bluuebunny/crossref_metadata_2025 huggingface dataset:
Formulas and Numerical Tables for Overlap Integrals
Authors: Mulliken R. S. , Rieke C. A. , Orloff D. , Orloff H.
Published: January 2005

Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μa+μb)R/aH , R being the interatomic distance, and t=(μa—μb)/(μa+μb). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra-atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2-quantum s, p hybrid AO's.

Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non-hybrid S values. It is shown how S values corresponding to orthogonalized Slater AO's and approximate S values for SCF (self-consistent-field) AO's can also be obtained as linear combinations of the Slater-AO S values. S values for carbon-carbon 2pσ- and 2pπ-bonds using SCF carbon AO's have been computed (see Table in Section Vb); they correspond to stronger overlap than for Slater AO's. Non-localized MO group-orbital S values are also discussed, and are illustrated by an application to H2O. The use of the tables to obtain dipole moments for electronic transitions in certain cases is also mentioned. The use of the tables to obtain S values for various specific atom-pairs and bond-types, and resulting conclusions, will be discussed in another paper.
Measurements of Normal Burning Velocities and Flame Temperatures of Bunsen Flames
Authors: Andersen J. W. , Fein R. S.
Published: January 2005

Stroboscopically illuminated particle tracks are used to accurately measure normal burning velocities of laminar flames. The precision of the measurements is increased by the use of a constant-velocity profile nozzle which gives a straight-sided Bunsen cone. Normal burning velocity data are presented for 3.7 to 5.3 percent propane-air mixtures. The value for the stoichiometric flame was determined to be 44.8 cm/sec.

From stroboscopic and streak photographs of particle tracks it is possible to obtain the maximum flame temperature and temperature distribution in the flame front. Measurements from the two types of photographs are combined with the equation of continuity and the equation of state to obtain the flame temperature. The flame temperature for a stoichiometric propane-air flame was determined to be 2220°K. An extension of this method is used to obtain an approximation of the temperature distribution in the flame front.
Some Properties of van der Waals' Liquids
Authors: Wall Frederick T. , Krigbaum William R.
Published: January 2005

A theoretical consideration of the volume of a van der Waals' liquid suggests some new rules, comparable to that of Trouton, relating coefficients of expansion and compressibility to heats of vaporization. According to the simplest and most reliable of these new relationships, the product of the coefficient of cubical expansion and the heat of vaporization, αΔHv, is the same for many liquids and equal to about 10 cal./deg. It is further shown that at a given temperature, ΔHv2β/V is also constant where β is the compressibility and V the volume of the liquid. Certain corollary rules are derived by combining the above two with each other and with Trouton's law. These new rules should prove of some value in estimating compressibilities and heats of vaporization from coefficients of expansion.
A Normal Coordinate Analysis of the Planar Vibrations of Substituted Ethylenes. I. CH Bending Modes
Authors: Torkington P.
Published: January 2005

A normal coordinate analysis of the planar vibrations of some substituted ethylenes is carried out. Thirteen compounds are studied, including mono-substituted and 1:1- and cis- and trans−1:2-disubstituted ethylenes. Various solutions for the CH bending force constants are obtained and correlated. Some attempt is made to study the range of allowed solutions, and to examine the coupling of the different coordinates in the potential function.
Physical Properties of Polonium. I. Melting Point, Electrical Resistance, Density, and Allotropy
Authors: Maxwell Charles R.
Published: January 2005

Measurements on the electrical resistance, thermal coefficient of electrical resistance, melting point and density of polonium are reported. An abrupt change in the electrical resistance near 100°C indicates that polonium exists in two allotropic forms. Observations which indicate that the temperature for crystal transformation is a function of the size and history of the specimen are reported.
Physical Properties of Polonium. II. X-Ray Studies and Crystal Structure
Authors: Beamer William H. , Maxwell Charles R.
Published: January 2005

Structures are proposed which account for the powder diffraction patterns obtained from samples of polonium containing various amounts of lead. Unusual temperature effects are recorded for α-polonium. It is suggested that the Pb and Po are present in interpenetrating primitive cubic lattices which are indistinguishable because the atomic numbers are nearly the same.
The Dimensions of Chain Molecules Containing Branches and Rings
Authors: Zimm Bruno H. , Stockmayer Walter H.
Published: January 2005

Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light-scattering measurements.
The Mercury Photo-Sensitized Hydrogenation of the Butenes and the Photolysis of Di-n-butylmercury
Authors: Moore Walter J. , Wall Leo A.
Published: January 2005

The Hg–3P1 photo-sensitized hydrogenations of isobutene, butene−1, and butene−2 have been studied from 24 to 300°C at an H2:C4H8 ratio of 10:1. Mass spectrometer analyses of the products have led to the following conclusions: (1) When a H atom adds to isobutene, the tertiary butyl radical is formed. Any isobutyls decompose immediately into methyl and propene. (2) Addition of a H atom to butene−2 produces little sec.-butyl, mostly methyl plus propene. (3) Addition of a H atom to butene−1 produces considerable sec.-butyl. Any n-butyls decompose into ethyl and ethene. (4) The isomeric constitution of the octanes suggests that radicals add to olefinic double bonds at the carbon atom with highest electron density. Products from the photolysis of di-n-butylmercury at λ=2537A indicate that n-C4H9=C2H5+C2H4 has an activation energy of around 35 kcal.
Hexacovalent Bond Orbitals I
Authors: Duffey George H.
Published: January 2005

