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Volume 26, Issue 3, 01 March 1957

Comparison of Methods for Computing Bond Orders and Electron Densities
View Description Hide DescriptionThe molecular orbital energy levels, charge distributions, and mobile bond orders for o‐, m‐, and p‐toluidine in the ground state have been evaluated by three procedures: (1) the simple semiempirical LCAO with neglect of overlap; (2) the semiempirical LCAO method with one cycle of self‐consistency iteration; (3) the semiempirical LCAO with inclusion of overlap integrals. It is observed that all three methods give closely similar values for the bond orders and charge distribution, and it is thus concluded that the simple method is as adequate to obtain these quantities as any of the refined methods. The dependency on the nitrogen Coulomb parameter of the total pi‐electron energy, of the energy of highest occupied orbital, of the charge distribution, and of the dipole moment for o‐toluidine are reported and compared with the first‐order perturbation predictions. These calculations were accomplished on the Oak Ridge electronic computer, ORACLE.

New Approach to the Quantum‐Mechanical Analysis of the Electronic Structures of Molecules. The Method of Deformed Atoms in Molecules
View Description Hide DescriptionA modification of Moffit's method of atoms in molecules is here proposed. In this treatment, the modified atomic functions X are introduced, which are made up from the exact eigenfunctions of atoms modified by correction factors so as to take account of the deformation of atoms in molecules. The advantage of these basic functions X is as follows. Firstly, the difficulty caused by the correlation energy in atoms can be removed by the use of the experimental atomic term values just as in Moffitt's method. Secondly, the common effective charges for neutral and ionic structures can be applied for the convenience of calculating the interaction operators, which sometimes produces serious errors in Moffitt's method. Moreover the improvement on the original Heitler‐London treatment—corresponding to Wang's or Weinbaum's work for the hydrogen molecule—can be expected. Then, it is discussed how to determine these modified atomic functions in order that the results appertain to the good range in spite of the rather simple calculation.
The energy loss of atoms in molecules, induced by the deformation, is corrected, and the interatomic interaction energy is calculated by the use of the approximate functions composed of the orbital functions, where the molecular orbital method can be utilized for saving the difficulty of the higher order permutations. Then the unsatisfactory results, obtained in the calculation of Li_{2} by utilizing the common effective charges in Moffitt's method, are improved.

Application of the Method of Deformed Atoms in Molecules to the Hydrogen Molecule
View Description Hide DescriptionThe method of deformed atoms in molecules, which has been proposed in the preceding paper, is applied to the hydrogen molecule. Two structures, the neutral and ionic ones, are considered. It is assumed that the best approximate functions are made up from the hydrogen‐like functions, and favorable correction factors are sought so as to bring about the results appertaining to the good range. Energy drops of 1.5∼1.7 ev are then obtained, which are satisfactory results as compared with that of 0.16 ev in Moffitt's method. Discussion is given about the function of the ionic term, in which the axial correlation is taken into account.

Studies in Nonequilibrium Rate Processes. I. The Relaxation of a System of Harmonic Oscillators
View Description Hide DescriptionAs a part of an investigation of nonequilibrium phenomena in chemical kinetics a theoretical study has been made of the collisional and radiative relaxation of a system of harmonic oscillators contained in a constant temperature heat bath and prepared initially in a vibrational nonequilibrium distribution. An exact solution has been obtained for the general relaxation equation applicable to this system and expressions have been derived for the relaxation of initial Boltzmann distributions, Poisson distributions, and δ‐function distributions as well as for the relaxation of the moments of the distributions. Using the latter result, explicit expressions are given for the relaxation of the internal energy of the system of oscillators and for the time dependence of the dispersion of the distributions.

Effects of Pressure on Ultrasonic Relaxation in Liquids
View Description Hide DescriptionMeasurements of sound absorption as a function of pressure in carbon disulfide and glycerol indicate that the relaxationeffects causing the compressional losses in these liquids react differently to pressure changes. In CS_{2} the relaxation frequency increased with increasing pressure. In glycerol the relaxation frequency dropped as the pressure was increased. These results are consistent with the view that different relaxation mechanisms exist in associated and nonassociated liquids. The direction of the pressure changes in each case is in accord with the view that thermal relaxation is the cause of compressional loss in nonassociated liquids and that structural relaxation is the predominant factor in associated liquids.
A detailed study of the thermal relaxationeffects in CS_{2} showed that the variations in relaxation frequency with pressure could not be adequately explained by Kittel's theory of thermal relaxation in liquids.
Theoretical considerations of the relaxational part of the specific heat indicated that it should be only slightly pressure dependent.

