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Volume 49, Issue 6, 15 September 1968

Fine Structure in Energy‐Distribution‐Difference Ionization‐Efficiency Curves
View Description Hide DescriptionRefinements in the experimental application of the energy‐distribution‐difference (EDD) method for resolving fine structure in ionization‐efficiency curves are presented. These include data acquisition and computer‐processing techniques by which first‐differential EDD curves can be obtained with a good signal‐to‐noise ratio. Using these techniques, a study has been made of the fine structure observed in the first‐differential EDD ionization‐efficiency curves of C_{2}H_{2} ^{+} and Xe^{+} near their thresholds. Distinct “steps” are resolved in the first‐differential ionization‐efficiency curve of C_{2}H_{2} ^{+}. The energy separations between these steps agree quite well with energy separations between vibrational levels of the C_{2}H_{2} ^{+} ion determined by photoionization techniques. However, the relative cross sections for these processes determined by electron impact are drastically different from those reported for photoionization. Possible explanations for these differences are discussed. The electron‐impact results for xenon indicate that a large portion of the cross section between the and states of Xe^{+} is due to autoionization from known Rydberg levels.

Theoretical Study of the Geometry and Spectrum of Nitrous Oxide
View Description Hide DescriptionA series of ab initio SCF MO calculations is carried out for the nitrous oxide molecule as a function of internuclear angle in both NNO and NON arrangements. Investigation of the results of these calculations indicates that this molecule favors the nonsymmetric NNO arrangement mainly as a result of the net stabilization its occupied MO's derive from having the more electronegative oxygen atom at the terminal position of the system. Generalization of this point leads to a qualitative explanation for the almost universal preference of triatomic molecules for equilibrium structures in which the most electropositive atom of the three lies at the middle position of the system. The calculations are also employed to discuss the applicability of general rules governing questions regarding the geometry of symmetric triatomic molecules to analogous problems concerning the nonsymmetric members of this family. Finally, a large‐scale CI calculation for the linear equilibrium geometry of NNO is carried out in order to obtain a detailed list of assignments for the absorption lines in the electronic spectrum of this molecule.

Electron‐Diffraction Study of Ammonia and Deuteroammonia
View Description Hide DescriptionThe gas‐phase structures of NH_{3} and ND_{3} molecules were determined by the sector‐microphotometer method of electron diffraction. The following internuclear distances and mean amplitudes with estimated standard errors were obtained: For NH_{3}, , and for ND_{3}, , with the parameter representing bond‐stretching anharmonicity fixed at 1.0 × 10^{−5} and 0.5 × 10^{−5} Å^{3} for N–H and N–D, respectively. Effects of anharmonicity and isotope differences in the structural parameters analogous to those in CH_{4} and CD_{4} were observed. The and bond distances calculated from the above distances are found to be consistent with the corresponding and distances derived from the spectroscopicrotational constants of Benedict and Plyler. The isotope effects reported by Bell and by Halevi for the dipole moment and polarizability of ammonia are discussed briefly in the light of the present results.

Theory of Temperature‐Dependent g‐Tensor Splittings in p‐Phenylenediamine–Chloranil
View Description Hide DescriptionA theory is developed to interpret the unusual temperature dependence of the g‐tensor splittings—the electron paramagnetic resonance lines narrow slightly as they merge into a single line—observed in the paramagneticorganic crystalp‐phenylenediamine–chloranil. Dipolar interactions are shown to delocalize the magnetic excitations over magnetically inequivalent chains of radicals. The tensor for a delocalized excitation is calculated in terms of the tensors of the radicals over which it is delocalized. The splittings decrease, and finally vanish, as the interchain dipolar field becomes sufficiently strong to delocalize the excitation entirely. The dipolar field strength depends on temperature through the strong magnetic dilution arising from large, antiferromagnetic, intrachain exchange. The theory, which accounts for the entire temperature range of the spectrum, is contrasted with the qualitatively different line merging predicted by random modulation among fixed frequencies (i.e., localized excitations), which necessarily leads to an initial line broadening greater than the line shift.

