation in a liquid crystal. Results are shown for the special case of a molecule with absorption and emission moments parallel to the long axis. Finally results for continuous illumination type experiments are obtained.
TL;DR: In this paper, the anisotropic Rayleigh and the allowed Raman spectra of carbon disulphide over the normal liquid range are described, and the Raman reorientation times are qualitatively well predicted by the Stokes-Einstein-Debye formula with slip boundary conditions.
Abstract: Measurements of the anisotropic Rayleigh and the allowed Raman spectra of carbon disulphide over the normal liquid range are described. The Raman reorientation times agree well with N.M.R. values and are qualitatively well predicted by the Stokes-Einstein-Debye formula with slip boundary conditions, although significant departures are found. The Hubbard relationship is obeyed. A careful comparison of the Rayleigh and anisotropic Raman intensities indicates that the orientational correlation parameter (g 2) decreases with increasing temperature. Using values of g 2 obtained in this way the ratio of the Rayleigh and Raman reorientation times is shown to be consistent with a small value for the correlation in angular velocity between molecules. The vibrational dephasing time is found to be roughly constant with temperature in contrast with the predictions of the theories for this quantity. An attempt is made to correlate its behaviour with that of the collision induced Raman spectra of CS2.
TL;DR: In this article, the electron density distribution of solid chlorine is determined from high resolution X-ray diffraction intensity measurements at 90 K. The deformation density reveals a torus of non-bonding density at 0·31−0·37 e/A3 encircling the Cl-Cl bond somewhat in the back of each of the Cl atoms.
Abstract: The electron density distribution of solid chlorine is determined from high resolution X-ray diffraction intensity measurements at 90 K. Deformation densities are calculated from the observed X-ray data and parameters obtained from a high order refinement of data with sin ϑ/λ > 0·65 A-1. Refinements including the population of multipole density functions are used to calculate model deformation densities and the asymmetry of the electric field gradient. Inclusion of third and fourth cumulant thermal parameters results in a significant improvement in the fit to the experimental data. The deformation density reveals a torus of non-bonding density at 0·31–0·37 e/A3 encircling the Cl-Cl bond somewhat in the back of each of the Cl atoms. A double peak of 0·22 e/A3 is found in the bonding region of the experimental deformation density similar to the bonding density found in S8. This feature is not properly reproduced in density maps based on the atom-centred multipole functions. The calculated distribution of er...
TL;DR: A theory of neutron diffraction in polycrystalline specimens of sulphur hexafluoride (SF6) and carbon tetrabromide (CBr4) was developed and applied in the interpretation of the neutron results as discussed by the authors.
Abstract: An investigation of the plastic phases of polycrystalline specimens of sulphur hexafluoride (SF6) and carbon tetrabromide (CBr4) by neutron elastic scattering and neutron diffraction experiments is reported. A theory of neutron diffraction in plastic crystals, which treats the Bragg scattering and the diffuse scattering from a unified point of view, is developed and applied in the interpretation of the neutron results. The Debye-Scherrer peaks are analysed, both by a cumulant expansion technique and a cubic harmonic analysis, to determine the crystal structures of the plastic phase which are found to be body-centred cubic (space group Im3m) for SF6 and face-centred cubic (space group Fm3m) for CBr4. The bond-orientation distribution function, f(Ω), has maxima in the directions for SF6 and in the directions for CBr4. Since, in both cases, f(Ω) is appreciably different from zero for all orientations, it is apparent that significant thermal reorientation takes place in both these crystals. The tr...
TL;DR: In this paper, the authors extended the theory of polar polar polarizable molecules with renormalization and derived exact formal expressions for the pressure, entropy and internal energy at three levels of renormalisation.
Abstract: The theory of fluids of polar polarizable molecules is extended using the previous formalism based on renormalization. Exact formal expressions are derived for the pressure, entropy and internal energy at three levels of renormalization. Thermodynamic perturbation theory is developed, and numerical estimates are made for polar polarizable hard spheres. The effect of the polarizability α on the Helmholtz free energy A predicted by the two renormalized versions is much larger than the prediction of the unrenormalized version, which is in essential agreement with the unrenormalized perturbation theory of McDonald. The renormalized theories predict a strong dependence on the anisotropy of α, while no such dependence is predicted by the unrenormalized theories. The numerical values and the dependence on the anisotropy of α are in good agreement with the results of the more complicated perturbation treatment of Patey and Valleau, which requires detailed knowledge of a rigid polar reference system obtainable onl...
