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Volume 70, Issue 9, 01 May 1979

A solution of the Debye–Smoluchowski equation for the rate of reaction of ions in dilute solution
View Description Hide DescriptionReactions of isolated ion pairs in solution have been modelled using the Debye–Smoluchowski equation for diffusion and conduction. An activation step was incorporated using a partially reflecting boundary condition. The method of matched expansions and the Abelian theorem of Laplace transforms was used to give an approximate solution of the Debye–Smoluchowski equation. Numerical integrations based on the finite‐difference method confirmed these approximate analytic formulas.

Water: Anomalous compressibilities to 1.9 kbar and correlation with supercooling limits
View Description Hide DescriptionA new high pressure volumetric technique, which employs a fine glass capillary as joint sample chamber and pressure vessel is described. Because of the small samples used, it is suitable for supercooled liquid studies. The compressibilities κ_{ T } of water and of D_{2}O have been determined over the applied pressure range 0.1–190 MPa (1–1900 bar) at temperatures in the range of 25–30°C. The anomalous low temperature increases in κ_{ T } reported earlier for H_{2}O at 1 bar are found at higher temperatures in D_{2}O, as expected. In both liquids, increases in pressure cause the anomalous regions to be displaced to lower temperatures. The displacement per unit pressure change increases with increasing pressure. As found previously, the low temperature data conform to an empirical equation κ_{ T }=A (T _{ s }/T−1)^{−γ} where T _{ s } is a characteristic temperature now found strongly dependent on pressure.High pressure data are inadequate to yield both T _{ s } and γ parameters reliably but, when γ is assigned a pressure‐independent value, the best fit T _{ s } values vary in each case with pressure in a manner strikingly similar to that of the homogeneous nucleation temperature, confirming a previously suspected relation between the two quantities. Preliminary attempts to separate the total compressibility into ’’normal’’ and ’’anomalous’’ parts suggest that the exponent γ is close to unity, as found previously for the anomalous component of the expansivity.

Energy disposal in thermal‐energy charge transfer reactions determined by kinetic energy measurements of product ions: Ne^{+}+O_{2}→O^{+}+O+Ne and Ar^{+}+O_{2}→O_{2} ^{+}+Ar
View Description Hide DescriptionThe possibility of deducing reaction mechanisms from kinetic energy released in the products is discussed for thermal energy ion‐molecule reactions. An experimental method based on ICR spectrometry is described, allowing for the first time kinetic energymeasurements of ions produced in thermal energyreactions. Application to charge transfer from Ne^{+} and Ar^{+} to O_{2} is presented. Ne^{+} produces O^{+} ions with 0.55 eV mean KE, corresponding to the O^{+}(^{4} S°)+O(^{1} D) dissociation limit of O_{2} ^{+}, while Ar^{+} produces O_{2} ^{+} molecular ions with 1 eV mean KE corresponding to ground state ions in rather high vibrational states (?∼8–10). With Ne^{+} the results can be accounted for in the framework of a (quasi) resonant charge transfer process while with Ar^{+}charge transfer involves electronic into kinetic energy transfer.

Thermal energy charge transfer from He^{+} to O_{2} : Kinetic energy, nature, and reactivity of the O^{+} product ions
View Description Hide DescriptionFrom kinetic energy measurements in an ICR cell, the charge‐transferreaction between thermal He^{+} and O_{2} is shown to produce 64% of ground state O^{+} ions with 1.8 eV kinetic energy, and 36% of electronically excited O^{+}* with 0.3 eV kinetic energy. These O^{+}* react with O_{2} with a rate constant of 6.5×10^{−10} cm^{3}s^{−1}. The nature of this excited state,^{2} D° or ^{2} P°, is discussed. A resonant, long‐distance electron jump explains all the experimental data.

