Index of content:
Volume 80, Issue 8, 15 April 1984

Detection of small polydispersities by photon correlation spectroscopy
View Description Hide DescriptionWe consider dilute suspensions of homogeneous polydisperse spherical particles for which the Rayleigh–Gans–Debye (RGD) approximation is valid. For two model particle size distributions we calculate the dependence on scattering vector Q of the average scattered intensity I(Q) and the effective diffusion coefficient D _{ e }(Q) obtained from the first cumulant measured by photon‐correlation spectroscopy. If the mean particle radius R̄ is large enough (≳170 nm) that the intensity form factorP(Q R̄) shows at least one minimum in the accessible range of Q, we find that D _{ e }(Q) exhibits a characteristic variation with Q which is very sensitive to the sample polydispersity. Under favorable conditions it should be possible to measure polydispersities (standard deviation/mean size) as small as 0.01. These theoretical considerations are supported, at least qualitatively, by experiment. We also discuss briefly the effect of relaxing the RGD approximation and the implications of this work for the more common PCS probes of polydispersity such as Laplace transformation of the light scatteringcorrelation function.

Angle resolved photoelectron spectroscopy of the valence shells in HI and CH_{3}I as a function of photon energy from 13 to 90 eV
View Description Hide DescriptionAngle‐resolved photoelectron spectroscopy was carried out on the valence shells of HI and CH_{3}I over a photon energy range of 13–90 eV with the use of synchrotron radiation. From these data, partial cross sections and angular distribution parameters were obtained for bands corresponding to the 1 ^{2}Π and 1 ^{2}Σ^{+} states of singly ionized HI and the 1 ^{2} E, 1 ^{2} A and 2 ^{2} E states of singly ionized CH_{3}I. Calculations were carried out on HI for the same parameters with the use of the multiple scatteringXα method. The results, both experimental and theoretical, are examined in terms of the Cooper minimum. Clear evidence for minima in both the cross sections and β values are found for the lone‐pair orbitals. Bonding orbitals involving the iodine 5p subshell also show minima in the energy dependence plot of the β values, but the effects are less pronounced. These results are compared with similar studies on chlorine‐containing molecules. The lone‐pair orbitals showed spin‐orbit resolved bands in the photoelectron spectra. The behavior of these spin‐orbit split states are examined for their differences in β values and branching ratios as a function of photon energy up to 35 eV.

Internal coordinate formulation for the vibration‐rotation energies of polyatomic molecules. II. Symmetric top molecules with a threefold axis
View Description Hide DescriptionThe theory of vibration‐rotation interactions in symmetric top molecules with a threefold axis has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. General expressions for the inertial coefficients, Coriolis coupling coefficients, and vibrational kinetic energy anharmonic coefficients have been derived for planar and nonplanar XY_{3} molecules. A Van Vleck perturbation scheme is used to obtain the theoretical vibration‐rotation and vibration anharmonic spectroscopic coefficients. Applications are made in the analyses of the empirical spectroscopic coefficients for BF_{3} and NH_{3} in the determination of incomplete sets of improved anharmonic potential energy coefficients. In many respects it is found that the curvilinear internal coordinate approach to vibration‐rotation interactions has advantages over the Cartesian displacement coordinate approach for angle bending modes in the symmetric top molecules.

Resolution of the exchange anomaly in triplet exciton ion radical salts
View Description Hide DescriptionThe temperature dependence of the D and E zero‐field splitting parameters in the triplet‐exciton‐containing ion radical salt (φ_{3}AsCH^{+} _{3})(TCNQ)^{−} _{2} has been measured at low temperatures and used to correct observed splittings at higher temperatures where triplet–triplet exchange is present. Analysis of the exchange effects from the thermally corrected splittings leads to an exchange activation energy (0.110 eV) and frequency factor (1.4×10^{1} ^{1} Hz) in good agreement with those obtained from previous width measurements.

Rotational relaxation rates for the OCS J=0–1 pure rotational transition broadened by argon and helium
View Description Hide DescriptionWe have recorded time‐domain coherence decay and population decay signals for the pure rotational OCS J=0–1 transition broadened by argon and by helium using pulse methods based on Stark switching of the molecular resonance frequency. The signals have been analyzed to yield the pressure dependence of the two decay rates (1/T _{2} and 1/T _{1}) and their dependence on the absorber (OCS) speed. For comparison, using a potential which has been used several times in the literature for these systems, IOS (infinite order sudden approximation) scattering results are given. These calculations give substantial agreement on the ratio of the speed dependence of the relaxation rate to the rate itself, but fail to predict the rates quantitatively, especially for helium, or the relationship between the argon and the helium results. Because the IOS is expected to be accurate for these systems, the helium potential is ruled out by these data.

