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Volume 53, Issue 10, 15 November 1970

Viscosity, Thermal Conductivity, and Diffusion Coefficient of Ar–Ne and Ar–Kr Gaseous Mixtures in the Temperature Range 25–700°C
View Description Hide DescriptionThe paper presents new relative measurements of the viscosity of argon, neon, and krypton and of the binary mixtures Ar–Ne and Ar–Kr, all at atmospheric pressure, in the nominal temperature range 25–700°C, and with a precision of ± 0.1%. The oscillating‐disk method was employed. The experimental data were used to calculate the binary diffusion coefficient for the mixtures, and the thermal conductivity of the pure gases as well as the mixtures. The data for the pure gases can be correlated separately with the aid of a suitable potential of the 6‐n family, and optimum values of the parameters , , and are given for each of them. The same data can be correlated equally well with the aid of a universal, empirical expression for the collision integral with two individual parameters, and , being adequate to describe each gas separately. The conventional combination rules as well as those proposed by Kalelkar and Kestin [J. Chem. Phys. 52, 4268 (1970)] have been tested, and it was found that the latter represent the results as well as the expression for mixture viscosity in terms of the viscosity of the pure components and the coefficient of binary diffusion. Wassiljewa coefficients have been evaluated for the representation of the viscosity and the thermal conductivity of the mixtures.

NMR, Calorimetric, and Diffraction Study of Molecular Motion in Crystalline Carboranes
View Description Hide DescriptionMolecular motion of two nearly icosahedral molecules, ortho‐ and meta‐carborane, in the solid state has been studied by x‐ray diffraction, calorimetric, and NMR techniques. At 25°C the powder diffraction patterns for both crystals are consistent with a fcc unit cell of dimension 9.86 Å containing four molecules. For both isomers the corresponding molecular site symmetry is higher than the molecular symmetry, implying molecular orientational disorder at this temperature. That the orientational disorder is of a kinetic nature is confirmed by NMR measurements. The protonresonance line second moment at 25°C is 0.711 ± 0.051 G^{2} for o‐carborane and 0.82 ± 0.10 G^{2} for m‐carborane. This can be compared with a line second moment of 0.630 G^{2} calculated assuming rapid isotropic molecular reorientation and a line second moment of 34 G^{2} calculated for the rigid lattice. For both isomers the observed second moment is much smaller than calculated assuming rotation about the molecular twofold axis, implying rapid reorientation between thermodynamically indistinguishable orientations. Measurements above and below room temperature were made only for the ortho isomer. A phase transition was observed at 4.0 ± 3.0°C both by calorimetry and x‐ray diffraction. The associated transition enthalpy and entropy were respectively 0.84±0.05 kcal/mol and 3.0 e.u. The protonresonance line second moment observed at − 0.6°C is 1.13 ± 0.1 G^{2}, implying a rather general molecular reorientation between indistinguishable molecular orientations at this temperature in the low temperature phase. With decreasing temperature the line second moment rapidly increases in the vicinity of − 80°C. At − 98°C, the lowest temperature measurement, molecular reorientation is still rapid enough to significantly narrow the resonance line. No high entropyphase transition was found by calorimetric measurements from below the 4°C transition to − 130°C, indicating either that an order–disorder transition lies below − 130°C or that for kinetic reasons the ordered phase is not attained, necessitating a nonzero entropy at 0°K. On increasing temperature above 25°C, no change was observed in line second moment until about 200°C. Above this temperature the linewidth and second moment decrease due to rapid molecular translational diffusion. Apparent activation parameters for molecular rotation and for translational diffusion have been obtained from linewidth measurements.

Anisotropy of the Singlet Transitions of Crystalline Anthracene
View Description Hide DescriptionThe reflection spectra of three faces of crystalline anthracene in the region 5000–1820 Å have been observed at room temperature, and the corresponding absorption spectra have been derived by a Kramers–Kronig analysis. The results for face (001) agree with previous direct absorption work. For faces (201̄) and (1̄10) the Davydov splittings of the 3800‐Å transition are found to be substantially different from those observed for the (001) face. The strong 2500‐Å transition gives rise to reflection bands which are 1.5–2.0 eV wide. These bands are examples of metallic reflectivity which had previously been observed only for some organic dye crystals. For radiation incident upon the (201̄) and (1̄10) faces the splittings of the strong transition are smaller by nearly an order of magnitude relative to that observed in the case of the (001) face. These results are interpreted as strong evidence for the dependence of dipole sums on the relative orientation of the wave vector k to the transition moment d. The experimental observations are compared with the dipole theory of exciton states in molecular crystals. Qualitative agreement between dipole calculations and experiment is good, and quantitative differences are attributed to the presence of higher multipole and electron exchange effects. It is estimated that these nondipolar interactions contribute approximately − 1600 cm^{−1} to the total Davydov splitting of the intense 2500‐Å transition.

