Volume 57, Issue 4, 15 August 1972

Vibrational and Other Corrections to the Nuclear Quadrupole Moment of ^{14}N in Ammonia
View Description Hide DescriptionThe field gradient at the nitrogen nucleus has been evaluated for the NH_{3} molecule using two different rather accurate electronic molecular wavefunctions. The vibrational correction has been obtained by averaging the field gradient for the two totally symmetric vibrations of the C _{3v } point group computed at a number of geometrical configurations. In addition, a careful analysis has been carried out to assess the effect of the electronic quadrupolepolarization and other higher order effects. The value for the nuclear quadrupole moment of ^{14}N in ammonia so obtained is .

Kinetics of the Reaction of O(^{3} P) Atoms with Benzene
View Description Hide DescriptionThe kinetics of the gas phase reaction of O(^{3} P) atoms with benzene was investigated using fast flow techniques. Specific rate constants were obtained using two separate systems, one with ESR detection to monitor the decrease in O(^{3} P) atoms and the other with mass spectrometry to follow the change in benzene concentration. The rate constant computed with respect to O(^{3} P) removal is much larger than that obtained in the mass spectrometer studies and this is believed to result from further reactions of oxygen atoms with radical species produced in the initial O(^{3} P)+C_{6}H_{6} interaction. On the basis of the mass spectrometric studies a specific rate constant for the reactionof was obtained over the temperature range of 255–305°K. A negligibly small kinetic isotope effect was observed in competitive experiments with C_{6}H_{6} and C_{6}D_{6}. The results obtained are interpreted in terms of a rate determining step involving the addition of oxygen atoms to the benzene ring followed by subsequent isomerization and/or decomposition reactions.

Influence of Surface Charge and Surface Structure on the Sublimation of Ionic Crystals
View Description Hide DescriptionThe formation of charged defects in ionic crystals is shown to be accompanied by the formation of surface defects: kinks. The resultant defect pairs contribute to a Debye‐Hückel charge distribution at the surface.Surface charge,surface structure, and crystal defect equilibria are found to be interrelated and to influence sublimation rates. The theory is applied to the case of sublimation of II‐VI compounds and compared with experiments.

Quantum Mechanical Scattering of Asymmetric Molecules. II. Comparison between the Systems He–D_{2} and He–HT
View Description Hide DescriptionExact quantum mechanical coupled channel calculations have been performed in order to compare the rotating potential model for heteronuclear molecules with an asymmetric mass distribution, and the usual potential with anisotropy terms for homonuclear molecules. The scattering cross sections of He–D_{2} and He–HT show no difference in shape, apart from some quenching of the orbiting resonances. There is, however, a significant difference in absolute magnitude, due predominantly to inelastic processes. In the inelastic cross sections, the effect of the shift of the center of mass from the center of interaction in asymmetric molecules counteracts the effect of a change in moment of inertia.

Elastic Constants of the Nematic Liquid Crystalline Phase of p‐Methoxybenzylidene‐p‐n‐Butylaniline (MBBA)
View Description Hide DescriptionThe bend and splay elastic constants of MBBA were measured over its nematic temperature range. The ratio of the two constants is . The temperature dependence of the elastic constants is found to be adequately described by the simple mean‐field models. A comparison is made between viscosity coefficients obtained from the elastic constants and light scatteringspectra and from classical viscosity measurements. A method proposed for the measurement of twist elastic constants is evaluated and an upper limit of this constant of MBBA as a function of temperature is reported.

Scattering by an r ^{−2n } Potential in the Born Approximation and Application to Dipole‐Quadrupole Scattering
View Description Hide DescriptionBy using the Born approximation, an analytic formula is derived for the phase shifts δ_{ L } for scattering by a potential with an r ^{−2n } tail. The low‐energy properties of the phase shifts are discussed, and an expansion of tan δ_{ L } in powers of k is presented. The dipole‐quadrupole r ^{−8} potential is discussed as a special case.