TL;DR: In this paper, it is argued that quantum mechanical corrections will lead to a local mode splitting which is predicted to decrease in magnitude along any given stretching vibrational progression, and to be larger for a given quantum state of D2O than for H2O.
Abstract: Classical trajectory calculations on a realistic potential for the stretching vibrations of the water molecule are used to demonstrate the existence of stable local vibrational modes, which occur in degenerate pairs. The proportion of phase space occupied by such modes increases with increasing energy, with a clearly characterized (0, 2) local state in a local quantum number assignment. It is argued that quantum mechanical corrections will lead to a local mode splitting which is predicted to decrease in magnitude along any given stretching vibrational progression, and to be larger for a given quantum state of D2O than for H2O.
TL;DR: In this article, the authors extended the techniques for the rapid computation of energies of three-dimensional neutral periodic assemblies of charged particles to semi-infinite arrays and assemblies of ions in infinite filsm.
Abstract: The techniques for the rapid computation of energies of three-dimensional neutral periodic assemblies of charged particles are extended to semi-infinite arrays and assemblies of ions in infinite filsm. The results will be useful for simulation of ionic movements in fast-ion conductors and dense colloidal dispersions.
TL;DR: In this article, an improved HFD potential for krypton is presented, with known long-range behaviour, fitted to second virial, viscosity and thermal conductivity data, with the best overall predictive ability for dilute gas, bulk and micro-scopic data.
Abstract: An improved potential for krypton is presented. It has the simple but realistic form used by Aziz and Chen for argon based on the HFD potential suggested by Ahlrichs et al. The potential, with known long-range behaviour, was fitted to second virial, viscosity and thermal conductivity data. The potential appears to have the best overall predictive ability for dilute gas, bulk and micro-scopic data.
TL;DR: In this article, a new linear magneto-optic effect predicted earlier by the authors is considered in liquids composed mainly of chiral molecules, which manifests itself as a change in the refractive index, which is proportional to the scalar product (B. k), where k is the photon wave vector and B, the external quasi-static magnetic field.
Abstract: A new linear magneto-optic effect predicted earlier by the authors is considered. The effect appears in liquids composed mainly of chiral molecules. Phenomenologically the new effect manifests itself as a change in the refractive index, which is proportional to the scalar product (B . k), where k is the photon wave vector, and B, the external quasi-static magnetic field. The constant of the new effect has been calculated. The expression obtained contains matrix elements of electric and magnetic dipoles and electric quadrupoles taken between electronic wave-functions of the molecule. A simple interpretation of the mechanism for the new effect is given. The cascade mechanism for a contribution of the first order terms to the observable constants of the second order effects is treated. In particular, the corrections to magnetostriction and Cotton-Mouton constants due to the Faraday effect are determined. It is shown that the cascade mechanism does not contribute to the observable value of the new magnetorefr...
TL;DR: In this paper, the structure of the interface of an argon-like fluid in equilibrium with its own vapour at 110 K was studied using the Monte Carlo method, and the two components P N(z) and P T (z) (normal and tangential) of the pressure tensor P(r) for the planar interface were determined in the simulation.
Abstract: The structure of the interface of an argon-like fluid in equilibrium with its own vapour at 110 K is studied using the Monte Carlo method. The two components P N(z) and P T(z) (normal and tangential) of the pressure tensor P(r) for the planar interface are determined in the simulation. The normal component is a constant along the direction perpendicular to the surface (the z-direction) and is equal to the hydrostatic pressure. The tangential component varies across the surface. The surface tension γ, and the surface of tension z s are determined. The location of the surface of tension is compared with the location of the Gibbs equimolar dividing surface, and the results are used to determine the curvature dependence of the surface tension for spherical droplets. The results are compared with theory.
TL;DR: In this article, the authors developed a method based on the non-equilibrium molecular dynamics of Ashurst and Hoover [1] which calculates the spectrum of stress-stress correlation with greater efficiency than has hitherto been possible.
Abstract: Accurate computer simulation calculations of hydrodynamic transport coefficients are notoriously expensive. In this paper we develop a method based on the non-equilibrium molecular dynamics of Ashurst and Hoover [1] which calculates the spectrum of stress-stress correlation with greater efficiency than has hitherto been possible. The calculation shows that a potential function for methane, due to Williams [2], predicts a zero frequency shear viscosity within 10 per cent of the experimental value. The spectrum of stress-stress correlation gives clear evidence of a t -3/2 long-time tail. It is shown that the spectrum is not a monotonic decreasing function of frequency. This has not been seen in computer simulation before but is in agreement with the mode-coupling prediction of Bosse et al. [3].
