Volume 57, Issue 6, 15 September 1972

Collision Broadening of Rotational Spectrum
View Description Hide DescriptionThe problem studied is the rotational absorptionspectrum of linear molecules of moment inertia I in a simple nonpolar buffer gas. The focus is on the behavior of the spectrum as the buffer gas pressure and the associated collision frequency ν is increased. Four regions are distinguished. (1) , there are sharp lines with a van Vleck‐Weisskopf line shape; (2) , the contributions from overlapping lines are summed analytically. The ratio of minimum to maximum absorption in the weakly oscillatory spectrum is computed. (3) , This is the classical inertial region where there is a single maximum in the absorption per cycle. We compute its position as it moves from an angular frequency (2kT/I)^{1/2} to lower frequencies with increasing collision frequency. (4) , this is the region where the Debye frequency profile is valid, with the peak of absorption at an angular frequency (1/ν) (2kT/I). The calculations are based on a kinetic equation for the density matrix with a single relaxation time, no position change, collision model. We also compute the time dependent correlation functions needed in the theory of the rotational Raman effect of linear molecules.

Photoequilibrium and the Decay Mechanism in Dinitrobenzyl Pyridine Photochromism
View Description Hide DescriptionThe maximum intensity of photochromic color change in 2‐ and 4‐(2′, 4′‐dinitrobenzyl) pyridine solutions is controlled by a photon equilibrium. The equilibrium has been approached from both sides by means of irradiation. Solutions of the compound almost entirely in the form of its colored modification have been prepared. In the absence of photon activated decay, which is controlling in experiments where the preparation is made photolytically, these solutions decay thermally to the ordinary form by two mechanisms, the relative importance of which depends on temperature and pH.

Hydride Ion Transfer and Isotope Effects in CD_{4}‐Silane Ion Molecule Reactions
View Description Hide DescriptionHydride ion transfer is identified as an important mechanism in the reactions of methane and deuterated methane primary ions with silane. The pathway for these reactions is shown not to involve the production of a long lived intermediate. However, it is shown that addition reactions proceeding through a long lived intermediate show relatively little isotopic scrambling. Furthermore, it appears that the probability of losing a H atom is very much higher than that for losing a D atom from such an intermediate.

Torsion‐Vibration‐Rotation Interactions in Methanol. IV. Microwave Spectrum of CH_{3}OH in the Excited CO Stretching State
View Description Hide DescriptionThe branch and the doublet have been observed for the first excited CO stretching mode in the microwave spectrum of normal methanol. A value for the excited state barrier to internal rotation of is required to reproduce the Q‐branch origin frequency of 47 929.9 MHz, with reasonable limits on geometry changes assumed. This value is consistent with previous infrared results.

Another Hard‐Sphere Equation of State
View Description Hide DescriptionA basic form for a Pade approximant of the hard‐sphere equation of state is proposed. This form incorporates both high and low density limiting behavior and can easily be extended to include any further virial coefficients as they are calculated. Furthermore, addition of a simple term converts the approximant into an accurate equation for hard‐sphere fluids. Hard‐sphere solid behavior can also be estimated using a modification of the approximant, although the results are not as satisfactory as those of the high density hard‐sphere equation of state.

Dielectric Constant and Molar Polarizability of Compressed Gaseous and Liquid Fluorine
View Description Hide DescriptionIn this paper we present accurate wide‐range measurements of the dielectric constant of saturated liquid fluorine from 70 to 140°K and of compressed fluid fluorine at temperatures between 100 and 300°K at pressures to . The data are combined with previously measured densities to determine the molar polarizability and its dependence on density and temperature. The density range examined extends to nearly 3 times the critical density. The molar polarizability is found to increase initially with density and then decrease. Current theories of the dielectric constant are found to give satisfactory qualitative interpretation of the density dependence of the molar polarizability but do not give satisfactory quantitative predictions.

EPR Study of Diphenylnitroxide in Benzophenone
View Description Hide DescriptionA complete anisotropicEPR study of diphenylnitroxide imbedded in a benzophenone single crystal is presented. The ^{14}N hyperfine tensors are . The gtensors are , where x, y, and z lie along the N–O axis, the line drawn between the centers of phenyl rings, and a direction perpendicular to the x and y axes, respectively. The isotropic values obtained from the molten mixed crystal, a supercooled liquid, are . The study implies that the unpaired π* electron is delocalized into the phenyl rings. The bonding character of the radical is discussed.

