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Volume 66, Issue 7, 01 April 1977

The determination of the potential function governing the low frequency bending mode of disiloxane
View Description Hide DescriptionThe Raman spectra (10–3500 cm^{−1}) of gaseous and solid disiloxane and disiloxane‐d _{6} have been recorded. The infrared spectra of the gas from 4000 to 30 cm^{−1} and of the solid from 4000 to 450 cm^{−1} have been investigated. An examination of the low frequency Raman spectrum of the gas under moderately high resolution conditions (1.0 cm^{−1}) revealed a Q‐branch series for each molecule attributable to the double jumps of the anharmonic, low‐frequency skeletal bending mode. The observed Q‐branches were assigned with the help of a potential function of the form V (cm^{−1}) =1.07±0.02 q ^{4}−21.9±0.3 q ^{2} for the ’light’ compound and V (cm^{−1}) =0.973±0.015 q ^{2}−19.2±0.4 q ^{4} for the deuterated compound, where q is one of the reduced polar coordinates q and φ. These functions lead to barriers to linearity of 112±5 and 95±5 cm^{−1}, with the ground state energy levels at 42.6 and 37.8 cm^{−1}, respectively. Transformation of the potential functions to dimensioned form by using the reduced masses for the bending vibration gives an average equilibrium skeletal angle of 149±2°. The vibrational data have been interpreted in terms of G ^{†} _{36}molecular symmetry for the gaseous state, consistent with the concept of the quasilinear molecule, while the spectra of the solid state indicate a bent skeleton. Resolvable fine structure on two perpendicular bands in the infrared indicate very nearly free internal rotation in disiloxane.

A search for the infrared fundamental of matrix‐isolated XeF
View Description Hide DescriptionVarious xenon/fluorine mixtures were photolyzed in solid argon matrices and examined in the infrared spectral region with either a Fourier transformspectrometer or with a grating spectrometer. After photolysis, a strong peak was observed at 215 cm^{−1} in addition to the known XeF_{2}(ν_{3}) peak at 549 cm^{−1}. The appearance of the same two bands in Ar matrices containing the vapors over XeF_{2} indicated the assignment of the 215 cm^{−1} band to XeF_{2}(ν_{2}). The fundamental of XeF was not observed either because it is masked by the XeF_{2}(ν_{2}) peak or because it has a small infrared absorption coefficient.

Relaxation processes and spectra in liquids and dense gases
View Description Hide DescriptionThe spectral response of a molecule dissolved in a liquid or dense gas is calculated using a correlation function approach. It is shown that the characteristicspectra of the molecule can be used as a probe of the molecular motions and the dynamic structure effects. A method developed by Blume and Kubo which assumes the solute–solvent interaction parameter to be a stochastic process is employed. The induced Q branch in the vibration–rotation spectra of polar molecules is discussed as an example and the cases in which the rotational relaxation of the molecule is determined by either the dynamic structure or by collisional processes are obtained in the appropriate limits.

Semiclassical theory of electronic transitions in molecular collisions: Combined effects of tunneling and energetically inaccessible electronic states
View Description Hide DescriptionThe semiclassical theory of collision‐induced electronic transitions is extended to describe tunneling and the effect of energetically inaccessible states. The powerful technique of analytic continuation is utilized to yield very good agreement with exact quantum mechanical results on some model systems. The inaccessible states have a significant effect on transmission coefficients and thus can be important in semiclassical studies of molecular reactions.