A set of six equivalent orthogonal bond orbitals of type snp1+2md5−n−2m are considered. The fact that these are of trigonal prism symmetry is pointed out. Calculations were made of the bond strengths and angles at various values of m with n set equal to one and at various values of n with m set equal to zero.
The Infra-Red Spectrum of C2H6
Authors: Smith Lincoln G.
Published: January 2005

The infra-red spectrum of C2H6 gas has been studied in the region between 1.6 and 13μ with a spectrometer of high resolving power. From measurements on four resolved ∥ bands the value IB0 = (42.234±0.011)×10−40 g cm2 has been obtained for the large moment of inertia in the ground state. From measurements on the three fundamental ⊥ bands the best value at present available for the small moment of inertia is IA = 10.81×10−40 g cm2. Because of uncertainties concerning the perturbations of degenerate state ν8, of which a semi-quantitative explanation which is apparently basically correct has been obtained, this value is provisional but appears to be fairly reliable. With these values of IB0 and IA, if one assumes C–C = 1.55A, one obtains C–H = 1.098A and ≰HCC = 109° 3′. From the considerations of the perturbations of state ν8 and of the frequencies and line spacings of the combination ⊥ bands, spectroscopic evidence indicating that the configuration of C2H6 is staggered (point group D3d) has for the first time been obtained. Also from these considerations the reliable value ν8 = 1472.2 cm−1 and the values ν4 = 290 cm−1 for the torsion frequency and ν12 = 1190 cm−1 for the ``uncertain'' frequency have been obtained. The latter two values are perhaps somewhat more reliable and not inconsistent with values obtained previously by other methods. These and other results are summarized in Figs. 1 and 14 and in Tables XII—XV.
Concerning the Work of Polarization In Ionic Crystals of the NaCl Type. I. Polarization around a Single Charge in the Rigid Lattice
Authors: Rittner E. S. , Hutner R. A. , Pré F. K. du
Published: January 2005

Previous work is reviewed, and the Mott-Littleton method of treating the rigid lattice case is extended with some modification to higher order approximations. Numerical results are given for their hypothetical monatomic crystal and for NaCl.
The Planar Vibrations of Benzene
Authors: Crawford Bryce L. , Miller Foil A.
Published: January 2005

A normal coordinate treatment has been carried out for the planar vibrations of benzene and its deuterium derivatives. By using the latest assignments of Ingold and co-workers, eighteen of the twenty-six harmonic force constants have been determined.
Internal Rotation I A Product Rule for Cis- and Trans-Isomers
Authors: Bernstein H. J.
Published: January 2005

The assumption of equal force constants in the potential functions of cis- and trans-forms leads to a product rule for the planar vibrations of rotational isomers.

The rotational isomers of symmetrical dichloro- and dibromoethane are trans- and ``gauche.''
Internal Rotation II The Energy Difference between the Rotational Isomers of 1,2-Dichloroethane
Authors: Bernstein H. J.
Published: January 2005

From the variation of the intensities of infra-red bands with temperature the value of ΔH0 for the reaction C2h dichloroethane →C2 dichloroethane is found to be 1250±50 cals. per mole. The probable energy difference between the isomers is 1100±50 cal. per mole. A tentative assignment of all the fundamentals has been made.

Peak intensities and integrated intensities yield the same results within the limits of the experimental error. The ratio of the number of C2 molecules to the number of C2h molecules at room temperature is 0.29.
The Statistical Mechanical Theory of Surface Tension
Authors: Kirkwood John G. , Buff Frank P.
Published: January 2005

A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approximation to the superficial density of molecular pairs, the Lennard-Jones potential and the Eisenstein-Gingrich radial distribution function, the surface tension, surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquid argon at 90°K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolman's quasi-thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature.
The Kinetics of the Rapid Gas Reaction between Ozone and Nitrogen Dioxide
Authors: Johnston Harold S. , Yost Don M.
Published: January 2005

An apparatus has been designed and constructed which will rapidly mix two gaseous reactants, isolate them in a reaction cell, and, by means of light absorption, follow the course of the reaction photoelectrically in one-tenth of a second or less. The output of the photoelectric tube is recorded by a time-exposure photograph of the screen of an oscilloscope.

The kinetics of the fast reaction between ozone and nitrogen dioxide was studied over a tenfold range of concentration of each reactant. The rate law was found to be −d(O3)/dt=k(NO2)(O3)over the entire course of the reaction. From the temperature coefficient of the rate of reaction the energy of activation was found to be 7.0±0.6 kilo-calories per mole. A mechanism is proposed to account for the observations.
Zinc Sulfide Phosphor Constitution and Its Effect on Electron Traps
Authors: Garlick G. F. J. , Wells A. F. , Wilkins M. H. F.
Published: January 2005

The phosphorescence and thermoluminescence of zinc sulfide phosphors are governed by the mechanism of electron trapping in the phosphor crystal lattice. Experiments have been carried out to find the effect of phosphor constitution and method of preparation on the numbers and the energy distribution of electron traps. In order to investigate the traps, use has been made of the thermoluminescence vs. temperature characteristics of the phosphors.

