Volume 65, Issue 6, 15 September 1976
Index of content:

Computer molecular dynamics studies of a chemical instability
View Description Hide DescriptionComputermolecular dynamics studies are carried out on a binary mixture of hard disks in which one species can convert to the other by photoinduced transition or by collision‐induced reactions. Phenomenological rate laws are postulated for a simple model system which is then shown to possess multiple steady‐state concentrations under suitable conditions. The computer results for a 450‐disk system show that such solutions do exist, and that in general the postulated rate equations adequately describe the system behavior. Concentration fluctuations are examined and found to agree with the predictions of a master equation. Fluctuations are found to be enhanced near a point of marginal stability.

Absolute rate of the reaction of O(^{3} P) with hydrogen sulfide over the temperature range 263 to 495 K
View Description Hide DescriptionThe technique of flash photolysis coupled with time resolved detection of O via resonance fluorescence has been used to obtain rate constants for the reaction of O(^{3} P) with H_{2}S at temperatures from 263 to 495 K and at pressures in the range 10–400 torr. Under conditions where secondary reactions are avoided, the measured rate constants for the primary step obey the Arrhenius equation k= (7.24±1.07) ×10^{−12} exp(−3300±100/1.987 T) cm^{3} molecule^{−1} sec^{−1}. The results are discussed and comparisons are made with previous work and theoretical predictions. Experiments with D_{2}S show that the reaction exhibits a primary isotope effect, in support of a hydrogen abstraction mechanism.

Picosecond stimulated Raman effect in ethanol
View Description Hide DescriptionTime delays in the stimulated Raman emission from ethanol, excited with a mode locked Nd^{3+}glass laser, have been studied using echelons associated with a Kerr cell. By taking into account group velocity variations in all the dispersive media traversed by the light beam, the true time resolution of the spectrum has been determined. Our results indicate that there is no time delay between the Stokes, Rayleigh (laser pulse), and anti‐Stokes bands. With regard to the Stokes and Rayleigh bands, this agrees with a theoretical prediction for our experimental conditions.

Oscillating CO oxidation on a Pt surface
View Description Hide DescriptionA phenomenological model is proposed for the kinetics of oscillating oxidation of CO on SiO_{2}‐supported Pt pellets. The numerical solutions are in qualitative agreement with experiments. The surface temperature, as opposed to the ambient temperature, plays a crucial role.

Nucleation in a nonuniform vapor
View Description Hide DescriptionConventional nucleation theory describes nucleus formation in a uniform vapor as the addition or loss of single molecules from clusters of a given size. However, under nonuniform conditions, clusters can also be removed by diffusing away from the region of interest. Although there are many practical situations in which nucleation does occur under nonuniform conditions, the conventional theory cannot account for the loss of clusters by diffusion. It is therefore the purpose of this paper (1) to formulate a new theory which does include loss by diffusion and (2) to make a quantitative study of the diffusion effect in order to delineate the range of conditions under which it becomes important. The new theory is derived in the context of a typical diffusioncloud chamber by considering the diffusion loss from the narrow slab where nucleation occurs. The supersaturations which give rise to a unit steady rate of nucleation are then compared w i t h and w i t h o u t the diffusion term for model compounds under a variety of conditions. These quantitative studies on typical model compounds show that the diffusion effect first becomes important for vapor pressures as low as 10^{−8} torr. Thus, in the cloud chamber, nonuniformities do not cause serious errors. More importantly, in polluted atmospheres, even very low concentrations of vapors of involatile organic substances (e.g., sulfinic acids) can nucleate and give rise to the particulate matter commonly found in photochemicalsmog.

