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Volume 60, Issue 6, 15 March 1974

Application of ^{129}I Mössbauer spectroscopy to a metal iodide: [Ru(cp)_{2}I] I_{3}
View Description Hide DescriptionThe 27.8 keV transition of ^{129}I was used to study the bonding in [Ru(cp)_{2}I]I_{3}. The nuclear quadrupole coupling constants, isomer shifts relative to the source, asymmetry parameters, full widths at half‐maximum, intensities, and asymmetries in the recoilless fraction were obtained for each of the three inequivalent iodide sites. The Mössbauer parameters for the triiodide anion agree with both NQR and Mössbauer studies on other compounds containing the triiodide anion.

On the problem of hard squares
View Description Hide DescriptionIt is usually thought from computer studies that the partition function of hard squares on a crossed square lattice has all its zeros in the left half complex plane. From the study of a simpler problem we argue that, although not impossible, this is very unlikely.

Close‐coupling approach to gas‐solid energy transfer
View Description Hide DescriptionThe inelastic scattering of a gas molecule from a solid surface is treated quantum mechanically and in three dimensions using the close‐coupling formalism. Energy transfer processes involving internal states of the molecule and one‐phonon states of the solid are included as well as arbitrary diffractions. The phonon quantum number is replaced by a continuous variable. The dependence of the unknown wavefunction on this continuous variable is expressed as an expansion in a complete set of known functions having this continuous quantum number as argument. This substitution results in the continuously infinite set of coupled differential equations being replaced by an infinite set of discrete coupled equations. Truncating this set after a finite number of terms leads to finite sets of coupled equations which are solved by standard techniques. In applying this procedure to a simple example (which, nevertheless, provides a stringent test of the method) reasonably accurate results are obtained with a basis set of only 25 functions describing the continuous quantum number. On the basis of this test, it is suggested that this method appears to be practical for computing accurate gas‐solid one‐phonon energy transfer probabilities and should be most useful when many one‐phonon states are involved in the collisions (thereby complimenting ``near‐specular'' energy transfertheories).

Theoretical investigations of the reaction dynamics of polyatomic systems: Chemistry of the hot atom (T* + CH_{4}) and (T* + CD_{4}) systems
View Description Hide DescriptionAn unadjusted computation of the reaction dynamics in the (CH_{4} + T*) and (CD_{4} + T*) systems has been carried out. The six‐body potential‐energy surface has been obtained from the equilibrium thermodynamic and spectroscopic data for reactants and products, the results of all‐valence electron INDO and all‐electron, ab initio SCF and CI quantum calculations, and previously formulated three‐ and four‐body valence‐bond (VB) potential surfaces. The computed saddle‐point geometries for axial abstraction and inversion displacement are in good to excellent agreement with previous ab initio CI calculations. The saddle‐point energies are in fair to good agreement. Computed fundamental vibration frequencies for CH_{4} are in excellent accord with ir and Raman data. Reaction cross sections as a function of relative translational energy for abstraction, displacement, and fragmentation in (CH_{4} + T*) and (CD_{4} + T*) systems have been computed by quasiclassical trajectory analysis. Calculated thresholds are in quantitative agreement with experiment. The abstraction and displacement reaction dynamics are examined and discussed. Hot‐atom yield ratios in both systems have been determined through solutions of the integral reaction probability equation. Computed results for nuclear recoil tritium incident upon CH_{4} are in quantitative agreement with experiment. Yield ratios for [CD_{3}T/DT] obtained by photolysis of TBr are in excellent accord with experiment at all photolysis energies. Abstraction yields in CH_{4} are computed and found to be in good agreement with experiment. The low energy (40–65 kcal/mole) displacement cross sections are found to be too low by a factor of 2–3.