Polarization Dependence of Three‐Photon Phenomena for Randomly Oriented Molecules
View Description Hide DescriptionWe examine the polarization dependence of phenomena involving the interaction of three photons and a molecule, in the regime where the interaction is complete before the molecule has time to rotate. We obtain an explicit general formula for the orientation average of the observed intensity, which will be applicable to a randomly oriented sample of molecules. The results apply to simultaneous three‐photon absorption, hyper‐Raman or double quantum scattering, or other simultaneous three‐photon effects in fluids. In viscous media the results apply to sequential three‐photon absorptions or to simultaneous two‐photon absorption followed by fluorescence, and to three‐step photochemical processes in solid matrices. An experimental procedure is given for determining all the available molecular parameters of such processes. Certain simplifications of the general procedure arise in special cases. In all cases the formulas obtained are of the form , where I is the intensity of the effect, are the polarization vectors, T is the three‐photon tensor, the are a set of polarization parameters, the Q_{j} (T) are a set of molecular parameters, and M_{ij} is an averaging matrix. The P_{i} , M_{ij} , and Q_{j} are given explicitly for all cases considered. Thus the polarization dependence problem has been reduced to a linear algebra problem.

Doppler Broadening of Positron Annihilation Photons in Silver Halide Crystals Following High Energy Implantations of C^{5+}, N^{5+}, O^{6+}, and S^{6+}
View Description Hide DescriptionThe Doppler broadening of positron annihilation photons detected by a Ge(Li) detector was employed to probe the interactions of positrons in high purity AgCl and AgBr (95%)+AgCl sheet crystals that had been exposed to 10^{11}‐10^{13} ions cm^{−2} of implanted^{12}C^{5+}, ^{14}N^{5+}, ^{16}O^{6+}, or ^{32}S^{6+}. The narrowing of the Doppler broadened spectrum varied with the implanted ion, the concentration of the dopant, and the composition of the halide crystals. The decrease in linewidth is attributed to the electronic environment of the defects, and an increased probability of annihilation of near‐thermal positrons with conduction electrons relative to annihilation with core electrons.

Electric Resonance Spectroscopy of Hypersonic Molecular Beams
View Description Hide DescriptionA hypersonic nozzle beam(Mach 19) of HCN molecules was studied by electric resonance spectroscopy. Translational temperatures of 4°K and rotational temperatures of were found from a 283°K nozzle source. The monoenergetic character of the beam and the rotational cooling lead to an order of magnitude increase in signal‐to‐noise ratios. The absence of an appreciable velocity dispersion and a homogeneous radiation field allowed a critical comparison with theoretical two‐level resonance lineshapes. An SF_{6} diluent was used to reduce the beam velocity by one‐half and increase spectral resolution over a thermal (effusive) source. SF_{6} vibrational relaxation was observed. Chemically interesting species can be formed: ArXe, XeHCl, (HCl)_{2}, (HCN)_{ x }, and (HF)_{ x }.

Photophysical Processes in Polymers. V. Triplet Depletion in Solid Vinylnaphthalene Polymers and Copolymers
View Description Hide DescriptionThe results of a study of triplet energytrapping at 77°K are presented for vinylnaphthalene polymers and copolymers with styrene and methyl methacrylate. Delayed emission spectra originating from traps both intrinsic and extrinsic to the polymer chains are identified. In the solid polymers both intramolecular and interchain triplet energy migration occur, with eventual transfer to a trap at collisional distances of about 15 Å. Extrinsic traps lead to phosphorescence and delayed fluorescence, while traps that are part of the polymer chain lead to delayed exciplex fluorescence. In the model compound 1‐ethylnaphthalene, only extrinsic trapping phenomena are observed. The influence of concentration on trapping phenomena in both polymers and the model compound is considered from the standpoint of chain or molecular aggregation.

Lattice Vibrations in Ammonium Chloride in the Low‐Temperature Ordered Phase
View Description Hide DescriptionA rigid‐molecule model is used to analyze the lattice vibrations in ammonium chloride in the ordered phase (III). The ammonium and chlorine are treated as rigid ions with a partial charge, and short‐range forces out to the third nearest neighbor are considered. The model is shown to give a good fit of the neutrondispersion curve data on ND_{4}Cl at 85°K. Lattice frequency spectra are computed and decomposed into components associated with chlorine vibrations and ammonium translations and librations. Comparison with a recent shell‐model calculation shows that the numerical results are quite similar. The present results are also used to discuss the lattice heat capacity, mean square displacements, and incoherent neutron scattering.

Concept of Activation Energy in Unimolecular Reactions
View Description Hide DescriptionAn exact expression is derived, valid for all pressure regions, for the activation energy of a unimolecular reaction. Because of the reaction, the distribution of reactant molecules among vibrational levels deviates from a Boltzmann distribution; this deviation is explicitly taken into account. In the high‐pressure limit, the expression reduces to a well‐known form: due originally to Tolman. In the low‐pressure limit our expression contains terms which do not appear in Tolman's formalism. These are a term E^{M} which depends on the deviation from a Boltzmann distribution, and a term E^{Q} which arises from the thermal average of energy‐dependent vibrational cross sections. It is shown that the low‐pressure expression for E _{act} does indeed yield an energy fairly close to the energy at which conversion from reactant to product occurs. An approximate analytic expression for E _{act} is obtained for the case that the cross sections for vibrational energy transfer can be approximated by a truncated harmonic oscillator model. A numerical study of the thermal decomposition of N_{2}O, using SSH theory to evaluate collision rates, shows that both E^{M} and E^{Q} make important contributions to the final value of E _{act}. It is also shown that the steady‐state approximation can lead to serious error in calculating low‐pressure rate constants and activation energies at high temperatures.