Exactly solvable models for vibronic coupling in molecular spectroscopy. I. Nontotally symmetric harmonic mode
View Description Hide DescriptionMolecular vibronic coupling is studied on a model consisting of two electronic states coupled by one vibrational mode. If adiabatic potentials corresponding to the two states are available (e.g., from experiment), the model can be solved exactly in terms of a coupling function defined implicitly and self‐consistently by means of a chosen or calculated diabatic potential. Alternatively and equivalently, the model can be formulated and solved in terms of one adiabatic and two diabatic potentials. In the harmonic‐oscillator approximation, the coupling function reduces to one parameter modulated by the electronic energy separation. Near the limit of weak vibronic coupling, the model reduces to the well‐known linear Herzberg–Teller approximation. A formally equivalent but complementary linear perturbation approximation is developed for strong coupling. For intermediate coupling, where both of these perturbation schemes are shown to fail, the model is solved by two complementary numerical procedures of which at least one converges quickly for any given set of physically acceptable parameter values. Detailed results are presented for coupling through a nondegenerate, non‐totally‐symmetric normal mode. Energy level diagrams as well as absorption and emission spectra are calculated for the full range of coupling parameters and energy gaps compatible with the harmonic approximation. The results show anomalous level spacings, intensities, and isotope effects, especially under intermediate‐coupling conditions. The anomalies can be qualitatively understood on the basis of avoided crossings in energy‐level correlation diagrams. As an example, the model is used for a qualitative explanation of anomalous intensity variations of the ^{1} L _{ b } transition in aromatic hydrocarbons.

Librational motion and phase transition in sodium azide
View Description Hide DescriptionThe librational motion of N_{3} ^{−} ion in the α and β phases of sodium azide is described in terms of an effective field treatment for rotational excitations. A rigid lattice model incorporating both electrostatic and short‐range interactions is employed. The order–disorder aspects of the phase transition in sodium azide are discussed in terms of the pocket state model. The estimated q=0 librational frequencies are compared with the results of Raman scatteringmeasurements. The calculated tilt angle for the azide ion in the α phase is found to agree with experiment. The model provides additional evidence for a small amount of order–disorder character of the α–β phase transition in sodium azide superimposed on its structural aspects.

I* (5 ^{2} P _{1/2}) quenching by hydrogen halides
View Description Hide DescriptionThe total quenching rates of electronically excited iodine (I*,5 ^{2} P _{1/2}) by HF, HCl, HBr, and HI have been measured. Two techniques were used to observe the temporal behavior of the I*: (1) absorption of the 206.2 nm resonance line and (2) I* emission at 1.315 μm. Close agreement between the two methods supports the modified form of the Beer–Lambert relation for data analysis in the absorption technique. Rate constants for quenching by HF, HCl, HBr, and HI are 3±1×10^{−12}, 6.5±0.9×10^{−15}, 1.58±0.07×10^{−13}, and 5±1×10^{−14} cm^{3} molecule^{−1} sec^{−1}, respectively. I* quenching by HF and HCl is shown to be consistent with the efficient electronic to vibrational (E–V) energy transfer mechanism known to exist for Br* (4 ^{2} P _{1/2}) quenching by hydrogen halides. Quenching by HBr and HI is too rapid to be consistent with the E–V argument and is probably dominated by reactive channels.

Variational time‐dependent Hartree–Fock calculations. III. Potential curves for two‐electron molecular systems
View Description Hide DescriptionTime‐dependent Hartree–Fock calculations of excitation energies,oscillator strengths, and related properties are reported for the molecules H_{2} and HeH^{+}. For a wide range of internuclear separations, the results are in accord with more refined comparison data. The comparison demonstrates that the time‐dependent Hartree–Fock method yields accurate molecular properties over a range of internuclear distances.

Electronic transitions in CS_{2}: A systematic assignment based on solid phase spectra
View Description Hide DescriptionThe 115–300 nm absorptionspectrum of solid CS_{2} reveals four previously unidentified maxima at 4.53, 5.13, 8.08, and 9.88 eV. The first three can be systematically assigned as ^{3}Π_{ g },^{1}Π_{ g }, and ^{3}Π_{ u } excitations. The fourth correlates with the CS_{2} ^{+}(A ^{2}Π_{ u }) ionization potential of the free molecule.

