Volume 37, Issue 4, 15 August 1962

Mössbauer Effect in Iron (III) Acetylacetonate and Chemical Consequences of K Capture in Cobalt (III) Acetylacetonate
View Description Hide DescriptionThe resonance absorption of 14.4 keV gamma rays in Fe^{57} (Mössbauer effect) has been observed in Fe(III) and Co(III) acetylacetonate, the former used as an absorber against a source of Co^{57} diffused into metallic chromium, the latter as a Co^{57} labeled source against an K_{4}Fe(CN)_{6} (38%Fe^{57}) absorber. The Fe(III) acetylacetonate absorber spectrum shows a single broad line (Γ_{½}=1.83±0.09 mm sec^{—1}) with an isomer shift of 0.50±0.09 mm sec^{—1}. The Co(III) acetylacetonate source shows a complex spectrum which can be resolved into a single peak assigned to Fe(III) and a quadrupole split pair of lines assigned to Fe(II). These data are interpreted in terms of the chemical consequences following K capture in Co^{57}, and suggest a twofold preference for the stabilization of the higher charge state in the Co(III) acetylacetonate matrix. No evidence for ionic charge states higher than 3+ is observed, and it is assumed that these species—if formed as a consequence of the prior nuclear event—have been reduced to the observed states in times short compared to 10^{—7} sec.

Derivation of Physically Significant Nonbonded Interaction Constants in Hydrides by a Modified Urey—Bradley Analysis
View Description Hide DescriptionPrevious Urey—Bradley (U.B.) analyses of vibrational spectra have suggested that intramolecular repulsions between atoms are generally large and similar, at a given distance, to intermolecular nonbonded interactions. Hydrogen, however, has been found to exhibit anomalously low intramolecular repulsions according to conventional U.B. analyses. In the present modified analysis completely general quadratic force fields, corrected for anharmonicity, are resolved into the sum of U.B. fields and additional interactions neglected in conventional U.B. analyses. The assumptions required for evaluation of the central force components are discussed. It is found for a series of hydrides that explicit inclusion of stretch—stretch interactions over and above those implied by nonbonded repulsions markedly alters the analysis and yields H···H interactions interpretable in terms of large repulsions entirely comparable with those calculated using intermolecular force laws. Such large repulsions are compatible with structural, thermochemical, and kinetic data. While they cannot be separated from effects of hybridization solely on the basis of quadratic force constants, they provide an alternative explanation for effects commonly ascribed to hybridization and more specialized interactions.

Crystal Structure of CsMnF_{3}
View Description Hide DescriptionA single‐crystal x‐ray diffraction study shows that CsMnF_{3} has the hexagonal BaTiO_{3}‐type structure. The space group is P6_{3}/mmc. The unit cell with a=6.213 Å, c=15.074 Å contains six formula units. Each cesium atom has 12 fluorine neighbors at an average distance of 3.13 Å. One third of the manganese atoms occupy the centers of fluorine octahedra that share their corners with other octahedra as in the perovskitestructure. The remaining two thirds of the manganese atoms are in distorted fluorine octahedra that each share one face and three corners with other octahedra; these manganese atoms are in pairs 3.00 Å apart. The average Mn–F distance in the octahedra is 2.13 Å.

Theoretical Interpretation of Reactions Occurring in Photochlorination
View Description Hide DescriptionThe Arrhenius A and E factors of over 60 elementary reactions in photochlorination systems have recently been evaluated experimentally in this and other laboratories. In this article a uniform treatment of most of these reactions is given by activated complex theories. Two parameters are fit to the data from two activation energies. The other activation energies follow the expected trend for reactions of chlorine atoms with hydrocarbons, but the reactions of chlorine atoms with chlorinated hydrocarbons do not follow the expected trends. For reactions with activation energy, the theory accounts very well for the magnitudes and trends of the Arrhenius A factors. For reactions with no activation energy, the activated complex theory as used by Gorin accounts for the order of magnitude of the rate constants of the group as a whole, but it fails to account for several pronounced trends in the data and is judged to be of no predictive value. For certain limited types of chemical reactions and over restricted ranges of experimental conditions, activated‐complex theory is judged capable of predicting some kinetic factors. The range of predictions is small, but is not zero.