These experiments show that pure zinc sulfide and zinc sulfide activated by silver and manganese possess similar ``shallow'' electron trap configurations after preparation and that these configurations are not markedly dependent on the particular activator. However, the introduction of copper impurity to zinc sulfide causes a marked change in the number and distribution of electron traps and is responsible for the long afterglow of these phosphors. Investigations of the effect of firing temperature and crystal form on the electron traps show that below the blende-wurtzite transition temperature (1020°C) the proportion of deep traps increases with firing temperature but that above this temperature the trap distribution is independent of the firing temperature or of fluxes and excess of sulfur. Experiments attempting to show that these traps were due to stoichiometric excess of zinc gave inconclusive results, but it is clear that the deep electron traps which produce the long afterglow characteristics of zinc sulfide are due both to the presence of copper impurity and to some change produced in the zinc sulfide lattice at high temperature without copper being present.

Other studies have been made of the effect of the mixed crystal proportions in the ZnS–CdS–Cu phosphor system on the electron traps. At high CdS contents some relatively deep electron traps are produced. Measurements of the fluorescence vs. temperature characteristics of the above phosphors show how the phosphor constitution and firing temperature affect the temperature at which the thermal quenching of fluorescence becomes appreciable.
Thermal Diffusion in Hydrogen-Hydrocarbon Mixtures
Authors: Drickamer H. G. , Downey S. L. , Pierce N. C.
Published: January 2005

Thermal diffusion data have been obtained on a series of mixtures of hydrogen plus hydrocarbons. The results indicate that ``collision diameter'' for these unlike molecules is considerably smaller than the mean collision diameter of the pure compounds. This is consistent with the high critical pressure of such mixtures.
The Application of Ultrasonic Waves to the Study of Electrolytic Solutions II. The Detection of the Debye Effect
Authors: Yeager Ernest , Bugosh John , Hovorka Frank , McCarthy John
Published: January 2005

The existence of the alternating potentials which Debye predicted should accompany the passage of ultrasonic waves through an electrolytic solution has been established experimentally by means of a stationary acoustical field. The effect has been shown (i) to depend on velocity variations within the ultrasonic waves, (ii) to be a function of the electrolyte, and (iii) to be independent of concentration for practical purposes in the range 0.005 to 0.0005 molar for uni-univalent electrolytes. These characteristics are in agreement with theoretical considerations.
The C–C Bond Energy in Ethylbenzene
Authors: Szwarc M.
Published: January 2005

The pyrolysis of ethylbenzene in the presence of excess of toluene has been shown to be a unimolecular process, the rate-determining step being C6H5·CH2·CH3→C6H5·CH2·+CH3·.The methyl radicals were removed by a reaction with toluene, yielding CH4 and benzyl radicals, and the quantity of methane obtained was a measure of the extent of the decomposition of ethylbenzene. The energy of activation and the frequency factor were estimated experimentally at 63.2 kcal./mole and 1.0·1013 sec.−1, respectively. Taking the D(C–C)C6H5·C2H5 at 63.2 kcal./mole and using this value in conjunction with the value reported previously for D(C–H)C6H5·CH3 and the relevant thermochemical data, we calculated the D(C–H)CH4 at 102.9 kcal./mole.

The results of the thermal decomposition of ethylbenzene in the absence of toluene have been investigated, but it has been found unsuitable for kinetics studies because of a complicating chain process.

A short discussion on the frequency factors of these unimolecular reactions is given.
An Asymptotic Expression for the Energy Levels of the Asymmetric Rotor. III. Approximation for the Essentially Degenerate Levels of the Rigid Rotor
Authors: Golden S. , Bragg J. K.
Published: January 2005

Formulas are given for an approximation to the energy values of the levels of the asymmetric rotor when the latter are essentially twofold degenerate. The method of arriving at these formulas follows that described recently, in which the energy matrix is examined under conditions where J→∞. In contrast to the latter method, however, the present approximation considers those levels for which (in the limiting symmetric cases) |K| is very nearly equal to J. With these restrictions, the energy matrix of the asymmetric rotor assumes a form that can be related to that which may be obtained from a perturbed harmonic oscillator.
The Rotatory Diffusion Constants of Flexible Molecules
Authors: Riseman Jacob , Kirkwood John G.
Published: January 2005

Using the model and methods of a previous paper, the average components of the rotary diffusion tensor of a flexible molecule are calculated. The results obtained are found to be related to both the intrinsic viscosity and to the translational diffusion constant. In particular the rotatory diffusion constant of the molecule as a whole is shown to be a simple function of the intrinsic viscosity. The theory developed, in conjunction with the theory of intrinsic viscosity and translational diffusion coordinates the result of the various hydrodynamical physical methods used in high polymer research.
Substituted Borazole Spectra: Gain and Loss of Aromatic Character
Authors: Rector C. W. , Schaeffer G. W. , Platt J. R.
Published: January 2005