Spectra and kinetics of the Rb_{2} molecule
View Description Hide DescriptionIn an effort to evaluate the potential of the Rb_{2} molecule as a high power laser system, spectra of the A ^{1}Σ_{ u } to X ^{1}Σ_{ g } band have been taken in absorption and fluorescence, using 10^{20} atom/cm^{3} of noble gas as a buffer. The potential curves for both molecular states were estimated from the temperature dependence of the normalized absorption, using the classical Franck–Condon principle. The rate constant for molecular formation of the A ^{1}Σ_{ u } state is estimated to be 9×10^{−32} cm^{6}/sec using xenon as a buffer gas. However, this estimate was made on the basis of the normalized fluorescence which was emitted in that band. There appears to be a significant amount of nonradiative loss from that state, as evidenced by its low fluorescence efficiency compared to the RbXe molecule. Therefore, our estimate of the molecular formation rate could be low by as much as a factor of three. These nonradiative losses might be due to predissociation from the a ^{3}π to the repulsive χ ^{3}Σ state. This question must be more thoroughly investigated before any attempt is made to lase this molecule.

A temperature dependence kinetics study of the reactions of Cl (^{2} P _{3/2}) with O_{3}, CH_{4}, and H_{2}O_{2}
View Description Hide DescriptionThe technique of flash photolysis–resonance fluorescence has been utilized to study the temperature dependences of two chlorine atom reactions of considerable fundamental importance to stratospheric chemistry. These reactions have been studied using a wide range of experimental conditions to ensure the absence of complicating secondary processes. The reactions of interest with their corresponding rate constants are expressed in units of cm^{3} molecule^{−1} s^{−1}: Cl+O_{3}→ClO O_{2} (k _{1}), ΔU°_{298}=−164 kJ mol^{−1}, k _{1} = (3.08±0.30) ×10^{−11} exp[−(576±60/R T)], (220–350) K; Cl+CH_{4}→CH_{3}+HCl (k _{2}), ΔU°_{298}=−164 kJ mol^{−1}, k _{2} = (7.44±0.75) ×10^{−12} exp[−(2437±110/R T)], (218–401) K. In addition, the followong reaction was studied at 300 K: Cl+H_{2}O_{2}→HCl+HO_{2} (K _{3}), ΔU°_{298}=−56.8 kJ mol^{−1}, k _{3}?5.8×10^{−13} (±factor 2.0), 300 K. A direct implication of the new rate data is the need to revise downward by a factor of 2.4 to 3 the magnitude of the ozone perturbation predicted by earlier model calculations due to the presence of ClO_{ x } species in the stratosphere.