Transient Solvated Electron, Hydroxyl, and Hydroperoxy Radicals in Pulse‐Irradiated Crystalline Ice
View Description Hide DescriptionNeutral, crystalline ice samples were pulse irradiated in order to study phase and temperature effects on the properties of transient intermediates produced in radiolyzed water. These studies demonstrate that optical absorption bands with peaks near 670, at 280 ± 5, and at 230 ± 8 nm are detectable. The transient visible absorption is attributed to a solvated electron. Its spectrum, though unaffected by phase change, is influenced by temperature, being −1.2 × 10^{−3} eV/deg. also depends on temperature, decreasing markedly from −5° to −40°C, but only slowly thereafter. The decay of , which is second order at −14°C and partly first order from −40° to −100°C , becomes slower with decreasing temperature. Over‐all spectral, yield and kinetic considerations indicate that is structurally similar to , forms via pre‐existing traps, and though immobile as a unit, decays both by reaction with H_{3}O^{+} and by means of an equilibrial, mobile partner . These findings are viewed in terms of the polaron theory and other models for the solvated electron. The transient 280‐nm absorption is assigned to a hydrogen‐bonded hydroxyl radical OH_{ t }·. ESR data showing chemical and kinetic characteristics similar to the optical results confirm this assignment. Its molar extinction coefficient at −196°C is estimated as [using (stable) = 0.8]. The over‐all OH_{ t }· decay is complex. After prolonged irradiation, pseudo‐first‐order kinetics representing reaction with H_{2} and/or H_{2}O_{2} is primarily observed. For low doses and at temperatures below −100°C, separate fast and slow decaying portions can be distinguished, the former attributable to H· reacting with OH_{ t }·, the latter to reaction involving only OH_{ t }·. Based on an empirical ‐order kinetic treatment for the slow decay is determined to be 5.7 ± 0.7 kcal/mole. Qualitatively, this decay and the reaction with products are reconcilable with a mechanism involving OH_{ t }· in equilibrium with a mobile species OH_{ m }·. Second‐order kinetic behavior observed at −14°C ( appears to be may also be consistent with this scheme. The full transient yield at −131°C is estimated to be 1.2. These findings imply that OH· is structurally different in both phases, but chemically similar. The relatively stable absorption at 230 nm is ascribed to HO_{2}·. Spectral, chemical, and possibly, ESR evidence support this identification. Its yield is low, and it decays only very slowly at −14°C.

Neutron Diffraction Study of Ice Polymorphs. I. Ice IX
View Description Hide DescriptionThe neutron diffraction spectrum of polycrystalline D_{2}O ice IX has been obtained and it is in agreement with a proton‐ordered structure for this ice. Values of the tetragonal, pseudocubic lattice parameters were found to be at 80°K. A computer‐generated least‐squares fitting of the intensities of the 38 observed reflections gave the scale factor, thermal parameter, and the oxygen and deuteron position parameters. The O–O–O bond angles are appreciably distorted from the tetrahedral angle in this high‐pressure polymorph.

Zeeman Study of the ^{35}Cl NQR Spectrum of Chlorobenzene
View Description Hide DescriptionA Zeeman study of the nuclear quadrupole resonance spectra of ^{35}Cl using frozen samples of chlorobenzene has been carried out at 77°K. The experimental lower limit obtained for the asymmetry parameter at the chlorine site is 0.10 ± 0.01. A theoretical estimate of the value using Bersohn's analysis yields a value of 0.092 in agreement with experiment.