The far ultraviolet spectra of N-trimethyl, B-trimethyl, and B-trichloroborazole in n-heptane solution are compared with previous spectra of borazole and of the organic analogs, benzene and mesitylene. By N-substitution the negative charge on the boron atoms of the borazole ring is increased, increasing the double-bond character and the spectral resemblance to a benzene derivative. By B-substitution, the opposite effect is produced, increasing the spectral resemblance to a saturated compound. The physical and chemical properties of these borazoles show corresponding behavior.
Absorption Intensities of Ethylenes and Acetylenes in the Vacuum Ultraviolet
Authors: Platt J. R. , Klevens H. B. , Price W. C.
Published: January 2005

The spectra of three octenes, cyclohexene and 2,3-dihydropyrane, and of octyne−1 and −2 were obtained in n-heptane solution to 1700A. Intensity measurements on ethylene vapor to 1550A enable the contribution of the Rydberg bands to be separated from that of the continuum. The f-values in ethylene and the octenes are about 0.30, agreeing with Mulliken and Rieke's theoretical prediction within the experimental uncertainty of about 20 percent. The f-values of the octynes are about the same, but those of cyclohexene and dihydropyrane are about 0.20.
Spectral Resemblances in Azulene and Naphthalene
Authors: Mann D. E. , Platt J. R. , Klevens H. B.
Published: January 2005

The spectrum of the odd-ring compound azulene, C10H8, from 1730A to 7000A, is compared with that of its regular isomer naphthalene from 1600A to 3500A. The 5 band systems found in azulene seem to correspond, with respect to vibrational structure, intensity, and sequence to the 5 found in naphthalene, except that the former are all shifted to lower frequencies. The lowest band is shifted the most, about 17,000 cm−1, and its absorption gives azulene its blue color. This band has quite different properties from those of the lowest band in the blue compound pentacene. The observed energy levels are compared with LCAO predictions of the lowest states in naphthalene (Coulson) and azulene. The qualitative agreement is good.
The Mechanism of the Photo-Chemical Decomposition of Diethyl Ketone
Authors: Dorfman Leon M. , Sheldon Zachary D.
Published: January 2005

The photo-chemical decomposition of gaseous diethyl ketone in light of 3130A has been investigated at 56°C and 120°C over a wide range of absorbed intensities. The quantum yield of butane was found to increase with increasing intensity, while the quantum yield of total C2 hydrocarbons was found to decrease with increasing intensity. On the basis of a kinetic analysis of these data, the proposed free radical mechanism for the decomposition of this ketone is adequately substantiated.

Assuming zero activation energy for the recombination of ethyl radicals to form butane, the activation energy for the disproportionation of ethyl radicals has been determined as E=4.8 kcal./mole, and that for the reaction of an ethyl radical with a diethyl ketone molecule to form ethane has been found to be E=4.1 kcal./mole.
The Metastability of the Lowest Excited Singlet Level of Naphthalene
Authors: Kasha M. , Nauman R. V.
Published: January 2005

The fluorescence lifetime of naphthalene has been determined by direct observation to be on the order of 10−6 sec. The comparatively weak absorption band on the long-wave-length side of the ultraviolet spectrum of naphthalene is thereby established as a separate electronic transition to a metastable level, and as the lowest singlet-singlet transition. This weak absorption band and the fluorescence and phosphorescence bands of naphthalene in rigid glass solution at 77°K are presented. The absorption (Prikhotko) and fluorescence (Obreimov and Shabaldas) spectra of single crystals of naphthalene at 20°K are reinterpreted in terms of the above results; in particular, the lowest singlet-singlet band in the crystal is shown to be the 31060 cm−1 band. An anomalous crystal absorption band at 29945 cm−1 is accounted for in terms of absorption to an excited triplet state. A π-electron energy scheme for naphthalene for the experimentally observed singlet and triplet levels below 50000 cm−1 is given.
Statistical Mechanics of Adsorption. V. Thermodynamics and Heat of Adsorption
Authors: Hill Terrell L.
Published: January 2005

The thermodynamics of an adsorbate on an inert adsorbent is discussed in some detail. Heats of adsorption are given particular attention in an attempt to clarify and extend the available methods in this field. It is found that the true equilibrium ΔH=TΔS of adsorption for adsorbate molecules is given by (∂ lnp/∂T)[open phi]=−ΔH/RT2,where [open phi] is the two-dimensional spreading pressure.