Further Selection Rules for Excitation by Electron Impact at Small Momentum Changes
View Description Hide DescriptionAt kinetic energies in the range 300–500 eV, there is an accumulation of experimental evidence that the Born approximation does not hold when term symbols are the same in the initial and final states. In the present research, it is shown that deviations from the Born approximation at small momentum changes are proportional to a series of matrix elements of operators, the first (and dominant) term involving an operator which is invariant under the operations of the symmetry group of the scatterer. This accounts for the observation in the first sentence of this Abstract. Selection rules for the next term in the series are also discussed.

Absolute Electron Collision Cross Sections for Two Forbidden Transitions in Nitrogen at Kinetic Energies of 300–500 eV
View Description Hide DescriptionAbsolute differential electron collision cross sections and generalized oscillator strengths have been measured for two forbidden transitions, and , in N_{2}. These measurements were carried out at electron kinetic energies of 300, 400, and 500 eV and at small scattering angles to facilitate extrapolation to zero momentum change. The Born approximation apparently holds for the excitation of the first transition but not for the second. Generalized oscillator strengths, however, extrapolate to the optical oscillator strength (zero) in both cases in accord with the limit theorem previously demonstrated.

Studies in Molecular Dynamics. VIII. The Transport Coefficients for a Hard‐Sphere Fluid
View Description Hide DescriptionThe diffusion coefficient, the shear and bulk viscosity, and the thermal conductivity have been evaluated by means of their Einstein expressions by molecular dynamics computation over the entire fluid region. The autocorrelation functions for the different transport coefficients as well as their various components (such as kinetic and potential) have been obtained also. The results are compared to the predictions of the Enskog theory which involves a nearly exponential autocorrelation function. The observed deviations from an exponentially decaying autocorrelation function persist for many mean collision times, indicating that highly collective effects must be involved. The largest deviations for the transport coefficients occur near solid densities for the viscosity which is about twice as large as the Enskog prediction and for the diffusion coefficient which is about a factor of 2 smaller. In conformity with the Stokes relation, the product of diffusion and viscosity is found to be nearly constant over the entire fluid density range and in nearly quantitative agreement with the theoretically predicted constant using slipping boundary conditions. The deviations from the Enskog theory for the thermal conductivity are barely perceptible within the few percent accuracy of the data. The same is true for the bulk viscosity with its larger inaccuracies.

Normal Coordinate Analysis and Force Constants of Nitrogen Trichloride
View Description Hide DescriptionA vibrational analysis has been performed for nitrogen trichloride based on a frequency fit of the ^{14}N and ^{15}N species. Force constants for several modifications of the Urey–Bradley force field (UBFF) are compared to the six constants of the general valence force field. Modification of the UBFF to include angle–angle and bond–bond cross terms results in an excellent agreement with the GVFF constants. The chlorine–chlorine repulsion force constant obtained agrees satisfactorily with the calculated Lennard‐Jones nonbonded interaction between two argon atoms.

Constrained‐Variation Method Applied to Helium‐Atom Wavefunctions
View Description Hide DescriptionThe constrained‐variation method is applied to helium‐atom wavefunctions, using precise Pekeris values of electron moments both as constraints and as tests of the effectiveness of the method. The conclusions support the basic premise that constrained‐variation wavefunctions may better represent the true electron densities in a system than do the corresponding free‐variation functions.

Direct Flow Measurement of Quenching Rates
View Description Hide DescriptionA relaxation method is developed which permits a direct measurement of quenching rate constants. An Al wire spiral is used to selectively quench which is normally present in discharged oxygen as a steady‐state intermediate. The characteristic time for the reestablishment of the steady state is used to determine wall and bimolecular quenching rates. With this method, absolute rate constants are obtained from relative intensity measurements of the emission at 7619 Å. The rate constant for quenching by H_{2}O is found to be 4.0 ± 0.6 × 10^{−12} cc sec^{−1}. Rate constants for a number of other quenchers are reported.