Analysis of the matrix induced changes in the optical spectra of matrix isolated noble metal atoms
View Description Hide DescriptionThe absorption spectra of the noble metal atoms Cu,Ag, and Au isolated in Ar, Kr, and Xe matrices have been measured as a function of matrix temperature in the range between 3 K and about 0.4 of the respective matrix triple point temperature. The spectra show a pronounced energy shift of the absorption peaks with temperature which is entirely reversible in well annealed matrices in the above‐given temperature range. These spectra were evaluated by crystal field arguments to obtain more direct information on the matrix influence, which is discussed in terms of difference in level shifts, change in spin–orbit splitting, and crystal field splitting. The results are then explained by a model in which the matrix atoms are treated as clouds of negative charge which introduce a repulsive potential in the region of the metal electrons when the metal atom is squeezed into the matrix cage. The change with temperature in the interaction between metal atom and matrix is discussed in detail. In addition, an unambiguous assignment of the optical transitions under consideration has been made for the metal atoms in the crystal field of the matrix.

Note on the Thomas–Fermi and Thomas–Fermi–Dirac model calculation of atomic polarizabilities
View Description Hide DescriptionThis paper discusses a recent calculation by Bruch and Lehnen of the static electric dipole polarizabilities of neutral inert gas atoms. These authors obtained the polarizabilities within the framework of statistical models by making use of an energy functional method. The method, as applied by Bruch and Lehnen, makes use of the exact solutions of either the Thomas–Fermi (TF) or of the Thomas–Fermi–Dirac (TFD) equations. This paper points out that a better agreement than the one obtained by Bruch and Lehnen between calculated and experimental values of the atomic polarizabilities can be obtained upon resorting to approximate (analytical) variational solutions of the TF and TFD equations. The improved agreement, in the case of the TF model, is attributed to the fact that the variational solution of the TF equation permits one to construct a radial electron density for a neutral atom that decreases with the distance from the nucleus exponentially. That this is an improvement is seen from the fact that in the exact TF model the radial electron density drops off with the distance from the nucleus as the inverse fourth power of this quantity. Essentially the same situation prevails in the case of the approximate (analytical) solution of the TFD equation, which makes use of the variational solution for a TF atom. In this case, the improved radial electron density manifests itself in a contraction of the atomic radius, relative to that which is obtained within the exact TFD model.

Dielectric studies in solid phase MBBA
View Description Hide DescriptionDielectricmeasurements have been made in the metastable solid phase of MBBA in the frequency range 1–100 kHz and in the temperature range −196 to 0°C. The results indicate a Debye‐type dispersion with symmetric distribution of relaxation times. The dielectric relaxation strength (Δε=ε_{0}−ε_{∞}) varies with temperature and shows a maxima at about −60°C. The results can be qualitatively explained by assuming the free rotation of the dipoles in the temperature range above −60°C and a restricted rotation of the dipoles (or restricted number of active dipoles) in the low temperature region.

Molecular dynamics of the rough sphere fluid. II. Kinetic models of partially sticky spheres, structured spheres, and rough screwballs
View Description Hide DescriptionThe rough sphere model is extended and suitably generalized to collisions between partially rough spheres, ’’spheres’’ with anisotropic mass distributions, and spheres with domains of roughness and smoothness distributed in such a way as to model polyatomic models. These models are used to compute various relaxation and correlation times. In addition, a model is devised for the interaction of a chiral molecule and nonchiral solvent molecules. This model is used to compute the couplings between translations and rotations. In treating the chiral systems we extend the independent binary collision model to the multivariate case.

Properties of helium isotopes adsorbed on uniform surfaces. I. Isolated atoms
View Description Hide DescriptionExperimental data are reported for the submonolayeradsorption of ^{4}He and ^{3}He on the basal plane of a graphitized carbon black and on this substrate after coating with one monolayer of solidified xenon. The results obtained for these four systems include heats of adsorption as a function of coverage, Henry’s law constants, and derived properties of an isolated atom interacting with the solid, such as the average energy, the Slater sum, and the nonconfigurational entropy. Theoretical calculations of the gas–solid potential energy surfaces are reported and compared with previous calculations. The eigenstates for ^{4}He and ^{3}He that have been obtained by other workers for these systems were then used in direct theoretical calculations of the experimental quantities. Comparison of theory and experiment is used to comment upon the choice of parameters in the calculated gas–solid potentials for these systems.