Configurational properties of self‐avoiding walks generated in the presence of an interacting solid barrier
View Description Hide DescriptionSelf‐avoiding walks confined to the diamond lattice were generated in the presence of an interacting solid barrier by the method of exact enumeration. The behavior of some configurational properties such as the mean‐square end‐to‐end distance, average maximum normal to the surface distance of the chains, average number of adsorbed segments, etc., was investigated as a function of the interaction energy ε. All properties studied were found to obey a simple asymptotic expression of the form <P_{N} >≃N ^{γ}, where P is a generalized configurational property and γ is a critical index. Some estimates of γ as a function of ε are reported.

Influence of pressure on the melting of rare gas solids
View Description Hide DescriptionA simple equation which predicts the influence of pressure on melting points and includes anharmonicity has been applied to the rare gas solids. This equation is shown to be useful in estimating the Grüneisen parameter γ_{ G }(T_{m} ) near the melting point.

Valence electron studies with Gaussian‐based model potentials and Gaussian basis functions. III Applications to two‐valence‐electron systems composed of combinations of Li, Na, H, or their unipositive ions
View Description Hide DescriptionA previously developed simple valence‐only electronic structuretheory based on atomic core model potentials and using flexible Gaussian valence basis functions is applied to the two‐valence electron systems Li_{2}, Na_{2}, NaLi, LiH, NaH, Li_{3} ^{+}, Na_{3} ^{+}, Li_{2}Na^{+}, LiNa_{2} ^{+}, LiH_{2} ^{+}, Li_{2}H^{+}, NaH_{2} ^{+}, Na_{2}H^{+}, and H_{2}, within the SCF MO model. Results for calculated equilibrium geometries and energy changes for certain chemical reactions are compared to the corresponding quantities from analogous all‐electron ab initio calculations. The model potential results are quite similar to those from the ab initio ones and are generally satisfactory for such a simple theory. There is a tendency toward slightly long internuclear distances (average deviation of all unique independent distances is +0.06 bohr) and slightly high energy of complex relative to separate constituents (average deviation of dissociation reaction energies is −2.1 kcal/mole) in these calculations relative to the all‐electron ones, the explanation of which will require future detailed analysis of both the model potential valence‐electron and the ab initio all‐electron calculations.

Studies on dielectric relaxation in some rotational isomeric molecules
View Description Hide DescriptionDielectricpermittivities and losses for 1,2‐ethanedithiol, 1,2‐propanedithiol, and 1,2‐dichloropropane in the liquid state have been measured at 1.62, 3.17, and 3.49 cm in the microwave region at different temperatures. The distribution parameter in 1,2‐propanedithiol was found to increase with increasing temperature in contrast to that in 1,2‐ethanedithiol and 1,2‐dichloropropane. A possible explanation for this has been suggested. The energy differences between the trans and gauche isomers in all the liquids obtained from the dipole momentmeasurements agree fairly well with those obtained from spectroscopic studies.

Vibrational analyses and barrier to internal rotation of CH_{3}CHBr_{2} and CD_{3}CDBr_{2}
View Description Hide DescriptionThe infrared spectra of gaseous and solid 1, 1‐dibromoethane and 1, 1‐dibromoethane‐d _{4} have been recorded from 140 to 3500 cm^{−1}. The corresponding Raman spectra of the liquid and solids have also been recorded and depolarization values have been measured. All spectra have been interpreted in detail and the 18 normal vibrations have been characterized on the basis of band contours, isotopic shifts, depolarization values, and normal coordinate calculations. The internal torsional mode was observed at 253 cm^{−1} in the far infrared spectrum of gaseous CH_{3}CHBr_{2} and the assignment was confirmed by the shift with deuteration. The threefold barrier to rotation was calculated to be 4.3 kcal/mole. This determination allows a comparison of the barriers for a series of bromoethanes.

