Volume 40, Issue 12, 15 June 1964

Virial Coefficients and the Classical Theory of Fluids for the Square‐Well Potential
View Description Hide DescriptionThe term g _{2}(r) proportional to the square of the density in the expansion of the radial distribution function in powers of the density has been evaluated for a square‐well potential for the Born—Green—Yvon integral equation, the Kirkwood integral equation, the Percus—Yevick integral equation, the hyperchain approximation, and an integral equation derived by Meeron. The square‐well potential used has a hard‐core diameter of σ and attractive diameter of 2σ. Each g _{2}(r) is then used to calculate D_{p}, the fourth virial co‐efficient calculated from the pressure equation, and D_{c}, that calculated from the compressibility equation, for the above five liquid theories. This allows a comparison over the entire temperature range, rather than at infinite temperature, the only value given by the previously used hard sphere potential. It is shown that the Percus—Yevick equation yields virial coefficients in best agreement with the exact value over a large temperature range. All the results presented are low‐order polynomials in f=exp(ε/kT—1), where ε is the depth of the well, and reduce to the hard‐sphere results when f goes to zero.

Geometry of the Transition‐Metal Dihalides: The Fluorides of Manganese, Cobalt, Nickel, Copper, and Zinc
View Description Hide DescriptionThe deflection of mass spectrometrically detected beams of CaF_{2}, MnF_{2}, MnCl_{2}, CoF_{2}, NiF_{2}, CuF_{2}, ZnF_{2}, ZnCl_{2}, and HgCl_{2} by an inhomogeneous electric field has been examined. As found previously, CaF_{2} deflects in the manner expected for a polar molecule. The remaining molecules listed were found to be nonpolar. These observations are interpreted to imply that while CaF_{2} has a nonlinear equilibrium geometry the remaining species are linear. The result for HgCl_{2} is in agreement with a number of previous electron diffraction and spectroscopic studies.

Convergence of Fugacity Expansion and Bounds on Molecular Distributions for Mixtures
View Description Hide DescriptionWe have generalized the methods developed recently by Groeneveld and Penrose for a one‐component system to obtain a lower bound on the domain of convergence of the Mayer fugacity expansion of the pressure,where z _{α} is the fugacity of the αth component, α=1,•••, ω. This series is convergent forwhereand where the interaction potential φ_{αβ}(r) of a pair of particles of Species α and β satisfiesfor all α, x, and s. [For a positive interparticle potential, φ_{αβ}(r)≥0, Φ=0.] Consequently the system remains in a single phase in this region. We have also generalized the inequalities of Lieb, Penrose, Lebowitz, and Percus to this case. For positive potentials upper (lower) bounds are gotten for the pressure and the distribution functions by expanding in a Taylor series up to terms of even (odd) total order in the fugacities.

Stark Effects on the Nuclear Quadrupole Coupling of ^{35}Cl in Sodium Chlorate
View Description Hide DescriptionThe changes in the electric‐field‐gradient tensorq induced by an applied electric fieldE and stress δ are described by the relation . The magnitudes and absolute signs of the five independent components of R ^{σ} for ^{35}Cl in NaClO_{3} were measured at 77°K and related to the absolute atomic configuration of the crystal. The numerical values are in units of 10^{9} cm^{—1}, R _{111} ^{σ} = —0.42, R _{222} ^{σ} = —2.43, R _{333} ^{σ} = —2.22, R _{113} ^{σ} = —1.53, and R _{123} ^{σ} = +3.53, with respect to the following coordinate system at a Cl site. The positive x _{3} axis points from Na^{+} to ClO_{3} ^{—}, i.e., towards the [111] direction that develops a positive piezoelectric charge for a tension σ_{33}. The positive x _{1} axis passes through an oxygen site and x _{2} completes the right‐handed set in the plane of the oxygen triangle. The electric field effects at constant stress and at constant strain are nearly equal. They are attributed to variations in the electron orbitals of the chlorate group and to changes in the ionic lattice sums outside this group.

