bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Theory of the Structure of CH4 and Related Molecules: Part III
Authors: Van Vleck J. H.
Published: November 2004

(1) Use of Johnson's formulas for sp3 levels in conjunction with existing experimental data makes it doubtful whether the 5S state of the carbon atom is only 1.6 volts above the ground state, as often assumed in the literature. (2) A formula is derived for the energy of the ``valence state'' of the C atom, which is a linear combination of sp3 levels wherein the spins are paired with those of attached atoms. This state is characteristic of tetravalent carbon compounds involving four electron pair bonds, and is shown to involve an increase of about 7 volts in the internal energy of the C atom over that in the ground state. (3) Because of this increment, the net or observed bonding energy is less than the gross or true inter-atomic bonding energy. The gross energy per bond is probably greater in CH3 than in CH4 although the reverse is true of the net. (4) A critical comparison is given of the Slater-Pauling theory of directed valence and the nondirectional Heitler-Rumer |theory based on a 5S state of the C atom. The former leads to much firmer bonds. (5) The assumption of electron pairing, made in Part II, is shown to be well warranted in CH4, as it yields an energy value which is very nearly the same as the deepest root of Eyring and colleague's more exact cubic secular equation. (6) The energies of CH4 and 4CH are compared in the light of theory.
Potassium Superoxide and the Three-Electron Bond
Authors: Neuman Edward W.
Published: November 2004

The highest oxide of potassium is shown to be paramagnetic, with a susceptibility corresponding to the formula KO2, the crystals being supposed to contain O2 ions in a 2II state. The electronic structure :O lim ..:⃛O lim ..:− is proposed for the superoxide ion. It is suggested that the substance be called potassium superoxide rather than tetroxide.
The Structure of the Hypophosphite Group as Determined from the Crystal Lattice of Ammonium Hypophosphite
Authors: Zachariasen W. H. , Mooney R. C. L.
Published: November 2004

The crystal structure of ammonium hypophosphite was examined in order to determine the size and shape of the hypophosphite group. The crystals are orthorhombicholohedral with the dimensions of the unit cell; a = 3.98A, b = 7.57A, c = 11.47A. There are 4 molecules NH4(H2PO2) in the cell, and the space group is Acmm(Vh21). The complete structure is given by the following parameter values: 4 N in ±(0¼0), 4 P in ±(u10¼) with 2πu1 = 195° ±5°; 8 O in ±(u20v2) with 2πu2 = 125° ±5° and 2πv2 = 49° ±2°; 8 H in ±(U3v3¼) with 2πu3 = 290° and 2πv3 = 51°; 16 H in ±(xyz). The parameter values for phosphorus and oxygen were determined directly from the observed intensities of reflections, whereas the hydrogen values are based upon reasonable assumptions. The hypophosphite group has the shape of a distorted tetrahedron; two of the tetrahedral corners being occupied by oxygen atoms and the other two by hydrogen atoms. The phosphorus to oxygen distance is 1.51A and the angle between the phosphorus to oxygen bonds 120°. The distance from phosphorus to hydrogen is 1.5A and the angle between the P–H bonds 92°. Each ammonium radical is surrounded by four oxygen atoms at a distance of 2.81A and by four hydrogen atoms at a distance of 3.08A. There is strong indication that the ammonium radical is not rotating, and that hydrogen atoms of the NH4-groups are linked to the surrounding oxygen atoms as well. The hydrogen atoms of the hypophosphite group behave toward ammonium as if they were H— ions.
The Solution of Problems Involving Permutation Degeneracy
Authors: Serber Robert
Published: November 2004

Matrix methods are developed for calculating the energy levels of many electron systems. These methods are based on the intimate relation between the energy matrix and the irreducible representations of the symmetric permutation group. Part I deals with the ``pure matrix method,'' which involves explicit calculation of the matrices representing the permutations. The permutation matrices are given for states of various multiplicities arising from configurations of eight or fewer electrons. From these we obtain a very convenient orthogonal representation of the energy matrix. In particular, for symmetrical polyatomic molecules, it is shown that correct labelling of the orbits leads directly to a partial factorization of the secular determinant. A systematic procedure is given for determining just how this factorization can be achieved. Part II takes up the ``algebraic method,'' which makes use of algebraic relations satisfied by the permutations. Explicit representations of the permutations are not required if this method is employed. The procedure is illustrated by the four elecron problem, including non-orthogonality corrections. The interactions between configurations can also be calculated by the algebraic method. For symmetrical polyatomic molecules, the group of symmetry operators which commute with the Hamiltonian function can be used to obtain the secular equation in a factored form. The factorization is complete in the group theory sense. A number of illustrative examples are worked out, the energy levels of all multiplicities being found for the hexagonal (benzene) configuration, the configuration of eight similar orbits at cube corners, and the body-centered cube. The singlet levels of the tetrahedral (methane) configuration are also given.
``Isotopic Equilibria'' in the Hydrogen-Hydrogen Oxide System
Authors: Crist R. H. , Dalin G. A.
Published: November 2004