Thermodynamic properties of ZrO (g) and HfO (g); a critical examination of isomolecular oxygen‐exchange reactions
View Description Hide DescriptionThe thermodynamic properties of ZrO(g) and HfO(g) have been determined by mass‐spectrometric studies of five isomolecular oxygen‐exchange reactions of the type M(g)+M′O(g)=MO(g)+M′(g) involving the gaseous atoms and monoxides of yttrium and thorium. Third law values of the standard free energies of formation over the temperature range 2000–2800 K are adequately (within 2%) expressed by the linear equations ΔG°_{ f }(ZrO,g)=13 040−16.04T, ΔG°_{ f }(HfO,g)=9930−14.68T. Uncertainties of ±1 kcal mol^{−1} are estimated. Third law analyses of the data yield the enthalpies of formation at absolute zero, ΔH°_{0}(ZrO,g)=21.4, and ΔH°_{0}(HfO,g) = 18.5 kcal mol^{−1}, and the dissociation energies at absolute zero, D _{0}(ZrO)=180.7, and D _{0}(HfO)=188.9 kcal mol^{−1}, with uncertainties of 1–2 kcal mol^{−1}. The equilibrium constants for the isomolecular reactions in this and in previous studies were obtained from ion currents and relative instrumental sensitivities that were approximated from the mean square radii of the gaseous atoms and the squares of the interatomic distances of the gaseous monoxides; the use of these parameters was shown to improve the closure among several thermodynamic cycles by as much as 2 kcal mol^{−1}

Floating ellipsoidal Gaussian orbital computations on small molecules
View Description Hide DescriptionElectronic structure calculations on H_{2}, HeH^{+}, , HeH^{−}, LiH, BeH^{+}, Li_{2}, BH, CH^{+}, HBH^{+}, HBeH, HLiH^{−}, LiHLi^{+}, HBH^{−}, HCH, and HNH^{+} are performed using the floating ellipsoidal Gaussian orbital (FEGO) method and optimizing geometries. The resulting electronic energies; nuclear geometries; and shapes, sizes, and locations of orbitals are compared to the corresponding floating spherical Gaussian orbital values. The results suggest that energetics and bond angles are more accurately described by the FEGO computations. Bond lengths are predicted to be longer in the FEGO method. A discussion of the role of lone pair electrons in both methods is given.

Configuration coordinate model for the hydrated electron. III. Diffusive motion
View Description Hide DescriptionThe diffusive motion of the solvated electron is treated by use of the configuration coordinate model. The configuration coordinate diagram appropriate to the diffusive motion of the hydrated electron is constructed by calculating the total energy of the hydrated electron under a series of orientational polarization functions which are appropriately chosen. The diffusive motion of the hydrated electron is discussed in terms of this diagram. The calculated activation energy of diffusion is 0.16 eV, which is in excellent agreement with experiment.

Excited molecular terms of the alkali‐rare gas atom pairs
View Description Hide DescriptionNumerous excited molecular terms for the various alkali‐rare gas atom pairs have been determined. The semiempirical potential model of Baylis has been used with some modifications in the calculation of the molecular terms; in particular, a large number of atomic states are included in our calculation, which ensure the stability of the calculated molecular terms. Our results show that coupling among molecular terms is very important and gives rise to structure in the excited potential energy curves. Comparisons between our results and other theoretical and experimental data are made.

Rate constant of OH + H_{2} = H_{2}O + H from 1350 to 1600 K
View Description Hide DescriptionTransient OH maxima were observed in the shock‐initiated combustion of rich (H_{2}:O_{2}:Ar = 10:1:89) hydrogen‐oxygen‐argon mixtures. Computer simulations of the reaction profiles were used to compare an assumed mechanism and set of rate constants with the experimental results. The expression k _{3} = 5.2×10^{13} exp(−27 kJ/RT) cm^{3} mol^{−1} · s^{−1} was derived for the reaction OH + H_{2} = H_{2}O + H over the temperature range 1350–1600 K. The expression k _{3} = 10^{7.50}T^{1.77} exp(−12.7 kJ/RT) cm^{3} mol^{−1} · s^{−1} was derived combining our results with those of previous investigations spanning the temperature range 300–1800 K.