An energetically low‐lying silacyclopropyne isomer of SiC_{2}
View Description Hide DescriptionWe have discovered a low‐lying cyclic isomer of Si–C–C which is best described as a three‐membered ring with a weak carbon–carbon triple bond. In these theoretical studies a double zeta plus polarization basis set was used initially. At the self‐consistent‐field (SCF) and two‐configuration (TC) SCF levels of theory the ring structure is a transition state leading to linear Si–C–C. A configuration interaction (CI) treatment at the SCF optimized cyclic geometry, however, show it to lie 1.1 kcal/mol below the linear structure. Extension of the basis set to include a second set of d functions on each atom gives a final prediction that the ring structure lies ∼5 kcal below linear SiCC.

Visible spectroscopy of jet‐cooled SiC_{2}: Geometry and electronic structure
View Description Hide DescriptionSiC_{2} has been prepared in a supersonic molecular beam by laser vaporization of a siliconcarbide rod within a pulsed supersonic nozzle. Rotational analysis of the 0‐0 band of the well‐known 4980 Å band system of this molecule reveals that, contrary to previous assumptions, the molecule is triangular in both the ground and excited electronic states. In both states the molecule is of C _{2V } symmetry with a C–Si–C angle between 40° and 41°. The correct assignment of the spectrum is Ã ′B _{2}←x̃ ′A _{1}. The carbon–carbon bond length is 1.25 Å in the ground state, suggesting that the molecule is best understood as a silicon atom bound to the side of a triply bonded C _{2} fragment. The optical transition moment is polarized along the b axis of the molecule which is parallel to the carbon–carbon bond axis. In the Ã ^{1} B _{2}excited state the carbon–carbon bond opens up to 1.30 Å consistent with a π*←π excitation of the carbon–carbon triple bond. The silicon–cargon distance is measured to be 1.81 Å in the x̃ ^{1} A _{1} state, lengthening to 1.88 Å in the Ã ′B _{2}excited state. In addition, the ionization potential of SiC_{2} was determined to lie between 8.91 and 10.38 eV.

Conformational kinetics of methyl nitrite. II. Phase dependence of kinetic parameters
View Description Hide DescriptionTemperature and pressure dependent exchange broadened NMR spectra of gaseous methyl nitrite are consistent with the following kinetic parameters for the s y n–a n t i conformational interconversion: E _{act} (∞), 12.2(4) kcal/mol; E _{act} (bimolecular), 9.6(2) kcal/mol; ΔH ^{‡}, 11.7(4) kcal/mol; ΔG ^{‡} _{298} 11.97(7) kcal/mol; and ΔS ^{‡} _{298} , −0.9(4) cal/mol K. Kinetic parameters for interconversion in the neat liquid and in a 1% solution in CS_{2} are slightly higher: E _{act}; 12.9(2); ΔH ^{‡}, 12.4(2) kcal/mol; ΔG ^{‡}, 11.81(8) kcal/mol; and ΔS ^{‡}, 2.6(2) cal/mol K. These remarkably small solvent effects indicate that dielectric effects on conformational dynamics in this system are nearly equal in magnitude and opposite in direction to solvent internal pressure effects.

Calculation of partial widths and isotope effects for reactive resonances by a reaction‐path Hamiltonian model: Test against accurate quantal results for a twin‐saddle point system
View Description Hide DescriptionWe calculate the partial widths of three collisional resonances in a collinear system with mass combinations HFH and DFD on a low‐barrier modelpotential energy surface. We compare accurate quantal results to results obtained with a reaction‐path Hamiltonian model in which the resonances are interpreted as quasibound states trapped in wells of adiabatic potential curves and their decay probabilities are calculated by semiclassical tunneling calculations and a Feshbach golden‐rule formula with the decay mediated by an internal centrifugal interaction proportional to the curvature of the reaction path. The model successfully predicts when vibrationally nonadiabatic decay dominates over the adiabatic mechanism for decomposition of the resonances and it predicts the nonadiabatic partial widths with an average error of 25%.

