A validity test of the WCA perturbation theory for two-dimensional Lennard-Jones fluids

The potential energy and pressure are obtained from molecular dynamics simulations of two-dimensional Lennard-Jones fluids over a wide range of densities and temperatures, thus testing the validity of first-order (high temperature approximation) and second-order Weeks-Chandler-Andersen theory. The pressure results, which are very important for a subsequent analysis of adsorption theories, are very much affected by that approximation, especially at low densities and, surprisingly, at very high densities. For the potential energy the effect is smaller, and the approximation gives good results at intermediate and high densities even at low temperatures. The conclusion is that the second-order term of the Weeks-Chandler-Andersen theory is needed for theoretical calculations of the pressure, except at very high temperatures and intermediate densities. Nevertheless, the first-order term gives good results for the potential energy except at low densities. All these findings are necessary for a complete analysis of the validity of the Weeks-Chandler-Andersen theory and its consequences in the study of the adsorption of rare gases onto flat surfaces.     

To What Extent are “Atoms in Molecules” Structures of Hydrocarbons Reproducible from the Promolecule Electron Densities?

The “atoms in molecules” structures of 225 unsubstituted hydrocarbons are derived from both the optimized and the promolecule electron densities. A comparative analysis demonstrates that the molecular graphs derived from these two types of electron densities at the same geometry are equivalent for almost 90 % of the hydrocarbons containing the same number and types of critical points. For the remaining 10 % of molecules, it is demonstrated that by inducing small perturbations, through the variation of the used basis set or slight changes in the used geometry, the emerging molecular graphs from both densities are also equivalent. Interestingly, the (3, ?1) critical point between two “non‐bonded” hydrogen atoms, which triggered “H?H bonding” controversy is also observed in the promolecule densities of certain hydrocarbons. Evidently, the topology of the electron density is not dictated by chemical bonds or strong interactions and deformations induced by the interactions of atoms in molecules have a quite marginal role, virtually null, in shaping the general traits of the topology of molecular electron densities of the studied hydrocarbons, whereas the key factor is the underlying atomic densities.     

Mixing rules for binary Lennard–Jones chains: theory and Monte Carlo simulation

Theoretically-based van der Waals one-fluid (vdW1) mixing rules are derived for Lennard–Jones (LJ) chain mixtures. The rules provide equivalent one-fluid segment parameters for LJ size (σ) and energy () parameter as well as chain length (m) based on the parameters of the individual mixture components and the component mole fractions. The mixing rules are tested by performing Monte Carlo simulations of eight different binary mixtures and the equivalent vdW1 pure fluid, each at three densities. The simulations test the effects of changing LJ size parameter, LJ energy parameter and chain length individually and together. The effects of mole fraction and density are also examined. The mixing rules are tested for accuracy in predicting compressibility factors and radial distribution functions. It is found that the vdW1 rules provide excellent agreement when size and energy parameter are varied. Good agreement is found for mixtures with different chain lengths. The discrepancy is worst at very high densities when all component parameters are varied simultaneously.     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

The theory of gradient elution under hydrostatic equilibrium in liquid chromatography. Part 3: Using solvents of different densities

Gradient elution under hydrostatic equilibrium is extended to the treatment of the case where the two liquids have different densities. Analytic expressions are derived only for the cases where both mixing chamber and reservoir have constant cross-sectional areas. As in the case where the densities of the liquids are equal, pressigned concentration gradients can be duplicated quite satisfactorily by combining a mixing chamber having a constant cross-sectional area and a reservoir having an area which changes linearly with reservoir height. A numerical example is given to illustrate the use of the derived equations.     

Action des derives du phosphore trivalent sur les composes α-cyano α-halo carbonyles : Orientation de la reaction entre un anion enolate et un cation halophosphonium

The factors responsible for the orientation in the reaction between an anion derived from an α-cyano α-haloketo compound with an halophosphonium cation are determined. Steric effects are important, but electronic effects are not negligible. This reaction is controlled more by frontier electron densities for cations derived from trialkyl or triarylphosphines than for cations derived from trialkylphosphites or trisdime´thylaminophosphine.     

Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Intra- and intermolecular topological properties of amino acids: a comparative study of experimental and theoretical results

The charge densities rho(r) of the six amino acids L-Asn.H(2)O, DL-Glu.H(2)O, DL-Lys.HCl, DL-Pro.H(2)O, DL-Ser, and DL-Val were determined from high-resolution X-ray diffraction experiments at 100 K using synchrotron radiation and area detection (CCD) techniques. Bond topological parameters derived from these densities and from those of six additional amino acids published earlier are compared to each other and to the results of ab initio calculations. Experimental and theoretical properties for each chemically equivalent bond are in a fair agreement, and their variances are of similar magnitude. A noticeable outlier is the positive curvature of the density at the bond critical point, for which no correlation between the experimental and theoretical values can be established. The location of nonbonded valence shell charge concentrations derived from the crystalline densities scatter in a wider range than those obtained for the isolated molecules.     

Molecular geometry and symmetry from a differential geometry viewpoint

Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron density functional graphs (the so-called DFG equivalence introduced in our previous work) are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density scale; the classes of DFG equivalence are the orbits of a group of linear operators operating in the space of electron density functions. Within the symmorphy framework, the symmetry group is derived from the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densities of molecular conformations. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 669–678, 1997     

Expansion formulae for two-center charge densities of integer and noninteger n generalized exponential type orbitals with hyperbolic cosine and their use in evaluation of multicenter multielectron integrals

The expansion formulae are derived for the two-center charge densities of integer and noninteger n generalized exponential type orbitals with hyperbolic cosine (GETOHC) in terms of corresponding charge densities of generalized exponential type orbitals (GETO) presented in our previous paper. The general formulae obtained for the GETOHC charge densities are utilized for the evaluation of multicenter multielectron integrals appearing in the Hartree–Fock–Roothaan (HFR) and explicitly correlated theories when the GETOHC are employed as basis functions.     