Polarization of the Electret
View Description Hide DescriptionThe internal charge distribution of the carnauba wax electret has been determined by a sectioning method: After polarization and cooling samples are cut into sections of different thickness. These are reheated and the ensuing discharge currents are measured. The total released charge, as determined by numerical integration of the corresponding current—time curve, gives the polarization of each section. A macroscopic space chargepolarization would give charge values which, with decreasing thickness of sections, go to zero; a uniform volume polarization would give values which are independent of thickness. Measurements gave constant values and therefore prove the existence of a uniform volume polarization of the electret.

Work Function Changes Produced by Chemisorption on Surfaces with Different Types of Adsorption Sites
View Description Hide DescriptionA simple model describing the changes in work function produced by chemisorption on a surface possessing two types of adsorption sites is presented. Equations for the change in work function as a function of the amount of gas adsorbed are given, and curves for the cases of CO and N_{2} adsorbed on the (113) plane of tungsten are compared with recent experimental results.

Effect of Inert Salts on Equilibrium and Rate Constants for Ionic Reactions
View Description Hide DescriptionEmpirical evidence is given to show that individual ion activity coefficients can be written as logγ_{ t }=Z _{ t } ^{2} G(S)+[ν_{1}α_{1t }+ν_{2}α_{2t }]C, where ν_{1} and ν_{2} are the number of ions of type 1 and 2 formed from one formula of the supporting electrolyte,C is the formal concentration of the electrolyte,Z _{ t } is the charge of the ion t, G(S) is a function of the medium only, α_{1t } is a function of the ion‐size parameter for ions 1 and t, and α_{2t } is a similar function of the ions 2 and t. The equation is applicable only if the concentration of ion t is small in comparison to the concentration of electrolyte. Mayer's theory predicts that the above equation, when used to calculate experimentally observable quantities, should be correct to within good accuracy for ion‐size parameters between 5.5 and 8.5 Å in a 1–1 supporting electrolyte and for higher‐charged electrolytes at ionic strengths above about 0.2. Using this equation one can calculate the ratio of the rate constant for the bromacetate—thiosulfate reaction to that for the peroxydisulfate—iodide reaction at infinite dilution from data obtained in MgSO_{4}, Mg(NO_{3})_{2}, Na_{2}SO_{4}, and NaNO_{3} solutions at concentrations between 0.25 and 2F. The value obtained under these conditions is within experimental accuracy of the value obtained by extrapolation to infinite dilution from ionic strengths below 0.02.

Sequential Filling of a Line by Intervals Placed at Random and Its Application to Linear Adsorption
View Description Hide DescriptionA line with integral length n is filled sequentially at random with nonoverlapping intervals of integral length a, their end points having integer coordinates. It is shown that, as n tends to infinity, the average value of the length left vacant tends asymptotically to (n+a) A _{1}(a) while its variance tends to (n+a) × aA _{2}(a), where A _{1}(a) and A _{2}(a) are constants whose values are given numerically for all a; these asymptotic results are accurate to four significant figures for n/a>8. Some results are also given for the (average) relative numbers of vacant spaces of length i=0, 1,..., a—1.
With certain restrictions, the above results can be applied to the complete adsorption of linear molecules which when once adsorbed remain fixed in position in the line troughs of suitable crystal surfaces such as (110) on an fcc crystal or (112) on a bcc crystal. These restrictions concern the way in which the molecule sits in equilibrium on the underlying crystal sur face.

Low‐Energy Electron Diffraction Study of Silicon Surface Structures
View Description Hide DescriptionLow‐energy electron diffraction data are presented for superstructures on the clean (100) and (111) surfaces of silicon, and for structures formed by a monolayer of iodine and a monolayer of phosphorus on the (111) surface. Conventionally defined structure factors, modified for atomic structures a few layers thick, have been used to analyze two of these structures with results which are very probably correct. Insufficient data are apt to be the most serious limitation of the technique in structure determination. Observed transitions for the clean surface structures are described and results are presented for transition temperatures and rates of reaction of the surfaces with iodine and with phosphorus as a function of temperature and pressure. Iodine appears to be adsorbed in the ionic state and the calculated Si–I distance is about 3.2 Å. The data show that the physical and chemical properties of a siliconsurface at low temperatures depend very much on thermal, chemical, and mechanical history, and the models presented explain this in considerable detail. Multilayeradsorption of iodine and phosphorus, disordered transition structures, and etching effects were also observed. The stable clean siliconsurface has silicide properties, and reaction with hydrogen, mercury, and molybdenum is limited to a few active sites under conditions accessible in this work.