Quantum mechanical close coupling approach to molecular collisions: Averaged definite parity j _{ z } approximation with Clebsch–Gordan weights
View Description Hide DescriptionThe new averaged definite parityj _{ z }(ADPj _{ z }) approximation is considered in detail from the standpoint of the exact body frame CC cross section equations. These cross section equations are decomposed into contributions from the various possible orbital angular momenta and projections of the total angular momentumJ onto the scattering vector. This decomposition then permits a clearer examination of the quantities actually approximated in j _{ z }‐conserving approximations. The various contributions to the exact cross sections are regrouped into components having the same form as the j _{ z }CCS and DPj _{ z } approximate equations. It is found that the labeling of j _{ z }CCS amplitude densities by an orbital angular momentum quantum number enters in a very natural way and in fact that o n l y labeling by l̄ is permitted for consistency. Further, it is shown that o n l y the amplitude density is approximated and this d o e s n o t require the body frame T‐matrix to be diagonal in j _{ z }. After the approximate amplitude density is substituted into the exact partial cross section expression, the resulting equations for the partial cross sections σ^{ J }(j _{0}→j) lead to an average over the effective orbital angular momenta with weights w ^{ J } _{ lλ}(j ‖j _{0}) =〈l0jλ‖Jλ〉^{2}[(2l+1)/(2J+1)]. A similar analysis of the definite parity partial cross section leads to an average over the effective orbital angular momenta of the proper parity with weights w ^{ J p } _{ lλ}(j ‖j _{0}) =〈l0jλ‖Jλ〉^{2}[(2l+1)/(2J+1)][2/(1+δ_{λ,0})]. This enables one to include effects of the various turning points associated with values of l satisfying ‖J−j‖⩽l ⩽J+j. The present method of including parity through the values of l averaged also can correctly describe situations where the odd parity partial cross section is larger than the even parity partial cross section. The result is an approximation which describes definite parity partial cross sections, integral cross sections, and differential cross sections with very high accuracy. Finally, the ADPj _{ z } is a general method for which other averaging weights are possible. The previously obtained constant weight version is compared to the present Clebsch–Gordan weight version by applying both to He+H_{2} collisions. Results for definite parity partial cross sections and integral cross sections are used as the basis of the comparison.

Identification of the partial wave parameter and simplification of the differential cross section in the j _{ z }CCS approximation in molecular scattering
View Description Hide DescriptionThe identification of the partial wave parameter ? of the J _{ z }CCS approximation in molecular scatteringtheory is considered, and it is shown that if one chooses ?=l′ (the final orbital angular momentum) rather than ?=J (the total angular momentum) the full body‐fixed expression for the scattering amplitude reduces directly to the simple formula used by McGuire and Kouri. Results are cited that show that ?=l′ is not only simple, but physically reasonable, and gives much better results than ?=J.

Classical and quantum centrifugal decoupling approximations for HCl–Ar
View Description Hide DescriptionThe centrifugal decoupling approximation previously employed in quantum mechanics is extended to classical mechanics. Both classical and quantum centrifugal decoupling (CCD and CD, respectively) calculations are performed for HCl–Ar. Total cross sections are obtained from the CCD and CD calculations. The CCD and CD total cross sections are shown to be in good agreement with the corresponding exact classical trajectory (EC) and close coupled (CC) cross sections, respectively. The conservation of the projection (Ω) of the rotational angular momentum along the body‐fixed z‐axis is studied as a possible explanation for the success of the CCD and CD approximations in predicting total cross sections. By examining the CC body‐fixed S‐matrix elements and studying the behavior of Ω during the course of an exact classical trajectory, it is found that Ω is conserved o n l y under very limited conditions. Detailed examination of the calculations shows that the CD approximation may be good even when Ω varies rapidly.

