Theoretical and analytical radial distribution function for dense fluids

The ‘identical particles in quasi-mean potential energy field’ assumption was used to derive the approximate theoretical and analytical radial distribution function (RDF) for dense fluids through solving the two-body Schrödinger equation and using the first-order perturbation method. The theoretical and analytical expressions of RDF can save much computation time in calculating the thermodynamics properties of fluids and may make the statistical mechanics theories comparable with the equation of state method that is currently widely used in physics, chemistry and technology. The calculated properties for argon by this RDF fit well with the experimental data of reference over a very wide range of conditions, including dense fluids (liquid phase and dense gas), critical point, and dilute gas, in which the pair potential and the Axilrod-Teller three body interaction were considered. The extensive practical application of this model for science and technology needs further investigation.     

A SAFT model for associating Lennard-Jones chain mixtures

The recently proposed equation of state of statistical associated fluid theory (SAFT) is extended to associating Lennard-Jones (LJ) chain mixtures. In this extension, a new radial distribution function (RDF) for LJ mixtures is derived around the LJ potential size (σ _ij ). The RDF expression is completely analytical and real. Comparisons with computer simulation data under various conditions indicate that the RDF is very accurate up to its first peak. The new RDF, together with a previously established equation of state for LJ mixtures, is employed to study LJ chain mixtures by combining with Wertheim's first-order perturbation theory. The resulting equation of state is tested satisfactorily against computer simulation data for both non-associating and associating LJ chain mixtures, with a performance similar to its predecessors for pure LJ chains and LJ mixtures. The SAFT model is uniquely featured by being totally mixing-rule free and by being adjustable at both chain bonding and association sites. Moreover, the SAFT model is formulated very generally, so that it is applicable to both homonuclear and heteronuclear chain mixtures.     

A comparative study of non-polar solvents effect on dielectric relaxation and dipole moment of binary mixtures of mono alkyl ethers of ethylene glycol and of diethylene glycol with ethyl alcohol

Dielectric relaxation and dipole moment of binary mixtures of homologous series of mono alkyl ethers of ethylene glycol and of diethylene glycol, i.e., mono methyl, mono ethyl and mono butyl ethers of ethylene glycol (ROCH₂CH₂OH) and mono methyl, mono ethyl and mono butyl ethers of diethylene glycol (ROCH₂CH₂OCH₂CH₂OH) with ethyl alcohol (C₂H₅OH) of different concentrations were studied in dilute solutions of benzene, dioxane and carbon tetrachloride at 35 °C. Permittivity (ε′) and loss (ε″) at 10.1 GHz, static dielectric constant ε_o at 1 MHz and high frequency limiting dielectric constant ε_∞ = n_D² at optical frequency of these molecules and their binary mixtures at different concentration were measured in dilute solutions of non-polar solvents. The average relaxation time τ_o, relaxation times corresponding to overall molecular reorientation τ₁ and group rotations τ₂ were determined using Higasi's single frequency measurement equations for dilute solutions. The evaluated values of relaxation times and free energy of activation ΔF were used to explore the solvent effect on molecular dynamics of these polar binary systems in non-polar solvents. The excess inverse relaxation time and excess free energy of activation were determined to confirm the existence of hydrogen-bonded heterogeneous cooperative domains of the ethers and alcohol molecules at different concentration their binary mixtures in non-polar solvents. The dipole moment of the binary mixtures was evaluated using Higasi's and Guggenheim's equation for dilute solutions. The evaluated values of dipole moments and computed dipole moment values using a simple mixing equation of the polar molecules binary mixture were used to explore the effect of non-polar solvent environment on heterogeneous molecular interactions between ethers and alcohol molecules. The effect of number of carbon atoms in the molecular structure of these homologous series molecules was also considered for the interpretation of various evaluated dielectric parameters.     

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

The rotation-vibration Hamiltonian for an equilateral triangular X₃ molecule is derived in terms of the three curvilinear stretching coordinates Δr_i, and expanded in the form of a power series in the variables y_i = 1 ? exp(-aΔr_i), where a is a molecular parameter obtained from the potential function. The reason for the use of the variable y_i is twofold: Stretching potentials exhibit a much stronger convergence in the y_i than in the Δr_i, and a Hamiltonian expressed in the y_i can be diagonalized in a straightforward fashion using a Morse-oscillator basis set as we do here. Using a published ab initio potential surface we have expanded it as a polynomial in the y_i, and have calculated variationally the rotation-vibration energies of H₃⁺ and D₃⁺ using a symmetry-adapted Morse-oscillator-rigid symmetric top basis set. The results indicate that an expansion of the potential function to quartic terms in the y_i might be adequate, and that satisfactorily converged energies can be obtained with a relatively small basis set. The molecule H₃⁺ is the simplest polyatomic molecule. Inspection of the Appendix of this paper shows that the rotation-vibration Hamiltonian used here is one of the more complicated ones.     

