Index of content:
Volume 68, Issue 2, 15 January 1978

A reactive collision model for use in kinetic theory
View Description Hide DescriptionPresented here is a classical model for the reactive collisions A+BC→AB+C that is simple enough to be incorporated into kinetic theory calculations. This model involves a combination of reactive and nonreactive impulsive interactions between the participating particles. For the reactive impulse we use a generalization of the DIPR model proposed by Kuntz, Mok, and Polanyi. The nonreactive part of the interaction includes initial and final rigid‐sphere‐like repulsions between the reactants and the products, respectively. The angular momenta of AB and BC are taken into account. When the reactive impulse dominates the double differential cross sections reported here agree better with the results of molecular beam experiments than those generated by the latest version of DIPR, as proposed by Kuntz. The scattering is backward.

Mass and momentum transport in dilute reacting gases
View Description Hide DescriptionA formal kinetic theory and illustrative model calculations are presented for a mixture of four species coupled together by the two chemical reactions A+BC?AB+C. The cross sections for reaction are not restricted to be small and so the reactive collisions can not be treated as if they were small perturbations, but must be dealt with on an equal par with nonreactive events. To describe the dynamics of the reactive collisions we use an extension of the DIPR (direct interaction, product repulsion) model which takes into account rotational–translational exchanges of energy and, in a cruder way, vibrational excitation as well. Because the dynamics of these reactive events are not derived from a Hamiltonian, care must be exercised to insure that the condition of microreversibility is satisfied. A moment method is used to extract from the kinetic equation estimates for the nonequilibrium corrections to the reaction rates and for the changes of viscosity and diffusion coefficients due to the chemical reaction. Calculations reveal that the reaction rates can differ by as much as 80% from estimates based upon the assumption of an equilibrium distribution over reactant states. Furthermore, reaction can alter the coefficients of viscosity and diffusion by 10% or more. It is shown that the Onsager relations for the diffusion coefficients are valid only when chemical equilibrium prevails.

Enskog theory for chemically reacting fluids
View Description Hide DescriptionPresented here is a theory of nonequlibrium processes for a dense fluid composed of chemically reactive, rigid‐sphere molecules. Explicit consideration is given to the relocations of the molecular centers of mass that result from the occurrence of reaction and the accompanying rearrangements of chemical bonds. The collision operators are separated into source and flux parts in order to produce equations of motion which faithfully mimic those of continuum mechanics. As a consequence of this we are led naturally to the discovery of ’’collisional transfer’’ contributions to the mass fluxes of the reactive species. To transform these concepts into a computationally tractable theory we invoke the approximate Enskog functional relationship between the singlet and pair‐space distribution functions. This is followed by the development of a procedure for estimating the nonequilibrium corrections to the reaction rates as well as the coefficients of viscosity and diffusion, with special attention being devoted to the collisional transfer contributions to the species’ mass fluxes.

Kinetic theory of simple reacting spheres
View Description Hide DescriptionDilute and dense gas Enskog theory calculations are reported for a fluid composed of simple reacting spheres. Results for the dilute gas provide qualitative confirmation of previous calculations based on the MIRS (multiple interaction, reacting sphere) model. At high densities the viscosity and ’’empirical’’ diffusion coefficients vary almost linearly with the heat of reaction. The diffusion coefficients associated with the collisional transfer or ’’surface reaction’’ contributions to the component mass fluxes depend very strongly on density. For small heats of reaction and large densities this novel mechanism can completely overshadow regular diffusion. The transport coefficients associated with this surface reaction term fall into two categories, those with numerical values which tend to zero for large heats of reaction and those which increase rapidly as the exothermicity rises. The mass fluxes of reaction products belong to the latter category.

