Volume 42, Issue 12, 15 June 1965

Proposed Theory of Calculating the Energy of Negative‐Ion Resonant Elastic Scattering States and of the Pre‐Ionization States of Electronic Spectroscopy
View Description Hide DescriptionIn elastic electron‐impact experiments, with the subsequent formation of negative ions and pre‐ionization spectral theory, similar theoretical problems arise. In both, autoionizing states of lifetime 10^{−14} to 10^{−12} sec are of basic importance, and also the variation principle is not applicable to the problem of the calculation of the energy. We propose here an approximate variation principle for calculating their energies and wavefunctions. The ideas are based on physical and nonanalytic arguments and tested successfully on the problem of elasticscattering of electrons by the hydrogen molecule, with an explanation of the H_{2} ^{—}resonances observed by Simpson et al. and the H^{—}resonance observed by Schulz.

Use of Gaussian Functions in the Calculation of Wavefunctions for Small Molecules. III. The Orbital Basis and Its Effect on Valence
View Description Hide DescriptionFurther calculations on N, H, NH, and NH_{3} are used as a guide for the selection, in general, of symmetry types and screening parameters of Gaussian atomic orbitals in an LCAO—SCF—CI scheme. The paper also examines the sensitivity of predicted valence properties to the choice of orbital basis and to the amount of configuration interaction included.

Cross Sections for Dissociative Ionization of Molecules by Electron Impact
View Description Hide DescriptionCross sections for dissociativeionization have been measured as a function of electron energy from threshold to 1000 eV in nine gases (H_{2}, D_{2}, N_{2}, CO, NO, O_{2}, CO_{2}, N_{2}O, and CH_{4}) by collecting those ions reaching the ion collector after passing through a 0.25‐V retarding potential in a total‐ionization tube. Approximate correction is made for the effective solid angle subtended by the ion collector at the electron beam. The results are reported as the fraction of total ionization, and as absolute cross sections for dissociativeionization. At moderately high electron energies (>70 eV), the fraction of total ionization that is dissociated ions with kinetic energy in excess of 0.25 eV, ranges from ∼7% in H_{2} and D_{2} to ∼35% in N_{2}O, with other gases intermediate.

Oscillator Strength of the CN Red System
View Description Hide DescriptionThe red system of CN is produced in emission by running a pulsed electrodeless discharge in acetonitrile. The extrapolation at zero acetonitrile pressure of the fluorescence decay time is accepted as the lifetime of the A ^{2}Π state of CN. The lifetime values vary slightly from one vibronic level to another. The dependence of the electronic part of the transition moment over the nuclear coordinates is deduced from this variation. A value of 3.4×10^{−3} is recommended for the oscillator strength f(0, 0) of the CN red system.

Crossed‐Beam Investigation of N_{2}D+ Production in N_{2}+—D_{2} Collisions
View Description Hide DescriptionThe reaction N_{2} ^{+}+D_{2}→N_{2}D^{+}+D has been studied in a crossed‐beam experiment. The angular distribution of the secondary ions was determined with a movable quadrupole mass filter. Differential cross sections have been obtained within the energy range 7.5 to 57.5 eV.
Total cross sections for this reaction have been determined using another crossed‐beam apparatus in which the product ions are collected in toto. Total cross sections were also derived from the angular measurements, but less reliance is placed in these values.

Calculation of the Total Cross Section from Angular Measurements in Crossed‐Beam Experiments
View Description Hide DescriptionThe total cross section is written as the sum of an integral taken over the scattered intensity measured in the plane of the initial velocity vectors and a correction term which itself is the sum of two integrals of the center‐of‐mass (c.m.) differential cross section. One of these integrals is taken from 0 to ε, the other from π—ε to π, where ε is the angle between the center‐of‐mass velocity and the relative velocity. In certain atomic or molecular scattering experiments, the angle ε is small; for these cases, it is shown that only a small error is made by dropping this correction term. This error is estimated for the case of isotropic scattering and for the case of glory scattering. In the latter case, the range of parameters for which the method is useful is given. In the event that the shape of the differential cross section is known a priori, the correction term can be calculated and the total cross section found exactly.