The relation of the work of Rowley and Innes to the present paper is considered.
The Equations of Radioactive Transformation in a Neutron Flux
Authors: Rubinson William
Published: January 2005

The standard equations of radioactive transformation are generalized to include the case where radioactive nuclei are subject to transformation by neutron absorption in addition to spontaneous decay. Opportunity is taken to derive the equations by a simple method which avoids recourse to the formal methods of solving differential equations. A method is pointed out whereby one may write simply by inspection the equation for the activity of a species which is descended from an ancestral species through a chain of any combination of decays and neutron absorptions. Some problems are solved as illustration.
Raman Effect, Infra-Red Absorption, Dielectric Constant, and Electron Diffraction in Relation to Internal Rotation
Authors: Mizushima San-ichiro , Morino Yonezo , Watanabe Itaru , Simanouti Takehiko , Yamaguchi Shigeto
Published: January 2005

The relative intensities of Raman lines of 1,2-dichloroethane were determined in the gaseous state as well as in the liquid state. The result combined with that of the dipole measurement in the gaseous state enabled us to determine the equilibrium isomeric ratio of the trans- and the gauche molecules, which was in good agreement with that obtained from the absorption measurement of infra-red spectra. This ratio could also explain satisfactorily the result of an electron diffraction experiment made by us for the vapor of 1,2-dichloroethane. The statistical entropy of dihalogenoethanes was calculated from the molecular data and was compared with the third law entropy obtained from the thermal measurement. The frequencies of torsional oscillation about the C–C bond as axis were determined by the difference method and were found to be in agreement with the lowest frequencies of the observed Raman spectra.
Motions of Molecules in Condensed Systems: V. Classification of Motions and Selection Rules for Spectra According to Space Symmetry
Authors: Winston Harvey , Halford Ralph S.
Published: January 2005

A classification of the motions of a crystal is made on the basis of space symmetry, with the aid of the Born-Karman boundary conditions. It is shown that the selection rules for fundamentals arising from this classification are the same as those derived by the unit cell analysis of Bhagavantam and Venkatarayudu. A relation between the unit cell and site analyses is investigated which makes it possible to obtain the unit cell results by means of the usually simpler site method. A space symmetry criterion for the appearance of composite transitions is established, and some of the effects expected on the basis of this criterion are discussed. The character tables for space groups are described.
The Quantum Mechanics of Chemical Kinetics of Homogeneous Gas Phase Reactions II. Approximations for Displacement Reaction between an Atom and a Diatomic Molecule
Authors: Golden S. , Peiser A. M.
Published: January 2005

The quantum mechanics of a displacement reaction: AB+C→A+BC, has been considered and the results have been applied to the reaction: H2+Br→H+HBr at 500°K. The potential energy of the reacting system is based upon the London approximation as modified by Eyring and Polanyi. The absolute rate has been found to be a sensitive function of the coulombic energy fraction; when this fraction is taken to be 30 percent, the absolute rate is in essential agreement with the observed value. This agreement can only be regarded as fortuitous, however.

Several results have been derived which are not sensitive to the fraction of coulombic energy and furnish, therefore, a more stringent test of the present formulation. It has been found that the variation of the absolute rate with temperature, as calculated at 500°K, compares favorably with the observed variation. Approximately 95 percent of the rate comes from hydrogen molecules in the first excited vibrational state. The contribution from hydrogen molecules in various rotational states is given. The distribution of the initially formed hydrogen bromide molecules has been found to be representable by a pseudo-canonical distribution function of the rotational quantum number, in which the ``rotational temperature'' is approximately one-half the initial temperature.
The Properties of 86-Second I(136)
Authors: Stanley Charles W. , Katcoff Seymour
Published: January 2005

A short-lived iodine which was discovered by Strassmann and Hahn as a U fission product was shown to have a half-life of 86±1 seconds. It emits 6.5-Mev beta-rays and 2.9-Mev gamma-rays. The fission yields in U235, Pu239, and U233 are 3.1 percent, 1.9 percent, and 1.7 percent, respectively. A mass assignment to 136 has been shown to be the most likely one. The observed 86-sec. I activity does not originate from a Te parent whose half-life is greater than 20 seconds.
Electron Deficient Compounds. II. Relative Energies of ``Half-Bonds''
Authors: Rundle R. E.
Published: January 2005

It is suggested that the tendency to make use of all low energy orbitals is the underlying principle of electron-deficient bonding. Simple theoretical arguments, limited to the special case of two electrons and three orbitals, are given to show that this principle is a direct consequence of quantum-mechanical theories of valence.

Two half-bonds are shown to be of lower energy than a single bond plus an unused low energy orbital in most cases. The tendency to form half-bonds should be most important in symmetrical cases, and particularly where the electronegativities of all atoms involved are equal, e.g., the boron hydrides and H3+.

Certain consequences of the proposal to the fields of organo-metallic compounds, catalysis, and molecular rearrangements are pointed out. It is suggested that at low temperatures complexes may exist between molecules with excess orbitals and molecules with no unshared pairs.
Vibration Frequencies and Binding Forces in Some Silicate Groups
Authors: Matossi Frank
Published: January 2005

Frequency formulas for some atomic groups occurring in silicates (Si2O7, Si3O9 ring, SiO3 chain, SiO2 network) are computed, using simplified force systems, and force constants are calculated. The strong force between the O atoms connecting the SiO4 groups of the Si3O9 ring is especially remarkable. Further observations are necessary to indicate the choice of less simple force systems.
Comparison of Relations between Covalent Bond Order, Energy, and Interatomic Distance for Carbon-Carbon Bonds
Authors: Kavanau J. L.
Published: January 2005

The results given by the relations of Bernstein, Gordy, and the author between interatomic distance and energy and order are compared for carbon-carbon bonds. The predictions of these relations for the benzene and graphite bond orders are compared with the results given by quantum mechanical calculations, while those for the energies are compared with experimental values.
The Heats of Vaporization of Uranium Hexafluoride
Authors: Masi Joseph F.
Published: January 2005

Vaporizations of uranium hexafluoride were carried out in a heavy-wall, nickel-plated calorimeter. Measurements of the heat of vaporization of the solid were made at seven temperatures and of the liquid at four temperatures, covering the range from 4° to 90°C. The apparatus was tested before beginning the measurements by obtaining the heats of vaporization of water at three temperatures.

