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§ 1. The object of this communication is to partially realise the hope expressed at the end of my paper of July 1 and July 15, 1889, on the “Molecular Constitution of Matter”:—“The mathematical investigation must be deferred for a future communication, when I hope to give it with some further developments.” The italics are of present date.Following the ideas and principles suggested in §§ 14–20 of that paper (referred to henceforth for brevity as M. C. M.), let us first find the work required to separate all the atoms of a homogeneous assemblage of a great number n of molecules to infinite distances from one another. Each molecule may be a single atom, or it may be a group of i atoms (similar to one another or dissimilar, as the case may be) which makes the whole assemblage a group of i assemblages, each of n single atoms.

An exact expression for the solvent diffusion coefficient in a pore that is so narrow that two molecules cannot get around each other is derived. The theory states that the diffusion coefficient for a pore that contains n molecules is simply equal to the diffusion coefficient a molecule would have if it were all alone in the pore ( D °) divided by n . The theory is very general. Two different models that can be used to determine D ° are described. An exact experimental test of the theory is carried out by the use of computer simulation (molecular dynamics). It is shown that as long as the density of molecules in the pore is not too high, the experimental results are not significantly different from the theoretical preditions. These experimental results also test the theory presented in the first paper of this series and provide strong support for those results.

The application of computer technology in carbon-13 magnetic resonance spectroscopy has resulted in much improved signal detection through Fourier transform and time averaging techniques. These advances have compensated for the less favourable gyromagnetic ratio and relatively low (1.1 per cent) natural abundance of the carbon-13 isotope, and carbon-13 magnetic resonance methodology may now be employed in a variety of chemical studies. Two very different applications are reviewed in this paper to illustrate the diversity of the method.

The pressure-induced infrared fundamental band of hydrogen in H2–rare gas mixtures was recorded over a wide range of temperatures (77–300 K) and densities (5–1200 amagat) using pressures up to 2000 atm. By assuming appropriate line shapes for overlap- and quadrupole-induced transitions the band profiles could be computer analyzed in terms of essentially three parameters, δd, δc, and δq. The value of δd, the half-width of overlap-induced transitions, was found to be density independent, thus indicating the very short range of this induction process. The half-width, δc, of the intercollisional interference dip for overlap-induced transitions increases with the density, ρ, according to the equation, [Formula: see text]. The collision cross section for overlap induction, calculated from the linear coefficient a, is ~10% greater than the Lennard–Jones σ12. The relation of δc to the diffusion coefficient D12 of H2 molecules in the rare gas is discussed. Data on the half-width δq of quadrupole-induced transitions will be analyzed in paper II of this series.

In a previous paper we have derived a number of simple approximations for the thermodynamic and structural properties of liquids. Here we test these approximations by applying them to models for ionic solutions and atomic liquids and comparing the results with those obtained from Monte Carlo and molecular dynamics simulations. In particular, the pair‐correlation functions for 1–1 primitive model aqueous ionic solutions are calculated using the EXP approximation. The internal energy for 2–2 salts is obtained from the ORPA+B2 approximation. The pair‐correlation function for the Lennard‐Jones fluid is calculated with the EXP approximation. In all cases the results obtained agree closely with those obtained from computer experiments. Thus, the ORPA+B2 approximation for the free energy and the EXP approximation for the pair correlation function provide a theory that is both very accurate and applicable to a wide variety of classical fluids.

Numerical calculations of the dynamic scattering function $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$, the intermediate scattering function, and the van Hove distribution function $\mathrm{G}(\stackrel{\ensuremath{\rightarrow}}{\mathcal{r}}, t)$, based on an approximate expression for $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$ proposed in an earlier paper, are presented. The liquid structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ and first two even moments of $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$, which are needed as input, are obtained by means of the Percus-Yevick equation with a Lennard-Jones potential, making the calculation entirely self-contained. The calculation is applied to the liquid-argon case studied through molecular dynamics by Rahman; comparisons with these results and those of experiment show good qualitative agreement. A brief description of the numerical procedure is included.

We have improved the free‐volume model for molecular transport in dense fluids, as developed in earlier papers, by taking account of the variable magnitude of the diffusive displacement. The development is carried through in a way which may display more clearly the relation between the free‐volume model and the Enskog theory. Implicit in the free‐volume development is the association, on the average, of a correlation factor f(a) with each magnitude, a, of the displacement. It is assumed that f(a) is a step function which is zero, because of the predominance of back scattering, for a a.* This corresponds to dividing the displacements sharply into two categories, one “gaslike” and the other “solidlike.” Molecular dynamics computations have shown that the self‐diffusion coefficient in the hard‐sphere fluid at the highest densities is falling precipitously, with increasing density, away from the Enskog values. It appears that this density trend, which was attributed to back scattering, ...

Magnetic resonances have proved to be a convenient tool to study the problem of local molecular dynamics in liquid crystals, In this paper three different approaches will be presented.

In the present paper some preliminary results obtained in the study of molecular dynamics of ethylene adsorbed ōn activated charcoal. by slow neutron scattering, are presented.