The electronic states of Ar^{+} _{2}, Kr^{+} _{2}, Xe^{+} _{2}. I. Potential curves with and without spin–orbit coupling
View Description Hide DescriptionThe low‐lying states of Ar^{+} _{2}, Kr^{+} _{2}, and Xe^{+} _{2} have been investigated using the POL CI method. Spin–orbit coupling has been included with a simple atoms‐in‐molecule approach. The calculated dissociation energies for the ground I (1/2)_{ u } states of Ar^{+} _{2} and Kr^{+} _{2} are in good agreement (10% error) with experiment, while the agreement is slightly worse (20% error) for Xe^{+} _{2}. The well depth decreases from 1.19 eV in Ar^{+} _{2} to 0.79 eV in Xe^{+} _{2} mainly because of spin–orbit effects. As expected, the calculated bond distances increase from Ar^{+} _{2} to Xe^{+} _{2} as the atoms increase in size. The first excited state,I (3/2)_{ g }, possesses a small well (0.12 eV) at larger distances (3–4 Å) in all the rare gas dimer ions. The higher excited states arising from the lowest asymptote are more repulsive. There are three dipole‐allowed transitions from the ground state. The I (1/2)_{ u }→I (3/2)_{ g } transition, which occurs in the near infrared, is very weak in accordance with propensity rules based on changes in Ω. The I (1/2)_{ u }→I (1/2)_{ g } transition occurs between 700–800 nm and grows dramatically in intensity from Ar^{+} _{2} to Xe^{+} _{2} because of spin–orbit effects. The predicted increase in intensity is in excellent agreement with experiment. Finally, the I (1/2)_{ u }→I I (1/2)_{ g } transition is very strong with the intensity decreasing slightly for the heavier rare gas dimer ions. The absorption maxima are predicted at 319, 339, and 375 nm for Ar^{+} _{2}, Kr^{+} _{2}, and Xe^{+} _{2}, respectively, which are to be compared with the experimental values of 292 and 325 nm for Ar^{+} _{2} and Kr^{+} _{2}, respectively. The theoretical values for the peak absorption cross sections are in good agreement with experiment for Ar^{+} _{2} and Kr^{+} _{2}. Thus, although the calculated wavelengths for the peak absorption are too long by 20–30 nm, the size and shape of the calculated absorption bands should be in good agreement with experiment. Finally, a comparison is made between the a b i n i t i o SCF potentials for the ^{1}Σ^{+} _{ g } state of Ar_{2}, Kr_{2}, and Xe_{2} with the potentials predicted by the electron gas model.

Excess electrons in condensed media: Theory of optical absorption spectrum in molecular solutions
View Description Hide DescriptionA theoretical formalism is developed for analyzing the spectra of excess electrons in pure molecular solids and liquids. A perturbation decomposition of the Hamiltonian allows the expression for the band shape I (ω) to be written as a sum of a zeroth order part, proportional to dipole transition matrix elements and corresponding Franck–Condon factors, and perturbation terms containing effects of electronhopping and their fluctuations. By using several physically motivated approximations (e.g., the temporally localized nature of electronic transitions which allows a short‐time expansion of the time dependence of operators), the expression for I (ω) can be expressed in terms of solvent structure information and the electron–solvent interaction potential. From the general expressions for I (ω) a simplified model was developed in the special case of systems for which bound‐to‐bound transitions are dominant. This model has been successfully applied to the spectra of excess electrons in ethanol and anthracene glass, thereby providing some optimism for the potential use of the general formalism derived here.

’’Proximity effect’’ in radiationless transitions
View Description Hide DescriptionThe quantum statistical approach to relaxation phenomena was employed in a numerical investigation of the effect of vibronic interaction between the first and second excited states on the radiationless decay rate of the first excited state. It is shown that the vibronically active out‐of‐plane modes may be the dominant accepting modes for the radiationless transitions of N‐heterocyclics with close‐lying nπ* and ππ* excited states. The decay rate was found to vary with the strength of nπ*–ππ* vibronic interaction, the nπ* and ππ* separation, the energy gap between the initial and final electronic states of the radiationless process, and isotopic substitution, in a manner which is consistent with experimental observation.

A quasiclassical trajectory study of the energy transfer in CO_{2}–rare gas systems
View Description Hide DescriptionComputational methods are presented for the study of collisions between a linear, symmetric triatomic molecule and an atom by three‐dimensional quasiclassical trajectory calculations. Application is made to the investigation of translational to rotational and translational to vibrational energy transfer in the systems CO_{2}–Kr, CO_{2}–Ar, and CO_{2}–Ne. Potential‐energy surfaces based on spectroscopic and molecular beam scattering data are used. In most of the calculations, the CO_{2} molecule is initially in the quantum mechanical zero‐point vibrational state and in a rotational state picked from a Boltzmann distribution at 300°K. The energy transfer processes are investigated for translational energies ranging from 0.1 to 10 eV. Translational to rotational energy transfer is found to be the major process for CO_{2}–rare gas collisions at these energies. Below 1 eV there is very little translational to vibrational energy transfer. The effects of changes in the internal energy of the molecule, in the masses of the collidants, and in the potential‐energy parameters are studied in an attempt to gain understanding of the energy transfer processes.