Experiments are described in which the distribution of deuterium between hydrogen and water vapor at equilibrium at 800°K is investigated. The equilibrium constants of the reactions necessary to describe the system H2, HD, D2, H2O, HDO and D2O are calculated and the amount of each constituent calculated for various concentrations of deuterium. The distribution of deuterium between the hydrogen and the water is calculated and found to agree with the experimental data.
The Approximations Involved in Calculations of Atomic Interaction and Activation Energies
Authors: Coolidge Albert Sprague , James Hubert M.
Published: November 2004

The assumptions underlying the computation of interaction energy among several atoms, and especially of activation energies, have been analyzed and discussed for the case of small overlapping of the one-electron wave functions involved. Some formal justification has been found for several types of approximation which have hitherto been used without adequate examination. Computations of the energy of several three-electron systems are presented as material illustrating the applicability of some of the assumptions to typical cases. It is concluded that in general any modification of the complete Heitler-London treatment of the system may lead to errors comparable in magnitude to the quantity to be computed. The so-called ``semi-empirical method,'' which involves many such modifications, owes its success to a happy cancellation of errors, and, until some theoretical explanation of this cancellation is found, it must assume the status and responsibilities of a purely empirical method.
Formation of Negative Ions in Gases by Electron Attachment Part I. NH3, CO, NO, HCl and Cl2
Authors: Bradbury Norris E.
Published: November 2004

With the same method and apparatus employed in the study of negative ion formation in O2 by electron attachment, the results have been extended to all the common diatomic gases and NH3. No negative ions are formed in NH3 below an X/p of 7.5; beyond that point they are formed with increasing probability as the energy of the electrons increases. The phenomenon is interpreted as dissociation of the molecule with the formation of NH— at an electronic energy of approximately 3 volts, the NH3 molecule having itself no electron affinity. No negative ions could be formed in CO at the electronic energies available, and the molecule is presumed to have no electron affinity. Negative ions are formed by electron attachment in NO, the probability increasing with decrease in electronic energy. A linear variation in probability of attachment with pressure is also observed in NO which is due to a collision with a pair of NO molecules held together by weak attractive forces. Negative ions are formed in HCl with a probability which increases with increasing electronic energy suggesting that dissociation of the molecule occurs here as well. Similar results are obtained in Cl2 where it has been known that the energy of the attachment process must be more than sufficient to dissociate the molecule. The experiments indicate several types of attachment processes which can occur in gases and the possibilities of energy dissipation in ion formation. In general the most favored process is the carrying off of the energy by a third body involved in the process.
The Infrared Absorption Spectra of Nitrogen Dioxide and Tetroxide
Authors: Harris Louis , King G. W.
Published: November 2004

The absorption spectra from 1 to 4μ of pure NO2–N2O4 mixtures in a long tube were examined with a rocksalt and a quartz spectrometer. Several new bands were discovered from 1.9 to 4μ in the spectra of both NO2 and N2O4. The NO2 bands were analyzed as combinations of two fundamentals. The N2O4 bands were interpreted as combinations and harmonics of reported fundamentals. Three bands of N2O4 lie at shorter wave-lengths than correspond to the work of dissociation into 2 NO2. A study of the symmetry properties shows that only those models where the NO2 groups are joined by the nitrogen atoms would give rise to the observed infrared spectrum. Some features of the spectrum seem to be in favor of the existence of molecules where the NO2 groups do not lie in the same plane.
Dielectric Constant Studies. IV. The Moments of Some Inorganic Compounds
Authors: Malone Mary G. , Ferguson A. L.
Published: November 2004

The moments of some inorganic compounds have been determined, some in more than one solvent and the best values are believed to be: for SbCl3, 3.12; SbBr3, 2.47; SbI3, 1.58; AsI3, 0.96; AsBr3, 1.60; PI3, 0.0; AsF3, 2.65; and LiClO4, 7.84 Debye. The dielectric constant of solid AsF3 was measured and found to be 5.7. The moments of the molecules measured have been calculated from the electronegativity of the elements and compared with the measured values. A fair agreement is found with deviations greatest for molecules of highest polarizability and possessing large moments. The electronegativity values were deduced from the measurements of the hydrogen compounds or from their periodic relationship.
Determination of the Speed of Flames and the Temperature Distribution in a Spherical Bomb from Time-Pressure Explosion Records
Authors: Lewis Bernard , von Elbe Guenther
Published: November 2004

