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Volume 54, Issue 6, 15 March 1971

Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. IV. A Study of Doublet Stability for Odd Linear Polyenic Radicals
View Description Hide DescriptionThe doublet stability conditions for the restricted Hartree–Fock (HF) solutions of the simple open‐shell case (i.e., one electron in addition to the closed shell) are applied to the π‐electronic models of the odd linear polyenic radicals, using the Pariser–Parr–Pople‐type semiempirical Hamiltonian. It is found that symmetry‐adapted restricted HF solutions for linear polyenes with carbon atoms are always doublet stable while those with carbon atoms may be unstable for large enough coupling constants (i.e., the ratio of two‐electronic part of the Hamiltonian to the one‐electronic part). In fact the HF solutions for the latter systems are generally doublet unstable already for the currently used values of the semiempirical parameters or a very small lowering of the absolute value of the resonance integral (i.e., ∼0.1 − 0.3 eV) is sufficient to yield instability for any type polyene. The instability, in fact, occurs already for the allyl radical, which is studied in a considerable detail. The doublet stability of the solutions for the type polyenes is explained on the basis of symmetry properties of corresponding Kekulé structures. The symmetry‐nonadapted restricted HF solutions are calculated for illustration of their properties and possible multiplicities.

Experimental Determination of the Excitation Function for the Reaction: H+n‐C_{4}D_{10}→HD+C_{4}D_{9}(sec)
View Description Hide DescriptionThe excitation function for the formation of HD was determined by means of a nonequilibrium bulb method in the relative energy range of ∼ 0.5–1.7 eV. Hydrogen atoms of various well‐known initial kinetic energies, 0.35, 0.48, 0.67, 0.92, 1.15, 1.67, and 2.05 eV, were generated by the photodissociation of HI and HBr in the presence of either n‐C_{4}D_{10} or n‐CD_{3}–(CH_{2})_{2}–CD_{3}. Temperature variation studies performed at the lowest source energy allowed an estimate, 0.35 eV, for the sec‐abstraction threshold energy. The excitation function was related to the measured HD yields through an integral equation, derived previously. The cross section rises from threshold to a maximum value (∼ 0.35 Å^{2}) at about 1.2 eV with an energy dependence intermediate between that predicted by the familiar line‐of‐centers and step function models, and then decreases with increasing energy. The results are compared with other experimental and theoretical studies.

Optical Properties of Six‐Member Carbon Ring Organic Liquids in the Vacuum Ultraviolet
View Description Hide DescriptionOptical data for incident photon energies 2.0–10.6 eV are reported for 1,3‐cyclohexadiene, cyclohexene, and cyclohexane in the liquid state. New measurements of the optical constants of liquid benzene over this energy region are included for comparison. An interpretation of the data is made in terms of molecular excitations of and electrons and collective oscillations of the electrons in the liquids.

Explicit Solution for the Wavefunction and Energy in Degenerate Rayleigh–Schrödinger Perturbation Theory
View Description Hide DescriptionThe Rayleigh–Schrödinger perturbation series for the energy and wavefunction are derived for the case that the zeroth‐order state is degenerate. The solution, embodied in four “rules,” is a generalization of the nondegenerate formulas of Huby and Brueckner. The derivation consists of redefining the unperturbed Hamiltonian and the perturbation (in a particular way) so as to remove the degeneracy, then rearranging the terms in the nondegenerate series in the new perturbation according to the order in the old perturbation. The “choice” of “correct” zeroth‐order functions falls out in a natural way, as do the components of the wavefunction in the degenerate unperturbed subspace. The solution given here is not directly related to the degenerate problems solved previously by Kato and by Bloch, in that their solutions do not lead directly to the Rayleigh–Schrödinger series for the energy and wavefunction. The present solution is more related to the one given by Hirschfelder (both being solutions of the same problem), but it differs in not involving the recursively defined operators , in being expressed in terms of quantities directly related to the unperturbed Hamiltonian and the perturbation, and in the method of derivation. (An explicit representation of Hirschfelder's is given in Appendix C.)