Molecular theory of solvated ion dynamics
View Description Hide DescriptionWe present a simple molecular approach for understanding the dynamics of a single ion in a polar solvent. The approach is based on a heuristic development starting from a resolution of the force–force correlation function of a Brownian ion, into parts depending on the attractive ion–solvent interaction and a repulsive, hard core ion–solvent interaction. We show that in the limit of infinitely weak, long range attractive ion–solvent interactions the molecular theory reduces to the phenomenological dielectricfriction picture for the drag on an ion. The molecular theory also gives sensible results in the case of strong, short range attractive interactions. In this case the theory essentially indicates that the drag on the ion reduces to the drag on a composite body, i.e., a solventberg consisting of the ion and the molecules in the first solvation shell.

Spinodal decomposition in a binary liquid mixture
View Description Hide DescriptionLight scattering was used to study phase separation near the critical temperature T _{ c } in a critical mixture of 2,6‐lutidine and water. This system has an inverted coexistence curve, so that a quench into the two‐phase region is produced by an upward jump in temperature. The scattered intensity I (q,t) was recorded at various angles and at a number of quench depths ΔT _{ f } =T _{ f }−T _{ c } in the range 0.5≲ΔT _{ f }≲2.5 mK. Here T _{ f } denotes the final temperature. The initial temperature was also varied, and no initial‐state effects were observed. One set of experiments employed a cell of very short optical path (0.1 mm) to minimize multiple scattering at the sacrifice of quenching speed. In another set, emphasis was placed on achieving a temperature jump in roughly 0.1 sec so that phase separation could be followed in its early stages. For ΔT _{ f }≲1 mK, the change in the measured ring diameter (q _{ m } ^{−1}) with time, is in fair agreement with the nonlinear theory of Langer, Bar‐on, and Miller. However, the intensity of the ring, I (q _{ m },t), increases faster than this theory predicts. The measurements also reveal that the results depends significantly on the quench rate as well as quench depth.

Depolarized light scattered near the gas–liquid critical point of Xe, SF_{6}, CO_{2}, C_{2}H_{4}, and C_{2}H_{6}
View Description Hide DescriptionWe report an experimental study of depolarized Rayleigh light scattered at 90° by two isotropic fluids (xenon and sulfur hexafluoride) and three anistropic fluids (carbon dioxide, ethane, and ethylene) near their respective gas–liquid critical points. All measurements were performed along the critical isochore, in the single phase region, that is to say for T≳T _{ c }. The depolarization ratios, as shown by theory, are separable into two contributions. Far from the critical temperature single scattering of light is predominant but near the critical point double and multiple scatterings become the main phenomena. From measurements of polarized intensities in the temperature range corresponding to double scattering, the cross sections or the compressibility factors were calculated when a choice of a theoretical expression for the Rayleigh ratio was made.

EPR spectroscopic determination and interpretation of g _{∥} of Gd^{3+} in single crystals of the lanthanide ethyl sulfate nonahydrates
View Description Hide DescriptionHigh‐precision measured values of g _{∥} for Gd^{3+} dilutely substituted in single crystals of 13 lanthanide ethyl sulfate nonahydrates at room temperature (297.3 K) are presented. It is shown that, within the experimental uncertainties, the present observations are entirely accounted for in terms of a model invoking purely magnetic dipolar interactions between the Gd^{3+} guests and the host structures. On this model, the shift of g _{∥} depends upon the identity of the lanthanide host, the sample shape, the temperature, and the Gd^{3+} composition. Moreover, values of the shifts of g _{∥} at 77.2 K predicted by this model are in agreement, within the experimental uncertainties, with the 77.2 K data of Gerkin and Thorsell [J. Chem. Phys. 57, 2665 (1972)]. Consistent with this model, values of g _{∥} for spherical samples of 2.0×10^{−3} mole fraction Gd^{3+} in 14 of the lanthanide ethyl sulfate nonahydrates at 297.3 K and at 77.2 K are presented.