Photoelectron and far‐ultraviolet absorption spectra of nonaromatic azomethine compounds
View Description Hide DescriptionThe far‐ultraviolet absorption and He I photoelectron spectra of seven compounds containing either the nonconjugated azomethine group with alkyl substituents only or the conjugated C=C–C=N or C=N–N=C unit have been measured. The n and π ionization potentials (IP) as well as the bands due to π*←n and π*←π transitions are readily identified. The Rydberg bands can be approximately located at observed shoulders of broad bands using the IP’s and the usual ranges of term values but the diffuse character of these spectra makes exact assignments difficult.

Classical trajectories for the H+H_{2} reaction on a spline‐generated potential energy surface
View Description Hide DescriptionUsing a functional form based on rotated Morse curves, cubic splines are used to fit the Shavitt–Stevens–Minn–Karplus (SSMK) potential surface for the collinear H+H_{2}reaction. The fit obtained by this method is shown by contour maps and difference maps to be excellent. The deviations which do occur are shown to result from the limitations of the method but also from an error in the SSMK function. Classical trajectories carried out on the spline‐fitted surface show good agreement with the results obtained from the analytical SSMK surface, including a point‐by‐point matching of most of the individual trajectories. The reactivity bands and total reaction probability agree closely with the two methods. The spline‐fitted potential function is more economical to use than the analytical function and is easily adjusted to give different surface features, which may be varied in an independent manner.

Conformation maps of some saturated six and seven membered rings
View Description Hide DescriptionUsing a new semirigid model, conformation maps of cyclohexane, p‐dioxane, m‐dioxane, and cycloheptane are recalculated. The ideal out‐of‐plane coordinates are used together with in‐plane coordinates and are found to give the correct energies of all the significant conformations of six membered rings and of the chair–twist–chair form of cycloheptane. Conformation maps display higher symmetry than maps previously reported.

The vibrational deactivation of HF(v=3) and HF(v=2) by H atoms
View Description Hide DescriptionThe rate of HF(v=2 and 3) removal by H atoms was measured at T=295 K. The measurements were performed by laser‐induced fluorescence in a discharge flow tube in which H atoms were produced by a microwavedischarge. The absolute H‐atom concentrations were measured by isothermal calorimetry with a Pt wire coil as a catalytic probe. A small fraction of the injected HF(v=0) was pumped first to HF(v=1) and subsequently to HF(v=2) and HF(v=3) by the multiline output from a pulsed HF transverse excitation atmospheric (TEA) laser. The exponential decay times of the HF 3–0 fluorescence with and without the microwavedischarge and the measured H‐atom concentrations were used to calculate a removal rate of 6.3×10^{13} cm^{3}/mol‐sec for HF(v=3). This rate is ∼400 times faster than the deactivation of HF(v=1) by H atoms and ∼100 times faster than the deactivation of HF(v=2) also reported in this study. Thus, it many account for the low laser output from the higher vibrational levels that has been observed in pulsed HF lasers. There are several vibrational deactivation processes and reactions that may contribute to the measured removal rate. The present results bear directly on the construction of potential energy surfaces used for theoretical predictions of upper level deactivation rates.

Studies on bond dissociation in CH_{4}, NH_{3}, and H_{2}O by the multiconfiguration self‐consistent‐field method
View Description Hide DescriptionThe lowest potential curve for the dissociation of an X–H bond of an XH_{ m } molecule is calculated for CH_{4}, NH_{3}, and H_{2}O by the multiconfiguration self‐consistent‐field (MCSCF) method. The calculated well depth of the potential curve (in atomic units) obtained from the two configuration wavefunction constructed with MCSCF localized orbitals is 0.1707 for CH_{4} (0.1656 for NH_{3} and 0.1589 for H_{2}O). The value is in good agreement with the experimental value of 0.1619 (0.1610 for NH_{3} and 0.1879 for H_{2}O). This allows us to conclude that the potential curve of the dissociation process of any local bond in a polyatomic molecule may be satisfactorily reproduced by the use of the two configuration wavefunction constructed with MCSCF localized orbitals. This wavefunction gives very good asymptotic behavior at a dissociation limit.