Effect of Pressure on the Rates of Reaction of Solvated Electrons in Liquid Ethanol
View Description Hide DescriptionAt a γ radiolysis dose of in ethanol at 296°K the hydrogen yields in neutral ethanol were at 1 bar and 5.5 at 5.3 kbar; in 1 mM and 1 M sulfuric acid, independent of pressure. The electron scavengers nitrobenzene, acetone, and naphthalene reduce the hydrogen yields in neutral and acidic ethanol at 1 bar and 5.3 kbar; increasing the pressure greatly reduces the ease of scavenging the free ions but has only a small effect on scavenging efficiency in the spurs. Using as a standard the reaction with at 1 bar and averaged between 0 and 5.3 kbar, one obtains the following values for and , at zero ionic strength, +4.5; . The diffusion coefficient of solvated electrons in ethanol appears to correlate with the liquid viscosity; this is different from the behavior of electrons in alkanes. In ethanol for for . The free ion yield in ethanol is , independent of pressure from 1 bar to 5.3 kbar; the model of Freeman and Fayadh [J. Chem. Phys. 43, 86 (1965)] is consistent with this behavior and it predicts that G _{fi} in methanol and water are also independent of pressure.

Laser Raman Spectra of Solid and Molten NaNH_{2}: Evidence for Hindered Rotation of the Ion
View Description Hide DescriptionResults of a Raman study of solid and molten from 25–220°C are reported. Three bands are observed in both the solid (3267, 3218, and 1531 cm^{−1}) and the liquid (3267 dp, 3218 p, and 1550 p cm^{−1}), which are assigned to the three expected fundamental modes of with C _{2v } point symmetry. Additional bands were observed in the 300–700 cm^{−1} region for both the solid and the liquid. In the case of the liquid, the band envelope in this region was resolved into three Gaussian components, which are attributed to the hindered rotational modes of There was no evidence of intermolecular hydrogen bonding between ions.

Studies of the Triplet State of Carbonyl Compounds. I. Phosphorescence of β‐Diketones
View Description Hide DescriptionThe phosphorescence intensity of the diketone form and of one of the two chelated enol forms of β‐diketones in solution at 77°K depends largely on the solvent used. The phosphorescence of the diketone form (seen principally in polar solvent) is similar to that of aromatic monoketones and arises from a state. The phosphorescence of one of the two chelated enol forms in nonpolar solvent is emitted from a state as suggested by the external and internal heavy atom effects. However the shortness of the phosphorescence lifetime shows that the lowest triplet state is probably mixed with some higher energy triplet state of type. The diketone form seems much more luminescent than the chelated enol form. This result is consistent with the suggestion of Lamola [A. A. Lamola and L. J. Sharp, J. Phys. Chem. 70, 2634 (1966)] that a very fast radiationless decay takes place in molecules possessing an intramolecular hydrogen bond between the carbonyl oxygen and the hydroxyl hydrogen. The comparison of chelated enol spectra with those of crotonophenone and benzalacetone indicates that phosphorescent chelated enol has structure II, the other form being nonradiatively deactivated or nonexistent. Benzoyltrifluoroacetone gives a spectrum with a long lifetime which seems to originate from a nonchelated enol form.

Torsional Barriers in the Methyl Substituted Ethylenes
View Description Hide DescriptionThe far‐infrared spectra have been recorded from 350 to 33 cm^{−1} for propene, cis‐2‐butene, trans‐2‐butene, isobutene, 2‐methyl‐2‐butene, and 2,3‐dimethyl‐2‐butene, in the gaseous and solid states (−190°C). The Raman spectra of the liquids have also been recorded in the same frequency range. The bands corresponding to the torsional modes are assigned as appearing at 226; 195; 233 and 219; 183 and 144; 219 and 178; and 227, 201, 194, and 153 cm^{−1}, in the infrared spectra of propene, trans‐2‐butene, isobutene, cis‐2‐butene, 2‐methyl‐2‐butene, and 2,3‐dimethyl‐2‐butene, respectively, in the solid state. The corresponding barriers to internal rotation are 2.68, 2.21, 3.24, 1.82, 2.45, and 2.25 kcal/mole.