Combination Reactions of Imino Radicals in the Flash Photolysis of Isocyanic Acid
View Description Hide DescriptionThe flash photolysis of HNCO vapor yielded CO, N_{2}, and H_{2} in a ratio of 1/0.42/0.27, independent of HNCO pressure (7–40 mm) and flash energy (17–1150 J). From the mass balance, production of ammonia was implied; the stoichiometry was described approximately by 12 . It was concluded that the reaction 2NH→N_{2}H_{2} was much more important than 2NH→N_{2}+H_{2}, with the observed stoichiometry largely determined by the subsequent decomposition of N_{2}H_{2}.
The addition of ethylene or propane reduced the yield of CO (by competitive absorption of light), and reduced the value of N_{2}/CO, apparently for the most part by interfering in the decomposition of N_{2}H_{2} rather than by reacting with NH radicals. The effect on the hydrogen yield was complicated by the production of hydrogen by photolysis of ethylene and propane; in the HNCO—propane system, however, extra hydrogen definitely was produced, probably by the reaction of NH with propane.

Molecular Motion in Solid 1,2‐Dichloroethane
View Description Hide Description^{35}Cl pure quadrupole spin—lattice relaxation has been studied in solid 1,2‐dichloroethane over the presently accessible temperature range below 90°K. T _{1} for ^{35}Cl changes by about three orders of magnitude between 53° and 82°K, and shows the onset of a thermally activated rate process above 63°K. The activation energy for this motion is found to be 3.93 kcal/mole. The temperature dependence of the protonT _{1} was also examined. At values of H _{0} for which relaxation is not complicated by the temperature dependent cross relaxation with the chlorine spin system, the activation energy obtained from protonT _{1} data agrees with that from the pure quadrupole measurements.
An anisotropic least‐squares refinement was made using the 133°K. X‐ray data of Reed and Lipscomb and amplitudes were assigned to chlorine atom motions. The physical picture that emerges from the combination of these data is that the amplitude of over‐all motion is small below the heat capacity anomaly, relaxation being effected by a reorientation between two (or several) close minima 30° to 40° apart and separated by the above barrier. Near the heat capacity anomaly this precursor motion goes over into a large scale motion, still about the Cl–Cl axis, which has been previously described.

Low‐Frequency Vibrations of Crystalline Biphenyl
View Description Hide DescriptionThe spectrum of inelastically scattered slow neutrons has been obtained for polycrystalline biphenyl. Whereas translational modes account for the broad general features of the whole spectrum, the fine structure observed can be interpreted in terms of librational and q‐independent internal modes. The six theoretically predicted librations have been assigned. Moreover, one has good reasons to believe that the torsional internal mode, practically inactive in infrared and Raman, occurs in the INS spectrum at about 70 cm^{—1}.

Theory of Subexcitation Electron Scattering by Molecules. I. Formalism and the Compound Negative‐Ion States
View Description Hide DescriptionThe problem of slow‐electron scattering by molecules is treated formally with explicit consideration of the possible effects of the compound negative‐ion states. The formulation is based on the treatments for nuclear reactions and scattering, in particular the unified treatment recently advanced by Feshbach. The transition matrix for both direct and resonancescattering, describing the excitation of the nuclear motion of the target molecule, is obtained. The influence of the compound negative‐ion states on the equivalent scattering potential for resonancescattering is investigated in some detail.

Theory of Subexcitation Electron Scattering by Molecules. II. Excitation and De‐Excitation of Molecular Vibration
View Description Hide DescriptionThe proposed mechanism for the excitation and de‐excitation of molecular vibration by slow electron impact involving compound negative‐ion states as intermediates is studied in some detail in light of the theory presented in Paper I of this series. The absolute orders of magnitude of the cross sections for such collisional processes are calculated for the (N_{2}, e) system, where detailed measurements have recently been made for the excitation of the ground N_{2} molecules to various excited vibrational states. The observed multipeak structures for the excitation functions are accounted for. The energy dependence of the cross sections for the excitation and de‐excitation of a vibrationally excited N_{2} molecule exhibits similar multipeak structures in the same energy region. An interpretation of such multipeak structures is offered.