Vibration–Rotation Interaction Effects in Calculated Franck–Condon Factors. I. The Ionization of H_{2} and D_{2}
View Description Hide DescriptionComputed Franck–Condon factors for the ionization of H_{2} and D_{2} are reported which include previously neglected vibration–rotation interaction effects. Eigenfunctions were obtained by direct solution of the Schrödinger equation in which the exact centrifugal potential is explicitly included. Only and small states of the neutral molecule have been considered and attention is confined to those transitions for which . The results show a clear dependence of the computed Franck–Condon factor on rotational quantum number. For , this effect is small except for transitions to the uppermost vibrational states of the ion. For , the effect is substantial even for transitions to low‐lying vibrational states of the ion. By using a sum rule, it is shown that the probability of dissociativeionization exhibits a similar dependence on rotational state. Comparison of the present results for the case with previous computation shows that adiabatic corrections for nuclear motion, explicitly included in this work, have a wholly negligible influence on computed Franck–Condon factors.

Electron–Ion and Ion–Ion Dissociative Recombination of Oxygen. I. Electron–Ion Recombination
View Description Hide DescriptionThe rate coefficient for electron–molecular‐oxygen‐ion recombination is calculated quantum mechanically. The quantum treatment due to Warke is presented in detail. A simple one‐electron model is used. The positive molecular ion is approximated by a rotating dumbbell consisting of and , and the electron–atomic oxygen interaction is treated as the perturbation for the recombination process. In the one‐electron approximation, only six final continuum states are possible. By assuming that one of them, the repulsive of O + O, crosses at the ground vibrational state of O_{2} ^{+}, the overlap integrals are then carried out. The calculated rate coefficient, at , is close to the experimental results .

Electron–Ion and Ion–Ion Dissociative Recombination of Oxygen. II. Ion–Ion Recombination
View Description Hide DescriptionThe rate coefficient and the thermal cross section for the oxygen ion–ion dissociative recombination are calculated using the semiclassical formalism. The motion of the heavy particles (positive and negative ions) in their mutual Coulomb field is treated classically. At certain ranges of the ion–ion separation (determined from energy conservation), the electron tunnels from the negative ion to the positive ion. Using the experimental data on the electron binding energy of O_{2}−, this tunneling effect is calculated in the WKB approximation. It is found that the linewidth of the levels due to the dissociative effect is important for the electron tunneling and the molecular dissociation. The rate coefficients and the thermal cross sections have been calculated between 200° and 500°K, and have the orders of magnitude 10^{−8} − 10^{−7} cm^{3}/sec and 10^{−12} cm^{2}, respectively. We find that they both decrease as the temperature increases, and have the following approximate relations: . No direct laboratory data is available, but the theoretical results are in agreement with indirect observations from the ionosphere.

Perturbation Treatment of the Helium Ground State with Correlation in Zeroth Order
View Description Hide DescriptionPluvinage's method for calculating correlation energies of two‐electron atoms is modified so that a consistent perturbation calculation becomes possible. Correlation is thereby introduced into the wavefunction in zeroth order, and the cusp conditions between all pairs of particles are satisfied in zeroth order. The first‐order wavefunction is estimated variationally, and the resulting energy to third order is compared with that of Scherr and Knight and Midtdal for the systems H^{−}, He, and Li^{+}. The sensitivity of certain calculated properties to the accuracy of the first‐order wavefunction is examined in the case of He.

Dielectric Relaxation, Far‐Infrared Absorption, and Intermolecular Forces in Nonpolar Liquids
View Description Hide DescriptionMeasurements of dielectric constant and loss at 2.1‐mm wavelength have been carried out upon benzene, cyclohexane, n‐heptane, carbon disulfide, carbon tetrachloride, and tetrachloroethylene, and similar measurements at centimeter wavelengths have been carried out where needed. The infrared absorption spectra of the liquids were measured from 17–170 cm^{−1}. The points for dielectric absorption fit on a smooth curve drawn through the infrared absorption points. Similar measurements have been made upon several binary mixtures of these liquids.Measurements upon liquids to which very small quantities of water have been added show that the effect of water can be corrected for or disregarded. Relaxation times calculated from the dielectric constant and loss measurements are close to 1 × 10^{−12} sec for all of the liquids, which is the magnitude of the time between the collisions of a molecule in the liquid with its neighbors. Apparent dipole moments calculated for the molecules from these measurements are close to 0.1 D and in satisfactory agreement with values of the dipole moments calculated as induced by the quadrupole or octopole moments of neighboring molecules.