The scattering of the data on UF6 is about one percent. The measured heats of vaporization have been used to obtain a consistent correlation of the vapor pressures, heat of fusion, and triple point given in the literature. The results are expressed as vapor pressure equations and an equation of state for the saturated vapor. From these equations and the National Bureau of Standards values for the thermodynamic properties of the solid and liquid, the entropies of the ideal gas are calculated and compared with those given in the literature from spectroscopic data and molecular structure.
Magnetic Study of Some Hydrates
Authors: Prasad Mata , Dharmatti S. S. , Kanekar C. R. , Biradar N. S.
Published: January 2005

Magnetic susceptibilities of a number of hydrates have been measured by the Gouy technique. In several hydrates of the same salt it has been found that the deviation in the observed molecular susceptibility from additivity, per molecule of water of crystallization, is greatest in the hydrate containing the least number of molecules of water of crystallization and tends to decrease as the number of molecules of water of hydration increases. A relation has been shown to exist between the heat of hydration per molecule of water of crystallization and the deviation in χm per molecule, in these hydrates. The departure from the additivity rule in hydrates has been explained on the basis of bindings between the molecules of water of crystallization and the anhydrous salt.
The Asymmetric Rotor. VII. Extension of the Calculation of Energy Levels
Authors: Hainer R. M. , Cross Paul C. , King Gilbert W.
Published: January 2005

Various methods of computing the energy levels of the asymmetric rotor are reviewed for values of high angular momentum which are required in the interpretation of infra-red and micro-wave spectra. A table of values of J=11 and 12 is given and over the whole range of asymmetry −1≤κ≤1. Methods of using the Correspondence Principle, Mathieu functions, harmonic oscillator matrices, and power series expansions are discussed, and this survey indicates there is always a region of some degree of asymmetry where the exact value has to be obtained from the rigorous matrix-mechanical formulation. Methods of obtaining energy values for small intervals in κ from existing tables are also discussed.
Diffusional Boundary Value Problems Involving Moving Boundaries, Connected with the Growth of Colloidal Particles
Authors: Reiss Howard , La Mer Victor K.
Published: January 2005

A method is suggested for treating problems of diffusion which involve moving boundaries. This method is applicable when the flux of material through any surface in the diffusion field is considerably greater than the rate of change of concentration on that surface. The method is applied to two problems dealing with the growth of monodispersed aerosols and hydrosols.

The solution of the first of these problems indicates that, in a naphthalene-like aerosol system growing by means of the diffusion of vapor toward sinks (nuclei) which cannot support supersaturation, spontaneous nucleation will not occur if the number density of nuclei exceeds 100/cc.

The solution of the second problem permits the reproduction from theory of several curves due to Zaiser and La Mer which depict the rate of growth of sulfur hydrosols, therefore lending support to the idea that the particles grow by means of a simple diffusion mechanism rather than by a surface catalyzed deposition. The critical supersaturation concentration for sulfur in aqueous solution is c0=4.7×10−6 g/atom/liter,and the diffusion coefficient of S8 is D=2×10−6 cm2/sec.These values are in reasonable agreement with those estimated by independent means, although the diffusion coefficient seems to have about one-half the expected value. This indicates that a unit larger than S8 may be diffusing, e.g., a polythionate.
Note on the Influence of Structure on Internal Pressure in Polymeric Systems
Authors: Flory Paul J.
Published: January 2005

The development of the preceding paper is applied to the calculation of the internal pressure contribution arising from the nature of the polymer structure. A network structure imposes a positive (compressive) internal pressure which increases with the degree of interlinking. In polymers composed of finite molecules the internal pressure should, of course, decrease in proportion to the reciprocal of the molecular weight. A general formula for the dependence of the internal pressure on polymer structure is given which embraces both of these extreme cases and includes also imperfect network structures possessing unattached terminal groups. Magnitudes of the calculated internal pressure contributions are sufficient to alter the specific volumes perceptibly.
Raman Spectrum of Liquid Ethylene and Methane
Authors: Rank D. H. , Shull E. R. , Axford D. W. E.
Published: January 2005

A search was made for the missing frequencies in the Raman spectrum of liquid methane. ν2(e) was found and the harmonic of ν4(f2). Intense plates were obtained of the Raman spectrum of liquid ethylene. The polarizations of the lines in this spectrum were obtained. ω6, the only missing Raman active fundamental, was found in the position predicted by Arnett and Crawford.
The Energy of the Hydrogen Molecule
Authors: Gurnee E. F. , Magee J. L.
Published: January 2005