Mass Spectrometric Study of the Vaporization of Uranium Monophosphide
View Description Hide DescriptionThe vaporization of uranium monophosphide, UP, and its mixtures with uranium oxide, UO_{2}, have been investigated by Knudsen effusion techniques in combination with a mass spectrometer.
The vaporization of UP occurs by decomposition according toIf UO_{2} is present approximately in equimolar ratio with UP the principal reaction is according toThe partial pressures of P, P_{2}, and U over UP have been obtained from the silvercalibration for the temperature range of 1750°—2250°K. The temperature dependence of logKp for Reaction (1), where x=1 was determined to be the following:From the second‐law treatment, the heat of vaporization in kcal/mole of UP is obtained for Reaction (1) as 251.17±4.88 when x=1.
Vapor pressures derived from other methods, such as (a) from known dissociation energy of P_{2} and thermodynamic functions of P and P_{2}, and (b) from the amounts of sample evaporated are discussed.

Excitation Migration in One‐Dimensional Molecular Random Lattices
View Description Hide DescriptionMigration of electronic excitation energy is studied in two types of one‐dimensional random lattices, one whose chains consist of identically oriented but randomly spaced molecules, and one with equally spaced but randomly oriented molecules. Results of computer calculations show that the loss of periodicity suppresses migration of excitation and that the velocity of migration is not constant but a decreasing function of time.

Infrared Spectrum of Diboron Tetrafluoride in the Gaseous and Solid States
View Description Hide DescriptionInfrared spectra of B_{2}F_{4} are reported over the range 2.5 to 50 μ at small grating resolution for both the gaseous and polycrystalline states. Examination of band envelopes for the gas and of differences between gas and solidspectra indicates that a structural difference exists between gaseous and solid B_{2}F_{4}. It is suggested that the alteration is analogous to that observed for B_{2}Cl_{4} with the V_{d} or staggered configuration applying in gas and the V_{h} or planar configuration applying in the solid. Rough estimates are made for some of the principal potential constants.

Many‐Center Wavefunctions for the Hydrogen Molecule and the Hydrogen Molecular Ion
View Description Hide DescriptionMany‐center wavefunctions for the hydrogen molecule and the hydrogen molecular ion are constructed using basis sets composed of either 1s orbitals or spherical Gaussians. Emphasis is placed on minimization of the total molecular energy with respect to all available nonlinear parameters. In the case of the s‐orbital basis, all the many‐center integrals are computed without resort to approximation techniques. It is concluded that the basis set of spherical Gaussians is superior to that of 1s orbitals and that further work with these functions may prove fruitful.

Interaction Energies, Charge Exchange Cross Sections, and Diffusion Cross Sections For N^{+}–N and O^{+}–O Collisions
View Description Hide DescriptionPotential energy curves for the lower electronic states of the N_{2} ^{+} and O_{2} ^{+} molecules have been obtained from a semiempiricalvalence bond method which makes use of available spectroscopic data. From these curves the probability of charge exchange has been calculated, and from this the charge‐exchange and diffusion cross sections. The cross sections for the O^{+}–O collisions are in good agreement with the experimental values of Stebbings, but differ by about a factor of 3 from earlier theoretical estimates. Some consequences of this are discussed.

Pariser—Parr Theory: Quantum Mechanical Integrals from the Benzene Spectrum
View Description Hide DescriptionThe integrals which occur in Pariser—Parr ASMO—CI theory for carbon atoms at short internuclear distances (≤2.40 Å) can be derived from the spectrum of benzene [R. Pariser, J. Chem. Phys. 24, 250 (1956)]. Previously, various workers have uniformly neglected the highest singly excited configuration in the configuration interaction on the grounds of its high energy and because its inclusion destroys the simple linear formulas for the state energies of benzene. The effect of inclusion of this configuration on the spectral matching method of determining nearest‐neighbor β_{ pq }, γ_{ pq }, and γ_{ pp }, employing the ^{1} B _{2u }, ^{1} B _{1u }, ^{1} E _{1u }, and ^{3} B _{1u } states of benzene has been investigated. The major effect was lowering of [11  11] to a value near that expected theoretically when correlation effects are considered. The influence of the new parameters on spectral calculations was explored for benzene, cis‐ and trans‐butadiene, naphthalene, and azulene, and the major effect observed was in the energies of excited triplets. It is suggested that this set of parameters, derived consistently and solely from electronic spectra, will be useful for spectral calculations.