Electron Paramagnetic Resonance of Mn^{2+} in Ni(CH_{3}COO)_{2}·4H_{2}O and NiSO_{4}·7H_{2}O Single Crystals
View Description Hide DescriptionElectron paramagnetic resonance of Mn^{2+} has been studied in nickel acetate tetrahydrate [Ni(CH_{3}COO)_{2}·4H_{2}O] and nickel sulfate heptahydrate (NiSO_{4}·7H_{2}O) at 300°K. The Mn^{2+} was found to substitute for Ni^{2+} in both the systems and exhibit inequivalent magnetic complexes, two for the bimolecular Ni(CH_{3}COO)_{2}·4H_{2}O and four for the tetramolecular NiSO_{4}·7H_{2}O. Besides, the Mn^{2+}resonance lines exhibited a direct dependence of linewidth on the intensity of Zeeman field and a shift in value towards the lower side from the free‐spin value. These features have been explained in terms of the interaction of the Mn^{2+} ion with Ni^{2+} host ions.

Vacancy‐Limited Electron Transport in Rare‐Gas Solids
View Description Hide DescriptionAn expression is obtained for the mobility of conduction‐band electrons in rare‐gas solids when both vacancyscattering and phononscattering are effective. Deformation potential constants are obtained by a fit to experimental data. It is shown that large concentrations of vacancies which would result from the lowering of the vacancy formation energy by nonpairwise interatomic interactions might significantly affect the electronic mobility near the triple point of the solid.

Polymer Dynamics. V. The Shear Dependent Properties of Linear Polymers Including Intrinsic Viscosity, Flow Dichroism and Birefringence, Relaxation, and Normal Stresses
View Description Hide DescriptionUnder the physical requirement that the contour length of a polymer molecule remains constant irrespective of shear rate in the Rouse and Zimm theories and the Harris–Hearst theory, the shear rate dependence of intrinsic viscosity,flowbirefringence,flowdichroism, normal stresses, the relaxation of flowbirefringence and flowdichroism, and some quantities at zero shear rate have been calculated for molecules of different stiffness ranging from the rod to the flexible coil in solvents. Changes of hydrodynamic interaction with shear rate are not included. Comparing the present theory with the experimental results there is satisfactory agreement for stiff molecules such as the cellulose derivatives and DNA at low shear.

Ferroelectric Tungsten Bronze‐Type Crystal Structures. III. Potassium Lithium Niobate K_{(6−x−y)}Li_{(4+x)}Nb_{(10+y)}O_{30}
View Description Hide DescriptionFerroelectric K_{(6−x−y)}Li_{(4+x)}Nb_{(10+y)}O_{30}, with , and a Curie temperature of 613°K, crystallizes with a tungsten bronze‐type structure in the tetragonal system. The lattice constants are and at 298°K. The space group is . There is one formula per unit cell. The integrated intensities of 6578 structure factors, inside a reciprocal hemisphere of radius , were measured with PEXRAD. There are 998 symmetry‐independent Fmeas significantly above background. Isomorphism with Ba _{x} Sr_{(5−x)}Nb_{10}O_{30} allowed the metal atom positions to be deduced. Oxygen atom positions were obtained by Fourier series methods. Refinement of structural parameters by the method of least squares resulted in a final agreement factor . The structure is generally like that of other tungsten bronzes of formula , with the site occupied by 87% K and 13% Li, the site by 99% K and 1% Li, and the site by 94% Li and 6% Nb. The sites are fully occupied by Nb. X‐ray spectrochemical analysis and the present diffraction study suggest and for the nonstoichiometric formula above. Evidence for major positional disorder, excluding occupancy disorder, similar to that observed in Ba _{x} Sr_{(5−x)}Nb_{10}O_{30} and in Ba_{(4+x)}Na_{(2−2x)}Nb_{10}O_{30} is not present for K_{(6−x−y)}Li_{(4+x)}Nb_{(10+y)}O_{30}. The K/Li atom at the site is 12 coordinated with average K/Li–O distance of 2.833 Å. The K/Li atom at the site is nine coordinated with average K/Li–O distance of 3.024 Å. The Li/Nb atom at the site has three nearest oxygen neighbors at an average distance of 2.153 Å and six additional next‐nearest neighbors at an average distance of 2.542 Å. The two independent irregular NbO_{6} octahedra have an average Nb–O separation of 1.973 Å. The Nb atom displacements, of 0.167 and 0.160 Å from the nearest mean oxygen plane, may be compared with the value of 0.175 Å predicted from the parabolic relation with Curie temperature. All metal atoms are displaced from the mean planes of oxygen in the same sense, making the positive polarization direction parallel to the sense of this displacement.