TL;DR: In this article, the authors derived a closed expression for the orientation dependence of the long range interaction coefficients of linear molecules and then calculated the dispersion and induction multipole interaction coefficients for the systems H2-H2 and H2 He up to R -10 terms inclusive.
Abstract: We derive a closed expression for the orientation dependence of the long range interaction coefficients of Σ state linear molecules and then calculate the dispersion and induction multipole interaction coefficients for the systems H2-H2 and H2-He up to R -10 terms inclusive. The monomer states are described by SCF-LCAO wave functions with polarization functions optimized with respect to the different multipole polarizabilities. The anisotropy factors γ8 and γ10, describing the orientation dependence of the R -8 and R -10 terms, are approximately equal and much larger than γ6, due to the occurrence of the (completely anisotropic) mixed-pole terms.
TL;DR: A relatively simple tractable scheme for the evaluation of the isotropic intermolecular potential between two closed-shell systems, which contains one adjustable parameter, is proposed and tested using the He-He, Ne-Ne, Ar-Ar, Kr-Kr, and H2-H2 interactions as models.
Abstract: A relatively simple tractable scheme for the evaluation of the isotropic intermolecular potential between two closed-shell systems, which contains one adjustable parameter, is proposed and tested using the He-He, Ne-Ne, Ar-Ar, Kr-Kr, and H2-H2 interactions as models. The approach is based on expressing the potential as a sum of exchange (E x) and coulomb (E c) contributions. A semi-empirical approximation, which is a simple function of the first order coulomb energy (E c (1)), is used to represent E x. The representation for E c is based on E c (1) and a suitably universally damped asymptotic expansion of the second-order coulomb energy through O(R -10). The adjustable parameter formally occurs in the representation for E x and influences the balance between E x and E c in the representation of the potential. The results obtained for the model systems are in excellent agreement with reliable literature potentials, many of which contain several adjustable parameters, and suggest that the scheme proposed he...
TL;DR: The method of Widom has been used to calculate the chemical potential of liquid chlorine and bromine in Monte Carlo simulations based on the two Lennard-Jones centres potential as mentioned in this paper.
Abstract: The method of Widom [1] has been used to calculate the chemical potential of liquid chlorine and bromine in Monte Carlo simulations based on the two Lennard-Jones centres potential. The agreement between the computed and experimental entropies and vapour pressures over the range T* = 1 to 1·8 is satisfactory.
TL;DR: In this article, a molecular dynamics study based on two-Lennard-Jones (12-6) centers pair potentials, with reduced bond lengths in the range 0·5 ⩽l/σ⩽0[sbreve]d8, and with e, σ-parameters simulating liquid F2, Cl2, Br2 and CO2 (14) is extended to time correlation functions.
Abstract: The molecular dynamics study based on two-Lennard-Jones (12-6) centres pair potentials, with reduced bond lengths in the range 0·5 ⩽l/σ⩽0[sbreve]d8, and with e, σ-parameters simulating liquid F2, Cl2, Br2 and CO2 (14) is extended to time correlation functions. The calculated properties include: translational velocity and force self correlation functions; orientational self-correlation functions , a cross correlation function for P 2, angular momentum (J), and torque self-correlation functions. Diffusion constants (D) and rotational relaxation times (τ1, τ2, τ J ) have been evaluated and where possible compared with experimental data (D and τ J for F2, τ2 for Cl2). Calculations with 108 or 256 molecules are reported for several densities and temperatures for four model liquids. The nature of the one-particle motion is analysed qualitatively in terms of quasi-oscillations and -librations. It is difficult to fit the observed features into the framework of physical models proposed in the lite...
TL;DR: The second rank orientational correlation function g 2 and the effective polarizability anisotropy of liquids CS2, C6H6 and C6F6 were determined by combining data from the Rayleigh spectrum with Cotton-Mouton measurements on these liquids as mentioned in this paper.
Abstract: The values of the second rank orientational correlation function g 2 and the effective polarizability anisotropy of liquids CS2, C6H6 and C6F6 were determined by combining data from the Rayleigh spectrum with Cotton-Mouton measurements on these liquids in a way which avoids difficulties with the interaction-induced polarizability A detailed discussion of the errors associated with this procedure is presented The values are used to interpret the Kerr constants of these liquids The value of g 2 is combined with Rayleigh and Raman reorientational relaxation times to determine the dynamic orientational correlation parameter Comparison with previous values suggests the plausibility of calculating the effective polarizability in a dielectric model