Charge‐Transfer Self‐Complex Formed in Potassium Squarate Monohydrate
View Description Hide DescriptionThe x‐ray crystal structure analysis of the monohydrate of the potassium salt of squaric acid is reported. Squaric acid is the name given to 3,4‐diketocyclobutenediol. The main feature of the structure lies in the packing of the squarate anions. These are arranged in stacks with the planes of the anions almost parallel. Two of the carbon atoms, on neighboring anions, approach one another very closely, their separation being 3.237 Å (σ=0.012 Å). It is concluded that the structure represents a charge‐transfer self‐complex. The anion was found to have the expected D _{4h } symmetry with mean CO bond length of 1.259 Å (σ=0.007 Å) and mean CC bond length of 1.457 Å (σ=0.008 Å).

Atomic Emission of the Helium Afterglow
View Description Hide DescriptionThe spectral emission from a dc pulsed helium discharge for pressures from 5 to 20 Torr has been investigated during the early afterglow using interference filters with gated photomultiplier. The radiation transmitted by the filters consists generally of both atomic lines and molecular bands and after the termination of the active discharge shows characteristically an initial rapid decrease in intensity followed by a much slower rate. The rapid decrease is due to the atomic radiation, the slower to molecular. By subtracting the molecular emission from the total emission transmitted through an interference filter, the atomic emission is obtained. From the decay curves of the atomic emission, which is the result of collisional‐radiative recombination of He^{+}, and the known diffusion loss of He^{+}, the rate of conversion of He^{+} into He_{2} ^{+} is found to be 109±6 sec^{—1}·Torr^{—2}.

NMR of Isotopically Substituted Molecules. A Complete Analysis of the Spectrum of Acrylonitrile
View Description Hide DescriptionThe nuclear magnetic resonance spectra of ^{13}CH_{2}:CHCN and CH_{2}:^{13}CHCN appearing in their natural abundance in acrylonitrile have many proton transitions obscured by the much stronger protonresonances of CH_{2}:CHCN. Double‐irradiation experiments have been used to locate these missing lines and the ^{13}C transitions, and to assign them to the appropriate energy level diagrams. This has made possible three parallel independentanalyses by the iterative procedure, the identical proton—proton coupling constants providing a searching test of the validity of the solutions. The relative signs and magnitudes of the ^{13}CCH coupling constants have been determined, and small but significant shifts observed in the protonresonances, attributable to ^{13}C isotope effects. The chemical shifts of the ^{13}C nuclei have been related to the resonance frequency of protons in tetramethylsilane in the same magnetic field, with an accuracy of ±1 in 10^{8}.

Heat Content of Molten Uranium
View Description Hide DescriptionThe heat contents of γ‐phase uranium from 1205° to 1394°K and of molten uranium from 1415° to 1579°K were measured using a drop calorimeter.

Atomic‐Beam Scattering from Epitaxially Grown Gold Films
View Description Hide DescriptionThe spatial distribution of beams of He and Ar scattered by gold‐target films was examined mass spectrometrically during and after the formation of these films by evaporative deposition. By controlling the target temperature during the deposition of the metal, varying degrees of crystallographic orientation and surface smoothness were obtained. The metallic deposition rate was maintained high as compared with the impingement rate of background gas particles, resulting in approximate clean‐surface conditions during deposition. For rough polycrystalline films, only cosine scattering of He and Ar was observed. For smooth, well‐oriented films, specular scattering of He was observed during deposition. In this latter case, a gradual time‐dependent dispersion in He scattering was seen after deposition and is shown to result from the formation of adsorbed gas layers. For Ar scattered from a smooth goldfilm during deposition, a broad directed beam, displaced from the specular angle, is obtained, and very little dispersion occurs after deposition. This latter result is interpreted as being due to the greater interaction between Ar and gold, compared with that between He and gold, which masks the effects of adsorbed gases upon Ar scattering.