Solid L-α-alanine: Spectroscopic properties and theoretical calculations

A spectroscopic study of L-α-alanine in different environments is presented, with special emphasis on the neutral to zwitterion transformation of this amino acid. Spectra of room temperature solids as deposited from the vapour and in KBr pellets are compared and discussed revealing some discrepancies. An assignment is proposed based on theoretical calculations of the solid structure. Vapour deposits at 25 K are prepared both of pure alanine and of mixtures with polar (H₂O) and non-polar (CO₂, CH₄) components. The spectra of the solids contain IR bands which can be individually assigned to the neutral and to the zwitterion, and whose relative intensity variation can be used to follow the neutral to zwitterion transformation. The assignment of the spectrum of the neutral species is proposed, again with help from theoretical calculations of the single neutral molecule. The neutral/zwitterion ratio in deposits at 25 K varies between ～60% for pure alanine and H₂O mixtures and ～90% for non-polar matrices. This ratio drops when the solid is heated until the ionic species only remains at 200 K. The conversion process depends on the environment surrounding the alanine molecules.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary and ternary isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study for the first time systematically the dependence of the self-diffusion coefficients D_i (i = 1, 2, 3) in binary and ternary atomic isotopic mixtures on the particle mass ratios m*₂ = m ₂/m ₁ and m*₃ = m ₃/m ₁ at different reduced temperatures T* and reduced particle number densities n*, using a Lennard-Jones 12-6 potential and a hard-soft-spheres potential. In addition, the dependence of D_i values of binary mixtures on the mole fraction x ₁ = 1—x ₂ was also investigated for some thermodynamic states. The calculated values of D_i can be represented quantitatively by exponential estimates of the form D_i = D* _i (m*₂)^ex _i in the case of binary mixtures and D_i = D ⁰ _i (m*₂)^{ex _i} (m ₃)^{ext _i} in the case of ternary mixtures. D ⁰ _i are the self-diffusion coefficients in reference mixtures of mass ratios m*₂ = m*₃ = 1. The dependence of the exponents ex _i (m*₂, T*, n*, x ₁) of binary mixtures on m*₂, T*, n*, and x ₁ and the dependence of the exponents ext _i (m*₂, m*₃, n*) of equimolar ternary mixtures at T* = 1.8 on the exponents ex _i of the constituent binary mixtures and on m*₂, m*₃, and n* are discussed.     

A phenomenological theory of possible sequences of ferrotoroidal phase transitions in boracites

A phenomenological theory of the sequence of two second-order phase transitions with close temperatures is considered; such transitions occur in the Ni-Br boracite. The thermodynamic potential is written as a function of polarization P _i, magnetization M _i, and toroidal moment T _i vectors and fields E _i and H _i; T _i is treated as an order parameter. It is assumed that only one coefficient of T _i ² passes through zero as T decreases. The possibility of a sequence of two proper ferrotoroidal phase transitions along the T ₁ and T ₂ components is demonstrated. Spontaneous T _i, P _i, and M _i vector values and equations for susceptibility tensors (dielectric χ _ij = dP _i/dE _j, magnetic k _ij = dM _i/dH _j, and magnetoelectric α_ij = dP _i/dH _j = dM _j/dE _i) were obtained for three phases. Some of these values have well-defined anomalies in the vicinity of transitions. All possible sequences of ferrotoroidal phase transitions in boracites are considered. Depending on two potential coefficient values, these sequences may consist of one, two, or three such transitions.     

Loss calculations in weakly-guiding optical dielectric waveguides

The application of perturbation theory to a three-layer weakly-guiding slab waveguide composed of lossy dielectric media yields a simple formula for the attenuation coefficient α of a guided mode: α = (Σ³_i=₁a_iP_i)/ (Σ³_i= ₁P_i, where α_i, P_i are respectively the loss coefficient and model power in region i (i = 1, 2, 3). It is shown that this result can also be obtained from arguments based purely on geometric optics. The result is easily extended to apply to circularly-symmetric optical fibres where it yields confirmation of an earlier approximation for the power ratios P_i/(Σ²_i= ₁P_i).     