A method has been developed for determining the velocity of flame relative to the mass movement of the gases, in a closed spherical bomb from an analysis of the time-pressure record of the explosion. The speed of the flame can be evaluated at any moment during its progress from the center to the periphery of the bomb, as well as the temperature existing in the unburned phase, the temperature immediately behind the flame front, the temperature gradient from the latter point to the center of the bomb, and the pressure in the bomb at the same moment. Given a certain fraction burned of the total amount of gas, the volume occupied by the products can be determined for three conditions: (1) Before it has expanded against the rest of the unburned gas; (2) after it has expanded; and (3) when combustion is complete and it has been compressed by subsequent burning of gas nearer the periphery. Calculations of flame speeds, temperatures, etc., have been made and tabulated for explosions of mixtures of ozone and oxygen. The speed of flame increases from the center of the bomb to the wall. At the same time the pressure and temperature of the gas about to be burned increases. The temperature gradient in the gas from the center to the wall has been calculated when the combustion is complete. A complete diagrammatic description is given for one explosion. It is shown that the temperature gradient actually existing in the bomb does not affect the specific heat results obtained by the usual method of calculating the final temperature from the maximum pressure by means of the gas law. It is pointed out that the practical coincidence of the pressure curve with the zero line in the first part of the time-pressure record is not due to a time lag between passage of the spark and ignition, but to the small fraction of gas which has burned during this time.
Electron Diffraction by the Oxides of Nitrogen
Authors: Maxwell Louis R. , Mosley V. M. , Deming Lola S.
Published: November 2004

Electron diffraction has been obtained by the transmission of electrons (20–35 kv) through molecular beams of N2O, NO2, N2O4 and N2O5. The molecular structure determinations were made by using the complete electron scattering formula including the incoherent scattering. The results can be summarized as follows: (1) Nitrous oxide; for a linear model the separation of the end atoms was found to be 2.38±0.05A in exact agreement with Wierl's measurement on this structure. Unfortunately it is impracticable to distinguish between models of the form N – O – N and N – N – O. (2) Nitrogen dioxide; no diffraction rings were observed which is to be expected if the molecule is triangular with the N – O distance 1.15 to 1.3A. (3) Nitrogen tetroxide; the presence of one diffraction ring at (1/λ) sin θ/2 = 0.455±0.01 lead to the conclusion that the N – N distance is 1.6 to 1.7A for the model O2N – NO2. No definite angular relationship between the two planes containing the NO2 groups could be determined. (4) Nitrogen pentoxide; again only one diffraction ring was observed. It occurred at a slightly greater angle than for N2O4 giving (1/λ) sin θ/2 = 0.474±0.004. The symmetrical model O2N – O – NO2 with the N – O distance 1.3 to 1.4A gave a calculated interference pattern in best agreement with this result.
Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions
Authors: Kirkwood John G.
Published: November 2004

The electrical contribution to the chemical potential of an ion having an arbitrary charge distribution is calculated with the aid of the Debye-Hückel theory. The calculation is based upon a general solution in polar coordinates of the approximate Debye-Hückel equation, Δψ—κ2ψ=0. In addition, the Born relation between the free energy of solvation of a spherical ion and the dielectric constant of the solvent, is generalized to include ions of arbitrary charge distribution. Application of the theory to a study of the influence of simple electrolytes, and of the dielectric constant of the solvent on the solubilities of the aliphatic amino-acids in alcohol water mixtures, is discussed.
The Inter-Relations of Hydrogen and Deuterium Molecules
Authors: Gould Austin J. , Bleakney Walker , Taylor Hugh S.
Published: November 2004

It has been shown that neither stopcock grease nor water in a Pyrex or soft-glass vessel affect the concentration of hydrogen-deuterium mixtures. Diffusion through palladium gives a concentration of the isotopes which is about that to be expected from an atomic diffusion process. Desorption from charcoal at liquid air temperatures gives the concentration effect to be expected from a diffusion as molecules. Mercury, Pyrex and soft-glass surfaces at room temperature and charcoal at liquid air temperatures do not promote the reaction between hydrogen and deuterium. Chromium oxide and nickel-kieselguhr surfaces promote the reaction between hydrogen and deuterium in the temperature range between — 190° and 110°C. A palladium surface catalyzes the reaction at 270°C. Experimental values have been obtained for the equilibrium constant of the reaction between hydrogen and deuterium from the temperature of liquid air upwards, in accord with theoretical calculations by Urey and Rittenberg based on statistical mechanics.
The Line Absorption Spectrum of Crystalline KCr(SO4)2–12H2O
Authors: Spedding F. H. , Nutting G. C.
Published: November 2004

The line absorption spectrum of chrome alum has been photographed at five temperatures from 85° to 14°K. The variation with temperature of the intensities of certain of these lines suggests the existence of one or more excited lower levels. At 14°K a new group of faint, sharp lines appears near 4500A. A general discussion of the nature of energy levels in solids is presented and the possible energy states which could give rise to the observed lines are examined theoretically.
The Vapor Pressures and Derived Thermal Properties of Hydrogen and Deuterium
Authors: Scott R. B. , Brickwedde F. G. , Urey Harold C. , Wahl M. H.
Published: November 2004