Internal Rotation in Butane
View Description Hide DescriptionQuantum‐mechanical calculations within the Hartree–Fock framework and using two Gaussian basis sets are carried out on several conformations of the butane molecule. The smaller basis set predicts a transgauche barrier of 3.536 kcal/mole, an energy difference of 0.822 kcal/mole between the gauche and trans forms, and a barrier of 6.821 kcal/mole for interconversion of the two gaucheconformations. The values of these quantities as given by the larger basis set are 3.619, 0.761, and 6.834 kcal/mole. Taking the angle of rotation about the central bond to be 0 for the transconformation, the gauche form is predicted to occur at 110.9° for the smaller and at 111.3° for the larger basis set. The barrier to internal rotation of a methyl group is predicted to be 2.92 kcal/mole and 2.94 kcal/mole for the smaller and larger basis sets, respectively.

Vibronic Coupling in the Dimer
View Description Hide DescriptionA displaced oscillator model of vibronic coupling in the dimer is presented. Interpolation formulas for the vibronic eigenvalues and intensities are derived which are valid in both limits of weak intermolecular and weak vibronic coupling. The characteristic function of the intensity distribution function is also derived. The physical interpretation of these expressions is given.

Method for Calculation of the Conformation of Minimum Potential‐Energy and Thermodynamic Functions of Molecules from Empirical Valence‐Force Potentials—Application to the Cyclophanes
View Description Hide DescriptionA method for determining the conformation of minimum potential energy of molecules from empirical valence‐force potentials is presented. The energy is written in terms of valence coordinates, expanded through quadratic terms about an assumed geometry, and transformed to Cartesian coordinates. It differs from steepest‐descent methods in that the linear equations resulting from differentiation to find the minimum are solved directly to find a set of displacements. These displacements are used to calculate a new geometry, and the process repeated. It is found to converge rapidly in practice. In addition, the final coefficient matrix of the linear equations is used to calculate the vibrational frequencies of the molecule, and, along with moments of inertia from the final geometry, the gas‐phase thermodynamic functions are calculated. The method is illustrated by calculations of the structures, strain energies, and thermodynamic functions of four cyclophanes.

Si–Te System: Partial Pressures of Te_{2} and SiTe and Thermodynamic Properties from Optical Density of the Vapor Phase
View Description Hide DescriptionThe optical density between 2400 and 7000 Å of the vapor in equilibrium with Si–Te samples containing between 10 and 100 at.% Te was measured for sample temperatures between 500° and 940°C. The partial pressures of Te_{2}(g), , were obtained from the optical densities at 4357, 5000, and/or 5500 Å, where SiTe(g) does not absorb. A plot of vs shows the existence of a single compound, Si_{2}Te_{3}(c), whose homogeneity range falls within outer limits of 59.45 and 60.50 at.% Te and ends at a peritectic temperature of 892°C. X‐ray powder diffraction patterns indicate the Si_{2}Te_{3}(c) phase is the same as that previously identified by some authors as SiTe_{2}(c). The net SiTe(g) optical densities at 2708 and 2893 Å were determined and found to be in constant ratio to one another. For 0.4 Si(c) + 0.6 Te(1)→Si_{0.4}Te_{0.6}(c), the standard Gibbs free‐energy change is between 604° and 892°C. For the reaction , it is (700°–892°C).

