Volume 9, Issue 1, 01 January 1941
 SYMPOSIUM ON THE STRUCTURE OF MOLECULES AND AGGREGATES OF MOLECULES



Molecular Distribution
View Description Hide DescriptionVarious functions, by means of which the distribution of molecules in a system may be described, are defined, and the relations between them are derived. Equations, by means of which these functions may be calculated from a knowledge of the mutual potential energy between pairs of molecules, are also derived. The equations applicable to gaseous systems, which are derived by a development previously used in the theory of condensing systems, enable the calculation of the distribution functions by means of a power series in either the fugacity or the inverse volume. The coefficients of these power series are direct integrals involving the pair potentials between molecules. In condensed systems an alternative procedure is required. The equations then appear in the form of integral equations involving the unknown functions under the integral signs. These equations are not readily solved, due primarily to the difficulties of performing multiple coordinate integrations. By the use of functions involving the probabilities of population of virtual cells, the cell equation frequently used for the calculation of the thermodynamic properties of liquids is derived as a consequence of the method used here. The direct connection between the equations derived in the theory of condensing systems, and in the usual cell approximations, is thus established. The equations derived here, however, permit consistent use of the cell method to arrive at higher approximations. This development may possibly be of value in making numerical evaluations of the thermodynamic functions of liquids.

Theory of the Transition in KH_{2}PO_{4}
View Description Hide DescriptionPotassium dihydrogen phosphate contains phosphate groups connected by hydrogen bonds. Different possible arrangements of the hydrogens result effectively in different orientations of the (H_{2}PO_{4})^{—} dipoles. Since these have the lowest energy when pointing along the axis of the crystal, there is a tendency toward spontaneous polarization along this axis, resulting in the well‐known transition, similar to Rochelle salt, with polarization below the Curie point. The theory of this transition is worked out, using statistical methods to count the number of arrangements of hydrogens consistent with each total polarization of the crystal, and deriving the free energy. It is found that the theory predicts a phase change of the first order, with sudden transition from the polarized state at low temperature to the unpolarized state at high temperature, rather than the lambda‐point transition or phase change of the second order which is observed. However, the observed transition is confined to a very narrow temperature range compared to that predicted, for instance, by the Weiss theory, so that it seems as if it might be merely a broadened transition of the first order. It is suggested that the broadening may result from the irregular shifts of transition temperatures of individual domains in the crystal on account of stresses resulting from the large piezoelectric effect and the resulting deformation of the crystal below the transition point. The susceptibility above the Curie point comes out by the theory to be 4.33 times as great as it should according to the Weiss theory, a result which seems to be in general agreement with experiment. The entropy change in the transition is given by the theory as 0.69 unit, somewhat smaller than the observed value of about 0.8 unit. No explanation is suggested for this discrepancy.

The Sorting of Mixed Solvents by Ions
View Description Hide DescriptionThe electrostatic interaction of ions with nonelectrolytes is computed for ethanol‐water mixtures over the whole composition range by the Debye treatment which takes into consideration the heterogeneity of the solvent. A simple approximate relation is derived which may be extended to other solvents. The agreement with the experimental measurements is shown to be unsatisfactory. The possibility that the lack of agreement may be due to neglect of the discrete structure of the solvent is discussed qualitatively.

The Effect of the Rotation of Groups about Bonds on Optical Rotatory Power
View Description Hide DescriptionIt is shown that the numerical value of the optical activity of an optically active compound is markedly reduced if the groups surrounding the asymmetric atoms in the compound possess a threefold axial symmetry about the bonds connecting them with the asymmetric atoms. This threefold symmetry may be either inherent in the groups themselves, or it may be acquired by them through the free rotation of the groups about these bonds or by their orienting themselves to equal extents in each of the three possible equilibrium positions about each bond. The order of magnitude of the numerical value of the optical activity is thus a measure of the freedom of orientation about single bonds of the groups in an asymmetric molecule. That this effect is actually a dominant factor in determining the order of magnitude of the optical activity is proved by the contrast in the optical activities of cyclic and open chain compounds. It is shown to have an important effect on the temperature coefficient of optical activity and to lie at the root of the observed differences in the orders of magnitude of the rotatory powers of liquids and crystalline solids. The structures of certain sulphur compounds, polypeptides, and proteins are discussed in the light of the magnitudes of their optical activities.


The Influence of Intramolecular Atomic Motion on Electron Diffraction Diagrams
View Description Hide DescriptionA discussion of the influence of atomic vibrations and of free or hindered rotations of molecular groups in molecules on their scatteringproperties. The radial distribution curve is calculated and the results which may be expected from an analysis of this curve are indicated.

Potential Energy Functions for Diatomic Molecules
View Description Hide DescriptionThe usual Morse functions are determined from the energy of dissociation, the equilibrium separation of the nuclei, and the fundamental vibration frequency. Two additional spectroscopic constants, ω_{ e } x _{ e } and α_{ e }, are available for most of the common diatomic molecules and permit us to add a two‐parameter correction term to the Morse curve. Both the potential and the extended Morse curve of the Coolidge, James and Vernon type, agree with accurate potentials in those cases where they are known. Here x = 2β(r—r _{ e })/r _{ e }. The constants for the first of these potentials are easy to evaluate and are given for 25 common diatomic molecules. With only a few exceptions, the improved potentials lie above the Morse curves and the corrections for moderately large internuclear separations may amount to ten percent of the energy of dissociation. Our treatment is based on the work of Dunham and the analysis of Coolidge, James and Vernon.