Theory of Ultrasonic Thermal Relaxation Times in Liquids
View Description Hide DescriptionThe theory of thermal relaxation phenomena in liquids is considered from the standpoint that the mechanism of energy transfer in the liquid is the same as in a gas. This would mean that binary collisions and not cooperative action of the molecules are important. The data on ultrasonic relaxation in CS_{2} is considered. It is found that values predicted by use of the cell model, proposed for liquids and dense gases, in combination with binary collision theory give values for the pressure and temperature dependence of ultrasonic relaxation times which are in good agreement with experiment. Furthermore excellent agreement is found between the values of the probability of energy transfer per collision found in the liquid and gaseous CS_{2}. It also appears that the Schwarz‐Herzfeld theory which has been applied to gases can also be applied to liquids and dense gases. It is concluded that the mechanism of energy transfer in thermal relaxation is not affected by the change in state from gas to liquid.

On the Application of the Molecular Orbital Method to the Spectra of Substituted Aromatic Hydrocarbons
View Description Hide DescriptionThe MO theory of the spectra of substituted hydrocarbons is presented in rather general terms, with careful emphasis on the precautions to be observed in introducing the inevitable approximations. Previous treatments of the problem, notably by Sklar, Herzfeld, and Matsen, are then examined. Satisfactory calculaof energy‐level shifts are considered to require closer attention to the definition and dissection of the perturbed Hamiltonian. The most interesting intensity effects concern the enhancement of weak transitions: here earlier treatments do not satisfy the requirements of orthonormality of the perturbed MOs, and unjustifiably neglect interactions with intense transitions. The consequences of neglecting overlap in these calculations are discussed in an appendix.

Experimental Determinations of Charge Transfer Cross Sections and Secondary Electron Emission by Ion Bombardment
View Description Hide DescriptionThe method utilized by the authors for determining charge transfer cross sections has been improved and applied to symmetric and unsymmetric reactions involving the inert gases, N_{2}, H_{2}, CH_{4}, C_{2}H_{4}, C_{2}H_{6}, and C_{3}H_{8}. The cross sections were found to be about 20% higher than the values previously reported. The discrepancy can be explained by the fact that in previous experiments cross sections were determined from net chargemeasurements without taking full account of the secondary electrons impinging on the plate where the charge transfer ions were collected.
As expected from adiabatic hypothesis, the reactions involving mixtures of gases having nearly equal ionization potentials were found to have maximum cross sections for low‐energy ions. The interaction distances were calculated from the observed ion energy for which the cross sections are a maximum.
The method described here can be utilized to determine the secondary electron emission from a metal surface due to ion bombardment. Such determination has been made for a brass surface. Relating the variation of emission with the ion mass and energy, it is found that the emission varies inversely as the square root of the ion mass.

Vibration Spectrum and Heat Capacity of a Chain Polymer Crystal
View Description Hide DescriptionThe Born‐von Karman model for a chain polymer crystal previously studied by Stockmayer and Hecht is re‐examined using only analytic approximations rather than numerical methods. The analytic approach brings out many peculiar properties of the chain polymermodel that did not appear in the numerical treatment.
One branch of the frequency distribution g(v) is shown to be proportional to v ^{2} for the smallest values of v, approximately proportional to for slightly larger v, to v ^{½} for still larger v and to v ^{—½} in still a fourth range of small values of v. An accurate graph of g(v) is constructed for the entire range of frequencies using values of the force constants suggested by Stockmayer and Hecht. g(v) is shown to have approximate singularities of a type not anticipated by van Hove in his broad treatment of singularities for general systems. This anomalous behavior results from having strong valence forces resisting the bending of bond angles. A classification and description of various kinds of singularities that may arise for systems with strong valence forces are given in an appendix.

