Volume 36, Issue 6, 15 March 1962
Index of content:
36(1962); http://dx.doi.org/10.1063/1.1732758View Description Hide Description
A mechanism for excitation of molecular vibration by slow electron impact involving negative‐ion states as intermediates is proposed and discussed. It is believed that this mechanism is the most important energy loss mechanism for slow electrons for energy regions in which it occurs. Calculation of the vibrational excitation cross section using the proposed mechanism has been carried out for hydrogen molecules and the result is compared with the experimental observations. The estimated cross section is in the order of 1 A2.
Diffusion Kinetics in Radiation Chemistry. I. Generalized Formulation and Criticism of Diffusion Model36(1962); http://dx.doi.org/10.1063/1.1732759View Description Hide Description
A generalized formulation of the diffusion‐kinetic model of track effects in radiation chemistry is presented and criticized. It permits consideration of complex mechanisms, arbitrary initial distributions and radical correlation effects. Methods for the numerical integration of the associated differential equations on high‐speed electronic digital computers are given and their accuracy is examined. Several applications are suggested.
36(1962); http://dx.doi.org/10.1063/1.1732760View Description Hide Description
The general diffusion‐kinetic equations are applied to a one‐radical‐one‐solute model of the radiolysis of dilute aqueous solutions. The validity of the prescribed diffusion approximation is examined. Results of calculations of the effect on the molecular and radical yields of the following parameters are given: solute concentration, solute depletion, shape of initial radical distribution, radical density, diffusion coefficients, and rate constants. Conditions under which a straight track of equal and equidistant spherical spurs can be replaced by either isolated spherical spurs or an axially homogeneous cylindrical track are examined.
On the Use of Nonintegral Exponents in Elliptical Coordinate Wave Functions, with Special Reference to the Hydrogen Molecule‐Ion36(1962); http://dx.doi.org/10.1063/1.1732761View Description Hide Description
Introduction of arbitrary powers of the elliptical coordinate μ is shown to give a better approximate wave function for the hydrogen molecule‐ion than any previous function of comparable complexity. The three‐parameter two‐configuration functionis found to give an energy of —0.602566 a.u. and an equilibrium internuclear separation of 1.9956 a 0 compared with the results for n=0 of —0.602386 a.u. and 1.9966 a 0, respectively, and with the exact values of —0.60263 a.u. and 2.0 a 0, respectively. This agreement is maintained over a range of internuclear distances.
In the Appendix a discussion is given of various methods for computing kinetic energy integrals, and a special difficulty is pointed out that arises when functions in prolate spheroidal coordinates are employed.
36(1962); http://dx.doi.org/10.1063/1.1732762View Description Hide Description
Vapor transport of uranium from UC1.86 in a graphite crucible has been measured from 1930° to 2365°K by the Knudsen technique. In order to treat the data, unusual assumptions have been made concerning the thermal properties of carbides which hydrolyze to yield hydrocarbons. The gaseous uranium species is assumed to be monatomic. With the aid of these assumptions, the data have been treated by the third‐law method as well as by the second‐law method. Agreement between the two is considered good, and the ΔH 298° obtained for the processis 140.15±1.82 kcal/mole. Reasonable estimations for reactionentropies within the system lead to an upper limit of 0.5 kcal/mole for ΔH 298° for the reactionand hence a value of 119.8±2.8 kcal/mole is obtained as an upper limit for ΔH 298° of vaporization of uranium.
36(1962); http://dx.doi.org/10.1063/1.1732763View Description Hide Description
A molecular orbital self‐consistent field calculation is made for closed shell ions, LiHe+ and LiHe— as function of internuclear distance. The eigenfunctions obtained from these calculations were used to calculate the potential energy curves for the neutral Li–He. This system has some interesting properties. For example, these calculations suggest the probable quenching of certain excited states of an alkali metal when in close interaction with a rare‐gas atom. All of the curves obtained are repulsive except for the LiHe+ curve which has a shallow minimum and follows an expected 1/r 4 attractive potential. Fair values are obtained for the ionization energies of the Li and He atoms and the electron affinity of Li. These calculations indicate that open‐shell systems with few electrons can be treated by making the simpler SCF calculation on a closely related closed‐shell system and using the resulting eigenfunctions to calculate the energy of the closed shell system.
36(1962); http://dx.doi.org/10.1063/1.1732764View Description Hide Description
Pure quadrupole resonance of N14 in the α phase of solid nitrogen has been studied in the temperature range from 1.5° to about 34.5°K. The resonance frequency at 4.2°K is 3.4873±0.0001 Mc. The line shape and relaxation times at 4.2°K are discussed. A hydrostatic compression to 130 atm at 4.2°K gives (dν/dP)4.2=33 cps/atm. The temperature dependence of the resonance frequency below 20°K has been analyzed in terms of a modified Bayer theory in which account is taken of volume expansion. The torsional frequency of oscillation of the molecule is found to be ν t =1.12×1012 sec—1, and the quadrupole resonance frequency without zero‐point vibrations is ν0=4.16 Mc. The resonance frequency decreases very rapidly as the phase transition at 35.6°K is approached and pure quadrupole resonance has not been observed in the β phase.
