Perturbation theory for the angular correlation function

A perturbation expression for the angular pair correlation function g ⁽²⁾(r ₁₂, ω₁, ω₂) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g ⁽²⁾(r ₁₂, ω₁, ω₂) and the present expression is made for a system of two-dimensional point dipoles.     

Solvation of large dipoles

A model system consisting of one strongly polar molecule dissolved in a pool of 499 moderately polar particles is studied in a molecular dynamics experiment. A pair potential of Stockmayer type is used. The structure of the solution has been analysed in terms of g(R), f(R), h _Δ(R), h _D(R), g(R, x), and Voronoi polyhedra. Solvent-solvent spatial correlations are presented and compared to solute-solvent properties already discussed in part I. Voronoi polyhedra analysis is also used to define structural relaxation around solute or solvent particles unambiguously. The dynamics of the system is described by means of angular momentum, orientational, and velocity autocorrelation functions. The solute's influence on the dynamics of the solvent is analysed by a polyhedral decomposition of time correlation functions.     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .     

Implicit finite-size effects in computer simulations

The influence of periodic boundary conditions (implicit finite-size effects) on the anisotropy of pair correlations in computer simulations is studied for a dense classical fluid of pair-wise interacting krypton atoms near the triple point. Molecular dynamics simulation data for the pair distribution function g _N(r) ≡ g _N(r, θ, ?) N-particle systems, as a function of radial distance r, polar angle θ, and azimuthal angle ?, are compared directly with corresponding theoretical predictions [L. R. Pratt and S. W. Haan, J. Chem. Phys. 74, 1864 (1981)]. For relatively small systems of N = 60, 80, and 108 atoms, significant angular variation is observed, which is qualitatively, and in several cases quantitatively, well predicted by theory. Finite-size corrections to the spherically-averaged radial distribution function g _N(r), however, are found to be comparable to random statistical errors for runs of 10⁵ time steps.     

An approximate expression for the Wigner-Kirkwood ℏ4 quantum correction to the pair distribution function in a one-component plasma

We propose an accurate approximate expression for the exact ℏ⁴ quantum correction to the pair distribution function g₂^q(r₁₂) that we have derived recently in an OCP using Wigner-Kirkwood ℏ² expansion. Our expression, depending only the classical pair distribution function g₂^c(r₁₂), reproduces the behavior of Wigner-Kirkwood g₂^q(r₁₂) at order ℏ⁴, at small, intermediate and large r₁₂.     

The distance dependence and spatial distribution of the molecular quadrupole moments of P2, S2 and Cl2

The quadrupole moments (Θ) of the molecules P₂, S₂ and Cl₂ have been computed at the SCF, CASSCF and CASSCF + 1 + 2 levels of theory, using augmented correlation consistent basis sets. The convergence of Θ as a function of basis set and level of theory is discussed. The variation of Θ from the separated atoms to the equilibrium region is reported. Θ is written as the sum of a sigma and pi contribution, and inaccuracies in the SCF values for P₂ and S₂ are due to the poor representation of the pi system in the SCF theory. A reference state dependent quadrupole moment density, - ½(3cos² θ- 1)r ²δη(r; R), is defined whose integral is the mole2 cular quadrupole moment, and the spatial distributions of the density and its relationship to the density difference δη(r; R) are examined.     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

A statistical theory of orientational ordering at the free surface of a liquid of ellipsoidal molecules

The surface tension γ of a system of ellipsoidal molecules is evaluated approximately using a generalized Fowler-Kirkwood-Buff model. The pair potential is modelled as u(r/σ) where r is the centre of mass distance and σ is an angle dependent range parameter determined by the shape anisotropy of the molecule. It is shown that if the pair correlation function g scales as g(r/σ) γ can be mapped onto the value for a system of spheres, multiplied by an angular integral which takes into account approximately both the anisotropic molecular shape as well as possible orientational order. It is shown that γ is lowered when the orientational order parameter Q ≠ 0, implying that isotropic molecular liquids may be partially ordered near the free surface. The surface favours parallel ordering of rod-like particles in a direction in the plane of the surface. For plate-like particles, ordering with the plates in the plane of the surface is favoured. In both cases the anchoring energies increase sharply with the shape anisotropy of the molecule. These results are qualitatively consistent with the surface properties of non-polar nematic liquid crystals.     

Perturbation theory for equilibrium properties of molecular fluids

Perturbation theory for the angular pair correlation function g(r₁₂ ω ₁ ω ₂), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties. Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states. Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections. Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties. The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressibility, in agreement with the first-order theory. Molecular anisotropy has a relatively small effect on the configurational energy and on the Helmholtz free energy, but the effect is large for pressure and specific heat. The pressure is more sensitive to short-range anisotropic forces than the other properties, whereas the specific heat is particularly sensitive to the long-range anisotropic forces. Mean squared torques (derived from infra-red and Raman band moments) are very sensitive to the strengths of the anisotropic forces, and are more sensitive to higher terms in the multipole series than are the other properties. The structure factors for oxygen and nitrogen are found to be little affected by the anisotropic forces.     