Nonlinear population analysis from geminal expansion of pair densities

The nonlinear population analysis of pair densities introduced by one of us (R. B.) is reformulated using the geminal expansion of pair densities. The pair density in the geminal basis is idempotent and allows one to describe the bonding patterns as singlet-and tripletlike contributions while still conserving the statistical nature of the original formalism. The new approach is applied to the analysis of pair densities derived from semiempirical MNDO calculations. The resulting values of pair populations of several simple molecules are discussed. © 1995 John Wiley & Sons, Inc.     

A synopsis of empirical gel fraction analytical methods: Application of the Wanxi equation to polyethylenes irradiated in vacuo and in the presence of acetylene

Gel fraction data from linear low-density polyethylene (LLDPE) films and high-modulus polyethylene (HMPE) fibers, which had previously failed to give reasonable results when treated with Charlesby-Pinner and Saito-Kang-Dole theory, have been fitted to a modified form of the Wanxi equation. The fitting yields parameters that compare very well with literature values derived by the Wanxi equation, confirming that fracture and cross-linking densities are proportional to a power function (β) of the radiation dose. Extrapolated G(S) values have been obtained from LLDPE using the fit parameters and UV-Vis spectroscopy data. A brief synopsis of the empirical analytical methods available for gel fraction analysis is given. © 1994 John Wiley & Sons, Inc.     

Configurational probabilities for symmetric dimers on a lattice: an analytical approximation with exact limits at low and high densities

A new approach is developed for lattice density functional theory of interacting symmetric dimers at high temperatures. Equations of equilibrium for two-dimensional square and three-dimensional cubic lattices are derived for the complete set of configurations in the first three shells around the central dimer, and rules of truncation for higher shells are based on exact results from the mathematical theory of domino tilings. This provides exact limits for both low and high densities. The new model predicts contributions of particular configurations which are in agreement with Monte Carlo simulations over the whole range of densities, including agreement with pocket Monte Carlo simulations at high densities.     

29Si and 27Al MAS NMR spectra of mullites from different kaolinites

Mullites synthesized from four kaolinites with different random defect densities have been studied by 27Al and 29Si magic angle spinning nuclear magnetic resonance spectroscopy (MAS NMR) and X-ray diffraction (XRD). All these mullites show the same XRD pattern. However, 29Si and 27Al MAS NMR spectra reveal that the mullites derived from kaolinites with high defect densities, have a sillimanite-type Al/Si ordering scheme and are low in silica, whereas those mullites derived from kaolinites with low defect densities, consist of both sillimanite- and mullite-type Al/Si ordering schemes and are rich in silica.     

Densities,excess molar volume,isothermal compressibility,and isobaric expansivity of (dimethyl carbonate + n-hexane) systems at temperatures (293.15 to 313.15) K and pressures from 0.1 MPa up to 40 MPa

The densities of dimethyl carbonate, n-hexane and their mixtures were measured for 12 compositions at five different temperatures varying from (293.15 to 313.15) K and over the pressure range of (0.1 to 40) MPa. The densities of pure substances and their mixtures at atmospheric pressure were measured by a vibrating-tube densimeter. The densities at high pressures were measured by a variable-volume autoclave and precise analytical balance. The excess molar volume, isothermal compressibility, and isobaric expansivity were derived from the experimental densities.     

Advances in electric field and atomic surface derived properties from experimental electron densities

The present study is devoted to a general use of the Gauss law. This is applied to the atomic surfaces derived from the topological analysis of the electron density. The method proposed here is entirely numerical, robust and does not necessitate any specific parametrization of the atomic surfaces. We focus on two fundamental properties: the atomic charges and the electrostatic forces acting on atoms in molecules. Application is made on experimental electron densities modelized by the Hansen-Coppens model from which the electric field is derived for a heterogenic set of compounds: water molecule, NO(3) anion, bis-triazine molecule and MgO cluster. Charges and electrostatic forces are estimated by the atomic surface flux of the electric field and the Maxwell stress tensor, respectively. The charges obtained from the present method are in good agreement with those issued from the conventional volume integration. Both Feynman and Ehrenfest forces as well as the electrostatic potential at the nuclei (EPN) are here estimated from the experimental electron densities. The values found for the molecular compounds are presented and discussed in the scope of the mechanics of atomic interactions.     

Matrix elements for operators for physical quantities in one-configuration functions of radicals

Some basis vectors are constructed for singly and doubly excited configurations of molecules and radicals for the method of configuration interaction in the second-quantization representation. The matrix elements of the Hamiltonian are derived for these. A method is given for calculating bond orders, transition moments, spin densities, and electron densities on atoms in the configuration-interaction method. An analog of Brillouin's theorem is obtained for radicals.Read at the II-nd Ukranian Republic Symposium on Quantum Chemistry. (Kiev, Dec. 1968).     

Theoretical transient currents from two-component bipolar space-charge swarms in media

Using an arbitrary initial space-charge distribution consisting of two bipolar species of charge carriers of different but constant mobilities in a medium, relations for the electric fields and charge-carrier densities, are derived as functions of position and time. The highly nonlinear, one-dimensional equations, which are derived for swarms of charge carriers between parallel plane electrodes, include the effects of the space-charge fields. A general method is outlined which, in principle, can be used to generate second-order differential equations whose solutions predict the time-dependent current caused by the drifting bipolar space-charge swarm. A specific differential equation is derived for initial charge distributions in dielectric media which could be produced by a pulse of ionizing radiation of uniform intensity.