Volume 33, Issue 1, 01 July 1960

Madelung Constants of the Cubic Perovskite Structures
View Description Hide DescriptionA proof is given of a simple linear relation between the Madelung constant, referred to the lattice parametera, of a cubic perovskitestructure ABX_{3} with the ionic charges in the ratio +z:+(3—z):—1 and the corresponding Madelung constants for the NaCl, CsCl, and Cu_{2}O structures.

Note on Secondary Isotope Effects in Reaction Rates
View Description Hide DescriptionIt is shown that secondary kinetic isotope effects, for all isotopes with the possible exception of hydrogen isotopes, are expected to be small unless the force constants involving the isotopically substituted positions are considerably different in the transition state from those in the reactant. Cases involving secondary hydrogen isotope effects are investigated in detail for certain model reactions. It is concluded that hydrogen isotope effects do not constitute an exception to the above rule.

Lattice Vibrations in Alkali Halide Crystals. II. Potassium and Rubidium Halides; Cesium Fluoride
View Description Hide DescriptionVibrational frequency distributions for the potassium and rubidium halides and for cesium fluoride have been evaluated on the basis of the Born lattice theory by the use of Blackman's numerical sampling method. Both room‐temperature and extrapolated 0°K parameters have been used in the calculation. Specific heats, the corresponding Debye characteristic temperatures, and the moments of the distributions have been obtained directly from the frequencies. Comparison is made with experimental data and with other theoretical work.

Isotope Effects on Reaction Rates and the Reaction Coordinate
View Description Hide DescriptionThe high temperature limit of the reaction rate isotope effect is discussed. The Slater approach is compared in this respect to the transition state theory approach. There is no essential disagreement between the two approaches. The Slater assumption with respect to this limit for simple bond rupture represents a special case, however, and is not necessarily correct.

A One‐Center Wave Function for the Methane Molecule
View Description Hide DescriptionSlater orbitals, centered on the carbon nucleus and having variable orbital exponents and principal quantum numbers, are used to construct electronic wave functions for the ground state of the methane molecule of the formValues for the five linear coefficients, the seven orbital exponents, and the seven principal quantum numbers are determined by the variational method. The total molecular energy obtained from a one‐term wave function of this form is —39.50 a.u.; the five‐term result is —39.80 a.u.; the experimental nonrelativistic energy is —40.51 a.u. Comparison with a similar calculation for the neon atom indicates that most of the residual error is in correlation energy, and it favors the high value for the heat of sublimation of carbon.

On the Reciprocal Relations of Onsager
View Description Hide DescriptionGiven any linear relation between forces and fluxes in irreversible thermodynamics, it is shown that redefinition of forces and fluxes by linear combination yields a relation with symmetric matrix. The rate of production of entropy is unchanged by the redefinition. Thus, unless ``forces'' and ``fluxes'' are defined by some property more specific than mere occurrence in the expression for production of entropy, there is no content in the statement that the matrix of phenomenological coefficients is or is not symmetric.

Quantum Yield for Energy Transfer by Resonance
View Description Hide DescriptionThe theoretical prediction of quantum yields for electric dipole‐dipole energy transfer by resonance is discussed. The common approximation which neglects transfers from each donor to all but the nearest acceptor is extended so as to include transfers to the second‐nearest acceptor and, in the limit of very high acceptor concentration, to the third and fourth as well. The total quantum yield and the fractional yields due to transfers to the individual categories of nearest acceptors are evaluated, and the merits of the various approximations are discussed quantitatively.

Thermodynamic Properties of Unipositive Gaseous Elemental Ions
View Description Hide DescriptionThermodynamic properties of unipositive gaseous elemental ions were calculated from available energy level data for a range of temperatures from 100° to 50 000°K.

Thermodynamics, Stationary States, and Steady‐Rate Processes. V. A Collection of Corollaries
View Description Hide DescriptionA listing is made of a number of direct consequences of the ideas and procedures developed in papers I—IV of the series; the topics considered are reaction equilibria in concentration and in thermal fields, thermocells, steady bithermal mass flow, and compound linkages. Some general remarks about monothermal fields are relegated to an appended section.