Polymer dynamics in a binary critical mixture
View Description Hide DescriptionThe dynamic structure factor of a dilute solution of flexible polymer molecules in a binary mixture near the critical point is studied using mode coupling techniques. The strong concentration fluctuations of the solvent near the criticcal point lead to modifications of the hydrodynamic interactions between the monomer units in a chain. A set of equations is derived which describes the decay of the coupled solvent and polymer modes. The critical fluctuations of the solvent lead to a change in the wave vector dependence of the dynamic structure factor and a change in the center of mass diffusion coefficient of the polymer.

Raman spectroscopic studies of yttrium (III) chloride–alkali metal chloride melts and of Cs_{2}NaYCl_{6} and YCl_{3} solid compounds
View Description Hide DescriptionThe Raman spectra of molten YCl_{3}–A Cl (A=Cs, K, Li) mixtures have been measured at different compositions and temperatures up to 890 °C. The Raman spectra of polycrystalline Cs_{2}NaYCl_{6} and YCl_{3} were also measured from 25 °C to temperatures above melting. The factor group analysis of crystalline Cs_{2}NaYCl_{6} was used to identify the three Raman active modes (ν_{1}, ν_{2}, ν_{5}) of the YCl_{6} ^{−3} octahedra. For liquid mixtures rich in alkali halide, the predominant features of the spectra are characterized by a polarized and a depolarized band with frequencies near the ν_{1} and ν_{5} frequencies of the YCl_{6} ^{−3} octahedron and thus indicates the existence of such species in the melt. In melts containing above 25% YCl_{3} a new polarized band D appears in the spectra which shifts continuously and rapidly to higher energies with increasing YCl_{3} concentration. The frequency shift is attributed to a continuous distortion mechanism of the YCl_{6} ^{−3} octahedra by the neighboring yttrium ions. The c o n t i n u o u s frequency shift of the D band and a comparison of the liquid and solid Raman spectra of yttrium chloride suggest the existence of lattice‐type modes in these melts.

Surface structures of normal paraffins and cyclohexane monolayers and thin crystals grown on the (111) crystal face of platinum. A low‐energy electron diffraction study
View Description Hide DescriptionThe surfaces of the normal paraffins (C_{3}–C_{8}) and cyclohexane have been studied using low‐energy electron diffraction (LEED). The samples were prepared by vapor deposition on the (111) face of a platinum single crystal in ultrahigh vacuum, and were studied both as thick films and as adsorbed monolayers. These molecules form ordered monolayers on the clean metal surface in the temperature range 100–220 K and at a vapor flux corresponding to 10^{−7} Torr. In the adsorbed monolayers of the normal paraffins (C_{4}–C_{8}), the molecules lie with their chain axes parallel to the Pt surface and Pt[11̄0]. The paraffin monolayerstructures undergo order–disorder transitions as a function of temperature. Multilayers condensed upon the ordered monolayers maintained the same orientation and packing as found in the monolayers. The surface structures of the growing organic crystals do not corresond to planes in their reported bulk crystalstructures and are evidence for epitaxialgrowth of pseudomorphic crystal forms. Multilayers of n‐octane and n‐heptane condensed upon disordered monolayers have also grown with the (001) plane of the triclinic bulk crystalstructures parallel to the surface.n‐Butane has three monolayerstructures on Pt(111) and one of the three is maintained during growth of the crystal. Cyclohexane forms an ordered monolayer, upon which a multilayer of cyclohexane grows exhibiting the (001) surface orientation of the monoclinic bulk crystalstructure.Surface structures of saturated hydrocarbons are found to be very susceptible to electron beam induced damage. Surface charging interferes with LEED only at sample thicknesses greater than 200 Å.