Second‐Order Splittings in the ESR Spectra of Organic Radicals
View Description Hide DescriptionMore lines than can be explained by first‐order theory have been observed in the ESR spectra of several alkyl radicals in solution. The additional structure is predicted if the usual treatment is extended to second order in the coupling constants. This extension has been made in such a way as to eliminate the necessity of explicitly considering the 2^{ n } nuclear‐spin wave functions which occur with spin‐½ nuclei. The spectrum of the ethyl radical is used to demonstrate the agreement of actual spectra with the treatment presented here. A table is included which facilitates calculation of the second‐order structure in the spectra of radicals containing spin‐½ nuclei.

Bond Character in XY_{M}‐Type Molecules: Chlorine—Oxygen Compounds
View Description Hide DescriptionAn internally consistent LCAO—MO method is presented for determining the bond characters in XY_{M}‐type molecules involving second‐row elements. This treatment is based on Moffitt's ``atoms‐in‐molecules'' method, but utilizes valence‐state electronegativities of the atoms involved rather than the generally unavailable valence‐state ionization potentials and electron affinities. Results from the two methods compare favorably for C–O and S–O compounds.
Application of the method to the oxygen compounds of chlorine shows that the chlorine atom 3d orbitals may significantly participate in the π bonding. A successful correlation between the calculated total π‐bond orders and the Cl–O bond stretching force constants is obtained when a reasonable set of β(dπ) values is used, and the observed properties of the compounds are compatible with the calculated bond characters.

Some Theoretical Aspects of Bonding in N–F Compounds
View Description Hide DescriptionA separation of the effects of substituent groups into distinct σ and π contributions and the influence of the σ and π contributions on Hamiltonians and wave functions of various cores has proved useful for describing several diverse phenomena in N–F compounds.
(1) The ``anomalous'' difference in bond strengths in NF_{3} and NF_{2} where the N–F bond in NF_{3} is weaker than that in NF_{2}.
(2) The nonconstancy of the δ_{ K } value for F in ionization potentials of NF_{3} and CF_{3}, whereas other substituent group effects were constant.
(3) The similarity between the effect of F on ionization potentials of NF_{2} and of CF_{3}.

Effect of Molecular Shape on Nuclear Magnetic Relaxation
View Description Hide DescriptionThe dependence of magnetic relaxation processes upon molecular shape is examined by regarding the molecule as a rigid ellipsoidal body which shows anisotropic rotational and translational Brownian motions. The shape effects are examined based on particular mechanisms of relaxation: (1) intramolecular dipole—dipole interactions, (2) intermolecular dipole—dipole interactions, (3) anisotropic spin—spin couplings, (4) interactions of the nuclear moments with the local magnetic fields due to anisotropic shielding of the external field, and (5) electric quadrupoleinteractions. The relaxations caused by the first and second mechanisms are discussed in detail by taking a prolate spheroid as an example; the correlation time and the relaxation time are obtained as functions of the axial ratio. Saturations of multiple NMR lines are discussed; then, by taking the multiple lines of the three vinyl protons of acrylic acid as an example, the shape effect on the saturation, as well as an application of the saturation effects of multiplet lines to the assignment of a complex NMR spectrum, is discussed.

Microwave Spectrum of Chlorine Dioxide. III. Interpretation of the Hyperfine Coupling Constants Obtained in Terms of the Electronic Structure
View Description Hide DescriptionThe hyperfine coupling constants obtained from the microwave spectrum of chlorine dioxide are discussed in terms of the electronic structure of chlorine dioxide. It is found that these constants can be reasonably interpreted in terms of a simple molecular orbital model of chlorine dioxide in which the odd electron is in a b _{1} antibonding orbital.

Diffusional Contribution to the Total Flow from a Knudsen Cell
View Description Hide DescriptionIt has been recognized for sometime that the geometry of a Knudsen effusion cell influences the kinetics of the molecular effusion of the vapor from within the cell. However, no treatment has been reported of the contribution to the effusion current made by the surfacediffusion out through the orifice of the effusate adsorbed on the walls within the cell. The applicable integro‐differential equations which describe the steady‐state kinetics for both surfacediffusion and vapor effusion out through the orifice have been solved approximately. The derived relations predict that under specified conditions the diffusion flux for the orifice dimensions commonly employed may contribute an appreciable fraction of the total weight loss of the cell during an effusion experiment. If not taken into account, this diffusional contribution would yield equilibrium vapor pressures in excess of the actual values.