A simple two-parameter variational function has been used to calculate the energy of normal H2. The first parameter is the usual scale factor; the second parameter is a distance of displacement of the atomic orbitals (see Fig. 1). The best potential energy is obtained as approximately 96 kcal per mole for internuclear separation 1.45 a0. The behavior of the new parameter as a function of internuclear separation is discussed.
The Structure of Uranium Hexafluoride as Determined by the Diffraction of Electrons on the Vapor
Authors: Bauer S. H.
Published: January 2005

The structure of uranium hexafluoride has been redetermined by electron diffraction. Special precautions were taken to eliminate sample contamination; both sector and non-sector photographs were analyzed. Even casual inspection of the photographs and microphotometer traces shows that insofar as this type of measurement is concerned, the structure of UF6 is not a regular octahedron. The model which is in best agreement with the data is a distorted octahedron with three short (1.87A) and three long bonds (2.17A). However, a model with a center of inversion, possessing two short (1.87A), two medium (2.12A), and two long bonds (2.22A) cannot be eliminated.

The disagreement between the structures deduced from various technics is discussed, as are also possible experiments which might be done to resolve these differences.
The Mechanism of the Decomposition of Nitrous Oxide on Zinc Oxide as Catalyst
Authors: Wagner Carl
Published: January 2005

For the decomposition of nitrous oxide on metals and oxides, a tentative mechanism is indicated which involves quasi-free electrons as reactants and adsorbed oxygen ions as intermediate product. This mechanism is in accordance with experimental facts such as retardation by oxygen, a fractional order of the reaction with respect to nitrous oxide in the case of indium oxide as catalyst, and the decrease of the electrical conductivity of zinc oxide due to the presence of nitrous oxide. A mixture of zinc oxide and gallium oxide, however, has about the same catalytic activity as pure zinc oxide, although the electrical conductivity of the mixed catalyst is about fifty times greater than that of pure zinc oxide. This finding can be accounted for by the assumption that the reaction between nitrous oxide and electrons of the catalyst takes place in the vicinity of an adsorbed zinc ion or an anion vacancy.
Determination of the Concentrations of Cation and Anion Vacancies in Solid Potassium Chloride
Authors: Wagner Carl , Hantelmann Paul
Published: January 2005

The mobility of cation vacancies and the equilibrium concentration of cation and anion vacancies in solid potassium chloride are calculated from measurements of the electrical conductivity of pure potassium chloride and solid solutions of strontium chloride in potassium chloride.
Transference Numbers of Solid Potassium Chloride with Strontium Chloride, Potassium Oxide, and Sodium Sulfide as Additives
Authors: Ronge Grete , Wagner Carl
Published: January 2005

The transference number of cations in solid potassium chloride at 600°C has been found to be 0.88 in accordance with previous experiments of Tubandt, Reinhold, and Liebold. Addition of strontium chloride causes increase of the transference number approaching unity. Addition of potassium oxide and sodium sulfide, respectively, lowers somewhat the transference number of cations and accordingly increases the transference number of anions. These results are in accordance with the Schottky disorder model, but the presence of interstitial cations apart from cation and anion vacancies cannot be ruled out.
Equilibrium at Low Pressure in the Reduction of Barium Oxide by Carbon
Authors: Brown Callaway
Published: January 2005

An experimental scheme to investigate the reduction equilibrium of barium oxide by carbon is described and analyzed critically. Exploratory results at 950° support the analysis and indicate equilibrium at carbon monoxide pressures below 100μ with barium vapor pressures in the range 0.1 to 0.3μ. The resulting value for the free energy of formation of barium oxide is −114,000 cal. per mole.
Substituted Ethanes. II. Raman and Infra-Red Spectra of 2,3-Dibromo−2,3-Dimethylbutane and 2,2,3,3-Tetramethylbutane
Authors: Cleveland Forrest F. , Lamport James E. , Mitchell Richard W.
Published: January 2005

Raman displacements and infra-red absorption wave numbers for 2,3-dibromo−2,3-dimethylbutane and 2,2,3,3-tetramethylbutane (hexamethylethane) are reported, together with depolarization factors for the Raman lines and relative intensities for both the Raman lines and the infra-red absorption bands. The spectra were obtained in both benzene and CCl4 solutions and the infra-red measurements covered the region 400–5000 cm−1. The results indicate that both molecules possess a center of symmetry and that the structure is the same in the two solvents. The dipole moment of 1.01 D. obtained by Mizushima, Morino, and Miyagawa for 2,3-dibromo−2,3-dimethylbutane in CCl4 solution may be explained by oscillations of 48° amplitude about the equilibrium trans- position.
Ultrasonic Velocities of Sound in Some Metallic Liquids. Adiabatic and Isothermal Compressibilities of Liquid Metals at Their Melting Points
Authors: Kleppa O. J.
Published: January 2005

The ultrasonic velocities of sound at 12 mc in 12 pure liquid metals at their melting points under atmospheric pressure and in 4 equi-atomic liquid metallic mixtures have been determined by the use of the electronic pulse-circuit technique.