(1) The vapor pressure equations of liquid and solid, normal deuterium were determined by comparison of the vapor pressure of deuterium with that of liquid, normal hydrogen between 13.9° and 20.40°K. The triple and boiling points of deuterium were found to be 18.58° and 23.5°K, respectively. (2) The changes with time in the vapor pressures of liquid hydrogen and liquid deuterium at 20.4°K, resulting from ortho-para conversions, were investigated. The rate of change of the vapor pressure of liquid deuterium resulting from its natural, self-conversion was found to be less than 1/40th of the natural rate of conversion for liquid hydrogen. (3) From the vapor pressure equations of deuterium and an equation of state, its latent heats were deduced by the use of the Clausius-Clapeyron equation. Two equations of state for deuterium were used: (a) the empirically determined equation for hydrogen, and (b) an equation deduced from an equation of state of hydrogen of a form required by the Bose-Einstein statistics by including the effect of mass in such an equation. The first of these is believed to be the better approximation though the latter might be used with little change in results. The vapor pressure equation required by the third law of thermodynamics has been derived and by the use of the Debye theory values of the zero point energies and Debye Θ's are secured. These Θ's which are used to calculate the heat capacities of solid and liquid deuterium at constant pressure are calculated from the vapor pressure data. The difference between Cp and Cv is much greater for solid hydrogen than for solid deuterium indicating a larger coefficient of expansion in the case of hydrogen. This is to be expected because of the larger zero point energy of hydrogen. The heat capacity under saturation pressure of liquid deuterium is considerably less than that of hydrogen. A recalculation of the distillation data of Urey, Brickwedde and Murphy on the natural mixture of H2 and HD shows that they secured approximately the enrichment to be expected from the theory and experimental conditions.
Deviations from Ohm's Law in Weak Electrolytes
Authors: Onsager Lars
Published: November 2004

The effect of an external electric field on the electrolytic dissociation is computed kinetically from the equations for Brownian motion in the combined Coulomb and external fields. The result is an increase of the dissociation constant, by the factor K(X)/K(0) = F(b) = 1+b+(1/3)b2..., where the parameter b is proportional to the absolute value of the field intensity, and inversely proportional to the dielectric constant. In water at 25°, F(b) = F(1) = 2.395 for a field of 723 kilovolt/cm, while in benzene, the same increase of the dissociation constant is obtained for a field of only 21 kilovolt/cm. The theory is quantitatively confirmed by the deviations from Ohm's law which have been observed for solutions of weak electrolytics in water and in benzene. For solutions of salts in acetone, and for solid electrolytes such as glass, mica, celluloid, etc., the observed increments of conductance are smaller than those expected from the theory, but still of the predicted type and order of magnitude. The kinetic constants of dissociation and recombination can be computed separately on the assumption that the recombination proceeds as rapidly as the mutual approach of two ions due to the Coulomb attraction. The derivation is equivalent to that of Langevin, and leads to the same result. In the Langevin case, the coefficient of recombination is independent of the field; that of dissociation is increased by the factor F(b). Slower reactions may occur when a (chemical) rearrangement of the ion pairs is involved. In the most general case, it is necessary to consider the successive reversible reactions ions⇄pairs⇄molecules, where the former takes place with the Langevin velocity; only the reaction rate pairs→ions depends on the field. On the basis of this picture, the saturation phenomena observed in dielectrics are discussed in relation to the field effect.
The Vitreous State
Authors: Hägg Gunnar
Published: November 2004

The tendency of glass forming substances to supercooling is discussed in connection with the existence of large or irregular groups in the melts of such substances. If the size of these groups makes their direct addition to the crystal lattice difficult, and if the forces within them are so strong as to prevent a rapid disintegration of the groups, the melt will tend to supercooling and glass formation. In the inorganic glasses consisting of oxides of metalloids or the corresponding acids or salts, the formation of large or irregular groups is caused by the strong tendency of these metalloids to coordinate oxygen in a definite way. If the number of available oxygen atoms is smaller than necessary for the formation of discrete polyhedral groups with the required coordination, the polyhedra will be linked together sharing oxygen atoms. The resulting groups will delay crystallization and thus cause the formation of glass.
The Structure of Rhombic Sulphur
Authors: Warren B. E. , Burwell J. T.
Published: November 2004

From rotation and oscillation photographs with Mo Kα, rhombic sulphur is found to have the following cell and space group; a = 10.48A, b = 12.92A, c = 24.55A, Z = 128, space group Vh24(Fddd). The structure contains S8 molecules which are symmetrical puckered rings with S–S distance 2.12A and bond angle α = 105°. The atomic coordinates are determined by comparison of calculated amplitudes with visual intensity estimates from oscillation photographs. The relation of rhombic sulphur to the high temperature forms is discussed briefly.
The Infrared Absorption Spectrum of Methyl Deuteride
Authors: Ginsburg Nathan , Barker E. F.
Published: November 2004

