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Volume 66, Issue 3, 01 February 1977

Attenuation and single electron charge‐exchange cross sections of He^{+} on Ne and Ar in the 500–5000 eV energy range
View Description Hide DescriptionThe absolute total charge‐exchange cross sections of He^{+} on Ne and He^{+} or Ar have been measured using a parallel plate target ion collection method. The first set of collision partners have large but similar ionization potentials and the resulting cross sections agree reasonably well with theory. He^{+} on Ar collisions appear more complex, involving many interacting states. The resulting cross section does not show good agreement with existing two‐state theory. In addition, a lower limit to the total collision cross section of these same two collisions has been determined via incident beam attenuation measurements. For each of these collisions, the cross section was found to decrease monotonically with increasing ion velocity. In the He^{+} on Ar collision, the measured total and charge‐exchange cross sections were observed to coincide at energies above 3 keV.

Cooperative pseudo‐Jahn–Teller model for the sequence of ferroelastic transitions in barium sodium niobate
View Description Hide DescriptionA microscopic model is described which accounts for the sequence of two ferroelasticphase transitions in Ba_{2}NaNb_{5}O_{15}. It is shown that the phase transformations, which involve opposite symmetry changes on raising the temperature, can be explained on the basis of a cooperative pseudo‐Jahn–Teller mechanism. In the model, it is assumed that two d electrons localized on each niobium ion interact with their oxygen‐octahedral environment. The electronic energy levels, which are degenerate in a cubic symmetry, are partially split by the spontaneous polarization of this ferroelectric crystal. At each niobium site, the resulting ground and excited electronic levels are both coupled to the surrounding octahedra distortion by a pseudo‐Jahn–Teller interaction. Finally, the various octahedra distortions couple cooperatively to determine the ferroelastic spontaneous strain of the crystal. In the framework of this theory, the lowest transition at 110 K has its origin in the temperature dependence of the populations of the electronic excited states. At higher temperature (T≳573 K), the increase of the entropy restabilizes the undistorted paraelastic phase. Possible experimental tests of the model are discussed. In particular, it is predicted that observable changes, of definite sign, must occur in the transitions temperatures, either by application of a static electric field along [001] or by substitution of the niobium ions by Jahn–Teller inactive ions.

Pressure dependence of NMR proton spin–lattice relaxation times and shear viscosity in liquid water in the temperature range −15–10 °C
View Description Hide DescriptionThe NMRproton spin–lattice relaxation timesT _{1} and shear viscosities have been measured as functions of pressure in the temperature interval −15–10 °C. At low temperatures the low pressure boundary of the experiments is iceI, whereas iceV represents the high pressure extreme of our measurements. The initial compression at all temperatures covered in our study results in higher motional freedom of water molecules so that the pressure dependence exhibits a minimum in viscosity and a maximum in T _{1}. This is a consequence of significant distortion of the hydrogen bond network due to compression which also seems to weaken the hydrogen bonds. Further compression leads to restricted motional freedom due to increased packing of the molecules. This anomalous behavior of spin–lattice relaxation and shear viscosity with compression is more pronounced at lower temperatures since the hydrogen bond network is better developed at lower temperatures. In agreement with our earlier data covering the 10–90 °C temperature range, we find that compression under isothermal conditions distorts the random hydrogen bond network, leading to diminished coupling between the rotational and translational motions of water molecules. The data indicate that the Debye equation describes the relationship between the reorientational correlation time and shear viscosity at constant volume but is not applicable to describe the density effects on water reorientation. In general, pressure and temperature have parallel effects on many dynamic properties at temperatures below 40 °C and pressures below 2 kbar, whereas at higher temperatures and pressures their effects are just the opposite. Hard core repulsive interactions become more important than the directional interactions of hydrogen bonding at high compression.