Theoretical Investigations on the Light Scattering of Colloidal Spheres. I. The Specific Turbidity
View Description Hide DescriptionScattering cross sections, scattering coefficients and specific turbidities are calculated from the Mie equations for α = 0.2(0.2)7.0(1)15 and m = 1.05(0.05)1.30; and, in addition, for α = 22(2)32; 39(1)41 and m = 1.05, for α = 16(1)21 and m = 1.10, for α = 7.2(0.2)15.2 and m = 1.20. Thus, the calculations cover virtually all dispersed systems of ultramicroscopic or small microscopic nonabsorbing spherical particles dispersed in a liquid. The effect of α and m upon these functions is discussed and a few approximating equations are given and tested for the limit of α→∞. The most important features of the Mie theory are briefly discussed and compared with those of alternate approximating theories.

Herzberg Oxygen Bands in ``Air'' Afterglows and the Night Airglow
View Description Hide DescriptionThe ultraviolet A ^{3}Σ_{ u } ^{+}—X ^{3}Σ_{ g } ^{—} oxygen bands have been observed in emission from greenish‐white ``air'' afterglows containing 95–98% nitrogen and 2% to 5% oxygen. The afterglows were excited by an electrodeless rf oscillator and examined with a grating spectrograph having an f/2 camera and a dispersion of 30 A/mm. The mechanism of excitation of these bands in the afterglow may be either the reaction N+O_{3}→NO+O_{2} or the reaction N+NO_{2}→N_{2}+O_{2}. A comparison of the afterglow spectrogram with an ultraviolet night airglow spectrogram shows that bands arising from higher vibrational levels are more intense in the airglow than in the afterglow. Collisional de‐excitation can account for the lower vibrational temperature in the laboratory. The atomic nitrogen‐ozone reaction also may occur in the chemosphere between 60 and 90 km and may contribute to the excitation of the night airglow Herzberg bands. The atomic nitrogen at this level could come from daylight predissociation of NO and N_{2} and from the twilight dissociative recombination of ionized NO.

Density of Liquid He^{4}
View Description Hide DescriptionThe density of He^{4} under its own vapor pressure has been measured between 1.2°K and 4.4°K by a direct method. The results are given in smoothed tabular form and are compared with the results of previous measurements. An attempt has been made to derive a usable value for the critical density from the liquid and vapor densities at lower temperatures.

Sound Dispersion in Halo‐Methane Mixtures
View Description Hide DescriptionResults of studies of the dispersion of ultrasound in mixtures of CHClF_{2} in CF_{4} and of CHCl_{2}F in CClF_{3} at various concentrations are presented. In none of the eight mixtures studied is there evidence of multiple dispersion; each mixture exhibited a single relaxation time which falls between the relaxation times of the pure constituents. A simple method of averaging the various quantities entering into the prediction of collision lifetimes in the pure constituents is presented which yields lifetimes for the mixtures nearly matching those found by experiment.

Direct Correlation Functions for Argon
View Description Hide DescriptionDirect correlation functions as defined in the Ornstein‐Zernike liquid model have been calculated from the argon x‐ray scattering data corresponding to several points on the liquid‐vapor transition curve. Graphs of these direct correlation functions are presented along with an integral check on their general validity. It is concluded these correlation functions derived from the x‐ray scattering data are a reasonable representation of these functions.

Experiments on the Polarization and Decay of Electrets
View Description Hide DescriptionExperiments have been performed to test implications of a two‐charge theory of electrets. It was found that the persistent volume polarization of a number of dielectrics can be expressed by analytical functions which are linear in the applied field and exponential in time. The linear superposition of the effects of homocharge and heterocharge is demonstrated for some dielectrics and is shown to be violated for another, Lucite. The heterocharge and homocharge are demonstrated to be different but interacting entities, their interaction being given by the static field equations for a three‐layer capacitor. A major cause of electret decay is shown to be the self‐depolarization of the electret by its own electric field.

C^{13}‐Isotope Effect in the Photolysis of Ethyl Bromide
View Description Hide DescriptionThe photolysis of ethyl bromide in a tenfold excess of cyclopentane has been studied over the temperature range, 30 to 250°C.
Ethane is the principal volatile product of reaction. The quantum yield of ethane formation has been found to be unity at 30°C. An increase in apparent quantum yield to 1.5 at 250°C was observed. This increase is attributed to the greater absorption of the incident radiation at high temperatures.
The C^{12} enrichment in the ethane product was 1.0070±0.0008, and invariant in temperature. The isotope fractionation effect is explained on the basis of the higher absorption of C^{12}–C^{12}–Br over C^{12}–C^{13}–Br in the long wavelength region.