The six fundamental vibrational frequencies of methyl deuteride were observed and the fine structure of the bands resolved. The frequencies are v6 = 1156.3, v5 = 1306.8, v4 = 1477.1, v3 = 2205.25, v1 = 2983.0, v2 = 3031.0. From the fine structure of the bands, the moments of inertia are found to be IA=7.166×10−40 g cm2,IC=5.298×10−40 g cm2and the internuclear distances are C–H=1.093×10−8 cm,  H–H=1.785×10−8 cm.From the four previously known frequencies of methane and each of the frequencies of this molecule, the values of the five potential constants are computed. Three of the sets are consistent and agree well with the values found by Dennison and Johnston, but the other three sets have either negative or imaginary values. The frequencies from which these are calculated are the ones which take part in a resonance interaction which was not included in the theory. From the observed spacings of the zero branches of the perpendicular bands, extreme ranges of the rotation-vibration interaction factors are computed. An overtone, 2v4 = 2923, was also observed as were three frequencies of the molecule CH2D2, at 1036.0, 1090.5, and 1235.5 cm—1.
The Relation Between the Internuclear Distances and Force Constants of Molecules and Its Application to Polyatomic Molecules
Authors: Badger Richard M.
Published: November 2004

The relation between the internuclear distances and force constants found for diatomic molecules is discussed, and is shown to carry over to polyatomic molecules. It is shown that internuclear distances of polyatomic molecules can be predicted from vibrational data alone, with considerable accuracy.
Ultraviolet Absorption of Mixtures of NO, NO2 and H2O
Authors: Melvin Eugene H. , Wulf Oliver R.
Published: November 2004

In considerable amounts of NO containing small amounts of NO2 a continuous absorption occurs in the ultraviolet, obscuring both the absorption of NO and that portion of the absorption of NO2 which lies below 2500A. The behavior of this absorption with respect to temperature and the partial pressures of the constituents is rather convincing evidence that it is due to N2O3. When very small amounts of water are also present a group of bands occurs in the near ultraviolet, lying in the same region but not resembling the longer wave-length NO2 absorption. These bands appear diffuse under low dispersion but possess an ordered arrangement. With increase of temperature the intensity of the bands decreases rapidly. They begin in the vicinity of 3850A, extending to shorter wavelengths. The first members are broader and more diffuse than those that follow, indicating a predissociation process in the carrier, which is probably HONO.
The Group Relation Between the Mulliken and Slater-Pauling Theories of Valence
Authors: Van Vleck J. H.
Published: November 2004

By means of the group theory of characters, it is shown that there is an intimate relation between Mulliken's molecular orbitals and the Slater-Pauling directed wave functions. One can pass from the former to the latter by making a simple transformation from an irreducible to a reducible representation. Consequently the same formal valence rules are usually given by either method, and one can understand generally why wave functions of the central atom which are nonbonding in Mulliken's procedure are likewise never employed in constructing Pauling's ``hybridized'' linear combinations.
Valence Strength and the Magnetism of Complex Salts
Authors: Van Vleck J. H.
Published: November 2004

Certain complex salts, notably ferro- and ferricyanides, have susceptibilities much lower than those predicted by the Bose-Stoner ``spin only'' formula. The first interpretation was that given by Pauling on the basis of (I) directed wave functions. In the present paper it is shown that alternative explanations are possible with (II) the crystalline potential model of Schlapp and Penney, or with (III) Mulliken's method of molecular orbitals. In any of the theories, the interatomic forces, if sufficiently large, will disrupt the Russell-Saunders coupling, and make the deepest state have a smaller spin, and hence smaller susceptibility, than that given by the Hund rule. This situation is not to be confused with that in normal paramagnetic salts, such as sulphates or fluorides, where only the spin-orbit coupling is destroyed. The similarity of the predictions with all three theories is comforting, since any one method in valence usually involves rather questionable approximations. Because of this similarity, a preference between the theories cannot be established merely from ability to interpret the anomalously low magnetism of the cyanides. Covalent bonds, as in cyanides, seem to be more effective in suppressing magnetism than are ionic ones, as in fluorides, but so far the evidence to this effect is empirical rather than theoretical.
Symmetry Considerations Concerning the Splitting of Vibration-Rotation Levels in Polyatomic Molecules
Authors: Wilson E. Bright
Published: November 2004

The interaction of rotation and vibration and perhaps other effects may split degenerate vibration-rotation energy levels of symmetrical polyatomic molecules into a number of components. The permutation symmetry of molecules containing several identical atoms provides certain restrictions on this splitting. This paper discusses the maximum number of fine-structure components, their quantum weights when nuclear spins are taken into account, and the selection rule for transitions. All arguments are based solely on symmetry considerations so that no estimate of the magnitude of the splitting is given.
The Activated Complex in Chemical Reactions
Authors: Eyring Henry
Published: November 2004

The calculation of absolute reaction rates is formulated in terms of quantities which are available from the potential surfaces which can be constructed at the present time. The probability of the activated state is calculated using ordinary statistical mechanics. This probability multiplied by the rate of decomposition gives the specific rate of reaction. The occurrence of quantized vibrations in the activated complex, in degrees of freedom which are unquantized in the original molecules, leads to relative reaction rates for isotopes quite different from the rates predicted using simple kinetic theory. The necessary conditions for the general statistical treatment to reduce to the usual kinetic treatment are given.
Thermodynamic Functions of Tetramethylmethane
Authors: Kassel Louis S.
Published: November 2004