On the Coupling Scheme in Uranyl Complexes
View Description Hide DescriptionSimple theoretical considerations of the ligand field type have been applied to the electronic structure of insular uranyl complexes. The study of the consequences of equatorial ligation is used as a means to test the applicability of different coupling schemes for the isolated uranyl ion. From the analysis of the spectra of a large number of different uranyl complexes of D_{nh} symmetry, it was previously shown how the effect of equatorial ligation consists in lifting certain degeneracies of the free uranyl electronic energy levels and introducing variations in the corresponding transition probabilities. In this note the equatorial field operator is successively applied to uranyl wavefunctions derived in a Russell‐Saunders approximation, in an coupling approximation, and in an intermediate scheme. Only Russell‐Saunders coupling allows a satisfactory explanation of the observed splitting and intensity pattern.

Kinetic Theory of Droplet Growth in Nucleation
View Description Hide DescriptionA kinetic theory is presented for the mass flux to a liquid droplet surrounded by its pure vapor. When the mass flux Γ is expanded in terms of a parameter α which is the ratio of the droplet size to the mean free path (inverse Knudsen number), one obtains a series of the form The coefficients of the first three terms of this expansion are derived by solving the Boltzmann equation using a modified Knudsen number iteration procedure. It is shown that the coefficients are determined by integrals associated with sequences of successive collisions among a number of vapor molecules and the droplet. These collision integrals bear a close similarity to the collision integrals derived earlier from the generalizedBoltzmann equation for the density dependence of the transport properties of gases.

Reactions of and with HCl and HBr
View Description Hide DescriptionReactions of and with HCl and HBr were carried out in a flowing afterglow system at room temperature and the reaction rate constants were measured. The reaction is found to be nearly thermoneutral. The results lead to these values of electron affinities:. In addition, rate constants for the reactions of NO^{−} and with HCl are reported. A number of cluster ions were observed: , and Br^{−} (HNO_{3})_{1,2}.

Thin Film Reflection Spectroscopy. I. Determination of Optical Constants of Amorphous Selenium and As_{2}Se_{3}
View Description Hide DescriptionThe reflectivityspectra of thin films of amorphous As_{2}Se_{3} and Se have been obtained. The films were deposited on aluminum substrates and had a range of thickness from 2 to 50 μ. The frequency range covered by these spectra was from 650 to 40 wavenumbers (15 to 250 μ). Two methods have been used to determine the optical constants,N and K, from the reflectivityspectra. The first employs a single equation nonlinear regression analysis on the radiant reflectance equation. The second method uses a two equation maximum likelihood analysis on the real and imaginary parts of the amplitude reflectance equation coupled with a Kramers‐Kronig analysis of the phase angle. The real and imaginary parts of the complex dielectric constant, the absorption coefficient, the energy lossfunction and the transverse and longitudinal vibrational frequencies are then determined from the optical constants.

Pressure Dependence of Energy Transfer from Pyrene to Perylene
View Description Hide DescriptionThe efficiency of singlet‐singlet energy transfer between pyrene and perylene in polymethylmethacrylate decreases with increasing pressure, i.e., at 77°K the critical transfer distance R _{0} is 44 Å at 1 atm and 35 Å at 30 kbar. The factors responsible for the reduced efficiency at high pressure are in order of decreasing importance: the decrease in the fluorescence lifetime of the donor, the increase in the refractive index of the medium, and the decrease in spectral overlap of pyrene fluorescence and perylene absorption.