Electron energy loss spectroscopy of molecular fluorine
View Description Hide DescriptionWe have obtained electron energy lossspectra in molecular fluorine in the energy‐loss range 6–24 eV at scattering angles between 3 ° and 9 ° for an incident electron energy of 200 eV. For energy losses above 11.5 eV, our spectra are in excellent agreement with earlier electron scattering and photoabsorptionmeasurements and we resolve for the first time the vibrational levels of the F ^{1}Π_{ g } parity forbidden state, which is the lowest Rydberg state of F_{2} and serves as the lower level of the orange emission band system. We are able to unambiguously reassign vibrational quantum numbers to the F ^{1}Π_{ g } state, which have been in doubt for several decades. In the region 5–11.5 eV, of particular interest to F_{2} laser modeling, we are unable to find any electronic transition which cannot be attributed to minor, identifiable, impurities known to exist in F_{2}.

Action‐angle variables for quantum mechanical coplanar scattering
View Description Hide DescriptionA formulation of quantum mechanical scattering is presented with action‐angle variables. The theory is confined to coplanar three atom scattering which reduces to the consideration of three coordinates taking into account conservation of energy and angular momentum. The resultant partial differential equation is treated within a finite element formulation with the spatial elements taken as parallelopipeds. It is argued that the choice of the three independent coordinates in a calculation is not critical and no channel matching is required, although it could be included. A simple illustration with rotationally inelastic scattering is considered for the H+H_{2} system. The results are in good agreement with earlier close coupling calculations.

Non‐Markovian theory of activated rate processes. IV. The double well model
View Description Hide DescriptionThe transition rates associated with a particle moving in a double potential well under the influence of thermal noise and friction is considered as a generalization of Kramers’ theory of activated rate processes. We obtain expressions for these transition rates which are valid for all friction and for a general (non‐Markovian) interaction between the particle and its thermal environment. Nonthermal equilibrium effects in the steady state distribution in the well as well as effects of trajectories returning unrelaxed from the far wall are explicitly taken into account. The results reduce to all the previously obtained results of the single well model. We use the theory to analyze the experimental results of Hasha, Eguchi, and Jonas.

The reaction of NH^{+⋅} _{3} with H_{2}S: Dependence on the translational and internal energy of NH^{+⋅} _{3}
View Description Hide DescriptionThe reactions of vibrationally and of kinetically excited NH^{+⋅} _{3} ions with H_{2}S were investigated using a tandem ion cyclotron resonancespectrometer. NH^{+⋅} _{3} ions with internal energies ranging from 1–5 eV were generated by charge transferreactions, whose energy partioning is known. The charge transfer reagents used included Ar^{+⋅}, Kr^{+⋅}, Xe^{+⋅}, N_{2} ^{+⋅}, CO^{+⋅} _{2} , CO^{+⋅}, and O^{+⋅} _{2} . The ionic products formed in the reaction of excited NH^{+⋅} _{3} with H_{2}S were NH^{+} _{4} , H_{2}S^{+⋅} and H_{3}S^{+}. It is shown that the product distribution is sensitive to the NH^{+⋅} _{3} internal energy. At low internal energies, NH^{+} _{4} is the dominant product, while at 5 eV all three reaction products are of comparable intensity. Competition between formation of H_{2}S^{+⋅} and H_{3}S^{+} is effective only at NH^{+⋅} _{3} internal energies above 2 eV. The total rate constant was found to be 6±2×10^{−} ^{1} ^{0} cm^{3}/s and appeared to be independent of the internal energy of NH^{+⋅} _{3} . Kinetically excited NH^{+⋅} _{3} ions were formed using ICR double resonance and the effect on product distribution and total rate constant in the reaction with H_{2}S was studied. It is shown that kinetic energy exclusively drives the charge transfer channel. The total rate was independent of the NH^{+⋅} _{3} kinetic energy in the energy range of the experiment.

A semiclassical analysis of curvature corrections in quantal collinear reactive scattering
View Description Hide DescriptionThe orthogonal curvilinear coordinate system defined by periodic orbits is used to analyze the quantum mechanical approximation of vibrational adiabaticity in collinear reactive scattering. We show that with this system, the quantal close coupled equations decouple at an adiabatic barrier or well. The classical adiabatic frequency of a periodic orbit is shown to be the classical analog of the quantal adiabatic frequency at a barrier or well. Finally, we find that the success of the recently formulated DIVAH theory, in quantitative prediction of quantal resonance energies, is due to the fact that the diagonal correction terms appearing in this theory serve as curvature corrections. Adding the diagonal terms in the adiabatic approximation in radial coordinates compensates to a large extent for the difference in curvature of these coordinates and the system defined by periodic orbits. Numerical examples include the H_{3}, HMuH, and IHI systems.