For the pure metals the adiabatic and isothermal compressibilities have been computed. The compressibilities were generally found to be somewhat larger than for the corresponding solids at room temperatures. A calculation of Grüneisen's γ for the liquid metals shows that this quantity, in the case of normal metals, does not change appreciably on going from the solid state at room temperature to the liquid at moderately elevated temperature. These facts support the familiar view that the liquid metals at temperatures not far above their melting points are in a ``solid like'' state, and that equations of state for the solid state may be applicable to such liquids.
An Irregularity in the Solvent Powers of Paraffins
Authors: Hildebrand Joel H.
Published: January 2005

The solubility relations of n-heptane with f-heptane, iodine, sulfur, stannic iodide, and phosphorus are all accounted for within the usual limits of accuracy for regular solution theory by a solubility parameter 8.1 instead of the value 7.45 derived from its energy of vaporization per cc. Solutions of 2,2,4-trimethyl pentane with f-heptane and with iodine are similarly accounted for by the empirical value 7.45 instead of 6.85. Such an adjustment for paraffins is a practical alternative to the treatment used by Simons and Dunlap for the system n-pentane, ``pentforane,'' which they recently reported upon, and is, at the same time, consistent with their assumption that the exceptional behavior of paraffins is to be attributed to an irregularity in their mutual repulsions.
The Infra-Red Spectrum of Acetylene
Authors: Bell E. E. , Nielsen H. H.
Published: January 2005

New measurements of the infra-red absorption spectrum of acetylene between 16 and 2.5μ have established many new bands. A cooling experiment has demonstrated that the central line of the parallel band ν41+ν51 (1328.18 cm−1) belongs to a difference band, 2ν40+ν51—ν41 (1328.46 cm−1). Resolution sufficient to distinguish the center of the fundamental ν3 (3282.5 cm−1) from the combination band ν2+ν41+ν51 (3295.56 cm−1) has been obtained. An interesting Πu—Πg-band, identified as ν1+ν51—ν41, is shown. Frequencies of the infra-red inactive fundamentals are derived and many anharmonic coefficients are evaluated. Diagrams of the absorption regions and tables of the line frequencies are included.
Light Scattering by Concentrated Polymer Solutions
Authors: Debye P. , Bueche A. M.
Published: January 2005

The light scattered by benzene solutions of polystyrene up to a volume fraction of polymer of 0.62 has been measured. The results are compared with what was to be expected on the basis of recent thermodynamic theories for polymer solutions.

This comparison has led to the recognition of a new and rapid method for estimating molecular weights. The method also seems to be a convenient one for obtaining thermodynamic information.
Dodecahedral Octacovalent Bond Orbitals
Authors: Duffey George H.
Published: January 2005

Dodecahedral octacovalent bond orbitals of D2d symmetry are considered. The bond orbitals are divided into two groups which may differ widely in composition, the over-all composition remaining sp3d4. When the average orbital strength is greatest, it equals 2.981 and the orbitals of group one and group two differ in composition and strength. The concept of orbital strength does not allow us to exclude either the dodecahedral or the tetragonal antiprism structure in AB8 when A employs the sp3d4 configuration.
The Magnetic Anisotropy of Manganous Fluoride between 12 and 295°K
Authors: Griffel Maurice , Stout J. W.
Published: January 2005

The magnetic anisotropy of single crystals of MnF2, a typical antiferromagnetic substance, has been measured over the temperature range 12 to 295°K. At temperatures above 100°K the anisotropy is of the order of 0.1 percent of the susceptibility and the greater susceptibility is in the direction of the c axis of the tetragonal crystal. Below 70°K the anisotropy becomes extraordinarily large and the susceptibility in the direction of the c axis is smaller than that perpendicular to this axis. Within the limit of experimental error, the anisotropy was independent of field strength up to 10,000 gauss. From the present measurements, combined with those of previous investigators on the powder susceptibility, the directional susceptibilities parallel and perpendicular to the c axis have been calculated. As the temperature is lowered from 70 to 14°K, the perpendicular susceptibility increases by about 12 percent and the parallel susceptibility approaches zero at zero temperature. These results are discussed in connection with the theory of antiferromagnetism proposed by Van Vleck.
The Interpretation of the Dependence of Luminescent Efficiency on Activator Concentration
Authors: Johnson Peter D. , Williams Ferd E.
Published: January 2005

The previously published analysis (see reference 1) of the dependence of efficiency of substitutionally activated inorganic phosphors on activator concentration is generalized to include a wide variety of inorganic phosphors under various types of excitation. In addition to the optical excitation of the activator, the creation of conduction electrons and excitons, and the transfer of their energy to the luminescent and non-luminescent activator ions and to other impurities and lattice defects are included in the formulation. The dependence of efficiency on activator concentration of ZnF2:Mn under c.r., x-ray, vacuum u.v. and near u.v. has been measured and interpreted on the basis of the theory. Preliminary photo-conductivity measurements clarify the role of the conduction band in the luminescence of ZnF2:Mn. Also the dependence of the efficiency vs. activator concentration of both ZnF2:Mn and KCl:Tl on temperature has been measured and interpreted on the basis of the variation in activation energy for competing radiationless processes with distance between activator ions. In addition, other efficiency vs. activator concentration data previously published by other authors (see reference 8) on a variety of phosphors and at various temperatures can be correlated and explained with the general theory.