Thermodynamics, Stationary States, and Steady‐Rate Processes. VI. Forced Vaporization of Selected Liquids
View Description Hide DescriptionThe results of forced vaporization experiments are reported for water, carbon tetrachloride, benzene, methanol, and n‐butyl alcohol. The data, which were obtained at a monothermal temperature of 25°C and with a tapered tube having available areas from 0.2 to 3.4 sq cm, indicate a linear relationship between the logarithm of the steady pressure maintained above the liquid and the steady mass flow per unit area. A number of complicating features in the experimental arrangement are discussed briefly.

Absorption Spectra of Solid Xenon, Krypton, and Argon in the Vacuum Ultraviolet
View Description Hide DescriptionThe absorption spectra of solid xenon, krypton and argon at 4.2°K have been investigated between 3500 and 1200 A. In the region between 1510 and 1200 A solid xenon has four absorption bands, three of which lie within less than 800 cm^{—1} of atomic transitions, all being shifted to lower energy in the solid. Solid krypton has two bands between 1250 and 1200 A which lie within 900 cm^{—1} of atomic transitions but are shifted to higher energy in the solid. No absorption was found in solid argon at wavelengths longer than 1200 A. The experimental results are interpreted and discussed on the basis of valence type interatomic interactions in the excited states. It is predicted that the fluorescence spectra of these solids would be displaced to lower energy by about 1 ev.

Infrared Studies of Crystal Benzene. II. Relative Intensities
View Description Hide DescriptionIntensities of the absorption bands observed with a thin sample of polycrystalline benzene have been measured relative to the absorption of v _{20} at 1036 cm^{—1}. The gas‐phase‐allowed fundamentals are much the strongest bands in the spectrum. The relative intensities of these fundamentals are considerably different from the relative intensities in the gas or liquid phase. The experimental errors are discussed in detail with the conclusion that the observed difference in relative intensities are well outside any conceivable experimental errors. As a result, it is concluded that existing theories of spectra in condensed phases must be modified to predict different behaviour for each fundamental vibration. Finally, attention is drawn towards some of the anomalies still existing in the assignment of vibrational frequencies in the benzene molecule.

Theory of Hyperfine Interactions in Aromatic Radicals
View Description Hide DescriptionThe relation a_{H} =Q _{ρ} between the ring proton isotropic hyperfine splittinga_{H} and the unpaired spin density ρ on the carbon atom in an aromatic hydrocarbon radical is derived under even more general conditions than McConnell and Chesnut's.^{1} There are only three essential assumptions in the new theory: (a) that σ‐π exchange interaction is small; (b) that an antisymmetrised product U (π) V (σ), which allows π‐π and σ‐σ, but not σ‐π correlations, is a good first approximation to the ground‐state electronic wave function; and (c) that U (π) is formed exclusively of π‐orbital configurations, and V (σ) exclusively of σ ones. In the framework of our theory the unpaired spin density in the molecular plane arises entirely from σ‐electron excitations. The general relation a_{N} =tr(Q ^{ N } _{ ρ }) holds for any nucleus N, including C^{13} and N^{14}, which lies in the molecular plane. Here ρ is the π‐electron spin‐density matrix, and Q ^{ N } a hyperfine coupling matrix, whose elements depend on σ‐π exchange integrals and excited σ triplet states. The diagonal elements of Q ^{ N } for C^{13} are estimated in a simple way to be +41 gauss for the same carbon atom and —14 gauss for each next neighbor, while experimental data fit the values +41 and —6.9 gauss.