Measurements of T _{1} and T _{2} relaxation cross sections for HDO
View Description Hide DescriptionRotational relaxation cross sections for the 2_{20}, 2_{21}, and superposition states of HDO were measured using a beam maser spectrometer. Scattering gases used were H_{2}O, D_{2}O, HDO (50%), HCl, CH_{3}F, NH_{3}, OCS, CO_{2}, N_{2}, and Ar. For HDO–NH_{3} scattering, pure state cross sections were much larger than the superposition state cross section. For other scattering gases, pure state cross sections were slightly larger than the superposition state cross section.

Analytic representation of oscillations, excitability, and traveling waves in a realistic model of the Belousov–Zhabotinskii reaction
View Description Hide DescriptionOn the basis of their thorough investigation of the mechanism of the malonic acid–bromate–cerium reaction, Field and Noyes have proposed a simple model for the sustained oscillations observed in this system. In this paper, I present a scheme of analysis of their differential equations which yields simple analytic formulae characterizing: (a) the domain in parameter space of local asymptotic stability of the steady state solution, (b) the amplitude, period, and waveform of limit cycle oscillations, (c) the direction of bifurcation of small amplitude periodic solutions, (d) the existence of large amplitude stable periodic solutions simultaneously with a locally stable constant solution, (e) the threshold of excitation and transient response to perturbations from a globally, asymptotically stable solution, and (f) the spatial and temporal development of the concentrations of key intermediates in periodic traveling waves (plane, axisymmetric, and rotating‐spiral waves). These formulae facilitate the choice of parameter values to give reasonable agreement between model calculations and observed oscillations.

Fluorescence detected circular dichroism and circular polarization of luminescence in rigid media: Direction dependent optical activity obtained by photoselection
View Description Hide DescriptionThe fluorescence detected circular dichroism (FDCD) and circular polarization of luminescence (CPL) of rigid systems is related to molecular parameters. It is found that FDCD can yield the CD for light incident along the direction of the fluorescencetransition moment. The average CD can also be measured as in a fluid medium. From CPL measurements one can evaluate the optical activity for light incident along the direction of the absorptiontransition moment. Thus, photoselection provides a method for measuring the direction dependent CD or optical activity of a molecule without actually orienting the molecule.

Calculations of vibronic magnetic rotational strengths and oscillator strengths in the B _{1u } state of benzene
View Description Hide DescriptionVibronic oscillator strengths and magneto‐optical B values are calculated for the ^{1} B _{1u } state of benzene and benzene‐d _{6}. The calculations are performed for geometries displaced in the direction of normal coordinates which couple this state with electric dipole allowed states, using the CNDO/S method. Oscillator strengths and the sign of the summed partial B values associated with each vibration agree with experiment. The lack of a high resolution magnetic circular dichroism spectrum prevents more detailed comparisons of B values with experiment.

Perturbation theory for the radial distribution function in the presence of three‐body forces
View Description Hide DescriptionPerturbation theory is used to consider the effect of the three‐body potential on the radial distribution functiong (r). We find that the effective pair potential, u ^{eff}(1,2) =u (1,2)−k TρFg _{0}(1,3) g _{0}(2,3) f (1,2,3) d3, where g _{0}(i,j) is the true pair potential radial distribution function, is an appropriate model for the study of the effect of the triplet potential on the g (r). Dividing the effective pair potential into repulsive and attractive regions, the radial distribution function of the reference potential is evaluated. It is shown, by calculating the total g (r) for the effective pair potential that, to first order, the effect of the triplet potential on the g (r) is accounted for by its effect on the reference g (r). We find that the effect of the triple‐dipole potential on the structure of liquids at low temperatures especially near the triple point is substantial.

Self‐diffusion of liquid hydrogen and deuterium
View Description Hide DescriptionCoefficients of self‐diffusion are reported for liquid H_{2}, D_{2}, and H_{2}–D_{2} mixtures from the melting points to within about 10 °K of the gas–liquid critical points. The data are interpreted with the quasilattice theory for self‐diffusion with corrections for quantum mechanical tunneling. Satisfactory agreement is obtained between the theory and experiment for hydrogen as well as liquid argon.