The Q-sum corresponding to La Coste's eigenvalues for the rotational levels of tetramethylmethane has been expressed by the usual asymptotic expansion. The relatively large coupling terms between the various rotations cancel almost exactly in the Q-sum, so that the thermodynamic functions are scarcely affected by the coupling.
Anomalous Pressures and Vibrations in Gas Explosions. Determination of the Dissociation Energy 2H2O⇌2OH+H2
Authors: Lewis Bernard , von Elbe Guenther
Published: November 2004

Using thermodynamic functions of gases derived from band spectra, calculations have been made of theoretical explosion pressures in mixtures of hydrogen and oxygen containing various inert gases which are compared with explosion pressures observed experimentally by different investigators. Details of methods of calculation are given. In carefully dried mixtures of hydrogen and oxygen with excess hydrogen, the observed pressures are too low. This effect is eliminated by the addition of small amounts of water vapor to the original mixture which, according to an hypothesis advanced by Wohl and von Elbe, quenches the luminescence from OH radicals formed in the flame front. In mixtures containing excess oxygen or nitrogen the observed pressures are too high. The existence of a lag in the excitation of the vibrational energy levels of oxygen and nitrogen during the explosion period, as advanced by Wohl and Magat, is offered as explanation. The excitation lag is greater in oxygen than in nitrogen. Explosions of mixtures of gaseous ozone diluted with oxygen do not show this effect, even though the explosion time for approximately the same explosion temperature hardly differs from that of a hydrogen-oxygen explosion which shows the excitation lag. This is explained on the assumption that there is no appreciable lag in the transfer of vibrational energy between like molecules. A similar excitation lag apparently does not exist in H2O and H2. The phenomenon of time-variable heat capacities within the duration of an explosion may be used to explain the intense audible vibrations observed by the authors and others on exploding slow burning lean mixtures of hydrogen with air or oxygen within a certain concentration range. The possible bearing of this effect on the phenomenon of engine knock is mentioned. Explosions were made of mixtures of hydrogen and oxygen with helium as inert gas, which are free from both anomalous effects mentioned above and the energy of dissociation of the reaction 2H2O⇌2OH+H2 was calculated from the data obtained with the aid of accurate thermodynamic functions of the gases involved. The average of the results of six explosions was found to be 126,000±2000 calories per 2 moles of H2O. From this value one obtains H2O⇌H+OH−(114,400±1000) caloriesOH⇌H+O  −(104,160±1000) calories.
An Experimental Investigation of the Effect of Pressure on Phase Equilibria of Sodium Tungstate and of Related Thermodynamic Properties
Authors: Goranson R. W. , Kracek F. C.
Published: November 2004

In order to clarify some uncertainties concerning the physical properties of sodium tungstate the effect of pressure on phase equilibria to 1000 bars, the heats of inversion and of melting, and the specific volume (density) at 30° were determined. Sodium tungstate is trimorphous at atmospheric pressure, form I being stable from 695.5° (melting point) to 588.8°, form II stable from 588.8° to just below 587.6°, and form III stable below this temperature. The I⇌II inversion is estimated to take place at 588.8° with a heat change of 14 joules/gram but no volume change (independent of pressure). Because of the large amount of undercooling in the I→III inversion, the II⇌I transition could be obtained metastably to 613 bars. The III⇌I inversion takes place promptly and reproducibly on heating but not so on cooling, the temperature change being dependent in large measure on the past history of the charge. Heating curve values lead to the expression t = 588.8+0.025(p — 40) with a heat change of 105 joules/gram and volume change of 0.035 cm3/gram. The triple point lies at t = 588.8° and p = 40 to 80 bars. The II⇌III inversion is very similar in behavior to the I⇌III inversion; here t = 587.6+0.029 p on the heating curve. In order to represent specific volume as a function of temperature from 20° to 1300° the data of Jaeger and of Austin were also utilized. The published density of sodium tungstate was found to be in error and therefore a redetermination was made. The value obtained by us, 5.13±0.01, is 20 percent higher than that given by F. W. Clarke (J. L. Davis). The low-temperature modification expands from 0.1950 cm3/gram at 30° to 0.2032 cm3/gram at 587.6°. The salt inverts at this temperature, attaining the volume 0.2382 cm3/gram, and finally, it again increases in volume at the melting point, 695.5°, to 0.2565 cm3/gram.
The Statistical Weights of the Rotational Levels of Polyatomic Molecules, Including Methane, Ammonia, Benzene, Cyclopropane and Ethylene
Authors: Wilson E. Bright
Published: November 2004

A general method is described for calculating the statistical weights (degeneracies) of the energy levels of polyatomic molecules. Wave functions for a molecule are assumed to be expressible as linear combinations of products of the electronic, vibrational, rotational and nuclear spin functions. By using standard methods of group theory, the number of linear combinations of these products are found having the correct symmetry with respect to those permutations of identical atoms which are equivalent to rotations of the molecule. It is not necessary to find the combinations themselves. The molecules CH4, CD4, CH3D, CHD3, CH2D2, CH3X, CD3X, NH3, ND3, C6H6, C3H6 and C2H2 are treated. In addition noncombining species in polyatomic molecules and the splitting of energy levels due to the multiplicity of equilibrium configurations are discussed. Tables of statistical weights are given for the above molecules which could be used to interpret alternating intensities in rotation-vibration spectra or for more exact calculations of thermodynamic quantities than are usually made.
Electronic Structures of Polyatomic Molecules and Valence VI. On the Method of Molecular Orbitals
Authors: Mulliken Robert S.
Published: November 2004