Multiple IR photon laser induced reactions of cyclopropane
View Description Hide DescriptionThe multiple photon IR laser induced reactions of cyclopropane resulting from excitation of either of two fundamental vibrational modes has been demonstrated. In each case the products are typical of those formed with thermal excitation but the relative yields are not. The yield of the lowest energy barrier channel, isomerization, relative to higher channels, fragmentation, is dependent on the mode excited. Excitation of the C–H asymmetric stretch at 3.22 μm produces propylene with almost no fragmentation; excitation of the CH_{2} wag at 9.50 μm produces roughly equal yields of propylene and fragmentation products. Collisions play a critical role in this process. At 3.22 μm, the effect of collisions with argon is to increase yields of the fragmentation channel. As these collisions cannot add any significant amount of energy to the cyclopropane, it is concluded that the upper channel is opened due to intermode vibrational energy redistribution. At 9.50 μm, argon tends to favor the lower energy pathway. These results are consistent with an excitation that is initially nonstatistical or mode selective.

Molecular properties of N_{2} and CO_{2} as functions of nuclear geometry: Polarizabilities, quadrupole moments, and dipole moments
View Description Hide DescriptionA b i n i t i o static polarizabilities,quadrupole moments, and electronic energies of ground state N_{2} and CO_{2} have been calculated self‐consistently as functions of nuclear geometry in the Hartree–Fock approximation using the finite‐field method. In addition, permanent dipole moments for the infrared‐active vibrational modes of CO_{2} have been determined. For N_{2}, the effects of electron correlation on these molecular properties have been studied by performing generalized valence bond (perfect pairing) calculations with the same basis sets as were used in the Hartree–Fock calculations. These basis sets are constructed from energy‐optimized contracted sets of nucleus‐centered Gaussian‐orbitals to provide a flexible representation of the entire molecular charge cloud, including the highly polarizable outer regions. Results of these calculations are compared with experimental and other theoretical values where possible.

Triplet acetylene: Near infrared electronic absorption spectrum of the c i s isomer, and formation from methylene
View Description Hide DescriptionThe electronic absorptionspectrum in the gas phase of the metastable 1 ^{3} B _{2} state of acetylene has been observed. Its’ features, including rotational and vibronic structure as well as deuterium isotope effects, agree remarkably well with a b i n i t i o theoretical predictions for the 1 ^{3} A _{2}–1 ^{3} B _{2} electronic transition of the lowest triplet state in its c i s geometry. The metastable species was generated in the Hg‐photosensitized reactions of acetylene, ketene, and diazomethane. In the latter two cases it is probably formed by the reaction^{3}CH_{2}+^{3}CH_{2} →C_{2}H_{2}(1 ^{3} B _{2})+H_{2}.

Molecular and electronic structures of transition metal trifluorides
View Description Hide DescriptionQuantum mechanical calculations of the a b i n i t i o restricted‐Hartree–Fock type have been carried out on the molecules MF_{3} where M varies from Sc to Ni. Several electronic states were investigated for each molecule and in all cases the ground states were found to have high spin. The molecular structures were optimized and found to be trigonal planar (D _{3h }) except for CrF_{3}, found to be pyramidal (C _{3v }), and MnF_{3}, not investigated. Ionization potentials, electronic properties, and population analyses of the ground states have been obtained, and vibrational analyses of the out‐of‐plane modes have been carried out. The Jahn–Teller distortion of a low‐lying electronic state of CoF_{3} was worked out in detail.

Trajectory analysis of a kinetic theory for isomerization dynamics in condensed phases
View Description Hide DescriptionWe use an exact microscopic formalism to study the implications of a stochastic model of isomerizationdynamics in liquids. In the model, a reaction coordinate moves in a multistable potential and is coupled to a thermal bath via random collisions which occur with a specified average collision frequency. The nonlinear dynamics for this system is solved numerically. It is found that the usual linear rate law for isomerization is valid for any nonzero collision frequency if the activation barrier to reaction is sufficiently high. The reasons for this behavior are discussed at length. With appropriate parameter choices, we can draw conclusions concerning the t r a n s–g a u c h eisomerization of n‐butane in liquids. Transition state theory is found to overestimate the rate constant by at least a factor of 2 to 3 at any collision frequency. The collisional contribution to the volume of activation is calculated. At 1 atm, the result is an order of magnitude larger in size than the transition state theory activation volume. Furthermore, this collisional contribution has a strong pressure dependence that should be observable experimentally.