Comparisons of Morse and harmonic oscillator models for vibrationrotation excitation of H_{2} by Li^{+}
View Description Hide DescriptionMatrix elements of a potential for atomdiatomic molecule collision problems in three dimensions have been calculated using two models to describe the rotatingvibrating molecule. These models are the undistorted three dimensional harmonic oscillatormodel of Eastes and Secrest and a rotatingvibrating Morse oscillator. The most important difference between the two models is the presence of centrifugal stretching in the Morse oscillatormodel. A comparison of matrix elements is made which is applicable to any atomdiatom potential with a dependence on the vibrational coordinate in the form ξ, ξ^{2}, e ^{αξ}, and ξe ^{αξ}. In addition, the specific example of Lester's ab initio HartreeFock potential for Li^{+}–H_{2} is considered. Cross sections are calculated for Li^{+}–H_{2} with limited basis sets for the harmonic and Morse oscillator at 0.1, 2.0, and 3.26 eV relative kinetic energy.

Temperature dependence of the probability of vibration‐vibration‐rotation energy transfer in HCl (v = 2) + HCl (v = 0) ⇋ HCl (v = 1) + HCl (v = 1)
View Description Hide DescriptionEnergy transfer probabilities for the vibration‐vibration process HCl(v = 2) + HCl(v = 0)⇄HCl(v = 1) + HCl(v = 1) + ΔE = 102 cm^{−1} have been calculated in the temperature range of 300–1000°K assuming that ΔE is supplied or removed through the vibration‐rotation process. The interaction potential is assumed as the sum of repulsive, attractive, dipole‐dipole, and hydrogen‐bond energy terms. It is shown that the probability decreases nearly linearly with rising temperature between 300–600°K; this result agrees with experiment. After reaching a minimum value at 700°K, the probability increases with temperature. The temperature dependence is explained in terms of the contribution of molecular attractions including dipole‐dipole and hydrogen‐bond terms and the effect of translational motion on the vibration‐rotation process.

Nuclear magnetic resonance study of the transition metal monoborides. II. Nuclear electric quadrupole and magnetic shift parameters of the metal nuclei in VB, CoB, and NbB
View Description Hide DescriptionMeasurements are reported of the nuclear electric quadrupoleinteraction parameters (coupling constant and asymmetry) and the several anisotropicKnight shift parameters of the ^{51}V, ^{59}Co, and ^{93}Nbnuclear magnetic resonance spectra in VB, CoB, and NbB monoborides, respectively. A detailed account is given of the method of extracting these parameters from the experimental spectra. The quadrupole coupling constants and asymmetry parameters are ^{51}VB, 1.75 MHz, 0.95; ^{59}CoB, 25.2 MHz, 0.74; and ^{93}NbB, 20.4 MHz, 0.065. The isotropic components of the Knight shifts are all positive: ^{51}VB, 0.32%; ^{59}CoB, 0.69%; and ^{93}NbB, 0.24%. Despite the close similarity in the structures of these compounds, neither the quadrupole nor Knight shift parameters scale in a simple manner with the nuclear properties. Thus, even in the cases of VB and NbB, it appears that a rigid‐band type approximation furnishes a poor description of the actual changes in the electronic structure.

X‐ray scattering from diatomic molecules in the liquid state
View Description Hide DescriptionA version of the Steele‐Pecora equation suitable for use with diatomic molecules has been derived. Substitution of chlorine scattering factor coefficients and Percus‐Yevick distribution functions into this equation led to the determination of total scattered intensity functions expressed as sums of gas scattering, spherical, and angular intensity contributions. The angular contributions were shown to be experimentally significant in the regions of the first and second peaks at high densities . Temperature was shown to have only a slight effect on total intensity. g _{000}, g _{200}, and g _{220} were found to be the principal contributors to the intensity.