Reaction and deactivation of HCl (v=1, 2) by O atoms
View Description Hide DescriptionLaser‐induced fluorescence, following direct excitation of HCl (v=2), was used to measure the total deactivation rate constant for HCl (v=2) by O(^{3} P _{ g }) atoms as (5.2±0.4) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}. This is partitioned into a reaction rate constant of (1.5±1.2) ×10^{−12} cm^{3} molecule^{−1} sec^{−1} for HCl (v=2)+O(^{3} P _{ g }) →OH (v=1, 0)+Cl and a relaxation rate constant for HCl (v=2)+O(^{3} P _{ g }) →HCl (v=1)+O(^{3} P _{ g }) of (3.7±1.2) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}. The total deactivation rate constant for HCl (v=1)+O(^{3} P _{ g }) atoms, including reaction and relaxation, was measured to be (8.9±1.3) ×10^{−13} cm^{3} molecule^{−1} sec^{−1}. All measurements were carried out at 296±2 °K. The vibrationally enhanced chemical reaction rate constant for HCl (v=2) is roughly a factor of 10^{4} greater than the reaction rate constant for HCl (v=0) with O atoms. The reaction appears to occur adiabatically on the lowest triplet potential hypersurface. For HCl (v=2, 1)+O vibrational relaxation is faster than chemical reaction even though the total energy is well above the barrier to reaction.

Spectroscopic properties of polyenes. III. 1,3,5,7‐Octatetraene
View Description Hide DescriptionAbsorption and emission spectra of all‐t r a n s 1, 3, 5, 7‐octatetraene are presented along with fluorescence quantum yields and lifetimes. In solution, a gap of about 3000 cm^{−1} is found between the first band of the 1 ^{1} A _{ g }→1^{1} B _{ u }transition and the onset of the emission spectrum. Excitation spectra of concentrated solutions at 77 K show low‐lying bands in this gap, the lowest energy band being almost coincident with the highest energyfluorescence band. On the other hand, gas phase fluorescence spectra show no gap between the lowest energy 1^{1} A _{ g }→1^{1} B _{ u }absorption band and the first fluorescence band. The radiative lifetime in hexane is 220 ns at room temperature and 190 ns at 77 K. The radiative lifetime for the gas phase fluorescence is estimated to be longer than 150 ns. The solvent dependence of the absorption and emission spectra, the fluorescence lifetimes, and the vibrational frequencies observed in solution imply support for the conjecture of Karplus e t a l. that the lowest excited singlet state is of ^{1} A _{ g } symmetry. The solution data imply that the low‐lying state is about 6400 cm^{−1} below the 1^{1} B _{ u } level. On the other hand, the lack of a gap between absorption and emission and the long lifetime found for the gas phase are not compatible with this model.

High‐resolution infrared spectrum of the ν_{4} band of POF_{3} by laser Stark spectroscopy
View Description Hide DescriptionTransitions in the ν_{4} band of POF_{3} have been observed by means of an infrared laser Stark spectrometer resonating on the CO_{2} R (38) to R (54) laser lines near 10.1 μm. Many POF_{3} transitions were observed for this perpendicular band with both ΔM=0 and ΔM=±1 selection rules. Many of the lines were observed as Lamb dips. The spectral assignment was confirmed by the observation of a number of infrared‐microwave double resonances. Molecular constants obtained from analysis of the laser Stark spectra are ν_{4}=29768578.6±1.0 MHz, A _{4}=4803.06±0.16 MHz, B _{4} =4584.67±0.03 MHz, (Aζ)_{4}=2429.0±0.2 MHz, μ_{4} =1.8394±0.0004 D, and μ_{0}=1.8696±0.0004 D.