Thermal Generation and Spectrometric Measurement of Ba^{0} and Ba^{+} in a Hot Flame
View Description Hide DescriptionThe object of this program was formulation and laboratory study of a combustion system whose products contain both neutral (Ba^{0}) atoms and Ba^{+} ions. The system consists of tetracyanoethylene, hexanitroethane, and barium peroxide, all solids at room temperature. In a series of digital‐computer calculations, a mixture containing 8.0% BaO_{2}, 52.6% C_{2}(NO_{2})_{6}, and 39.4% C_{2}(CN)_{4} by weight was found suitable and chosen for experimental work. The calculated extent of ionization of barium in that mixture is 7.9%, at the adiabatic flame temperature of 3780°K. The mixture was prepared and pressed into strands of 1.65 g/cc density; its stability, sensitivity, and burning rate were studied. Flame spectrometry of the mixture yields line‐intensity temperature of 3310±50°K. The experimental extent of ionization of barium, determined by the relative intensities of the Ba^{+} and Ba^{0} lines, is 9.0%. The calculated equilibrium ionization at 3310°K is only 2.2%. The discrepancy between the measured and calculated degrees of ionization is ascribed to incomplete combustion of electron‐absorbing species, especially those containing the CN radical, which promote ionization of barium. Relevance of these laboratory studies to the performance of a scaled‐up burner releasing gaseous barium in the upper atmosphere is briefly discussed.

Motion of the H_{2}O Molecule in Barium Bromate Monohydrate
View Description Hide DescriptionThe PMR doublet splitting was measured for barium bromate monohydrate in the range 195° to 373°K. Two orientations of the crystal were used so as to observe the effects of torsional and rocking motions of the H_{2}O molecule. Torsional vibrations caused a decrease of about 0.47 G in splitting from low to high temperatures. The reduction was about 0.14 G for rocking motion. The root‐mean‐square amplitudes of the motion at 0°K were computed to be about 11° and 8° for the torsional and rocking motions, respectively. The torque constants were found to be about 16 and 30 kcal/mole·rad^{2} for torsion and rocking, respectively. The value of the proton—proton separation is 1.54 Å when results are corrected for motional effects.

Diffusion of Zn^{2+} in Single‐Crystal MgO
View Description Hide DescriptionDiffusion coefficients for Zn^{2+} in single‐crystal MgO have been determined in the temperature range 1000°—1650°C from concentration gradients obtained with the aid of electron microbeam probe spectroscopy. The variation of the diffusion coefficients with temperature yields an activation energy for diffusion of 1.85 eV, and D _{0}=1.48 10^{−5} cm^{2}/sec. The oxides display appreciable solidsolubility in one another, but the range of solid solution of ZnO in MgO greatly exceeds that for MgO in ZnO.

Orbital Radii of Atoms and Ions
View Description Hide DescriptionRadii corresponding to the principal maxima in the radial distribution functionsr ^{2}ψ_{ i } ^{2}(r) have been obtained for the ground states of all the atoms in the periodic table. The relativistic wavefunctions employed were solutions of the Dirac equations. Slater's ρ^{⅓} method for including exchange and Latter's method for the self‐interaction correction were used in ``creating'' the potential.
The radii corresponding to these maxima are used as measures of the size of each orbital. The relation between the orbital radii of the valence electrons is shown as plots for the first, second, and third series of transition elements.
In the elements below nobelium, only four maxima occur in the total charge‐density function. The relation of these maxima to the shell structure of the atom and the effect of shielding by outer electrons are discussed. The effect of the relativistic contraction on orbitals of low angular momentum is shown.