Time resolved ESR spectroscopy. IV. Detailed measurement and analysis of the ESR time profile
View Description Hide DescriptionAn ESR spectrometer for recording ESR signals with submicrosecond response time (R C=0.3 μsec) is described. Signals can be observed to within less than 1 μsec of the radiolysis pulse used to produce the radicals. The transient signals are observed directly in absorption for ease of analysis of their time dependence. Two modes of operation are possible: display of a spectrum at a fixed time after the pulse and the time profile at a fixed magnetic field. The latter mode (which was mainly used in this work) makes use of 100 data points in time, taken sequentially and averaged in a minicomputer. The magnetic field is computer controlled and is adjusted for changes in microwave frequency to maintain resonance. Analysis of the time‐dependent signals was by means of the Bloch equations so modified as to take account of changes in radical concentration with time, any initial magnetization upon radical formation, and CIDEP effects produced during radical decay. The ESR signal of the hydrated electron was observed at g=2.00033±0.00003 in irradiated solutions of SO_{3} ^{2−} and, by comparison of the observed time dependence with calculated curves, shown to have zero magnetization (or spin population difference) upon formation. Its apparent relaxation time was found to vary with radical concentration (dose), suggesting relaxation by Heisenberg spin exchange. Curves taken in the presence of CH_{3}CN were consistent with a reaction rate constant of 3.8×10^{7} M ^{−1} sec^{−1}, in agreement with optical data. Secondary radicals produced by reaction of e ^{−} _{aq} such as [^{−}O_{2}CCH=CHCO_{2} ^{−}]^{−}, ^{−}O_{2}CCH=?CO_{2} ^{−}, ?H_{2}CO_{2} ^{−}, CH_{3}? (O^{−})CO_{2} ^{−} were found to have zero initial magnetization while those formed from OH, such as ?O_{3} ^{−}, ?H_{2}CO_{2} ^{−}, and CH_{3}? (O^{−})CO_{2} ^{−}, showed curves indicating that the initial magnetization corresponded to the Boltzmann equilibrium as a result of relaxation of OH b e f o r ereaction. This behavior persisted for CH_{3}? (O^{−})CO_{2} ^{−} from 1M lactate, showing that the relaxation time of OH is <1 nsec. The markedly different ESR response observed for ?H_{2}CO_{2} ^{−} [or CH_{3}? (O^{−})CO_{2} ^{−}] produced from e ^{−} _{aq} or from OH shows very clearly that spin orientation is preserved upon reaction. Thus, the spin population of a radical such as OH (which cannot be observed directly) can be studied indirectly through the information passed to a reaction product. This experiment illustrates trapping as applied to spin populations. The reaction of both e ^{−} _{aq} and H with ^{−}O_{2}CC≡CCO_{2} ^{−} produces ^{−}O_{2}CCH=?CO_{2} ^{−}, and those radicals formed from H show initial magnetizations for the low‐ and high‐field lines corresponding to emission and enhanced absorption. This CIDEP is larger at lower concentration of ^{−}O_{2}CC≡CCO_{2} ^{−}, but some persists to very high concentrations. The increase at lower concentration must come from homogeneous radical–radical reaction of H atoms before reaction while that persisting at high concentration is probably produced by radical–radical reactions of H in the spur. Experiments with ?H_{2}CO_{2} ^{−} showed that the initial enhancement factors were inversely proportional to the first chemical half‐life at least up to a concentration where the enhancement was 3.6 and the half‐life was 15 μsec.

Translational and rotational relaxation
View Description Hide DescriptionThe translational relaxation and the translational nonequilibrium effects on the rotational relaxation are studied by solving the semiclassical Boltzmann equation with Monte Carlo simulation in the HCl–H_{2} system, where HCl formed in the exothermic reaction H+Cl_{2}→HCl+Cl with nonequilibrium rotational and translational distributions with an excess translational energy is dispersed in the heat bath of H_{2}. A simple hard sphere model with the line‐of‐centers cross section of upward rotational transition, the exponential model of downward transition probability proposed by Polanyi and Woodall, and the selection rule ‖ΔJ‖=1 is used. The explicit time‐dependent translational and rotational distributions from initial nonequilibrium to final equilibrium are obtained. Even when the translational distribution is far from equilibrium at the initial stage of rotational relaxation, the difference in the rotational distribution between translational nonequilibrium and equilibrium is less than 10% at the initial stage. Therefore, the estimation of the initial rotational distribution by Polanyi and Woodall with the master equation, where the translational equilibrium is assumed, is valid.

Isostructural phase transitions due to core collapse. I. A one‐dimensional model
View Description Hide DescriptionThis is the first of a two part study of a statistical mechanical system that exhibits an isostructural phase transition at high density and pressure. Here, in Paper I, we consider a one‐dimensional fluid; in Paper II we go on to treat the same system in three dimensions, using the approximation methods developed and tested here for one of the systems studied exactly by Stell and Hemmer [J. Chem. Phys. 56, 4274 (1972)]. Our pair potential φ (r) consists of a hard core of diameter d plus a shoulder of constant positive magnitude V _{0} for d<r<d (1+λ), to which a weak long‐range attraction term is added. We study the results of first‐order perturbation theory in V _{0}, as well as in f _{0}=exp(−βV _{0})−1, β= (k T)^{−1}, and find that used jointly they yield remarkably accurate results that promise to be similarly accurate in three dimensions, where an exact theory is lacking. In particular, we note that first‐order perturbation theory in V _{0} becomes rigorously exact in one‐dimension for fixed β as the density ρ approaches close packing; we argue (nonrigorously) that this result can be expected in any dimension. The first‐order theory in exp(−βV _{0})−1 is correspondingly good in the opposite limit of ρ→0.