Electrolytic Hydrogen Evolution Kinetics and Its Relation to the Electronic and Adsorptive Properties of the Metal
View Description Hide DescriptionA significant correlation between the logarithm of the exchange current densityi _{0} of the electrolytic hydrogen evolution reaction and the electronic work function φ is found for one group of metals. Another group of metals probably having a different relationship is distinguished. The relationship between logi _{0} and φ is explained as arising from the dependence of heat of adsorption upon φ. The bond strength D _{ MH} of the adsorbed hydrogen calculated from Pauling's equation is less than the experimental value, owing to the neglect of the image potential of H at the metal, but parallels the experimental values. D _{ MH} is dependent on the work function since the parameters D _{ MM} (the metal‐metal dissociation energy) and X_{M} (the electronegativity of the metal) are statistically significant linear functions of φ. For the metals Ta, Mo, W, Cu,Ni, Fe, Rh, Pd, and Pt (at high current densities) logi _{0} increases as the heat of adsorption of H decreases.
The heats of adsorption of H at Hg, Cd, Pb and Tl are low compared with the values for other metals having respectively similar work functions and the distinct relation, having a different direction, between logi _{0} and φ for these metals is explained.
Logi _{0} increases linearly with increase of d character for the metals Mo, W, Cu,Ni, Fe, Pd, and Rh. The correlation coefficient is 0.62. The relation to d character arises since the d character determines the heat of adsorption of H.
The usually observed Tafel slope of 0.12 is consistent either with the rate determining reactionorIf A is rate determining, i _{0} should increase with increase of the heat of adsorption of H; if B, the converse should occur. Hence, B is rate determining in acid solution for the metals, Cu,Ni, W, Mo, Ta, Fe, Pd, Rh, Pt (high current density) and A for the metals Hg, Tl, and Pb. The available stoichiometric number data support this conclusion, which implies that during steady evolution of hydrogen, a maximum coverage of the metal by adsorbed H occurs under the condition that the electrode is in contact with liquid water. A general theory of electrolytic reduction and electrode poisoning is given. A mathematical analysis of the dependence of the rate of the proton discharge reaction in terms of the heat of adsorption of H, MH bond force constants, and internuclear distance, is given.

Ionization Potentials of Some Molecules
View Description Hide DescriptionThe ionization potentials of eithty‐nine molecules have been determined by photoionization measurements. The results are tabulated and compared with those obtained by spectroscopic and electron impact methods. Uncertainties in interpretation and several discrepancies are discussed.

On the Second‐Order Decay of the Thermoluminescence of Polycrystalline Materials
View Description Hide DescriptionThe results of an isothermal decay and glow‐curve experiment for a thermoluminescent material having second‐order kinetics have been investigated. In contrast to the first‐order case, the location of the peak of the glow curve depends on the initial trap density. The effect of a distribution of trap densities for a polycrystalline material is investigated. It is found that for a narrow distribution function, a plot of the reciprocal of the square root of the light intensity versus the time in the isothermal decay experiment will give a straight line whose slope and intercept will depend on the distribution function. The location of the peak of the glow curve is not materially affected by the distribution function, and from its location and the energy of the trap depth, a parameter proportional to the initial trap density and independent of the optical efficiency can be determined.
Plots of first‐ and second‐order generalized glow curves are presented from which the parameters of an experimental curve can be determined.

Vibrational Intensities. VII. Ethane and Ethane‐d _{6}
View Description Hide DescriptionAbsolute intensity measurements have been made on the fundamental vibrations of C_{2}H_{6} and C_{2}D_{6}, using the extrapolation method of Wilson and Wells and using nitrogen at pressures up to 50 atmospheres to broaden the bands. The absorption coefficient was integrated against the logarithm of the frequency. Normal coordinates were calculated from the potential function of Hansen and Dennison, and were used to interpret the results in terms of quantities (∂p/∂S _{ i }) giving the change of dipole moment with respect to the symmetry coordinates S _{ i }. Consistency of data between the isotopes was used both to eliminate ambiguities in the interpretation, and as a criterion in separating overlapping pairs of absorption bands. The results have been interpreted in terms of bond effective moments.