Nonlinear Coupling among Critical Fluctuations: A Possible Source of Weak Divergences at a Critical Point
View Description Hide DescriptionIt is shown that a nonlinear coupling among critical fluctuations produces weak divergences in certain thermodynamic derivatives in agreement with the scaling law predictions. Moreover, restricting our analysis to quadratic terms in the order parameter fluctuations, an explicit expression is provided for the amplitude of the singularities. Weak divergences in binary mixtures are discussed in detail, including several exceptional cases, such as critical azeotropy. No divergence is predicted in general for the heat capacity at constant volume and concentration.

Sound Propagation near a Critical Point in Multicomponent Fluid Systems
View Description Hide DescriptionAs formulated by Fixman and by Kawasaki and Tanaka, the theory for sound propagation near a consolute critical point is inconsistent with the Wheeler and Griffiths thermodynamic bounds. A modification of the original version of the theory is proposed to avoid this difficulty. Sound propagation in binary mixtures is discussed in detail including special critical points such as critical azeotropy. Formulas for sound absorption and dispersion are also given for a multicomponent system in the general case. We found that, increasing the number of components, the magnitude of critical sound absorption and dispersion should decrease.

Microwave Spectrum and Ring‐Bending Vibration of 3‐Oxetanone
View Description Hide DescriptionThe microwave rotational spectrum of 3‐oxetanone, has been observed and assigned for the ground vibrational state, the first five excited states of the ring‐bending vibrational mode, and the two carbon‐13 isotopically substituted species. The features of the microwave spectrum indicate that the molecule has a single‐minimum ring‐bending vibrational potential and consequently a planar equilibrium configuration. Approximate models for the ring‐bending vibrational mode were set up and the vibrational potential function interpreted in terms of contributions from ring‐angle deformations and torsional interactions. The ^{13}C data were used to derive a partial substitution structure. With the carbonyl carbon being labeled C_{β}, the structural parameters determined in this way were The moment equations for the hypothetically planar molecule were solved to give some indication of the remaining parameters. Stark effectmeasurements yielded the dipole moment as for the common isotopic species in the ground vibrational state.

Perturbation Calculation of the Nuclear Spin‐Spin Coupling Constant in HD based on the Bare‐Nucleus Potential
View Description Hide DescriptionPerturbation calculations of the Fermi contact part of the electron‐coupled nuclear spin‐spin coupling constant (J) in the HD molecule have been performed in the bare‐nucleus potential. A very large Gaussian basis has been employed and, in addition, the effect on J of varying the HD internuclear separation has been considered. The term zeroth order in correlation, J _{0}, is in good agreement with an independent basis set study as is the geometric approximate to the coupled Hartree‐Fock value. The J _{0} and J _{1} values reported here differ significantly from those reported in a recent bare‐nucleus perturbation study using numerical H_{2} ^{+} orbitals. We give here a refined value of our previous Hartree perturbative results based on this larger atomic basis set.

Measurement of the Thermal Conductivity of Argon, Krypton, and Nitrogen in the Range 800–2000°K
View Description Hide DescriptionThe thermal conductivities of argon, krypton, and nitrogen were measured at 760 mm Hg in the temperature range 800–2000°K. Two thermal conductivity columns of different outside diameters were used in the experiments to provide an assessment of the convective heat transfer. In addition, potential leads were employed to minimize convection and end effects. The thermal conductivity values obtained were compared with existing data, with results of viscosity measurements, and with theoretical predictions.

Optimization of the Transferability of Atomic Hartree‐Fock Valence Shell Orbitals
View Description Hide DescriptionTwo procedures by which atomic valence shell orbitals may be transferred between atoms have been studied numerically. The one procedure optimizes the overlap between transferred and true orbitals, and the second, the electronic energy calculated with the transferred orbitals. The two procedures give significantly different results. Both improve on the results obtained in a previous study.

Hot Atom Reactions in the HBr–Br_{2}, DBr–Br_{2} Systems
View Description Hide DescriptionReactions of photochemically generated hot hydrogen atoms have been studied in HBr–Br_{2} systems at 185 and 229 nm and in DBr–Br_{2} systems at 185 nm. Kinetic analysis furnishes k _{3}/k _{2}—the rate coefficient ratio for the reactionsandAt 185 nm for HBr, , while at 229 nm . For DBr at 185 nm the ratio is . Complementary trajectory calculations have been performed on a semiempirical potential‐energy surface. The results of these calculations suggest that the observed variations in k _{3}/k _{2} arise primarily because the reaction cross section for Process (3) varies strongly with energy in the hot atom regime and is different for the HBr and DBr systems.