E.S.R. evidence for the planarity of the t-butyl radical

Monte Carlo calculations are reported for the radial distribution function g ₂(r; λ) of a fluid in which the intermolecular pair potential is [u ^ref(r) + λu ^p(r)], u ^ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ^ref(r) + u ^p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ³ = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g ₂(r; λ = 1) about g ₂(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y ₂(r; λ) = exp [βu(r; λ)] × g ₂(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (?g ₂/?λ)_λ=0, are presented. It is shown that these terms are individually large, but that (?g ₂/?λ)_λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (?g ₂/?λ)_λ=0 is highly sensitive to the approximation used to evaluate the individual terms.     

Perturbation theory for the radial distribution function

Perturbation theory is used to consider expansions for the radial distribution function, g ₂(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g ₂(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g ₂(r) is accurate at densities below about ρσ ³=0·5.     

Binary hard-sphere solute-solvent radial distribution function in the colloidal limit: exact calculation from an equation of state

An exact formula is derived relating the contact value of the solute-solvent radial distribution function for an additive binary hard-sphere (HS) mixture at infinite dilution, g ^∞ ₁₂(d ₁₂), to the mixture equation of state (EOS) (1 denotes the solvent and 2 denotes the solute). This result can also be considered to be a consistency condition involving approximations for g ^∞ ₁₂(d ₁₂) and for the mixture EOS. Employing three approximate HS mixture equations of state from the literature, we use our formula to derive corresponding analytical approximations for g ^∞ ₁₂(d ₁₂) In addition, new computer simulations were performed to obtain accurate results for g ^∞ ₁₂(d ₁₂) and for g ^∞ ₁₂(r ₁₂) at the solute-solvent diameter ratios {1, 3, 5, 7, 10, 20} and the reduced solvent density ρ? = 0.8. We compare our results for g ^∞ ₁₂(d ₁₂) with the simulation results and with the results of approximate analytical expressions for g ^∞ ₁₂(d ₁₂) proposed by several workers. The results obtained from our formula in conjunction with two of the EOS expressions considered are more accurate than all previously proposed approximations, with the exception of the approximation of Matyushov and Ladanyi [1997, J. chem. Phys., 107, 5815], which is of comparable accuracy.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

Studies of molecular motions and interactions in acetonitrile

Microwave and far-infrared absorption coefficients are reported for acetonitrile over the whole concentration range in carbon tetrachloride solution. The data have been used to compute dipole reorientational correlation functions and relaxation times as a function of concentration. These show that τ_1R ^T increases non-linearly as the acetonitrile concentration increases (in contrast to the values of τ_2R ^T obtained from light scattering measurements) and as the viscosity decreases. This behaviour is examined in terms of intermolecular correlations between rotating dipoles. Intensity data are used to provide a check on the importance of induced dipole absorption in the far-infrared spectra and to calculate ‘static’ correlation factors g ⁽¹⁾. Both g ⁽¹⁾ and the dynamic correlation factor f ⁽¹⁾ reflect the effects of strong molecular interactions in these solutions.     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

Molecular dynamics of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

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 ε, 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 <P _1,2(Î . Î(t))>, 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 literature. The parametrization in terms of memory functions will be reported in a subsequent paper.     

Calculating coefficients for a system of moment equations used to describe the magnetization kinetics of a superparamagnetic particle in a fluctuating field

A system of equations is derived for moments [averages of spherical harmonics 〈Y _l,m 〉(t)] that determine the dynamics of the magnetization M of a superparamagnetic particle in a fluctuating field. The system is derived by representing the Gilbert equation in a fluctuating field, and the corresponding Fokker-Planck equation for the distribution function of M, in terms of angular momentum operators, which in turn makes it possible to express the coefficients of the system of moment equations in terms of Clebsch-Gordan coefficients. Fiz. Tverd. Tela (St. Petersburg) 41, 2020–2027 (November 1999)     

Influence of reagent vibration on the stereodynamics of the Li + HF → LiF + H reaction

We investigate the influence of reagent vibration on the stereodynamics of the title reaction by the quasi-classical trajectory on the Aguado-Paniagua2-potential energy surface developed by Aguado et al. (J. Chem. Phys. 1997 106 1013). The cross sections and reaction probability as functions of the reagent vibration are calculated in the centre-of-mass frame. The product angular distributions of p(θ_r), p(φ_r), and p(θ_r, φ_r), which reflect the vector correlation, are also presented and discussed. The results indicate that the vector properties are sensitively affected by the vibrational excitation.     

Nd1.85Ce0.15CuO4－δ单晶c-轴方向电阻的低场行为

采用自助熔剂缓冷法成功地生长出了Nd_1.85Ce_{0. 15}CuO_4-δ单晶，其零场下零电阻温度约为21K. 在0—0.5T范围内分别测量了磁场平行和垂直样品表面的电阻转变曲线以及0.5T不同角度下的电阻转变曲线. 结果显示磁场平行和垂直样品表面时的转变温度T_p随磁场的变化均服从H=H₀(1-T_p(h)/T_p(0))²关系. 0.5T 关键词： 1.85Ce_0.15CuO_4-δ单晶')" href="#">Nd_1.85Ce_0.15CuO_4-δ单晶 输运性质     

Construction of the faithful irreducible representation for the subgroupG contained inS 7

Every element in the transitive subgroupG of order 42 contained in the symmetric group of degree 7 is expressed as an ordered product of powers of the basic permutationsg ₂ (1234567) andg ₈ (1) (243756). The only faithful irreducible representation forG is then given explicitly in terms of the six-dimensional matricesD(g ₂ ) andD(g ₈ ), obtained here with the aid of a simple computational algorithm.