The use of the method of nonlocalized molecular orbitals in building up a conceptual scheme or qualitative theoretical framework into which empirical data (chemical and spectroscopic) can be fitted, is emphasized. This should be distinguished from the use of the method, often with rough ``LCAO'' approximations (linear combinations of atomic orbitals), in semiquantitative calculations.
Molecular Constants and Potential Energy Curves for Diatomic Molecules
Authors: Huggins Maurice L.
Published: November 2004

By using the function U = Ce—a(r—re) — C′e—a′(r—re) with C = 10—12e—a(re—r12), and taking a = 6.0 × 108 cm—1, r12 values calculated from the band spectrum constants are nearly the same (1.46A) for all except highly excited states of all diatomic molecules containing only elements in the first row of the periodic table and having 12 or more electrons. This indicates that the repulsive term is nearly the same in all of these cases. This relation enables one to calculate, from experimental values of two of the molecular constants (e.g., ωe and ωexe) the magnitudes of others (e.g., re, Be and α). Calculated values of ωeye and ωeze are invariably small but not zero. The dissociation energy is (empirically) about 0.8 (C′ — C), calculated using a = 4.0 × 108 cm—1.
Electronic Structures of Polyatomic Molecules. IX. Methane, Ethane, Ethylene, Acetylene
Authors: Mulliken Robert S.
Published: November 2004

Electron configurations for the normal states of C2H6, C2H4, and C2H2 are given, and are used in interpreting observed ionization potentials. Excited orbitals of CH4 and the others are also discussed and tentative interpretations given for the ultraviolet spectra. ``Reduced'' interatomic distances are studied as a measure of overlapping and resonance of orbitals of different atoms or radicals.
The Absorption Spectrum of Diacetylene in the Near Ultraviolet
Authors: Woo Sho-Chow , Chu T. C.
Published: November 2004

The absorption spectrum of diacetylene gas was investigated down to λ1900A. In the region λλ2860–1900A more than eighty bands were found. Some regularities in the spectrum and the similarity with the cyanogen ultraviolet absorption spectrum are described. Resemblance between the diacetylene and cyanogen molecules is briefly discussed.
The Polarizability and Related Properties of Molecular Hydrogen and the Diatomic Hydrogen Ion
Authors: Hirschfelder J. O.
Published: November 2004

The polarizability of molecular hydrogen is calculated from both the Rosen and the Wang eigenfunctions by the variational method. The eigenfunctions of the perturbed molecule contain two parameters which are adjusted to give the molecule a minimum energy. The Rosen eigenfunction leads to a parallel polarizability 7.5×10—25 cm3 and a perpendicular polarizability 7.4×10—25 cm3. The Wang eigenfunction gives similar results. When only one adjustable parameter is used in the variational method, the formula for the polarizability is α=8(q12¯+q1q2¯)2a03 where q1 and q2 are the coordinates of electrons 1 and 2 in the direction of the applied electric field and a0 is the radius of the first Bohr orbit of atomic hydrogen. The magnetic susceptibility and the mean square dimensions of the hydrogen molecule are computed. It is found that the Kirkwood formula is applicable to the diatomic hydrogen ion and polarizabilities are obtained for many internuclear separations using the Guillemin and Zener eigenfunction.
Dielectric Investigations on Nitromethane and Chloropicrin
Authors: Smyth C. P. , Walls W. S.
Published: November 2004

The dielectric constants and densities of dilute solutions of nitromethane in heptane and of chloropicrin in heptane and in benzene have been measured and used to calculate the dipole moments of the solute molecules. The values thus calculated are considerably lower than those previously obtained in the gaseous state and are not well represented by the empirical equation of Müller. Measurement of the dielectric constant of pure liquid and solid nitromethane fails to show the existence of molecular rotation in the solid state. It is concluded, therefore, that the heavier molecule of chloropicrin does not rotate in the crystal.
The Electronic Structure of Diamond
Authors: Kimball George E.
Published: November 2004

The method of Wigner, Seitz and Slater has been applied to the determination of the electronic structure of diamond. It is found that the energy levels of the carbon atom are broadened into bands similar to the energy bands in metals. The 2s level of the atom splits into two bands, and the 2p level into six bands. The two 2s bands are completely filled by electrons and the two lowest of the 2p bands. The lowest unfilled band has a much higher energy than the highest filled band. The lack of electrical conductivity is explained and other properties of the diamond are discussed.
Electronic Structures of Molecules XII. Electroaffinity and Molecular Orbitals, Polyatomic Applications
Authors: Mulliken Robert S.
Published: November 2004