Ionic contribution to Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions

A theoretical treatment is performed of the mechanism (suggested in N. F. Bunkin andA. V. Lobeev, Z. Phys. Chem. 214, 269 (2000)) of ionic effect on the Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions. The mechanism consists essentially in that the fluctuation electric field caused by Brownian motion of ions dissolved in a liquid leads, because of the Kerr polarization effect, to fluctuations of optical anisotropy of the scattering medium. The spectral characteristics of the Rayleigh line wing are obtained using the fluctuation-dissipative theorem as applied to equilibrium thermal electromagnetic field. Expressions are derived for the integral intensity and spectral width (Δν) of the Rayleigh line wing in terms of parameters of liquid solution such as the temperature T, the viscosity η, the concentration of dissolved ions n _i, and the coefficient of their diffusion D _i. It is demonstrated that Δν ∝ exp(?W/2T), where W is the activation energy of ion mobility b _i = D_i/T. The possible region of validity of developed theoretical concepts as applied to the experimental data for the Rayleigh line wing in electrolytic solutions is discussed.     

Analysis of the relationship between the electron-capture and electron-loss cross sections for carbon ions

The electron-loss cross sections σ _{i, i + 1} and the electron-capture cross sections σ _{i, i ? 1} for carbon ions with energies of 35–330 keV/nucleon in hydrogen and neon are determined from experimental data. It is demonstrated that, for particle energies which satisfy the condition σ _{i, i + 1} = σ _{i, i ? 1} or σ _{i, i ? 1} = σ _{i ? 1, i} , the average equilibrium ion charge can be evaluated without solving the system of differential equations for charge exchange. The dependence of the average equilibrium ion charge on the ion energy is investigated for carbon ions.     

Study of cross sections for the loss of outer 1s, 2s, and 2p electrons by fast ions and atoms of light elements

In the case of light-element ions propagating with velocities V = 1.83 and 3.65 au in H₂, He, N₂, Ne, and Ar, the loss cross sections σ_{i, i+m} for m electrons (m = 1, 2, 3) are considered. The partial loss cross sections σ_i(nl) for one of the outer 1s, 2s, or 2p electrons are determined using the obtained data. It is shown that the experimental cross sections for the loss of the 1s and 2s electrons by positive ions qualitatively agree with the theoretical values calculated in the Born approximation. In the case of the ion velocity V = 1.83 au, the cross sections σ_i for 2p electrons are greater than the cross sections σ_i (1s) and σ_i (2s) by a factor of 1.2–3 for the same binding energies of electrons in the ion (I _nl > 20 eV). It is found experimentally that, at V = 1.83 au, the cross sections σ_i (2p) for I _nl ～ 10–20 eV are less than the cross sections σ_i (1s) by a factor of 2–3, which is probably caused by a decrease in the screening parameter (θ_2p < 1) of the outer shell of atoms.     

Fast approximate technique for the cumulative wavenumber model to modeling radiative transfer in a mixture of real gas media

In the cumulative wavenumber (CW) model, the total range of the absorption cross-section Cη is subdivided into the supplementary absorption cross-section of gray gases C_j, j=1,…,n, where n is the number of gray gases; and the wavenumber region is subdivided into intervals Δ_i=[η_i−1, η_i], i=1, 2,…,p, where p is the number of intervals. The intersection of the two spectral subdivisions is used to define the modeling of the fractional gray gas D_ij. In the CW model, we solve the radiative transfer equation (RTE) in every subinterval D_ij; then it is necessary to solve n x p times the spectral form of the RTE for complete spectral integration. In this work, the CW model is used with a numerical approximation technique based on additive properties of radiative intensity to reduce the solution of RTE to n new fractional gray gas D_j for complete spectral integration. The CW model was first coupled with the discrete ordinates method and the accuracy of the simplified technique and the algorithm was first examined for one-dimensional homogeneous media; results are compared with line-by-line calculations and it is found that the CW model with the simplified technique is exact for the homogeneous media examined. Also, the fast approach is tested in the diffuse reflecting boundaries case. The CW model is implemented in a bi-dimensional enclosure containing real gases in isothermal cases. Afterwards, this approximate technique is extended to non-isothermal and non-homogeneous cases; the results are compared with line-by-line calculations taken from literature and good agreement was found. The results obtained using the acceleration technique for the CW model agree with the results of original CW model. With this acceleration technique the CPU time decreases p times. Spectral database HITRAN and HITEMP are used to obtain the molecular absorption spectrum of the gases.     