Compton Profile of NH_{4}Cl
View Description Hide DescriptionThe Compton profile of x rays scattered from polycrystalline NH_{4}Cl has been measured and compared with theoretical profiles based on the superpositions (a) N+4H+Cl and (b) NH_{4} ^{+}+Cl^{−}. The molecular‐orbital wavefunctions of Moccia were used for NH_{4} ^{+}, and the electrons in N, H, Cl, and Cl^{−} were described by free‐atom wavefunctions. The experimental results were significantly different from the profile based on the model (a) and gave good agreement with the profile obtained from the superposition (b).

Vibrational Analysis of the Infrared and Raman Spectra of Oxalyl Bromide in the Crystalline and Fluid States
View Description Hide DescriptionThe vibrational spectrum of oxalyl bromide [COBr]_{2}, has been recorded between 4000 and 33 cm^{−1}. The infrared spectra of oxalyl bromide have been examined in the solid, liquid, and gaseous states, and the Raman spectra of the solid and liquid have been observed and qualitative depolarization ratios have been measured. The vibrational spectrum of the crystalline material has been interpreted on the basis of molecular symmetry and space group symmetry. Two of the three external lattice modes have been observed in the far‐infrared spectrum, and at least four of the six Raman active external lattice modes have also been observed. Six bands appear in the infrared and Raman spectra of the liquid/gaseous states which do not appear in the spectra of the solid. Thus, in the fluid states, molecules with both and molecular symmetries appear to be present. The enthalpy difference between the two isomers was determined by a variable temperature study to be 2.9 ± 0.1 kcal/mol with the trans isomer being more stable. A rough estimate of the equilibrium mixture at room temperature gives a value of 10% ± 5% for the cis isomer. The barrier restricting the internal rotation around the C–C single bond appears to be governed mainly by and terms of approximately the same order and in the range of 3 kcal/mol.

Dipolar Coupling and Molecular Vibrations in Crystals. IV. Frequency Shifts and Dipole Moment Derivatives
View Description Hide DescriptionThe internal vibrational modes of a dipole coupled crystal are discussed in terms of two models, a “back‐ground polarization” model which differs from the transition moment dipole coupled “resonant mode” model in that the additional induced dipolar coupling due to electronic polarization is included. The transverse–longitudinal mode splittings as well as factor group splittings are discussed in terms of these two models. The contribution to the frequency shifts from nonresonant modes is calculated and the effect of dipolar coupling on the overtone frequencies is examined. Dipole moment derivatives and static crystal field frequencies of the doubly degenerate stretching mode are calculated for a few rhombohedral crystals.

Modified Hamiltonians for Localized Orbitals and for the Removal of Degeneracies
View Description Hide DescriptionA single determinant approximate wavefunction can be improved by choosing a Hamiltonian of which it is an eigenfunction and applying perturbation theory. If is built up of orbitals which are eigenfunctions of a one‐electron operator , an appropriate choice of is . This paper discusses two modifications to . One consists of adding to an energy‐shift operator, and this has several applications the most interesting being the removal of any degeneracies in . The second consists of writing the new as where is different to . The can be chosen to have localized orbitals as its eigenfunctions, and this leads to a simple method of performing perturbation theory with localized orbitals. Some numerical examples are given.

Ion–Molecule Reactions by a Photoionization Mass Spectrometer. III. C_{3}H_{6}+n‐C_{4}D_{10} and Cyclo‐C_{3}H_{6}+n‐C_{4}D_{10} Mixtures
View Description Hide DescriptionIon–molecule reactions of the parent ions of propylene and cyclopropane (C_{3}H_{6} ^{+} and cyclo‐C_{3}H_{6} ^{+}, respectively), with deuterated n‐butane (n‐C_{4}D_{10}) have been studied by a photoionizationmass spectrometer.Ionizing radiation was Lyman alpha (1216 Å) which produced only one primary ionic species (C_{3}H_{6} ^{+} or cyclo‐C_{3}H_{6} ^{+}) in the mixture of C_{3}H_{6} and n‐C_{4}D_{10} or of cyclo‐C_{3}H_{6} and n‐C_{4}D_{10}. It has been found that, besides the two reactions, D^{−} and D_{2} ^{−} transfer, deuterium atom abstraction by C_{3}H_{6} ^{+} (or D atom transfer) takes place in each system. Reaction cross sections for all of these reactions have been determined at a field strength of 4.0 V/cm. These values in angstroms^{2} unit are: D^{−} transfer 13, D_{2} ^{−} transfer 7.1, D transfer 4.8 (C_{3}H_{6}+n‐C_{4}D_{10} system), D^{−} transfer 30, D_{2} ^{−} transfer 2.0, D transfer 8.1 (cyclo‐C_{3}H_{6}+n‐C_{4}D_{10} system).