Intramolecular electron transfer in simple model systems: A propagator study
View Description Hide DescriptionThe probability of site‐to‐site intramolecular electron or hole transfer as a function of time in simple model systems is calculated. Systems studied are the hydrogen molecule, allyl cation, and cyclopropenium ion, in the Hubbard model. We employ the method of electron propagators, using both exact and approximate (molecular orbital and valence bond)ground statewavefunctions. We conclude that the molecular orbital wavefunction affords a good description of the transfer process for a wide variety of systems. The utility of our approach for the calculation of electron transfer rates in which purely electronic effects are dominant is stressed.

Reactions between NO^{+} and metal atoms using magnetically confined afterglows
View Description Hide DescriptionA new method of studying thermal energy ion–neutral collision processes involving nongaseous neutral atoms is described. A long magnetic field produced by a solenoid in a vacuum chamber confines a thermal‐energy plasma generated by photoionization of gas at very low pressure. As the plasma moves toward the end of the field, it is crossed by a metal atom beam. Ionic products of ion–atom reactions are trapped by the field and both the reactant and product ions move to the end of the magnetic field where they are detected by a quadrupole mass filter. The cross sections for charge transfer between NO^{+} and Na, Mg, Ca, and Sr and that for rearrangement between NO^{+} and Ca have been obtained. The charge‐transfer reaction is found strongly dominant over the arrangement reaction that forms metallic oxide ions.

Partial summations and ESR line shapes in the slow tumbling region
View Description Hide DescriptionBeginning with the results of Hwang, Anderson, and Friedman we derive an expression for the line shape of a spin‐one system having an axially symmetrical isotropically tumbling g‐tensor and a zero‐field splitting term. The expression is in the form of a continued fraction and is obtained by a series of partial summations of subsets of an infinite set of graphs appropriate to the problem. We are able to vary the relative strengths of the g and Dtensors, thereby obtaining any mixture of the two. The expression allows us to go to arbitrarily slow tumbling rates with a minimum of computation.

Uniform quality Gaussian basis sets
View Description Hide DescriptionA direct optimization technique was applied to determine uniformly balanced, optimum (4^{ s }2^{ p }), (6^{ s }3^{ p }), (8^{ s }4^{ p }), and (10^{ s }5^{ p }) Gaussian basis sets for the first row atoms. These bases formally correspond to 2G, 3G, 4G, and 5G function representations per symmetry type per shell. The basis sets are throroughly balanced and all satisfy a rather rigorous quality criterion in terms of the local properties of the energy hypersurface over the space of the orbital exponents.

The infrared and Raman spectra of solid CH_{3}F and CD_{3}F: Crystal structure inferences
View Description Hide DescriptionInfrared and Raman spectra are reported for solid CH_{3}F and CD_{3}F, and infrared spectra of dilute solid solutions of each substance in the other are also reported, in the region of the internal fundamentals and at temperatures near 80 °K (infrared) and near 130 °K (Raman). The crystal structure, based on the splittings in the spectra, is believed to be centrosymmetric with four molecules in the unit cell, similar to that of methyl bromide and methyl iodide. The possibility of longitudinal optical modes appearing in the Raman spectrum is considered; several reasons lead us to reject this suggestion. Overtones and combinations are assigned, in both infrared and Raman spectra, and shifts between gas and solid phases are discussed.

Scattering of atoms by a stationary sinusoidal hard wall: Rigorous treatment in (n+1) dimensions and comparison with the Rayleigh method
View Description Hide DescriptionA rigorous treatment of the scattering of atoms by a stationary sinusoidal hard wall in (n+1) dimensions is presented, a previous treatment by Masel, Merrill, and Miller for n=1 being contained as a special case. Numerical comparisons are made with the GR method of Garcia, which incorporates the Rayleigh hypothesis. Advantages and disadvantages of both methods are discussed, and it is concluded that the Rayleigh GR method, if handled properly, will probably work satisfactorily in physically realistic cases.