Isostructural phase transitions due to core collapse. II. A three‐dimensional model with a solid–solid critical point
View Description Hide DescriptionWe give a theoretical treatment of isostructural phase transitions that result from partial collapse of the repulsive core of the interparticle pair potential. We use an approximation procedure that is tailored to the high‐density regime in which an isostructural solid–solid transition is found for a potential that is the sum of a hard‐sphere term and a repulsive shoulder term. A study is made of the transition and its critical point as a function of the potential parameters. We also give an extension of our theory to mixtures, as well as to the shouldered hard‐sphere potential to which a long‐range attractive tail is added.

Classical trajectory study of internal energy distributions in unimolecular processes
View Description Hide DescriptionThe method of classical trajectories has been used to study the flow of energy in a molecular system (similar to the molecules CD_{3}Cl and CD_{3}H) representing a chemical activation experiment. Energy distributions are obtained both before and after the breakup of the activated molecule by means of a correlation function technique. Four different potential energy surfaces are employed. It is found that the initial distribution of energy in the activated molecule may or may not be random, depending on the details of the particular surface. This distribution becomes random in less than 5×10^{−12} sec. The distribution of energy in the final product (CD_{3}) is found to be randomly distributed (as predicted by RRKM theory including angular momentum considerations) for a surface with no exit channel barrier or strong intermode couplings. When these special forces are present nonrandom energy distributions result. Product channel barriers result in an excess of translational energy and exit channel intermode couplings result in nonrandom vibrational distributions. Angular momentum considerations are found to be important in matching the predictions of RRKM theory with the calculations.

Coupled‐channel study of rotational excitation of a rigid asymmetric top by atom impact: (H_{2}CO,He) at interstellar temperatures
View Description Hide DescriptionA quantum mechanical scattering study is carried out to test a collisional pumping model for cooling the 6 and 2 cm doublets of interstellar formaldehyde. The Arthurs and Dalgarno formalism is extended to the collision of an s‐state atom with a rigid asymmetric top molecule and applied to rotational excitation of o r t h o formaldehyde by helium impact. Using a previously determined configuration interactionpotential energy surface, the coupled‐channel (CC) equations are integrated at 12 scattering energies between 20 and 95°K. Up to 16 o r t h o formaldehyde states, yielding a maximum of 62 CC equations, are retained to test convergence of computed cross sections. Resonance structure is obtained at ∼20.2, 32.7, and 47.7°K. The computed inelastic cross sections are averaged over a Maxwell–Boltzmann distribution and the resultant rates used to solve the equations of statistical equilibrium for the relative populations. The 6 and 2 cm doublets are found to be cooled o n l y upon inclusion of the j=3 doublet.

Theoretical studies of atmospheric molecules: SCF and correlated potential surface results for the X ^{2} B _{1} and ? ^{2} B _{2} states of H_{2}O^{+}
View Description Hide DescriptionSCF and MCSCF/CI calculations were carried out on the X ^{2} B _{1} and ? ^{2} B _{2} states of H_{2}O^{+}. Vibrational analyses based on second order perturbation theory were also performed. Computed equilibrium geometries, force constants, and low‐lying vibrational frequencies for both the SCF and MCSCF/CI surfaces are reported.

Molecular reorientation and shear viscosity in dense liquids
View Description Hide DescriptionThe viscosity dependence of reorientation correlation times τ_{ϑ} for a number of neat liquid monosubstituted benzenes and several symmetric top molecules has been analyzed in terms of Hu and Zwanzig’s hydrodynamic slip limit and also the parameter κ introduced by Kivelson. The slip limit predictions are improved by introducing a weighting factor which emphasizes molecular shape. The analysis of our high pressure data shows that the parameter κ is independent of pressure and temperature, in agreement with the results of other studies. The coupling between translational and rotational motions as characterized by κ is dominated by the molecular shape.