Volume 38, Issue 11, 01 June 1963

Molecular Orbital Studies of Diatomic Molecules. III. The Ground State of the Hydrogen Molecule
View Description Hide DescriptionA method of molecular orbital computation described in Papers I and II of this series are applied to the X ^{1}Σ_{ g } state of hydrogen. The potential curve is reported and the significance of the results is discussed.

Dipole‐Moment Function for Diatomic Molecules
View Description Hide DescriptionThe functional form of the dipole‐moment function of a diatomic molecule is investigated in the united‐atom and separated‐atom limits. The moment goes to zero as R ^{3} for an S or P united atom, and as R ^{5} for a D or F united atom. For separated atoms, the moment goes as R ^{—4} if at least one atom has a quadrupole moment, and as R ^{—7} otherwise. Evidence is given that simply combining the two limiting functional forms is insufficient to represent the actual dipole‐moment function.

Semiclassical Analysis of the Extrema in the Velocity Dependence of Total Elastic‐Scattering Cross Sections: Relation to the Bound States
View Description Hide DescriptionThe phenomenon of extrema in the velocity dependence of the total elastic cross section Q(v) for atom—atom scattering in the thermal‐energy region is shown to be a quite general one, whenever the interaction potential consists of both attractive and repulsive parts and the resulting well has a ``capacity'' for one or more discrete levels. The phase shift vs angular‐momentum dependence exhibits a maximum; since this maximum is a function of the de Broglie wavelength, the cross section exhibits an undulatory velocity dependence. A semiclassical analysis of the extrema velocities (and undulation amplitudes) is presented. Suitable plots are suggested from which one may deduce certain information on the interatomic potential and the diatom bound states. The following rule is proposed: the observation of m maxima in the elastic atom—atom impact spectrum implies the existence of at least m discrete vibrational levels of zero angular momentum for the diatom.

Investigation of a Fragmentation Model for n‐Paraffins
View Description Hide DescriptionA fragmentation model is postulated for the interpretation of n‐paraffin mass spectra. It is assumed that primary dissociations of molecule ions yield fragment ions containing at least half the total number of available carbon atoms. Any fragment ions retaining sufficient excitation energy can dissociate further, with the same product size limitations as in the primary processes. At each step, all possible dissociations are assumed to be in competition. Rate constants are calculated by the statistical theory. Breakdown curves are given for n‐decane, and described for other cases. The model can successfully account for observed patterns, their dependence upon the ionizing voltage, and the occurrence of several metastable ion peaks. However, other expected metastables do not appear, the requisite internal energy distributions cannot presently be reconciled, and the calculated amounts of fragment‐ion labeling from C^{13}‐enriched molecules are in disagreement with experimental results.

Corrosion of Tungsten and Iridium by Field Desorption of Nitrogen and Carbon Monoxide
View Description Hide DescriptionBy using an ultra‐high‐vacuum processed field ion microscope, two atomic adsorption sites of nitrogen and carbon monoxide were observed on tungsten and iridium surfaces. Field desorption of a nitrogen atom from a single site also removes the underlying tungsten or iridium atom. Field desorption of an adsorbed nitrogen molecule does not corrode the iridium substrate. Corrosion of both metals by field desorbing carbon monoxide is attributed to oxygen dissociated from the molecule by electron impact.

YH_{3} and YD_{3}: Heat Capacities and Thermodynamic Functions from 15° to 350°K and Infrared Absorption Spectra
View Description Hide DescriptionThe heat capacities of YH_{3} and YD_{3} were determined in an adiabatic calorimeter from 15° to 350°K. The heat capacity,entropy,enthalpy, and Gibbs free‐energy function for YH_{3} at 298.15°K are 10.363±0.021 cal deg^{—1} mole^{—1}, 10.019±0.020 cal deg^{—1} mole^{—1}, 1613.3±3.2 cal mole^{—1}, and —4.608±0.009 cal deg^{—1} mole^{—1}, respectively. The corresponding quantities for YD_{3} are 13.727±0.028, 12.028±0.024, 2024.8±4.0, and —5.237±0.010.
The infrared absorption spectra of YH_{3} and YD_{3} were taken in the range 400 to 4000 cm^{—1}. Maxima in the absorption bands of YH_{3} were observed at 1295, 920, and 640 cm^{—1} and in the absorption bands of YD_{3} at 1295/√2, 920/√2, and 640/√2 cm^{—1}. A reasonable assignment of these frequencies to Y—H and Y—D vibrations satisfactorily accounts for the difference between the heat capacities of YH_{3} and YD_{3} in the temperature range 50° to 350°K. The lattice parameters as determined by x‐ray diffraction for the hexagonal close‐packed trihydrides were a _{0} = 3.672±0.002 Å and c _{0} = 6.625±0.018 Å for YH_{3} and a _{0} = 3.659±0.002 Å and c _{0} = 6.586±0.019 Å for YD_{3}.