The transition of sulfur to a conducting phase
View Description Hide DescriptionCrystalline rhombic sulfur, an excellent insulator, has been converted to a conducting phase in 19 experiments. The cell resistance (initially determined by the boron nitride gasket) drops by at least six orders of magnitude at the transition; the sulfur resistivity itself has changed by a factor of 10^{−21} compared to its initial value. On the basis of a comparison technique utilizing a two sample cell with either ZnS and S pairs or S and GaP pairs, the transition pressure was shown to be between that for ZnS and for GaP. From interpolation of the forces for the three transitions, the transition pressure of sulfur to a conducting phase was found to be 175 kbars.

Intersystem crossing rates and saturation parameters in the triplet state for rhodamine, fluorescein, and acridine dyes
View Description Hide DescriptionThe saturation of the population in the triplet state T _{1} using a laser excitation ESR technique was observed directly at 77 K. The saturation parameters I _{sat} and the singlet‐to‐triplet intersystem crossing rate k _{ S T } were determined for acridine red (A O), rhodamine S (R S), rhodamine B (R B), rhodamine 6G (R6G), fluorescein disodium salt (F D S), 2′,7′‐dichlorofluorescein (D F), eosin Y (E Y), eosin B (E B), acridine orange (A R), and acridine yellow (A Y) in rigid ethanolic solutions. On the basis of the results, the intersystem crossing mechanisims of rhodamine (type R), fluorescein (type F), and acridine (type A) types of the ten dyes are discussed.

^{19}F shielding anisotropies of the fluoromethanes obtained from NMR studies in a smectic liquid crystal solution
View Description Hide Description^{19}F magnetic shieldinganisotropies of the fluoromethanes have been obtained from studies in a smectic liquid crystal solution using a pulsed FT NMR spectrometer. The value of Δσ obtained for methyl fluoride in the smectic phase is observed to be comparable in magnitude but higher in accuracy than the previous measurements obtained from theoretical, clathrate, molecular beam, and nematic single phase techniques, with the earlier value obtained using the nematic–isotropic two‐phase method being obviously in error. The shielding anisotropy measured for fluoroform is found to agree with the prior nematic two‐phase value, with the nematic single‐phase and clathrate values being considerably lower. The anisotropy measured in this investigation for methylene fluoride was found to be in disagreement with both previous values measured via molecular beam and nematic two‐phase techniques. It is shown that on transforming the experimental shielding anisotropy values obtained in this study along the C–F bond direction, that σ_{11}, the shielding component parallel to the C–F bond ,is essentially constant in magnitude for all three systems. In addition, it is also observed that from a knowledge of the signs of the orientation parameters that the absolute signs of the indirect proton–fluorine nuclear spin–spin coupling constants for the fluoromethanes are found to be unambiguously positive.

Internal conversions and relaxation dynamics in the CN radical in solid neon
View Description Hide DescriptionIn the present work we study the relaxation dynamics of the CN radical in solid Ne following selective excitation of individual vibronic levels of the A ^{2}π and B ^{2}Σ states. We demonstrate experimentally that when the molecule can relax by either vibrational relaxation or by internal conversions into lower lying levels of a nearby electronic state, the latter process is dominant. Neither near resonance nor perfect Franck–Condon overlaps are required for efficient internal conversions to occur. The rates of these conversions show qualitatively the exponential dependence on the size of the energy gap predicted by theory. The CN radical is stabilized in the solid Ne in several distinct trapping sites; its vibrational constants show negligible perturbation by the solid medium.

The molecular structure of a liquid–vapor interface: Comments on the integral equation approach
View Description Hide DescriptionA review of attempts to obtain interfacial density profiles by integral equation methods is presented. The first equation of the Yvon–Born–Green hierarchy is solved for ρ^{(1)}(z) for the vapor–liquid interface, using square‐well g ^{(2)}(r) data input generated by solving the second equation of the Yvon–Born–Green hierarchy. The method used in solving the first equation is discussed. Profiles are presented for three reduced temperatures spanning the vapor–liquid coexistence locus. The propertiessurface tension and surface excess internal energy are computed using statistical mechanical formulae and the ρ^{(1)}(z) and g ^{(2)}(r) data generated.