36(1962); http://dx.doi.org/10.1063/1.1732765View Description Hide Description
Three classical strong‐collision‐mechanism theories of unimolecular reactions, due to Slater, Kassel, and Giddings and Eyring have been rederived using Slater's new approach to rate theory. These derivations show the importance of the gap distribution problem, and help point the way toward further development of a nonlinear theory.
36(1962); http://dx.doi.org/10.1063/1.1732766View Description Hide Description
The hyperfine structure of the 32→33 and 52→53 rotational transitions of HDO, which fall at about 825 and 487 Mc, respectively, have been studied using microwavecavities as spectrometers. The experiments illustrated the usefulness of large Qcavities as spectrometers for this kind of work. The 32→33 transition was resolved into a symmetrical pattern consisting of a strong central line with six weak satellites on each side. The minimum full linewidth between half‐power points that was achieved was about 10 or 12 kc. The spectrum was fitted with C H=—46.6±0.3 kc, C D=—1.66±0.3 kc, and (eqQ)OD=310.3±3 kc. The 52→53 transition was resolved into a symmetrical pattern also, with a strong central line and three weak satellites on each side. The minimum full linewidth between half‐power points was about 6 kc. The spectrum was fitted with C H=—47.38±0.1 kc, C D=—2.42±0.1 kc, and (eqQ)OD=314.3±1.5 kc. A systematic comparison of the results with those obtained elsewhere on the 21→22 transition in HDO is made. The qualitative features of the spectra are consistent with what one would expect on the basis of existing theory, but the present state of the theory may be inadequate for explaining some of the quantitative details of the magnetic structure.
36(1962); http://dx.doi.org/10.1063/1.1732767View Description Hide Description
The f 7electrostatic matrices have been derived by the methods of Racah and are tabulated. A previous table of spin‐orbit matrix elements has been corrected and extended, and then used in a further analysis of the spectra of gadolinium salts. Finally, a tentative calculation has been made of the energy levels for the corresponding curium salts.
36(1962); http://dx.doi.org/10.1063/1.1732768View Description Hide Description
The definition of electronic energy in molecules is analyzed and, in its conventional form, it is shown to be in slight disagreement with experimental experience. By means of a proper treatment of the center‐of‐mass motion, a modified concept called reduced electronic energy is introduced and shown to give more satisfactory results. In particular, the hydrogen molecule and its isotopic analogues are used for a quantitative comparison of the two concepts with experimental results.
36(1962); http://dx.doi.org/10.1063/1.1732769View Description Hide Description
The Zeeman‐split quadrupolar resonances for Ba137 in BaBr2·2H2O were measured by using coincident enhanced protonresonance as a detector. The principal axes of the electric field gradient were found to be oriented thus: x parallel to b, y parallel to c, and z perpendicular to the bc plane. a, b and c are the crystallographic axes. The asymmetry parameter is 0.73±0.01 and the pure quadrupole resonance frequency is 24.38±0.03 Mc/sec.
36(1962); http://dx.doi.org/10.1063/1.1732770View Description Hide Description
The energy quantities for chemisorbing systems derived from calorimetry, isotherms, rate studies, and steady state measurements are analyzed. It is shown that if equilibration of the adsorbed layer occurs rapidly before evaporation (as it does for most metals) and the kinetic processes are properly identified, then the energy parameters deduced from thermodynamic and kinetic measurements are comparable.
36(1962); http://dx.doi.org/10.1063/1.1732771View Description Hide Description
The spectrum of 1,4‐dioxane shows strong absorption regions with intensity maxima at 55 500, 63 000, 69 500, and 72 000 cm—1, and an absorption region whose maxima is obscured by the last two absorption regions. A first ionization potential was located at 76 750 cm—1 (9.52 ev) which agrees with the value determined by electron impact (9.52 ev). The first electronic transition shows considerable virbrational structure, and the analysis of this structure indicates that the upper‐state vibrational frequencies are only slightly changed from those of the normal state. The other electronic transitions form a possible Rydberg series which converges to the first ionization potential.
1,3‐dioxane shows an absorption region with a maximum at 62 500 cm—1, and another very strong continuous absorption region beginning at about 67 500 cm—1. There is no apparent discontinuity in the region of the ionization potential. The electronic spectrum of 1,3‐dioxane showed no vibrational structure.
36(1962); http://dx.doi.org/10.1063/1.1732772View Description Hide Description
A method has been developed for following the kinetics of fast atomic reactions with a mass spectrometer. The method has been used to determine separately the rate constants for the following reactions which are relevant to an atomic nitrogen‐ozone system.These reactions have been used to interpret the observed changes of concentration with time for reactants and products of the N–O3reaction. The concentrations of N2O and NO2 in the system were below the detection limits of the mass spectrometer, which is consistent with predictions based on the above rate constants. Evidence was obtained for the production by reaction (2) of vibrationally excited N2 molecules having energies greater than 23.4 kcal/mole. Such energetic molecules are not present in significant quantities in discharged O2 or N2.