Matrix Elements for Vibration—Rotation Transitions in the HBr Overtone and Hot Bands
View Description Hide DescriptionThe strengths of the vibration—rotation lines of the first overtone, first hot band, and fundamental band of HBr have been measured by a curve of growth method, applying a correction for two overlapping lines devised by Sakai. The squares of the electric‐dipole matrix elements and for the lines have been calculated, and have been fitted, respectively, to a cubic and quadratic polynomial in m, using the method of least squares. The experimental results for all three bands are compared with the theory of Herman and Wallis. The fact that the experimental is less than that calculated from a linear dipole‐moment function clearly requires a positive value of M _{2}, the second derivative of the dipole‐moment function.
The squares of the matrix elements and are used to calculate M _{1} and M _{2}, the dipole‐moment coefficients, for Morse and anharmonic oscillators. Of all the possible sets of M _{1} and M _{2} obtained in each case, the one giving results in better agreement with is chosen. The chosen values of the dipole‐moment coefficients are M _{1}=+4.56×10^{−11} esu and M _{2}=+0.69×10^{−3} esu cm^{−1} for the Morse oscillator and M _{1}=+4.63×10^{−11} esu and M _{2}=−0.70×10^{−3} esu cm^{−1} for the anharmonic oscillator. Since the sign of M _{2} is positive, the Morse oscillator results are preferred.

Motions of Molecules in Condensed Systems. XIII. Polarized Infrared Spectrum of Single Crystals of Diacetylene
View Description Hide DescriptionThe polarized infrared spectra of single crystals of diacetylene, as well as those of the liquid and the vapor, are presented and analyzed. Modes forbidden activity in the vapor are observed in the spectra of the condensed phases, as are combinations of molecular fundamentals with lattice modes. The crystal and liquidspectra exhibit frequency shifts and band broadenings that are characteristic of hydrogen bonding. The crystal system is found to be either orthorhombic or monoclinic with two or more molecules in the primitive unit cell. The molecules are essentially coplanar and this plane is the only symmetry element that may be present at the site. An orthorhombic structure, of Space Group P22_{1}2_{1} with four molecules on sites of no symmetry, is proposed for the crystal.

Quadrupole Splitting of the Magnetic Resonance Spectrum of ^{9}Be in Chrysoberyl
View Description Hide DescriptionThe quadrupole coupling constant, the asymmetry parameter, and the orientation of the principal axes of the electri cfield gradient tensor were determined for the ^{9}Be sites in chrysoberyl. These values were found to be: η=0.90±0.01 and  eQφ_{ zz }/h =318±2 kc/sec. Two different types of sites were found for the beryllium. These two sites are equivalent. One of the principal axes was found to be parallel to the crystalline c axis.

Composition Change of Binary Compounds Under Conditions of Equilibrium and Vacuum Vaporization
View Description Hide DescriptionThe composition of binary compounds changes as a function of temperature when in equilibrium with the vapor. This change, for the IIB—VIA and IA—VIIA compounds is small, within the limits of solubility. The equilibrium vacancy concentrations are controlled by their free energies of formation. The composition changes in a different manner when the solid is heated in vacuum. Vacuum evaporation rates are controlled by the activation free energy of a surface reaction which, under proper conditions, may also control the bulk concentration of vacancies. Experimental verification of this effect is proposed. It has been shown that closed system vapor‐pressure measurements are extremely sensitive to minute changes of the solid composition. The measured apparent vapor pressure is a function of the reaction‐chamber volume for composition changes ≥2×10^{−8} mole/cm^{3}. In turn, the sensitivity of closed‐system vapor‐pressure measurements may be used for accurate determination of off stoichiometry.

Refractive Index and Lorentz—Lorenz Function for Saturated Argon, Methane, and Carbon Tetrafluoride
View Description Hide DescriptionBy means of the principle of minimum deviation, the refractive index was determined for argon, methane, and carbon tetrafluoride as saturated liquids from the triple point to the critical point. For argon, some measurements were also made on the saturated gas. For argon and methane, known values of the densities were used to compute the Lorentz—Lorenz function over the entire range of the saturation curve. For carbon tetrafluoride these computations were made only up to 0.7 of the critical temperature due to the lack of density data at higher values. The Lorentz—Lorenz function varies little with density and temperature for the three liquid phases. The argon measurements indicate definite increases in the Lorentz—Lorenz function on isothermal condensation.