Theory of Paramagnetic Excitons in Solid Free Radicals
View Description Hide DescriptionA linear chain of S=½ molecules with alternating intermolecular exchange integrals is used as a model to investigate the properties of paramagneticexcitons in solid free radicals from a theoretical point of view. The spin exchange Hamiltonian for the problem iswhen J>J′>0. In the limiting case that J≫J′, the exciton bandwidth is simply J′. For this case we have calculated (a) the fine‐structure splitting of the paramagneticresonance of isolated (noninteracting) excitons, (b) wave functions for a free exciton gas of arbitrary excitation density, (c) the magnetic susceptibility of the exciton gas, and (d) first‐order exchange interactions between excitations.
In the case that thermal energies are much larger than the exciton bandwidth, exchange interactions between excitations are simply proportional to the excitation concentration, but at temperatures corresponding to thermal energies less than the bandwidth, there is a ``Fermi hole'' type repulsion between the excitons that reduces the exchange interaction. In fact, the excitons behave somewhat like Fermi particles, except their number is not constant (depending on the temperature), and only one exciton may occupy a given momentum state, irrespective of spin. Also, when the exciton bandwidth is comparable to or larger than kT, it is predicted that the exciton fine‐structure splitting will be temperature dependent.
When J′ becomes comparable to J, then the elementary exciton takes on a complicated, distributed spin structure.

Equation of State of Classical Hard Spheres at High Density
View Description Hide DescriptionUnder certain conditions, an asymptotic expression for the equation of state of a classical mechanical system of N ν‐dimensional (ν=1, 2, or 3) hard spheres confined in a volume V is obtained in the formThis expression agrees with the leading term in V/V _{0}—1 of the usual free‐volume approximation for N = ∞. The conditions under which this conclusion is established are a restriction to a finite number of molecules N with periodic boundary conditions, and the requirement that as V→V _{0} the accessible configuration states approach a close‐packed configuration whose coordination number c satisfies the requirementSuch a limiting configuration, from which only an infinitesimal region of configuration space is accessible under an infinitesimal expansion, is called a stable configuration; the above restriction on the coordination number is a necessary condition for stability. The difficulties which appear as N→∞ are indicated.

Note on the ^{5}Σ^{+} _{ g } State of N_{2}
View Description Hide DescriptionAn approximate potential curve for the ^{5}Σ^{+} _{ g } state of the nitrogen molecule is proposed. The curve is based on the parameters D_{e} =1100 cm^{—1}, ω_{ e }=650 cm^{—1}, and r_{e} =1.55 Å, which were derived from a consideration of recent afterglow measurements and from an examination of the predissociations in the a ^{1}Π_{ g } and B ^{3}Π_{ g } states. The main features of the potential are in keeping with the trend of the ^{5}Σ^{+} _{ g } curve as proposed in the most recent theoretical work (see the accompanying paper by R. S. Mulliken).

Low‐Energy ^{5}Σ^{+} _{ g } States of the Nitrogen Molecule
View Description Hide DescriptionThe wave functions of the two ^{5}Σ^{+} _{ g } states of N_{2} derivable from configurationally unexcited (s ^{2} p ^{3}) atoms, one from ^{4} S+^{4} S atomic states, the second from ^{4} S+^{2} D states, are examined. With the help of empirical data on the normal state of F_{2}, to which the valence‐bond structure of the lower of the two ^{5}Σ^{+} _{ g } states is closely related, estimated potential curves for the two states are constructed. It is shown that for the lower ^{5}Σ^{+} _{ g } state, the theoretically expected curve agrees rather well with that deduced from empirical evidence {see Carroll's accompanying paper [J. Chem. Phys. 37, 805 (1962) ]}. The wave function of the ^{5}Σ^{—} _{ g } state from ^{4} S+^{2} P atoms is also given.

Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules
View Description Hide DescriptionThe equations usually given relating fluorescence lifetime to absorption intensity are strictly applicable only to atomic systems, whose transitions are sharp lines. This paper gives the derivation of a modified formulawhich should be valid for broad molecular bands when the transition is strongly allowed.
Lifetimes calculated by this formula have been compared with measured lifetimes for a number of organic molecules in solution. In most cases the values agree within experimental error, indicating that the formula is valid for such systems. The limitations of the formula and the results expected for weak or forbidden transitions are also discussed.