Infrared Spectroscopic Evidence for the Species HO_{2}
View Description Hide DescriptionInfrared absorptions observed following the photolysis of mixtures of HI and O_{2} in an Ar matrix at 4°K appear to be contributed by HO_{2} produced in the matrix. Studies on isotopically substituted systems support this assignment. The two oxygen atoms have been shown to be nonequivalent. Approximate force constants and thermodynamic functions for HO_{2} are tabulated.

Use of Catalytic Probes to Determine Atom Concentrations and Atom Diffusion Coefficients
View Description Hide DescriptionA simple analysis is presented for the perturbation of a stream of partially dissociated gas by a catalytic probe capable of completely removing all the atoms from the stream. The results of this analysis were confirmed by experiments on discharged O_{2}, which showed that for linear flow rates of several meters per second the atom concentration reaches 99% of the unperturbed value within 2.5 cm upstream from the probe. It is shown that such a probe can be used to measure atom concentrations, since the flux to the probe remains finite even though the atom concentration at its surface is virtually zero. No appreciable errors are introduced into relative concentration measurements required to obtain first order rate constants. Under suitable experimental conditions, absolute concentrations can be obtained which are negligibly different from the unperturbed values regardless of the order of the recombination processes. A method is described for using such a probe to obtain accurate values of atomic diffusion coefficients which does not require accurate knowledge of heterogeneous or homogeneous recombination rates.

Ion—Solvent Interaction in Mixed Solvents. II. The Viscosity of Electrolytes in Mixed Solvents
View Description Hide DescriptionThe viscosities of Na 2SO4, MgSO4, MnCl2, NaOCOCH3, Ba(OCOCH3)2, Mg(OCOCH3)2, and KOCOCH3 have been determined at 25°C in ethanol—water and acetone—water mixtures. Results have been interpreted as a function of solvated molar volume using an extension of Mooney's equation. Interaction coefficients have been calculated and correlated with the B coefficients of the Jones—Dole equation.

Vibrational Energy Transfer in Molecular Collisions Involving Large Transition Probabilities
View Description Hide DescriptionThe usual calculations of vibrational energy exchange in a diatomic gas make use of firstorder perturbation theory and are therefore limited to low transition probabilities. In actual practice, the thermally averaged transition probabilities in most gases are indeed small. However, this is partly because it is the relatively few molecules in the highvelocity ``tail'' of the velocity distribution which account for most of the energy exchange. The actual microscopic transition probabilities in these collisions may be too great to justify the perturbation method for many gases at high temperatures. We have therefore solved the timedependent Schrödinger equation based on a semiclassical collision, subject to an assumed form of potential, to get exact transition probabilities in a molecular collision. At low velocities, our result reduces to the perturbation result. A thermal average of our transition probabilities should eliminate errors due to use of the perturbation solution in previous calculations. For N_{2}, these errors only become important above 5000°K. For gases with lower vibrational frequencies such as O_{2}, or strong attractive forces such as NO, these effects become important at much lower temperatures.

Rectification Phenomena in Polycrystalline Phthalocyanines
View Description Hide DescriptionRectification was observed on polycrystalline samples of metal‐free, copper,nickel, and molybdenum phthalocyanines when these materials were sandwiched between different metal electrodes. The presence of a small amount of a liquid polar impurity proved essential for rectification, and it is suggested that the observed rectification is caused by the formation of an ionic space‐charge barrier in the vicinity of the least noble electrode. The highest rectification ratio observed was 500 and was obtained with copper phthalocyanine between a platinum and a silverelectrode and also between a silver and an aluminumelectrode. The effects of temperature, electrode material, and electrode size on the rectification ratio are given.