Shear Dependence of the Intrinsic Viscosity of Rigid Distributions of Segments with Cylindrical Symmetry
View Description Hide DescriptionThe theory of Hearst for the intrinsic viscosity of any segment distribution of cylindrical symmetry is used to calculate the shear dependence of such a model. Results are applied to the rigid rod and an approximate model of the random coil.

Liquid—Solid Phase Equilibria in the Hydrogen—Deuterium System
View Description Hide DescriptionThe phase behavior of mixtures of parahydrogen and normal deuterium, in the liquid and solid states, has been investigated. The calorimetric data show a continuous range of solid solutions from 8°K to the melting points. In the liquid—solid two‐phase region the system can be characterized by a continuous series of liquid and solid solutions. The experimental data show no evidence of the phase separation in the solid state previously reported by Kogan, Lazarev, and Bulatova.

Self‐Avoiding Random Walks. I. Simple Properties of Intermediate‐Length Walks
View Description Hide DescriptionA new method is presented for the rapid detection of self‐intersections in random walks generated by Monte Carlo processes. Reduction in required computer time made possible by this method allows the generation of walks containing significantly more steps than previously possible, thus corresponding to more realistic linear macromolecular dimensions. Results obtained by this method verify, for the tetrahedral lattice, a conjecture of Domb's that 〈R_{n} ^{2}〉, the mean‐square end‐to‐end distance, increases essentially as the 6/5 power of n, the number of steps in a walk. In addition, a new parameter 〈x_{n} 〉 the average maximum x‐axis extension of a walk, is calculated. The square of this parameter is found to have essentially the same exponential step dependence as 〈R_{n} ^{2}〉 and may be calculated more precisely than it. Further, 〈D_{n} ^{2}〉, the average maximum squared diameter of a walk estimated from 〈x_{n} 〉, having the property that essentially all of an average self‐avoiding walk of n steps is contained within a sphere of squared diameter 〈D_{n} ^{2}〉, is shown to be approximately 2.2 times 〈R_{n} ^{2}〉. The results presented are valid to 1700 steps.

Polarization Effects in the Two‐Photon Excitation of Anthracene Fluorescence
View Description Hide DescriptionThe polarization of the fluorescence of anthracene has been measured after two‐photon excitation with ruby laser light. The anthracene molecules were rigidly held in a 2×10^{−3} M solution in EPA glass at liquid‐nitrogen temperatures. For comparison, the polarization of the fluorescence was measured from one‐photon excitation at approximately twice the laser frequency. The measuredpolarization of the two‐photon excited light is in satisfactory agreement with the polarization as calculated from the Goeppert‐Mayer process involving a transition through an intermediate state. It is in disagreement with the polarization calculated in terms of the process recently suggested involving the A ^{2} term in the Hamiltonian. Thus the measurement of the polarization of the two‐photon fluorescent light appears to be one way of experimentally estimating the relative contribution of these two second‐order processes.
The concentration and intensity independent quantity δ, which is the ratio of the cross section to the laser flux, was found experimentally to be 0.9×10^{−51} cm^{4}·sec/atom·photon for anthracene molecules in a dilute glass.

Reaction of Atomic Hydrogen with Propylene at 77°K as Studied by Electron Spin Resonance
View Description Hide DescriptionHydrogen‐atom reaction rates with thin solid propylene films were studied at 77°K. Propylene was deposited on the walls of a quartz resonance cavity of an ESR spectrometer and hydrogen‐atom concentrations were monitored during reaction. The hydrogen atoms were produced in a 2450 Mc/sec microwave discharge external to the cavity and either diffused into or were pumped through the reaction zone.
The products of the reaction were found to be propane and 2,3‐dimethylbutane. The ratio of propane to 2,3‐dimethylbutane in the products increased as the average hydrogen‐atom concentration in the reactor increased. The product distribution and the variation of this distribution with hydrogen‐atom concentration may be explained by the following sequence of reactions: [Complex chemical formula]
The rate constantk _{1} was found to be 1.8×10^{6} cc/mole·sec at 77°K assuming that the monitored hydrogen‐atom concentration was equal to that in the reaction zone.