Intramolecular Distribution Functions Research Articles

A Born–Green–Yvon equation for flexible chain-molecule fluids. I. General formalism and numerical results for short hard-sphere chains

The Born–Green–Yvon approach is used to construct an integral equation for the site–site distribution functions describing the microscopic equilibrium structure of a fluid of flexible chain molecules. The multisite distribution functions appearing in this formally exact equation are related to the site–site functions via a set of site–site superposition approximations. Intramolecular distribution functions are approximated using exact results for an isolated chain molecule. Numerical results are presented for fluids of tangent hard-sphere 3-mers and 4-mers. These results, which include the site–site distribution functions over a range of densities, second virial coefficients, and the virial pressure equations of state, compare well with Monte Carlo data. In particular, the contact value of the average site–site distribution function is given quite accurately.

Structural Study of Liquid Ethylbromide Using Differential Anomalous X‐ray Scattering

AbstractSynchrotron radiation was used for a differential anomalous X‐ray scattering (DAS) study of liquid ethylbromide (C2H5Br). Two diffraction experiments were carried out at photon energies of 12500 and 13464 eV. The dispersion corrections were determined from photoabsorption coefficients obtained from an absorption experiment. After an elaborate and involved data evaluation and correction procedure a differential structure factor was obtained. The peak assignation in the differential atom pair correlation function (DAPCF) was verified by comparison with a theoretical intramolecular distribution function calculated from well known data of the intramolecular geometry of ethylbromide. In addition, a peak at 4.1 Å is found in the DAPCF, which may be assigned to an intermolecular Br—Br atom pair suggesting a strong dispersion interaction.

Numerical solution of RISM for homonuclear vibrating hard-dumbells

Numerical solutions of the reference interaction site model (RISM) for site-site radial distribution functions gαβ(r) of a fluid of vibrating harddumbells are carried out, using a method of direct substitution in Fourier space. Comparisons with molecular dynamics (MD) results for the same system are given. The intramolecular distribution functions obtained by MD are used in RISM to obtain the corresponding intermolecular site-site gαβ(r), which in turn are compared against the MD results. These numerical results and further algebraic analysis indicate that the intermolecular site-site correlation functions calculated with RISM, do not depend noticeably on the form of the intramolecular correlation function used in the calculation. Additional evidence on the equivalence of vibrating and rigid hard dumbells is given.

A novel theoretical approach to the conformational equilibrium of short-chain molecules in condensed phases

A novel theoretical approach to the equilibrium conformational structures of small non-polar chain molecules in dense liquid systems is presented. In contrast to the Pratt—Chandler theory it is essentially based on macroscopic thermodynamics. Explicit use is made of the formal equivalence of an ensemble of flexible molecules and a mixture of rigid conformers with variable composition. Employing the ideas of thermodynamic perturbation theory, the intramolecular distribution function of non-rigid particles is related to the hard core part of the residual chemical potentials of the conformers, which is readily evaluated from an accurate analytical equation of state for mixtures of hard molecules. The results thus obtained for the conformational equilibria of butane in the pure liquid state and in dilute solution in CC 4 are in good agreement with recent computer simulation studies.

A New Estimate of the H+ Ion Concentration in Pure Water. Part 1: A Critical Analysis of Current Treatments

AbstractIt is shown that attempts to determine the H+ concentration in pure water involve a search for a species which is not analytically well‐defined; thus appears the problem of what is the nature of the physical statements now available from pertinent measurements? Furthermore, it is demonstrated that both the conductance and the EMF determination of Kw erroneously involve an extrapolation from an aqueous solution to the pure solvent, water. Kw is not a strictly measurable quantity. Configurational definitions of the H+ and OH− ions are given which, using an intramolecular proton distribution function, essentially converts a statement concerning the distortion of a water molecule to species concentrations. The temperature dependence of the conventional Kw is also incorporated in the characterization of non‐analytical H+ and OH− ions.

A molecular dynamics and Monte Carlo study of solvent effects on the conformational equilibrium of n-butane in CCl4a),b)

We report on a computer simulation study of the gauche–trans conformational equilibrium of n-butane in liquid carbon tetrachloride solvent. The study is made possible by implementing an exact statistical mechanical theorem which relates the full intramolecular distribution function for a butane molecule to that of a hypothetical species which does not possess a large potential barrier separating the trans and gauche states. In addition to determining the trans–gauche equilibrium constant, the potential of mean torsion, that is, the reversible work required to alter the conformation is determined as a function of the dihedral angle. Recent theoretical work is compared with these computer experiments, and while qualitative agreement is found, the approximate theory overestimates the solvent effect. Finally, the change in solvent structure in response to a conformational change in the solute is determined.

Interaction site cluster series for the Helmholtz free energy and variational principle for chemical equilibria and intramolecular structures

The interaction site cluster series is derived for the Helmholtz free energy of a molecular mixture in which molecules can interconvert by chemical reactions. This series expresses the free energy as a functional of the single-molecule (intramolecular) distribution functions. Variations of this functional are studied. It is shown that when the total numbers of atoms in the mixture are fixed, the free energy functional is a minimum with respect to variations of the intramolecular distribution functions. Further, this variational principle is shown to be equivalent to the cluster series formulas derived earlier [J. Chem. Phys. 65, 2925 (1976)] for chemical equilibrium constants and intramolecular distribution functions of nonrigid molecules in condensed phases.