36(1962); http://dx.doi.org/10.1063/1.1732773View Description Hide Description
Approximate Hartree‐Fock calculations have been carried out on the 1Σ+ground state of hydrogen fluoride at three internuclear distances near equilibrium. Roothaan's method is used, with basis orbitals chosen to represent a reasonably good approximation to the atomic Hartree‐Fock orbitals and to allow for the principal polarization and distortion effects that must be expected when two atoms approach to within a chemical bond distance of each other. Total energies are comparable to calculated total Hartree‐Fock energies for the separated atoms, and the calculated binding energy is improved by a factor of nearly 3 over binding energy calculated with fixed atomic Hartree‐Fock orbitals. Thus this improvement can be attributed to polarization and distortion effects systematically neglected in earlier LCAO calculations. Physical and spectroscopicproperties of several electronic states of HF and HF+ are calculated, and are found to be in reasonable agreement with experiment. Localized ``exclusive'' self‐consistent orbitals have been calculated. They give a chemical picture of the structure of the molecule and make it possible to analyse the various contributions to the dipole moment, which is mainly due to the lone pair orbitals on the fluorine atom.
36(1962); http://dx.doi.org/10.1063/1.1732774View Description Hide Description
The gamma‐radiolysis of liquid methylcyclohexane has been studied over the dose range 0.40 to 35.0×1019 ev/ml. The initial 100 ev yields of the products are: H2, 4.80±0.07; (1‐methylcyclohexene+methylenecyclohexane), 2.65±0.15; (3‐methylcyclohexene+4‐methylcyclohexene), 0.83±0.10; open chain heptene′, 0.33±0.02; open chain heptene″, 0.31±0.04; bi‐methylcyclohexyl, 0.75±0.05; methylcyclohexylheptene, 0.13±0.02. Methylcyclohexyl‐methylcyclohexene was a secondary product, resulting mainly from reaction of methylenecyclohexane and partly from reaction of 1‐methylcyclohexene.
The values of the ratios of the olefin yields to the ``dimer'' yields in the cyclohexane and methylcyclohexane systems were compared with values of disproportionation to combination ratios for moderately bulky alkyl radicals in the gas phase. It was concluded that the major portions of the olefins and ``dimers'' in the radiolytic systems were formed by the disproportionation and combination of radicals. A steric hindrance effect probably has a small influence on the rate of the combination reaction.
It was illustrated that a polymerization reaction occurs, involving the olefinic products, although the polymer could not be characterized. The relative significance of the polymerization reaction increases with decreasing dose rate.
36(1962); http://dx.doi.org/10.1063/1.1732775View Description Hide Description
The effect of benzene on the radiolysis of liquid methylcyclohexane (MCH) has been studied over the benzene concentration range from 0.25 to 100 mole %. The dominant effect of benzene at low concentrations appears to be one of hydrogen atom scavenging. At higher concentrations, the transfer of energy (excitation or ionization) from activated MCH to benzene also becomes important.
As in the liquid cyclohexane system, there seem to be two major reactive species in γ‐irradiated MCH. One species, C7H14′, decomposes to produce ``cold'' hydrogen atoms that can be scavenged by benzene. The other species, C7H14″ or C7H14 +, produces hydrogen by a mechanism that is not subject to atom scavenging but which can be inhibited by an energy transfer process. The 100‐ev yields of the activated species in pure MCH are G(C7H14′) = 1.8±0.3 and G(C7H14″) = 3.0∓0.3. These compare with the cyclohexane yields G(C6H12′) = 2.4±0.3 and G(C6H12″) = 3.0∓0.3.
Reaction mechanisms have been proposed and tested against the experimental data.
36(1962); http://dx.doi.org/10.1063/1.1732776View Description Hide Description
A theory accounting for the effect of surfaceadsorption of molecules on losses occurring in acoustic boundary layers has been developed. Results of this theory show that such losses can be a sizable fraction of losses due to viscosity and thermal conductivity. Interpretation of recently obtained sound‐absorptionmeasurements in H2, He, Ne, N2, CO, O2, and Ar by this means permits direct determination of adsorption times for these gases. Comparison of these results with existing data is not conclusive, since most adsorptionmeasurements have been carried out at temperatures near that of liquid air whereas the data reported here was obtained at room temperature. In addition, it is almost certain that water vapor caused considerable contamination of the adsorbing surface.
36(1962); http://dx.doi.org/10.1063/1.1732777View Description Hide Description
In this paper we have shown that nitrogen is not adsorbed upon a (110) face of a nickel crystal at room temperature. In previous experiments it has been found that nitrogen is not adsorbed upon more densely packed crystal planes and upon polycrystalline surfaces. The new result extends the conclusion to the more open and chemically active (110) face.