Resonances by the complex coordinate method with Hermitian Hamiltonian. II. Error estimates
View Description Hide DescriptionUsing the Hermitian representation of the complex coordinate method that recently has been developed (Ref. 1), error estimates for the approximate resonance position and width are calculated. We prove here that for a given estimate of the resonance position and width the e x a c t solution is embedded in the surface of a crescent being part of an annular ring whose inner and outer radii can be obtained by variational calculations. An illustrative numerical example is presented.

Compensation effect in the dissociation of anharmonic oscillators: A model for catalysis
View Description Hide DescriptionThe differential form of the master equation for an anharmonic oscillator is solved in a steady‐state approximation to derive an expression for the rate constant for dissociation. A small increase of the anharmonicity parameter causes a decrease of activation energy and thus a very large increase in the rate constant. The energy of activation is nearly linear with the logarithm of the preexponential when the magnitude of anharmonicity varies. This compensation effect, along with the sensitivity of the rate constant to anharmonicity, suggests a relationship to catalyzed dissociation.

Finite duration of collisions and vibrational dephasing effects on the Ar broadened HF infrared line shapes: Asymmetric profiles
View Description Hide DescriptionThe existence of an asymmetry for the HF rovibrational absorption isolated lines induced by Ar pressure is clearly observed. This confirms the expected behavior based on a previous theoretical analysis of the finite duration effect on the molecular line shapes in the core region at moderate densities. The observed profile is well represented by the addition to the usual Lorentzian line shape of a dispersion component. This component is proportional to a characteristic parameter, linear with respect to the density of perturber and explicitly connected to the intermolecular potential. The a p r i o r i calculation of this parameter from an empirical potential leads to a super‐Lorentzian shape in the low frequency side in agreement with the experiment. Moreover, the expected increase of the asymmetry when going from the fundamental to the harmonic band is well observed. Such an increase results from the modification of the vibrational dephasing process due to molecular anharmonicities.

Temperature dependency of the affinity decay rate
View Description Hide DescriptionThe temperature dependency of the affinity decay rate of the reacting system was found to be analogous to the temperature dependency of the Helmholtz function of the equilibrium system. Consequently, standard‐state internal energies could be computed from the kinetic data and were found to be comparable to experimental internal energies.

A crossed molecular beam study of NO+O_{3}→NO^{*} _{2} +O_{2}: The effect of ozone rotational energy
View Description Hide DescriptionThe chemiluminescent branch of the reaction between NO and O_{3} to produce NO^{*} _{2} and O_{2} was studied by crossing a supersonic NO beam with a variable temperature effusive O_{3}beam and monitoring visible light emission. Signal was measured for two ozonebeam source temperatures, 300 and 181 K, and a ratio of S _{3} _{0} _{0}/S _{1} _{8} _{1}=3.0±0.4 was obtained. This ratio represents the effect of changing translational energy as well as internal O_{3} energy. The translational energy contribution to the signal ratio was calculated using a collision energy dependence of σ ∝ (E/2.3−1)^{2.05}, which was derived from experiments in which the temperature of the supersonic NO source was varied. The effect of vibrational energy was accounted for using published rate constant ratios. The remaining signal ratio of 2.3±0.3 is attributed to the effect of ozone rotational energy, which results in a dependence of (E _{rot})^{ n } where n=1.3–1.8.

Measurements of absolute total cross sections for charge transfer and electron detachment of halide ions on chlorine
View Description Hide DescriptionAbsolute total cross section measurements are reported for electron detachment and for reactive scattering between the halide ions (Cl^{−}, Br^{−}, and I^{−}) and chlorine gas Cl_{2}. The charge transfer and dissociativecharge transfer cross sections are found to be very large at their maxima, which occur at a relative collision energy of about 13 eV. The electron detachment cross section for I^{−}+Cl_{2} is anomalously low. Some energy loss spectra are reported for I^{−}+Cl_{2}. They exhibit substantial inelastic scattering which is consistent with the calculated potentials of Cl_{2}.