Thermodynamics of Rare‐Earth‐Carbon Systems. IV. The Lutetium‐Carbon System
View Description Hide DescriptionThe vaporization of the lutetium dicarbide‐carbon system has been investigated by the Knudsen effusion‐mass spectrometric technique over the temperature range 2100 to 2600°K. Lu(g) partial pressures, dissociation energies for LuC_{2}(g) and LuC_{4}(g) molecules, and the standard heat of formation for LuC_{2}(s) were obtained.

Correlation Functions for a Mixture of Gaussian Molecules
View Description Hide DescriptionThe Mayer series for the pair correlation functions of the Gaussian mixture has been determined to ninth power of the density (11‐point graphs). The model is a mixture of A and B in which the AA and BB interaction potentials are zero. The AB interaction is such that the Mayer f function, exp (−v _{AB}/k _{B} T) −1, is a negative Gaussian. The direct correlation functions and radial distribution functions are evaluated using Padé approximants. Comparison is made with solutions of the Percus‐Yevick and hypernetted chain equations.

Molecular Beam Electric Deflection and Resonance Spectroscopy of the Heteronuclear Alkali Dimers: ^{39}K^{7}Li, Rb^{7}Li, ^{39}K^{23}Na, Rb^{23}Na, and ^{133}Cs^{23}Na
View Description Hide DescriptionMolecular beam electric resonancespectra for several heteronuclear alkali dimers have been obtained for the transition in the J = 1, v=0 state in a supersonic beam. Values of the ground vibronic Stark coefficient and the nuclear quadrupole coupling constants eqQ were obtained. The values of were for ^{39}K^{7}Li, for ^{85}Rb^{7}Li, and for ^{39}K^{23}Na. Badger's rule was used to estimate B _{0} and to determine the following values for the molecular electric dipole moment:, and , where the errors arise from the uncertainties in the rotational constant. Electric deflection was used to obtain a value of μ^{2}/B for Rb^{23}Na of and hence for the dipole moment, while rf spectroscopy with power broadening was employed with ^{133}Cs^{23}Na to obtain for and hence for μ0. The translational and rotational temperatures in the supersonic beams were estimated from velocity scans and quadrupole voltage scans. An ionic model is used in a heuristic interpretation of the dipole moment results.

Effects of Screening and Polarization on Vibration‐Rotation Properties of H_{2}
View Description Hide DescriptionEight simple models of H_{2} in the ground state are examined through use of Dunham's formulas, numerical integration of the vibrational Schrödinger equation, and the WBK energy condition. These models provide four examples for studying the effects of variable screening and four examples for the effects of polarization on vibration‐rotation properties. At small v, variability of the screening parameter α correlates with positive curvatures of the ΔG and B_{v} curves; i.e., for the four models with both curvatures are negative, while both curvatures are positive for the four cases with α variable. The dominance of the quartic potential coefficient a _{2} in determining near‐equilibrium ΔG and B_{v} curvatures is pointed out. Near dissociation, the presence of polarization causes positive curvature of these two curves. In showing this, large fictitious values of the reduced mass are employed to provide several vibrational levels very close to the dissociation limit. The D_{v} curves have a pronounced minimum, similar to that of the experimental curve, for α variable but not for . In addition, the values of D_{v} and H_{v} are much closer to experiment for α variable than for .

Manifestations of Anharmonicity in the Specific Heat of Crystalline ^{63}Cu
View Description Hide DescriptionAccurate measurements of the specific heat of a high purity single crystal of ^{63}Cu have been carried out for T<50°K. The data are analyzed in terms of deviations from the specific heat of a physically realistic phonon model for ^{63}Cu. The sixth neighbor general‐force model determined for normal Cu at 49°K by neutron diffraction measurements has been adapted to ^{63}Cu by a scaling method. Precision calculations of phonon spectra were done for both general‐force and simple Leighton models. A statistical analysis shows deviation curve features are statistically significant with a minimum close to that of the theoretical quartic anharmonic contribution. Smoothed experimental C_{p} and C_{v} data are given for crystalline ^{63}Cu.