The use of electroaffinity data in the approximate estimation of the polarity coefficients of molecular orbitals and of the effective charges on atoms in polyatomic molecules is illustrated by application and extension of the results of XI of this series. Applications are made especially to CH4, CX4 and H2O, also to CH3X, NH4+, ClO4—, etc. Electronic structures are given first using localized, later using nonlocalized molecular orbitals. Comparisons are also made with Slater-Pauling electron configurations. Among tetrahedral molecules RA4, the homopolar part of the valence is shown to be in some cases nearly all s, in others nearly all p valence; in others both; and a varying part of the valence is heteropolar. Consideration of these facts suggests that the special stability of the tetrahedral type RA4 should be attributed rather to close packing associated with coordination number four than to special properties of the mixture of s and p valence.
Diffusion and reaction–diffusion in fast cellular flows
Authors: Pomeau Yves
Published: November 2004

Cellular structures, as the rolls generated by Rayleigh–Bénard instability, have always been an important topic in nonlinear science. The diffusion of a passive scalar in a given steady cellular flow becomes an interesting question in the limit of a large Péclet number, often realistic. The main result there is that the effective diffusion is somewhere in between the molecular diffusion and the “turbulent” diffusion. A new added twist to this is the reaction–diffusion case, where the front speed is the laminar propagation velocity (without flow) times the Péclet number to the power 1/4. I refine this last result and give the behavior of the prefactor in the Zel’dovich limit of a narrow reaction zone.
Dislocation dynamics in Rayleigh–Bénard convection
Authors: Walter Th. , Pesch W. , Bodenschatz E.
Published: November 2004

Theoretical results on the dynamics of dislocations in Rayleigh–Bénard convection are reported both for a Swift–Hohenberg model and the Oberbeck–Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven by the superposition of two independent contributions: (i) the Peach–Koehler force and (ii) an advection force on the dislocation core by its self-generated mean flow. Their competition allows to explain the experimentally observed bound dislocation pairs.
On propagation failure in one- and two-dimensional excitable media
Authors: Gottwald Georg A. , Kramer Lorenz
Published: November 2004

We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity, and scaling behavior. The results are compared with numerical simulations and show good agreement.
Nonlinear Hall effect for materials with weak thermoelectric power coefficients: Preliminary comparisons between theoretical results of the thermodynamic field theory and experimental data
Authors: Sonnino Giorgio , Peeters Philippe
Published: November 2004

This paper forms a part of a series of manuscripts which we intend to submit for publication in the near future, aiming to test the validity of the thermodynamic field theory (TFT), previously formulated, comparing the theoretical results with experimental data. In this particular case, we shall analyze the Hall effect. As known, when a magnetic field is applied at right angles to the direction of an electric current or a thermal gradient, galvano- and thermomagnetic effects appear in the material. In this paper, we shall show that if we study these effects in nonlinear regime, the TFT foresees an interesting effect: the nonlinear Hall effect. This prediction is herein submitted to experimental verifications. In this paper, we shall analyze this effect studying materials with weak thermoelectric power coefficients. We shall show the agreement between the theoretical predictions of the TFT and experiments. Experimental curves related to the nonlinear Hall effect allow us to determine the order of magnitude of the constant χ introduced in the TFT.
Anomalous inhibition of electron transport in laser–matter interaction at subrelativistic intensities
Authors: Kemp A. J. , Sentoku Y. , Cowan T. , Fuchs J. , Ruhl H.
Published: November 2004

Electron transport in femtosecond laser-irradiated solid targets is investigated by means of one-dimensional particle-in-cell simulations that include a model of collisional ionization, binary collisions and field ionization, while treating ions as individual particles. In particular, heat and particle fluxes in conductor and insulator targets are compared at the onset of relativistic laser intensities, i.e., at I=1017 W/cm2. Simulations show that fast electrons generate a longitudinal electric field of the order 1011 V/m in the bulk material that acts to inhibit heat flux in insulators, while the electric fields observed in metals are weaker and electrons penetrate deeper into the target. The bulk heat transport is found to be similar in both materials and mainly Spitzer-like, with a noticeable contribution by fast electrons.
Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation
Authors: Huepe Cristián , Riecke Hermann , Daniels Karen E. , Bodenschatz Eberhard
Published: November 2004

For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg–Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space–time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions.
Potential distribution of a nonuniformly charged ellipsoid
Authors: Kiwamoto Y. , Aoki J. , Soga Y.
Published: November 2004

A convenient formula is obtained for fast calculation of the three-dimensional potential distribution associated with a spatially varying charge-density distribution by reconstructing it as a superposed set of nested spheroidal shells. It is useful for experimental analyses of near-equilibrium states of non-neutral plasmas and for quick evaluation of the gravity field associated with stellar mass distributions.
How much information can one store in a nonequilibrium medium?
Authors: Coullet P. , Toniolo C. , Tresser C.
Published: November 2004

It has recently been emphasized again that the very existence of stationary stable localized structures with short-range interactions might allow one to store information in nonequilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and nonstorable information. This leads us to introduce a measure of the long-term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).