Low‐Temperature Magnetic Susceptibilities of Some Hydrated Formates of Cu^{++} and Mn^{++}
View Description Hide DescriptionThe magnetic susceptibilities of powdered specimens of Cu(HCO_{2})_{2}·4H_{2}O, Cu(HCO_{2})_{2}·2H_{2}O, and Mn(HCO_{2})_{2}·2H_{2}O have been measured by an audio‐frequency mutual‐inductance method between 1.3° and 4.2°K, and from 14° to 20°K. At hydrogen temperatures Cu(HCO_{2})_{2}·2H_{2}O and Mn(HCO_{2})_{2}·2H_{2}O exhibit Curie—Weiss behavior which, however, breaks down significantly in the helium region. The susceptibility of Cu(HCO_{2})_{2}·4H_{2}O rises to a pronounced peak at 16.8°K and is essentially constant below 4.2°K. The susceptibilities of single‐crystal Cu(HCO_{2})_{2}·4H_{2}O were measured along the three monoclinic axes in the same temperature intervals. χ_{ c } and χ_{ b } show sharp maxima at 16.8°, and are much larger in magnitude than χ_{ a }. The possibility of this salt becoming weakly ferromagnetic below 16.8°K is considered, as is the unusual indirect‐exchange coupling of Cu^{++} moments via formate groups.

Determination of Optical Constants from Reflection Bands Using Dispersion Relations
View Description Hide DescriptionA detailed study has been made of the Robinson and Price (Kramers—Kronig) method for determining optical constants from reflection data collected in regions of strong absorption. This method depends upon the fact that the phase shift at any given frequency can be expressed as an integral involving the reflectivityat all frequencies (0 to ∞). Although in practice reflectivity data are ordinarily available only in the immediate vicinity of a reflection band, a method is presented which can be accurately applied to that situation. The circumstances under which this procedure will be valid are outlined, and some differences from previous methods will be indicated. The following two experimental situations have been considered assuming that the reflectivities have been measured at normal incidence: (1) the sample is not covered by a window, (2) the sample is covered by a window whose (constant) refractive index is greater than the zero frequency refractive index of the sample.

Optical Constants and Absolute Intensities from Infrared Reflection Measurements. The 6.6‐μ Band of Liquid CS_{2} and the 13‐μ Doublet of Liquid CCl_{4}
View Description Hide DescriptionInfrared reflection spectra in the 6.6‐μ region of liquid CS_{2} and in the 13‐μ region of liquid CCl_{4} have been measured using a Perkin—Elmer Model 21 Infrared Spectrophotometer modified for double‐beam reflection operation. The measurements were made on samples covered by AgCl windows. The reflection data were analyzed by a new Robinson and Price procedure described in the paper immediately preceding this one. Optical constants (n and K) were obtained throughout the band, and the resulting absolute intensities are in good agreement with values previously obtained from dispersion data. It seems likely that our procedures are capable of giving reliable absolute intensities (5%—10%) for strong bands in condensed phases. This can be accomplished with reflection measurements of an accuracy (1%—2%) which should be obtainable without highly elaborate techniques.

On a Hole Theory of Fluids from Molecular Distributions
View Description Hide DescriptionA previously developed method connecting the molecular distributions inside a cell with the molecular distribution in the surrounding fluid is applied to the case of a cell small enough to occupy at most one molecule. It is then possible to arrive at explicit expressions for the thermodynamic functions of the fluid. The method has the advantage over current hole theories in that it eliminates the problem of the dependence of the free volume on the occupation number of neighboring cells. General properties of the resulting formulas are discussed.

1–0, 2–0, 3–0, Absorption Bands of Dense Forms of Pure CO and Its Solutions in N_{2} and Ar
View Description Hide DescriptionThe first overtone and the second overtone bands of pure CO as well as the first overtone band of CO in solution in the gaseous, liquid, and solid states of N_{2} and Ar have been studied. The method for obtaining under pressure long lengths of transparent solids is described. A principal band due to C^{12}O^{16} and a weak satellite due to the isotopes C^{13}O^{16} and C^{12}O^{18} have been found, and displacement of the maximum of the principal band and this satellite have been measured. The results are compared with those found for the fundamental by the condensed matrix method. The form of the band, in particular, its half‐width, as a function of temperature and density is discussed.