Vibronic Structure in the Fluorescence Lifetimes and Quantum Yields of Aniline Vapor
View Description Hide DescriptionAniline vapor has a well‐resolved vibronic absorptionspectrum in the region of the first excited singlet transition. By means of high‐resolution phase fluorimetry we have determined the spectrum of fluorescence lifetimes and quantum yields over the region from 300 to 275 nm with a bandwidth of 2.7 Å. The emission spectrum was not resolved. Relative values of quantum yields at different wavelengths were measured directly while absolute values were estimated from literature data. Quantum yields fluctuate between 0.3 and 0.6 and the reciprocal lifetime, , varies in the range (1.3 to 2.3) × 10^{8} sec^{−1}. shows sharply pointed minima whereas the quantum yields have maxima at the wavelengths of all major absorption peaks. The calculated intersystems crossing rate constants have minimum values at these wavelengths. These features are interpreted in terms of symmetry selection rules for spin–orbit and vibronic coupling.

Supersonic Molecular Beams of Alkali Dimers
View Description Hide DescriptionIntense alkali beams containing up to 30% mole fraction of K_{2}, Rb_{2}, or Cs_{2} have been generated from a supersonic nozzle expansion, with oven temperatures up to ∼ 900°K (corresponding to alkali vapor pressures up to ∼ 350 torr) and nozzle temperatures ∼ 50–300°K higher. The total beam intensity obtained reached ∼ 5 × 10^{17} particles sec^{−1}·sr^{−1}. An inhomogeneous deflecting magnet was used to separate the dimer and atom components of the beam, and the variation of dimer concentration with oven pressure and nozzle temperature were studied for a variety of nozzle sizes (throat diameters 0.04–0.15 mm). The velocity distributions of the atom and dimer components were also measured and found to be quite similar; the peaks occur at velocities up to 70% higher than the most probable atom velocity in the oven, and the widths are very narrow, corresponding to random translational temperatures as low as ∼ 30°K, and Mach numbers up to ∼ 15. A simple one‐dimensional theory of dimerization which takes into account vibrational relaxation and heat of condensation is found to be consistent with the data. It is shown that the observed velocity distributions and the variation of the dimer yield with pressure and nozzle diameter imply that most of the heat of condensation does not contribute to the beam acceleration but goes into vibrational excitation of the dimer molecules. A nominal value of ∼ 3 × 10^{−30} cm^{6} sec^{−1} at ∼ 600°K is obtained for the recombination rate constant for Cs+Cs+Cs→Cs_{2}+Cs. A reduced variable plot is provided which enables the theory to be applied to nozzle expansions of any substance for which the chemical recombination is governed by three‐body collisions.

Molecular Beam Kinetics: Reactions of H and D Atoms with Diatomic Alkali Molecules
View Description Hide DescriptionCrossed‐beam studies have been made of the reactions of H and D atoms with K_{2}, Rb_{2}, and Cs_{2}. The hydrogen atoms were generated by thermal dissociation of molecules in a tungsten oven at ∼ 2200–2900°K, the alkali dimers by association of atoms in a supersonic beam expanded from a nozzle at ∼ 900°K. Surface ionization detectors were unable to distinguish among alkali atoms, dimers, and alkali hydrides. However, a kinematic separation of reactive and nonreactive scattering proved to be feasible, owing to the disparity in reactant masses and parity in product masses. The angular distributions of reactive scattering peak at right angles to the initial relative velocity vector. A kinematic analysis indicates that only a small fraction of the available energy appears in product translational motion. This implies that either the vibrational and/or rotational excitation of the product alkali hydride is very high (∼ 30–40 kcal/mole), comparable to or possibly even larger than its dissociation energy, or the product alkali atom is electronically excited. Total reaction cross sections were estimated by normalizing the observed intensity of wide‐angle atom–atom elastic scattering to the hard‐sphere value. The nominal cross section obtained (no better than a factor of 2) is <̃ 50 Å^{2} for the H reactions. The D atom reactions show very similar product distributions, with total reaction cross sections larger by a factor of ∼ 2. Variation of the H and D beam temperature indicated the activation energy is negligibly small. The H atoms approach very rapidly compared with the sluggish vibrational and rotational motions of M atoms within M_{2}. From this it is argued that the observed scattering implies an anisotropic reaction probability, favoring configurations with the M_{2} axis perpendicular to the direction of approach of the H atom. Qualitative comparisons are also made with analogous dissociative electron attachment and photodissociation processes, and with an electron‐jump mechanism which involves formation of an intermediate H^{−}+M_{2} ^{+} ion‐pair.