High temperature expansion for the Gaussian core model
View Description Hide DescriptionExact series coefficients through eighth order are reported for the high temperature expansion of the Gaussian core model free energy. Although this expanison has a vanishing radius of convergence it can be summed by a Borel integral transform. It is demonstrated that this Borel transform has an intimate connection to ’’crystallites’’ in the stable fluid phase which causes it to display a replica of the distribution function for large crystallites. This last observation permits implementation of a transform subtractive procedure which generates metastable extensions of fluid properties into the supercooled regime below the thermodynamic freezing temperature.

The dissociation dynamics of internal energy selected C_{6}H_{6} ^{+} a)
View Description Hide DescriptionAbsolute fragmentation rates and average energy released in the gas phase dissociation of 2,4 and 1,5 hexadiyne have been measured by photoion–photoelectron coincidence. The decay rates over the metastable energy range, as measured by the asymmetric time‐of‐flight distributions of C_{4}H_{4} ^{+} and C_{3}H_{3} ^{+} fragments are identical, and equal to those measured by others for benzene. This indicates that over this energy range all three C_{6}H_{6} ^{+} isomers rearrange to a common ion structure prior to dissociation. Calculated rates based on the statistical theory suggest that the C_{6}H_{6} ^{+} ions fragment to all product channels by competitive pathways and that the existence of isolated states or noncommunicating isomeric structures is highly unlikely. Above this energy range, the branching ratios to the C_{3}H_{3} ^{+} and C_{4}H_{4} ^{+} fragments indicate that the 1,5 hexadiyne ion no longer isomerizes prior to dissociation.

Self‐consistent many‐body theory of π‐electron systems. II. Self‐energy effects
View Description Hide DescriptionIn the framework of the theory presented in a preceding paper (I) we analyze the electron self‐energy (SE) effects on the low energy spectrum and oscillator strength of ethylene molecule. The SE is expressed through the same degrees of freedom (the one‐body and two‐body Green’s functions) of the local field corrections (LFC) terms, which have been studied separately in I. The SE and LFC corrections are thus calculated by means of a self‐consistent procedure. All the calculations are carried out in the Pariser–Parr–Pole (PPP) model. The results show that the SE terms play a decisive role in the self‐consistent conditions, at least for the coupling constant g≳1.

Depolarized scattering of atomic fluids with variable polarizability
View Description Hide DescriptionThe calculated band shapes and intensities of the depolarized light scattering from dense systems of atoms interacting with either hard‐sphere or Lennard–Jones potentials are shown to agree qualitatively with experiment, if an empirical form for the pairwise polarizability distortion anisotropy is used.

Determination of the structure of ArCO_{2} by radio frequency and microwave spectroscopy
View Description Hide DescriptionThe species ArCO_{2} produced by adiabatic expansion is structurally characterized by molecular beam electric resonance spectroscopy. ArCO_{2} is shown to have C _{2v } symmetry. The spectroscopic constants obtained are: The derived structural constants for ArCO_{2} are: Comparison is made with a number of proposed Ar–CO_{2}intermolecular potentials. The determined force constants are shown to be poorly fitted by a spherical argon–oxygen interaction.

Low‐energy electron–molecule scattering: Comparison of coupled channel treatments of e ^{−}N_{2} scattering at 13.6 eV using various approximations to the static and exchange potentials and an approximate polarization potential
View Description Hide DescriptionWe consider vibrationally and electronically elastic electron scattering by N_{2} at 13.6 eV impact energy. We use four combinations (S, SP, SE, and SEP) of the static (S), exchange (E), and polarization (P) potentials, four target molecular orbital wave functions (INDO/1s, INDO/1s with double zeta core, and Cade–Sales–Wahl and Ermler a b i n i t i o), and two local exchange approximations (semiclassical and Hara free‐electron gas). We also consider the effect of using an accurate wave function for the spherical average and lowest order anisotropy and an INDO/1s wave function for higher order anisotropies, as well as other combinations. The effects of approximations to the various terms in the interaction potential and the target wave function are illustrated by calculations of the partial integral cross sections.