Anisotropy of the Carbon‐13 and Proton Hyperfine Coupling Constants in Organic Radicals
View Description Hide DescriptionA theoretical study of the anisotropy of the carbon‐13 and proton hyperfine coupling constants in organic radicals is presented in terms of a spin density formulation which uses the generalized product approximation specialized to valence‐bond wavefunctions. Both isotropic and anisotropic components of the ^{13}C and ^{1}H hyperfine coupling tensors are obtained for the methyl and ethyl radicals with inclusion of all valence electrons. Theoretical results for the methyl radical are also based on spin densities from self‐consistent‐field (SCF) molecular‐orbital theory in the approximation of intermediate neglect of differential overlap and from nonempirical spin‐restricted SCF calculations with configuration interaction. The calculated results are compared with the available experimental data, and they indicate that inclusion of contributions from the σ‐electron framework is essential. But in contrast to isotropic hyperfine coupling constants, components of the anisotropic hyperfine tensor are relatively insensitive to the spin density distribution. Factors which are also discussed are the importance of variation of the effective nuclear charge, radical geometry, contributions from inner shells, and off‐diagonal elements of the spin density matrix.

Ionic Collision Processes in Gaseous Ammonia
View Description Hide DescriptionRate coefficients for reactions resulting from collisions of NH_{3} ^{+} and NH_{2} ^{+} with NH_{3} have been measured as a function of primary ion translational energy over the energy range 0–8.0 eV. NH_{4} ^{+} was the only observed product of NH_{3} ^{+}/NH_{3} collisions. The rate coefficient drops sharply with increasing energy from 18.1 × 10^{−10} cm^{3} molecule^{−1}·sec^{−1} for thermal ions to 10.2 × 10^{−10} cm^{3} molecule^{−1}·sec^{−1} for ions with a maximum translational energy (KE) of 1 eV. Above 3 eV an essentially constant value of 8 × 10^{−10} cm^{3} molecule^{−1}·sec^{−1} is obtained. Collisions of NH_{2} ^{+}/NH_{3} result in the production of both NH_{4} ^{+} and NH_{3} ^{+}. With increasing ion energy below 1 eV the relative number of collisions which proceed via the less exoergic mechanism increases. Above 3‐eV KE the rate coefficient for the removal of NH_{2} ^{+} increases which is taken to indicate that in this energy range the cross section for electron transfer is greater than that for ion–molecule reaction. The rate coefficient for NH_{4} ^{+} production drops to an undetectable level at about 2‐eV KE rising again above 3‐eV KE. It is proposed that this new onset can be attributed to the endoergic reaction in which the neutral products are N+H and not NH as is supposed for the proton‐transfer process at lower ion energies.

Pulse Radiolysis Studies. XIX. Solvent Effects in Electron Transfer and Proton Transfer Reactions of Aromatic Molecule Ions
View Description Hide DescriptionAbsolute rate constants were determined, by the pulse radiolysis technique, for the electron transferreaction from an aromatic radical anion to a different neutral aromatic molecule: for a number of aromatic molecule pairs in ethanol, in ethylenediamine, and in diethylamine. The dependence of these rate constants upon the standard free energy for reaction of the pair and upon the dielectric properties of the solvent, as predicted by the theory of Marcus for electron transferreactions, is found to support this theory, at least semiquantitatively, over a limited range. The effect of solvent on the rate of protonation of the biphenyl radical anion by an alcohol: was studied for a number of mixed solvent systems, namely, ethanol–ethylenediamine, ethanol–cyclohexane, ethanol–triethylamine, ethanol–diethylamine, ethylene glycol–ethylenediamine, and ethylene glycol–triethylamine. In the alcohol–amine systems the first order rate constant for the protonation reaction was drastically reduced in amine‐rich solution and increased in alcohol‐rich solution. The rate constant was increased at all concentrations of cyclohexane in the ethanol–cyclohexane system. These effects of the presence of a second solvent were attributed to the formation of a hydrogen‐bonded complex between the amine and the alcohol, which reduces the rate in these systems, and to the solvent structure breaking effect of the cyclohexane, which increases the rate.

High‐Resolution Electronic Absorption Spectra of Diazanaphthalenes in the Vapor Phase
View Description Hide DescriptionThe absorptionspectrum of quinoxaline vapor for is presented. Two diffuse systems and a single sharp system are observed. A vibrational analysis of observed broad and sharp bands is given for the allowed electronic system, and a 0–0 band is assigned at 27 071 cm^{−1}. Characteristic band contours and correlation with low‐temperature polarization data allow the assignment of nine fundamental vibrations in the electronic excited state. Six ground electronic state fundamental vibrations are also assigned. The observed band contours and prominent frequencies of quinoxaline are compared with other diazanaphthalenes, and new spectral data for quinazoline and cinnoline are presented.