Gas-surface scattering from W(100): Kinetic energy dependence of the effective corrugation

Angular and velocity distributions have been obtained for the scattering of argon and N₂ from a W(100) surface for incidence energies, E_i, in the range 0.03–5.5 eV, and surface temperatures, T_s, from 90 to 1700 K. For E_i < 0.1 eV, we find broad angular distributions (> 60° FWHM) which are relatively insensitive to T_s and velocity distributions which are inconsistent with parallel momentum conservation, indicating a relatively corrugated interaction potential. Increasing E_i first causes a rapid narrowing in these distributions, but as E_i exceeds ~ 2 eV, they broaden again, as the effective corrugation again becomes large.     

A skew ray tracing approach for the error analysis of optical elements with paraboloidal boundary surfaces

Using the error analysis methodology developed by the current author in previous studies for optical systems comprising elements with flat boundary surfaces, this study examines the errors induced in a light ray's path as it is reflected or refracted at a paraboloidal boundary surface. In analyzing the light path, two principal sources of error are considered, namely (1) translational errors (Δx_i, Δy_i and Δz_i) and rotational errors (ΔΓ_i, ΔΨ_i and ΔΦ_i), which collectively determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed approach is verified using a generic parabaloidal boundary surface for illustration purposes. Overall, the results show that the proposed error analysis methodology provides a straightforward means of analyzing the performance of optical systems characterized by paraboloidal boundary surfaces such as headlight reflectors, optical telescope mirrors, flashlights and so forth.     

Ab initio potential energy curves and vibrational levels for the c, l, and i states of the hydrogen molecule

Potential energy curves for the hydrogen molecule in the c³Π_u, I¹Π_g, and i³Π_g state have been calculated in the Born-Oppenheimer approximation. Highly flexible wavefunctions have been used, and for each state the calculations have been carried out for 40 different internuclear distances in the region 1 ≤ R ≤ 12 a.u. For the Π_g states the wavefunctions are known to change their character around R = 5 a.u. The effect of this change on various components of the energy has been analyzed. The vibrational Schrödinger equation for all states has been solved for H₂, HD, and D₂. For H₂ the resulting energies are compared with the experimental values and it is shown that the adiabatic effects are likely to be responsible for the existing discrepancy between the theoretical and experimental values.     

Dunham potential energy coefficients of the hydrogen halides and carbon monoxide

The Dunham potential energy coefficients a_i, 0 ≤ i ≤ 6 (except 4 for HI) have been derived from spectroscopic data of hydrogen halides HF, HCl, HBr, and HI, and carbon monoxide in their ground electronic states. A full error analysis has produced standard deviations of both these a_i and further energy coefficients Y_lj. Comparison with experimental data shows good agreement; trends in the hydrogen halide series are discussed.     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces

This study applies skew ray tracing based on a 4×4 homogeneous coordinate transformation matrix and Snell's law to develop a detailed methodology for analyzing the errors of a ray's light path as it passes through optical elements with flat boundary surfaces. The error analysis methodology considers two fundamental sources of light path error, namely (1) the translational errors (ΔX_i, ΔY_i and ΔZ_i) and rotational errors (ΔΓ_i, ΔΨ_i and ΔΦ_i) which determine the deviation of the light path at each boundary surface in terms of the coordinate frame attached to that surface, and (2) the differential changes induced in the incident point and unit directional vector of the refracted/reflected ray by differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified using a solid glass corner-cube.     

First-principles cluster study of electronic structures, locations and hyperfine interactions of isolated atoms and ions in silicon

The electronic structures of the dilute transition metal (TM) impurities, V^2?+?, Cr^?+?, Mn^2?+?, and Mn⁰ in silicon have been studied using the Hartree–Fock (HF) procedure combined with many-body perturbation theory (MBPT). The systems studied involved the TM impurities at the hexagonal interstitial (H _i ), tetrahedral interstitial (T _i ) and substitutional (S) locations. Investigations of the binding energy and local potential energy surface of the TM impurity-Si systems indicate that the TM impurities are binding at the T _i location. Hyperfine interaction constants (A) of the TM impurities at the T _i and S sites are presented and compared with available experimental results (Woodbury and Ludwig, J Phys Rev 117:102, 1960a, Phys Rev Lett 5:98, b) from Electron Paramagnetic Resonance (EPR) measurements.