Interdependence of Spectral Line Breadth, Sound Velocity Dispersion, and Viscosity of Small Molecules in the Gas Phase
View Description Hide DescriptionAn examination of the data on bimolecular collisions of small molecules has produced several new insights and predictions. The data on viscosity, sound velocitydispersion, and spectral line breadths in the microwave, infrared, and Raman regions have been assembled for H_{2}, O_{2}, N_{2}, CH_{3}Cl, and HCN. These data have been put on an equivalent basis of calculated or observed spectral line breadth constants. When this is done, the relative importance of elastic and inelastic rotational collisions may be assessed.
The data on H_{2} are here used to predict a collisional narrowing of the ordinary Doppler linewidth; this narrowing effect can be found in the literature, where the significance of the extremely narrow lines has not been fully appreciated.
The line breadths observed in the microwave spectrum of oxygen are seen to be peculiar to some phenomenon which reorients electron spins but does not alter rotational states. Spin exchange is here identified as the most probably mechanism for microwave line broadening in O_{2}.
The differences between isotropic and anisotropic linewidths in the Raman spectra of H_{2}, O_{2}, and N_{2} indicate that a thorough theoretical treatment of Raman linewidths is required. Some additional experiments on line breadths in the Raman spectra of H_{2}, O_{2}, and N_{2} are suggested. The basic approximation in Anderson's impact theory for broadening of spectral absorption and emission lines is seen to be quantitatively invalid for self‐broadening of these homonuclear diatomic molecules. This is the approximation of classical (straight) paths.
Two new phenomena are predicted for the propagation of rotational energy in small polar molecules. The first of these is a separation of the rotational sound velocitydispersion into two regions for symmetrictop molecules. The region of lower frequency dispersion should account for R/2 of heat capacity, and be associated with changes in rotation about the unique axis of the molecule. Small polar molecules with large dipoles (particularly the alkali halide vapors) should also exhibit a peculiar form of energy propagation in the rotational degrees of freedom only. This ``roton propagation'' may also influence the behavior of shock waves in polar gases and the heat conductivity at very low pressures.

Atomic Screening Constants from SCF Functions
View Description Hide DescriptionThe self‐consistent‐field function for atoms with 2 to 36 electrons are computed with a minimal basis set of Slater‐type orbitals. The orbital exponent of the atomic orbitals are optimized as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1s, 2s, 3s, 4s, 2p, 3p, 4p, and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need of accounting for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the groundstate configuration and to the positive ions.

Molecular Interaction and Linewidth of Asymmetric Molecule SO_{2}. III. SO_{2}–CH_{3}Br and SO_{2}–SO_{2} Collisions
View Description Hide DescriptionThe linewidth of the 9_{1,9}→8_{2,6} transition of sulfur dioxide broadened by methyl bromide and sulfur dioxide itself has been measured at different pressures of the broadener. The measuredlinewidth for SO_{2}–CH_{3}Br collisions is 13.64 Mc/mm. The hard‐sphere collision diameter corresponding to this is 12.1 Å as compared to the kinetic collision diameter of 4.0 Å. The calculated width on the basis of Anderson's theory, assuming dipole—dipole interaction, comes out to be 22.4 Mc/mm, which is in disagreement with the experimental results. The measuredlinewidth for SO_{2}–SO_{2} collisions comes out to be 11.23 Mc/mm. The effective collision diameter for this is 10.5 Å.

Microwave Spectra and Structures of Difluoroethylenes
View Description Hide DescriptionThe microwave spectra of the C^{12} and C^{13} species of cis‐difluoroethylene‐d _{1} and cis‐difluoroethylene‐d _{2} have been investigated in the region of 8–36 kMc. Effective rotational constants for the ground vibrational state have been determined and are combined with previous microwave data to obtain the structural parameters: r _{CC}=1.324 Å, r _{CH}=1.089 Å, r _{CF}=1.335 Å, ∠FCC=122.1°, ∠HCC=124.0°.
The microwave spectrum of vinylidene fluoride has been reinvestigated and the rotational constants for C^{13} species obtained. These data lead to a structure: r _{CC}=1.315 Å, r _{CH}=1.079 Å, r _{CF}=1.323 Å, ∠FCF=109.1°, ∠HCH=121.8°.
A comparison of the structures with data for vinyl fluoride and ethylene shows that fluorine substitution produces a systematic shortening of both the CC and CF bonds.