Radiative lifetimes of the alkaline earth monohalides
View Description Hide DescriptionThe radiative lifetimes for a number of electronic states of the alkaline earth monohalide molecules MX, where M denotes Ca, Sr, or Ba and where X denotes F, Cl, Br, or I, have been determined directly from the rate of fluorescence decay with time using a pulsed dye laser as an excitation source. The measured lifetimes in nanoseconds are CaF: A _{1} 21.9(4.0), A _{2} 18.4(4.1), B 25.1(4.0); CaCl: A _{1} 29.4(1.8), A _{2} 28.4(2.6), B 38.2(3.9), C 25.0(2.1); CaBr: A _{1} 34.2(2.9), A _{2} 33.7(1.9), B 42.9(3.1), C _{1} 33.2(4.0), C _{2} 31.8(3.7); CaI: A _{1} 41.7(2.3), A _{2} 41.6(3.4), B 50.9(1.7); SrF: A _{1} 24.1(2.0), A _{2} 22.6(4.7); SrCl, A _{1} 31.3(2.7), A _{2} 30.4(3.6), B 38.8(2.1), C _{1} 26.1(1.9), C _{2} 26.0(1.6); SrBr: A _{1} 34.3(2.3), A _{2} 33.2(1.6), B 42.2(1.6), C _{1} 30.3(2.6), C _{2} 28.1(1.3); SrI: A _{1} 43.3(1.6), A _{2} 41.9(1.3), B 46.0(2.0), C _{1} 36.0(3.7); BaF: C _{1} 23.8(2.3), C _{2} 23.5(0.7); BaCl: C _{1} 17.5(0.8), C _{2} 16.6(0.6); BaBr: C _{1} 17.9(1.0), C _{2} 16.5(1.4); BaI: C _{1} 17.9(1.9), C _{2} 16.0(1.5), where A _{1}, A _{2}, B, C _{1}, and C _{2} denote, respectively, the A ^{2}Π_{1/2}, A ^{2}Π_{3/2}, B ^{2}Σ^{+}, C ^{2}Π_{1/2}, and C ^{2}Π_{3/2} states, and where the uncertainties, representing one standard deviation, are given in parentheses. The lifetimes of the CaX and SrX states are seen to be quantitatively similar, while those of BaX are quite different. No vibrational dependence of the lifetime for the BaI C _{2} state is observed for 0 ≤ ν′ ≤ 39. For other MX molecules the vibrational dependence of the lifetime could not be ascertained because the MX molecule was not produced in a sufficiently wide range of ground state vibrational levels. Various one‐electron models for the MX transitions are discussed. It is found that a consistent explanation of the transition moments can be obtained by assuming that the transition is between two nonbonding orbitals centered on the metal atom whose mixing coefficients in terms of a truncated metal atom basis set are adjusted to reproduce a subset of the experimentally determined transiton moments. For the X, A, and B states of CaX and SrX, the nonbonding orbital is primarily n s σ, n p π, and n p σ, respectively, in character; for BaX it is suggested that (n − 1)d π and (n − 1)d σ play an important role in the description of the nonbonding orbital in the A, B, and C states.

Multiple transition points in a semiclassical treatment of electronic transitions in atom(ion)‐diatom collisions
View Description Hide DescriptionA semiclassical treatment of multiple transition points for electronic transitions in atom(ion)‐diatom collisions is presented. The treatment, based on a theory by W. H. Miller and T. F. George [J. Chem. Phys. 56, 5637 (1972)], involves the semiclassical evaluation of a path integral connecting the initial and final states of a given collision. The evaluation considers first the classical limit of an electronic propagator, which is a function of the time development of the nuclear degrees of freedom, and then the classical limit of a nuclear path integral containing the electronic propagator. The treatment of multiple transition points in the electronic propagator is presented in analogy with the problem of motion over multiple barriers. For transition points close in time a uniform approximation must be introduced in the evaluation of the electronic propagator. This is distinguished from another uniform approximation which might be necessary in the evaluation of the nuclear path integral. The resulting forms of classical S matrix elements derived from these approximations are given, and their application to H^{+} + D_{2}collisions is discussed.