Excitation and quenching reactions in E‐beam excited He/H_{2}O and He/CH_{3}CN systems
View Description Hide DescriptionThis paper describes observations made in the afterglow of an electron beam discharge into high‐pressure mixtures of He/H_{2}O and He/CH_{3}CN and assesses the laser potential of these systems. Emission spectra and time histories at visible and near uv wavelengths were obtained spectroscopically. OH(A ^{2}Σ→X ^{2}Π_{ i }) emission (306.8?λ?310.9 nm) predominated in the He/H_{2}O system, and CN(B ^{2}Σ^{+}→X ^{2}Σ^{+}) emission (385.0?λ?391.6 nm) predominated in the He/CH_{3}CN system. The suggested pumping reactions operative in these systems are the dissociative charge exchange reactions He_{2} ^{+} + H_{2}O→OH(A)+HeH^{+}+He and He_{2} ^{+}+CH_{3}CN→CN(B)+CH_{3} ^{+}+2He. The rate constants for these reactions have been determined to be (1.3±0.2) ×10^{−10} and (1.1±0.3) ×10^{−10} cm^{3}/s, respectively. The He_{2} ^{+} quenching rate constants for H_{2}O and for CH_{3}CN were found to be (1.2±0.2) ×10^{−9} and (3.5±0.7) ×10^{−9} cm^{3}/s, respectively. The OH(A) quenching rate constant for H_{2}O was determined to be (4.2±0.4) ×10^{−10} cm^{3}/s, and the CN(B) quenching rate constant for CH_{3}CN was found to be (1.4±0.3) ×10^{−10} cm^{3}/s. The OH(A) yield (number of excited molecules produced/number of He^{+} ions formed) was found to be 11%; the CN(B) yield was 3%. Maximum laser efficiencies for these systems were calculated and determined to be 0.5% and 0.1%, respectively.

Prior statistical distributions for the collision of an atom with a diatom
View Description Hide DescriptionThe statistical theories of reaction rates play a major role in the formulation and use of the information theoretic approach in reaction dynamics. The statistical theory is used as the prior theory to which the actual rates should be compared. Since one can formulate many different statistical theories, one is faced with the problem of which to use in the information theoretic analysis. Four different theories are reviewed and analyzed for a collinear reaction. It is shown that of these the theory based on the assumption of equal rates for equal product flux in phase space leads to difficulties. Furthermore, a classical collinear calculation of a reaction on a potential surface with a deep well shows that the product state distribution of a reaction involving a long lived complex is well characterized by the statement of equal probability for equal product density in phase space. The implications of these findings on the information theoretic approach are discussed.

Molecular orbital description of silver clusters: Electronic structure
View Description Hide DescriptionElectronic properties derived from calculations of Ag clusters up to 39 atoms in size are compared with bulk properties calculated within the same theoretical framework. Density of states profiles (DOS) determined by extended Hückel theory show a broadening with increasing atoms in this range of sizes. The bulk periodic DOS compare favorably with other calculations. Oscillations in electron affinity, binding energy, and ionization potential for open and closed shells of electrons are observed for Ag clusters using the CNDO method.

Quantum corrections to the equation of state of a fluid using hard‐sphere basis functions
View Description Hide DescriptionWe develop the expansion for the Slater sum, using a hard‐sphere potential as a reference potential and the hard‐sphere wavefunction as a basis set, which replaces the usual Wigner–Kirkwood series. Expressions are given for the first and second quantum corrections to the free energy arising due to perturbation potential. Results are given for the first and second quantum corrections to the second and third virial coefficients. We find that the quantum corrections to the higher virial coefficients depend on the potential at the core as well as the shape of the well. The general expression for the third virial coefficient of a gas at high temperature is given by B ^{ q } _{3} =B ^{ c } _{3}+(5π^{2} d ^{6}/18)[(3/√2) B ^{I} _{3}(λ/d) +1.708 B ^{II} _{3}(λ/d)^{2}+⋅⋅⋅], where B ^{I} _{3} and B ^{II} _{3} are constants depending upon the shape and nature of the perturbation potential and equal to unity in the limit of the hard sphere [i.e., u _{ p }(r) →0].

Transient visible absorption in infrared saturable absorbing dyes
View Description Hide DescriptionAn optically generated transient absorbing state in the polymethine pyrylium dyes EK 9860 and 9740 is described. The broadband absorption is produced when solutions of the dyes are irradiated by a 1060 nm picosecond duration pulse. The absorbing state spans the wavelength range from ∼520 to ≳800 nm and is characterized by a molar extinction coefficient of ∼1×10^{4} and by a decay time as short as 13.4 psec (in 9860). The latter result and the 7 psec value previously reported for the recovery of ground stateabsorption at 1060 nm following excitation at the same wavelength are accommodated by a three level relaxation mechanism. This approach treats the visible absorption as arising from electronic transitions both from the first excited singlet state and from a transient intermediate level. Lack of structure in the transient visible absorption indicates that the transition populates high density bound statemanifolds or continuum states.