Force Constants in Some Organic Molecules
View Description Hide DescriptionConsistent normal coordinate treatments, involving force‐constants which are related to bond structures and which may be transferred from one molecule to another, are applied to hydrogen cyanide, methyl cyanide, and the methyl halides. The connection with previous treatments of acetylene, ethane, and methyl and dimethyl acetylene is discussed. A method of setting up such a consistent treatment is described, and a table of force constants for a number of bond structures is given. The structural significance of these force constants is briefly discussed.

Some Mathematical Methods for the Study of Molecular Vibrations
View Description Hide DescriptionDevelopments which reduce the labor of calculating the vibration frequencies of complex molecules are described. In particular a vectorial scheme is given for obtaining the reciprocal of the matrix of the kinetic energy in terms of valence‐type coordinates. A general rule for writing down the coefficients of the transformation to symmetry coordinates is derived together with a method of obtaining the kinetic energy reciprocal matrix () in terms of symmetry coordinates with a minimum of algebra. A treatment of redundant coordinates is developed. In addition, reduction of the secular equation by the splitting out of high frequencies, a new type of isotope product rule, and the determination of normal coordinates are discussed. The molecule CH_{3}Cl is worked out as an illustration.

On the Theory of Antiferromagnetism
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Overvoltage and the Structure of the Electrical Double Layer at a Hydrogen Electrode
View Description Hide DescriptionThe theory of absolute reaction rates applied to electrode processes leads to the equationfor the specific rate of discharge of ions. The question arises as to whether V should be the actual potential at the electrode or only the overvoltage. In the case of hydrogen ion discharge, it is found experimentally that the overvoltage should be used. On the other hand, the theory in its simplest form requires V to be the total potential. This paradox can be resolved by postulating the existence of two different electrical double layers at the electrodesurface, and two corresponding energy barriers over which the protons must pass. Provided that the barrier nearer the electrode is the higher, the overvoltage is essentially established across this layer, while the variation in equilibrium potential caused by variations in the hydrogen ion concentration of the solution is established across the outer double layer. Since the rate of discharge is determined by the potential difference across the inner double layer, the rate is determined by the overvoltage, and not by the total potential. The nature of these two energy barriers is also discussed. Both barriers may correspond to transfer of protons from water molecule to water molecule, or one may correspond to the actual discharge process in which a neutral hydrogen atom is formed. It does not yet seem to be possible to decide between these two alternatives, either theoretically or experimentally, but it seems most probable that both barriers correspond to proton transfers from water molecule to water molecule.

Optical Sensitizing of Silver Halides by Dyes III. The Relation of Sensitizing to the Absorption Spectra and Constitution of Dyes
View Description Hide DescriptionOptical sensitizing is related to dye structure in general, not confined to particular classes of dyes. While sufficiently strong adsorption to silver halide, and relative insolubility of the adsorbed dye are essential, they are not sufficient conditions. The absorption spectra of adsorbed dyes correspond to their spectra in solution, and are affected in the same way by structural changes, but are not identical therewith. The displacement of the spectrum should be referred to the absorption of the dye in the gaseous state at low pressures; examples are given. This displacement corresponds to an adsorption energy available for sensitizing, but this energy difference may not be available, and is not generally sufficient. For ``molecular'' sensitizing, planarity of the dye molecule appears to be essential, and the following conditions are deduced as necessary and probably sufficient for sensitizing: (i) Planar configuration of dye molecules, respectively of adsorbed dye ions, (ii) edge‐on adsorption of planar molecules oriented possibly orthogonally but more probably at an angle of 70° to a (111) plane of the crystal, and (iii) electronic transition in dye ion or dipole on absorption of a photon polarized in an azimuth defined by (i) and (ii). On these bases a hypothesis of coplanar coupling of electronic displacements in the dye and in a congruent plane of the silver halide lattice is advanced. It is suggested that this is a key factor in optical sensitizing by dyes, both for molecular and aggregate sensitizing. Certain other relations of constitution to sensitizing are discussed, including the influence of nuclear (perichrome) changes and of substitution.

The Thermal Reaction Between Hydrogen and Oxygen II. The Third Explosion Limit
View Description Hide DescriptionThe thermal high pressureexplosion of the hydrogen‐oxygen mixture (``third explosion limit''), occurring near atmospheric pressure at 560°C, was studied. In the p—T diagram, a section of the limiting curve was determined. The effect of a KCl coat on a Pyrex surface was observed. The investigation of the third explosion limit does not lend itself to a decision between the competing theories of the thermal hydrogen‐oxygen reaction.
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 LETTERS TO THE EDITOR


The Vibrational Energy Levels and Specific Heat of Ethylene
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Simultaneous Determination of Adiabatic and Isothermal Elasticities
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The Reaction of Hydrogen and Oxygen in the Presence of Silver. The Third Explosion Limit
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Thermal Conductivity of Liquids
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A Note on the Entropy of Fusion of Argon
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