Electrical Conductivity in Cholesteric Liquid Crystals
View Description Hide DescriptionThe conductivity and activation energies for conduction for three cholesteric liquid crystals in the solid,liquid‐crystal, and isotropic‐liquid state are presented to describe the transport properties and to observe the effects of varying degrees of order on the transport mechanisms. The conductivities vary from 10^{−10}–10^{−12} (Ω·cm)^{−1} between 25 and 125°C according to an Arrhenius temperature dependence with an over‐all average of the activation energies of 0.45 eV. The free carrier densities were also found to be exponentially dependent on temperature with an over‐all average carrier activation energy of 0.32 eV. These results are discussed in relation to both a band and hopping model of conduction. An unusually small discontinuity in conductivity and activation energy is observed at solid–liquid‐crystal and liquid‐crystal–isotropicliquidtransitions indicating that it is very likely that the same conduction mechanism is present in both the solid and liquid states. These observations agree with the results of measurements. The conductivities calculated from mobilities and carrier densities obtained from curves agree with the conductivities measured directly. The optical absorption spectra is presented between 200 and 1800 mμ.

Ultrasonic Velocity and Attenuation in Liquid Neon
View Description Hide DescriptionThe velocity and attenuation of 30‐MHz sound waves were measured in liquid neon from 25 to 37°K at pressures to 28 kg/cm^{2}. The values of the velocity, extrapolated to the vapor pressure curve, are from 1.5% higher at 25°K to 0.4% higher at 32°K than corresponding values reported for 2‐GHz sound waves. This negative dispersion is in agreement with recent predictions by Fleury and Boon. Values of the attenuation exceed the classical values calculated from the Navier–Stokes equation. This excess attenuation is attributed to a volume viscosity of the same magnitude as the shear viscosity. No anomaly in the temperature dependence of either velocity or attenuation was observed near the temperature where an anomaly has been reported for thermal conductivity, shear viscosity, and hypersonic velocity.

Glory Scattering in Molecular Collisions. II. Formal Expressions for the Total Inelastic Cross Section
View Description Hide DescriptionFormal expressions for the differential and total inelastic scattering cross section when two rigid diatomic molecules with orbital and nuclear spin angular momenta collide are obtained. An extended distorted wave treatment is used to simplify the results. The nondegeneracy averaged and degeneracy averaged cases are compared.

Collision Broadening of Rotational Absorption Lines. VI. Pressure Broadening of Microwave Absorption Spectra Involving Oxygen
View Description Hide DescriptionThe pressure broadening of microwave absorption lines by collisions involving O_{2} has been investigated using a method presented earlier for analyzing and evaluating microwavelinewidth parameters under conditions where impact‐theory assumptions are valid. A value of (1.16 ± 0.12) D· Å was obtained for the molecular quadrupole moment of O_{2} from linewidth data for broadening of NH_{3} inversion lines by O_{2}. This value is in reasonably good agreement with values determined by other methods, and should constitute an upper limit to the true value since only dipole–quadrupole interaction was considered in the linewidth calculations, This value of the molecular quadrupole moment of O_{2} was used to calculate linewidth parameters for H_{2}O–O_{2} broadening, OCS–O_{2} broadening, N_{2}O–O_{2} broadening, O_{2}–O_{2} self‐broadening, and the broadening of the 9– line of O_{2} by various foreign gases. These results are in general smaller than the experimental values, suggesting that the effects of higher‐order interactions are important in collisions with O_{2}.