Laser‐collision induced chemical reactions: Collinear exchange reaction model on two electronic surfaces
View Description Hide DescriptionA collinear model of bimolecular exchange reactions in the presence of an intense laser field coupling two electronic potential energy surfaces is developed. Close coupling calculations for two model systems were carried out as a function of the initial energy, E, the laser coupling, μ E _{0}, and the laser frequency, h/ω. It is shown that the reaction probability can be greatly altered for some systems by intense off‐resonant laser radiation. A suggestion is made for laser frequency up‐conversion using exothermic chemical reactions.

Determination of the electric field gradients for the two different nuclear sites of the cadmium atoms in b i s (thiosemicarbazide) cadmium(II) sulfate using gamma ray perturbed angular correlation spectroscopy on the ^{111}Cd isotope
View Description Hide DescriptionGamma ray perturbed angular correlationspectra of ^{111}Cd^{2+} in b i s (thiosemicarbazide)cadmium(II) sulfate and in b i s (thiosemicarbazide)zinc(II) sulfate have been recorded. From the measurements of ^{111}Cd in the cadmium complex of known structure two different sets of electric field gradient parameters have been evaluated. These observed quantities have been interpreted in a general ligand field model suitable to translate information about electric field gradients of metal ions of nd^{10} electronic configruation into chemical bondingproperties.

Vibrational relaxation of DF (v=1–4) in D_{2}, H_{2}, N_{2}, HF, and CO_{2}
View Description Hide DescriptionThe deactivation of the upper vibrational levels of DF by H_{2}, D_{2}, N_{2}, HF, and CO_{2} has been studied with the technique of laser‐induced fluorescence. The upper vibrational levels were produced by sequential photon absorption in which DF (v=0) was pumped first to DF (v=1) and subsequently to DF (v=2), DF (v=3), and DF (v=4) by photons from a pulsed multiline DF chemical laser. The deactivation rates (V−V+V−R,T) for all the collision partners except D_{2} scaled with vibrational level as v ^{ n } with n=1.9 to 2.0 for v=1 to 4. Similar studies have indicated the somewhat larger value of n=2.7±0.2 for HF (v) deactivation by diatomic molecules.

Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids
View Description Hide DescriptionThe fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non‐Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational–vibrational band shape is shown to be related to a correlation function for rotational–vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.

Species‐specific Raman spectroscopic measurements of concentration fluctuations in unsteady flow
View Description Hide DescriptionConcentration fluctuations of specific chemical species in unsteady mixed gas flow were studied by fast Fourier transform (FFT) analysis of Raman intensity. Average concentration and the amplitude and frequency distribution of fluctuations about that average (at a specific Raman shift) can be determined by the FFT/Raman technique. The fluctuation spectra can be modeled to yield information on the lifetimes, periodicity, amplitudes, and the statistical distribution of these in unsteady or turbulent motion. A simple burner with a concentric outer air sheath and inner CH_{4} jet was used in the preliminary experiments for both cold gas and flame studies. Interference from flame emission (uncorrelated to Raman scattering) was minimized by chopping the Raman exciting beam and observing the FFT signal near the chopper frequency. Peak height at the chopper frequency indicates average concentration, while the sidebands around this frequency contain information on the fluctuations in concentration of the species under observation. With the present system, fluctuations in the frequency range of 0–1 kHz having an amplitude of 5% of the average concentration of certain species whose average partial pressure is as little as 1% of atmospheric pressure could be measured. The fluctuations are observed from sampling volumes as small as ∼10^{−4} mm^{3} at any position in the flow. Improvements in the technique and extensions to other systems are discussed.