Radiolysis of Cyclohexane. I. Pure Liquid Cyclohexane and Cyclohexane‐Benzene Solutions
View Description Hide DescriptionThe radiation chemistry of pure liquid cyclohexane and of cyclohexane‐benzene solutions has been investigated. The cyclohexane radiolysis system appears to contain at least two distinct activated species, one of which (c‐C_{6}H_{12}″) is subject to ``protection'' by benzene while the other (c‐C_{6}H_{12}′) is not. The approximate yields of these two species, determined by kinetic analysis, are G(c‐C_{6}H_{12}″) = 3.0±0.4 and G(c‐C_{6}H_{12}′) = 2.5∓0.4. In addition to the usual products, cyclohexylcyclohexadiene and dicyclohexadiene have been measured in the cyclohexane‐benzene system. A mechanism has been proposed to explain the formation of the major products and the variation of their yields with benzene concentration.
A limiting case calculation for the upper limit of the rate constant for energy transfer between molecules in the present system (10^{13}—10^{14} liters mole/sec) agrees well with a similar calculation, recorded in the literature, for energy transfer in organic solution scintillators. Another limiting case calculation shows that the rate constant for energy transfer might also be considerably smaller than the above value.

Entropy Production in Chemical Reactions
View Description Hide DescriptionThe generalization of Prigogine and Glansdroff which states that the rate of entropy production is negative in the nonstationary state and zero in the stationary state is verified for reversible isomerization of ammonium thiocyanate and the isomerization of Δ^{α}‐pentenoic acid involving a monomolecular triangular reaction.

Kinetics of Excited Molecules. II. Dissociation Processes
View Description Hide DescriptionA detailed calculation of the rate of dissociation of an electronically and vibrationally excited molecule (photochemicaldissociation) is compared with the experimental data for ketene. The results are consistent with unimolecular reaction rate theory. However, the data are not accurate enough to provide unambiguous values for the parameters in the theory.

Nuclear Spin‐Lattice Relaxation in Solutions
View Description Hide DescriptionT _{1} for protons in C_{6}H_{5}Cl, C_{6}H_{6}, and C_{6}H_{12} has been measured as a function of concentration in solution with CS_{2} and CCl_{4}. T _{1} does not have the dependence on the solution viscosity suggested by the theory of Debye. The rotational relaxation times at infinite dilution are obtained by extrapolation, and the correlation times calculated from these results are compared with the values predicted by the rotating sphere model as well as an inner viscosity and microviscosity model. The inner viscosity model provides the best agreement with the experimental results. The correlation times are found not to be proportional to the volumes of the molecules but seem to be simply related to the moments of inertia as well as the masses of the molecules of interest and the masses of the solvent molecules. An approximate formula which provides good results for the systems above is suggested as τ=2Iηa/μkT, where I is the moment of inertia of the molecule of interest, η is the solventviscosity,a is the average radius of the molecule, and μ is the reduced mass of the solvent‐solute system.

Vibrational Transitions and the Intermolecular Potential
View Description Hide DescriptionTemperature‐dependence studies of vibrational collision lifetimes by the authors have indicated that the application of the Schwartz, Slawsky, and Herzfeld theory to substituted methane molecules with heavy surface atoms results in repulsive ranges which are shorter than those expected from a Lennard‐Jones 6:12‐type interaction. We have shown that the 28:7 potential suggested by Hamann and Lambert for quasi‐spherical molecules gives ranges which are in better agreement with experiment. Also, experimental relaxation times of CHClF_{2}‐argon and CHClF_{2}‐helium mixtures have been used to obtain the collision lifetimes for the CHClF_{2} molecule undergoing either argon or helium collisions. The results can be explained using the SSH theory, if the 6:12 ranges for helium and argon are averaged with the shorter experimental range for CHClF_{2}.

Theorem on Separability of Electron Pairs
View Description Hide DescriptionThe theorem that two functions Λ_{ A }(12) and Λ_{ B }(12) span subspaces which are mutually perpendicular if the functions are orthogonal to each other in the strong sense;is proved here. The theorem is important for the study of chemical bonds.

Isoelectronic Extrapolation of Electron Affinities
View Description Hide DescriptionAn expression based on theoretical considerations and containing three adjustable constants has been derived for the purpose of extrapolating ionization potentials along isoelectronic sequences. When used to extrapolate electron affinities of the elements of the first and second short period, the formula is found to yield results that are correct within the error limits of the experimental data at present available.