Intra‐ and Intermolecular Vibrational De‐excitation in Impulsive Atom–Diatomic Molecule Collisions
View Description Hide DescriptionThe de‐excitation of vibrationally energetic Morse oscillators via impulsive collision with an atom is discussed. In certain types of atom–oscillator systems intramolecular vibration‐to‐rotation energy transfer is more important than intermolecular vibration‐to‐translation transfer. Since the efficiency of this intramolecular de‐excitation has a different dependence on particle mass and collision energy than does the intermolecular de‐excitation, restricting consideration to the latter, e.g., using a collinear collision model, does not always lead to an adequate description of the de‐excitation process.

Perturbation Theory of the Hooke's Law Model for the Two‐Electron Atom
View Description Hide DescriptionThe Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The expansion of the correlation energy is compared with that for heliumlike atoms and found to be similar.

Perturbation Energies for the Hooke's Law Model of the Two‐Electron Atom
View Description Hide DescriptionThe Rayleigh–Schrödlinger perturbation energies for the ground state of the Hooke's law model atom are calculated through tenth order. The are expressed as singly infinite sums whose terms are obtained from recurrence relations. Very slow convergence limited the method to and below. The results are compared with those of Midtdal (1965) for heliumlike atoms, and it appears that the convergence of the Hooke series is more rapid. However, no recognizable patterns are observable in the Hooke through . The nature and position of the singularity determining the radius of convergence is discussed.

External Heavy Atom Perturbation of Vibronic Transitions in Singlet–Triplet Spectra
View Description Hide DescriptionThe high‐resolution phosphorescencespectra of a number of compounds were obtained at 4°K both in the presence and absence of external heavy atom perturbers. A comparison of the two cases demonstrates that only totally symmetric modes of the molecule are enhanced by the external heavy atom effect. This result implies that the enhancement mechanism is purely electronic in nature and involves no vibronic coupling. The results also suggest that the external heavy atom effect can be useful in aiding the assignment of complicated singlet–triplet spectra.

Collisional Destruction of the State of Mercury
View Description Hide DescriptionInclusion of collisional destruction mechanisms as sink terms in the theory of imprisonment of resonance radiation appears to have been neglected in the case of the 2537‐Å mercury line. In this paper, the Holstein photon transport equation is employed to determine the effect of destructive or self‐quenching collisions between resonance state and ground state atoms, processes in which the resonance state is converted to another excited state with the release of kinetic energy. These mechanisms seem to explain experimental work in which the decay constant of the 2537‐Å mercury line reaches a minimum and then increases with density. Comparison of theory with experimental data yields a cross section between 3.0 and 10.0 × 10^{−18} for the conversion of to metastable by two‐body collisions with . The sharp increase at high density of the decay constant of the 2537‐Å mercury line has not been predicted by previous theories but is a general consequence of the inclusion of collisional destruction mechanisms.

Oscillator Strength of the Resonance Transitions of Ground‐State N and O
View Description Hide DescriptionMultiplet oscillator strengths, , for the resonance triplets of N and O were determined using the line absorption method and measuring atom concentrations by chemical “titration.” For the NI triplet at 1200 Å, , and excellent internal agreement was obtained among the separately measured of the three lines. A value of (3 ± 1) × 10^{−11} cm^{3} sec^{−1} is required for the rate constant of the N+NO→N_{2}+O reaction in the analysis of the data. For the OI triplet near 1300 Å, the apparent increased sharply and reproducibly from 0.19 to 0.42 when the diluent gas in the discharge light source was changed from Ar to He, which indicates that excitation transfer is a major source of excitation in such Ar–O_{2} resonance lamps. The larger oscillator strength obtained with He–O_{2} light sources is in excellent agreement with results of lifetime measurements by other workers.

Glory Scattering in Molecular Collisions: Formal Expressions for the Total Cross Section
View Description Hide DescriptionAn extended distorted‐wave treatment is used to obtain formal expressions for the total cross section when two rigid diatomic molecules with orbital and nuclear‐spin angular momenta collide. Explicit expressions are obtained through second order, including the lowest‐order inelastic effects.