Bond‐Function Analysis of Rotational Barriers: Ethane
View Description Hide DescriptionThe barrier potential to internal rotation in ethane is examined with bond‐orbital wavefunctions. It is found that reasonable values of the barrier height are obtained over a wide range of bond polarities if the wavefunction is constrained to satisfy the Pauli exclusion principle. By contrast, for a Hartree product of local nonorthogonal bond orbitals, the barrier is very sensitive to bond polarity. On integration of the Hellmann–Feynman forces from the determinantal bond‐orbital functions along a path that requires only force differences between staggered and eclipsed ethane, barrier values are calculated that closely parallel the corresponding total energy differences; use of an alternative path introduces a much larger error into the force calculation. The bond‐function results are utilized to examine the question of error cancellation in barrier calculations and for a comparison with other studies of the ethane barrier. It is concluded that the dominant contribution to the barrier is the overlap (exclusion‐principle) repulsion between closed‐shell, localized C–H bond orbitals and that the direct electrostatic and dispersion force interaction between these orbitals is relatively unimportant.

Self‐Consistent Approximations in Kinetic Theory
View Description Hide DescriptionA method is explained for obtaining generalizations of Boltzmann's equation which are consistent with the macroscopic conservation equations to any desired order in the density. The important feature of the method is the use of correlated stream velocity functions and temperatures, which can be derived from the statistical mechanics of equilibrium. Generalized conservation equations are obtained which serve as consistency conditions in the determination of the generalized velocity distribution functions. A self‐consistent method of approximation to these functions is developed, and illustrated by the derivation of a form of Boltzmann's equation, correct to terms quadratic in the density, and valid even when bound states are possible.

Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates
View Description Hide DescriptionThe coordinates of earlier papers of this series are extended from linear collisions to reactions in three dimensions. Termed “natural collision coordinates,” they have a unique property of passing smoothly from those suited to reactants to those suited to products. Potential applications to bimolecular reactions are described.

Analytical Mechanics of Chemical Reactions. IV. Classical Mechanics of Reactions in Two Dimensions
View Description Hide DescriptionThe natural collision coordinates of Part III are used to treat the analytical mechanics of chemical reactions, AB + C→A + BC. Other than in Part II, the classical analytical mechanics of chemical reactions on a smooth potential surface have not been explored previously in the literature. A Hamilton–Jacobi formalism is used, apparently for the first time in calculating a reaction rate. The “vibrationally adiabatic” reaction serves as the zeroth‐order approximation and nonadiabatic corrections are obtained. Theoretical expressions yield the rotational and vibrational energy distribution of reaction products, angular distribution, and reaction probability, as a function of impact parameter, initial translational velocity of relative motion, and initial rotational–vibrational state of reactants. The results are not intended to apply to reactions which show very large excursions from vibrational adiabaticity. In the zeroth approximation (vibrational adiabaticity), an adiabatic separation of variables is achieved. Here, the vibrational action is constant; however, the rotational–orbital action changes by a known increment from one constant value to another, on transition of that motion into a bending vibration. The resulting “adiabatic” correlation shows several interesting features. For reactions in which there are no large mass ratios, the state of vibration of AB, of rotation of AB, and of orbital motion of AB + C correlate with the state of vibration of BC, of rotation of BC, and of orbital motion of A + BC, respectively. For reactions with unusual mass ratios, such as H + Cl_{2}→HCl + Cl, the correlation equations show instead the “adiabatic” transformation of Cl_{2} rotation into HCl + Cl orbital motion, thereby reflecting the expected result of angular momentum conservation. Had the rotational–orbital cross term in the kinetic energy been neglected, an incorrect correlation would have resulted in the latter case. Extension of the present work to three dimensions involves an added approximation, to be given in a subsequent paper. The expressions and method also permit comparison of one‐ and two‐dimensional computer results on a more similar basis and, because of certain similarities in computer results for energy distributions in two and three dimensions, perhaps comparison with experimental results on energy distributions. In conjunction with the computer results information can be obtained on various approximations, such as near adiabaticity. The present theory can also be used to analyze and perhaps extend various statistical‐type theories in the literature.