Volume 68, Issue 5, 01 March 1978
Index of content:

Collisional ionization between fast alkali atoms and selected hexafluoride molecules
View Description Hide DescriptionNegative ion products resulting from collisions between orthogonal, crossed beams of alkali metal atoms (Na, K, Cs), and the octahedral hexafluorides MF_{6} (M=S, Se, Te, Mo, W, Re, Ir, and Pt) have been examined in the energy range from ∼0 to 40 eV (lab). Studies of the dependence of the reaction thresholds upon the temperature of the target molecules SF_{6}, SeF_{6}, and TeF_{6} have provided electron affinities for these molecules; E.A.(SF_{6}) =0.46±0.2, E.A.(SeF_{6}) =2.9±0.2, and E.A.(TeF_{6}) =3.3±0.2 eV. Energy loss measurements of the alkali, A, in the reaction A+MF_{6}→A^{+}+MF^{−} _{6} at small scattering angles are consistent with these values. Measurements for SF_{4} together with temperature dependent thresholds for the formation of SF^{−} _{5} from SF_{6} and SF^{−} _{3} from SF_{4} combined with known bond dissociation energies for D (SF_{5}–F) and D (SF_{3}–F) yield electron affinity values for the SF_{ n } series; E.A.(SF_{6}) =0.46±0.2, E.A.(SF_{5}) =2.71±0.2, E.A.(SF_{4}) =0.78±0.2, and E.A.(SF_{3}) =3.07±0.2 eV. Lower limits of ∼5 eV for the electron affinities of MoF_{6}, WF_{6}, ReF_{6}, IrF_{6}, and PtF_{6} are implied by the detection of MF^{−} _{6} ions when only the thermal (T∼100 to 300 °C) alkali beam (atoms plus dimers) is incident on MF_{6}. The cross sections for charge transfer A+MF_{6}→A^{+}+MF^{−} _{6} are large at low energies which raises a question as to the mechanism of charge transfer since the zeroth order ground state covalent and ionic curves can never cross.

Generalized differential oscillator strengths for the electron impact ionization of helium determined for large and intermediate momentum transfers at 300 to 500 eV incident energies.
View Description Hide DescriptionDifferential oscillator strengths for the electron impact ionization (ejected electron energy=1 a.u.) of helium have been determined to ±6% accuracy for incident electron energies of 300 to 500 eV and

Molecular dynamics studies of Lennard‐Jones liquid mixtures. IV. Further calculation on the behavior of one different particle as a model of real fluid systems
View Description Hide DescriptionMolecular dynamics calculation has been made on Lennard‐Jones liquid mixtures containing 107 solvents and one solute, the attractive term, size, and mass of which are all different from those of solvent for the purpose of simulating real fluid system. The results were compared with those of our previous studies to discuss which factor is effective in determining static and dynamic properties. It was found that, although the position of the first peak of the solvent–solute radial distribution functiong _{12} is primarily dependent on the size of the solute, its height is much influenced by the strength of the attractive term. The attractive term and mass have also a small but nonnegligible effect on the velocity autocorrelation function and diffusion coefficient. A comparison of the present results with the diffusivity in real fluid systems has also been made.

Liquid‐state diffusion of Na_{2}O–CaO–SiO_{2} system
View Description Hide DescriptionThe concentration distributions after liquid‐state diffusion at 1200°C were measured by using an electron probe microanalyzer for two diffusion couples with an average composition of 16Na_{2}O⋅12CaO⋅72SiO_{2} (wt%). The diffusion profiles agreed satisfactorily with the theoretical profiles calculated by the five‐component diffusion equations derived from the Nernst–Planck equation with assumptions of two oxygen ionic species with differing diffusivities and the oxygen density conservation.

Cluster expansion of the wavefunction. Symmetry‐adapted‐cluster expansion, its variational determination, and extension of open‐shell orbital theory
View Description Hide DescriptionThe symmetry‐adapted‐cluster (SAC) expansion of an e x a c twavefunction is given. It is constructed from the generators of the symmetry‐adapted excited configurations having the symmetry under consideration, and includes their higher‐order effect and self‐consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open‐shell systems as well as closed‐shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher‐order effect and the self‐consistency effect. We have expressed some existing open‐shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo‐orbital theory which is an extension of open‐shell orbital theory in the SAC expansion formula.

Quantum corrections to classical photodissociation models
View Description Hide DescriptionAn unconventional time dependent formula for total photodissociation cross sections shows the importance of short time dynamics in direct photofragmentation. This is exploited to provide a systematic expansion in powers of h/ for the cross section. The lowest order term is a classical cross section which is shown to be an improvement upon the venerable reflection approximation. Terms to higher order in h/ lead to even greater improvements in accuracy as shown by simple numerical examples. Our formulas are directly applicable to polyatomic photofragmentation, and as a spinoff we derive the polyatomic generalization of the (diatomic) reflection method.

Vibrational anharmonicity in CF_{4}
View Description Hide DescriptionA simple anharmonic force field, consisting of a general quadratic force field in curvilinear coordinates, augmented with principal cubic and quartic valence‐bond stretching force constants based on a Morse function, has been determined by least‐squares adjustment to the vibrational energies of CF_{4}. Since this model did not give a value of the cubic normal‐coordinate force constant k _{344} in agreement with experiment, we considered a second force field identical to the first one except for the introduction of cubic stretch–bend–bend interaction force constants. These force fields have been used to calculate the tetrahedral anharmonic splittings of overtone and combination levels of CF_{4} and the calculated splittings have been compared with observed values determined by re‐examining the previously published infrared spectra of CF_{4} in liquid–argon solution.

Intensities of binary overtones and combinations in the infrared spectrum of CF_{4}
View Description Hide DescriptionThe intensities of the binary overtone and combination bands in the infrared spectrum of CF_{4} have been measured. The dipole strengths of the allowed two‐quantum transitions have been determined from the measured intensities and have been compared with the dipole strengths calculated from the anharmonic terms in the intramolecular potential‐energy function. The discrepancies between the observed and calculated dipole strengths have been used to estimate the second derivatives of the molecular dipole moment with respect to the dimensionless normal coordinates.

Rate constants for the reactions of O_{2} ^{+}, NO_{2} ^{+}, NO^{+}, H_{3}O^{+}, CO_{3} ^{−}, NO_{2} ^{−}, and halide ions with N_{2}O_{5} at 300 K
View Description Hide DescriptionThe reactions of N_{2}O_{5} with CO_{3} ^{−}, NO_{2} ^{−}, and the halide ions, F^{−}, Cl^{−}, Br^{−}, and I^{−}, have been found to be very fast (k∼10^{−9} cm^{3} s^{−1}) at 300 K and to produce the NO_{3} ^{−} ion. It is inferred from the thermochemistry of the halide reactions that the neutral products must be XNO_{2}. The positive ions O_{2} ^{+} and NO^{+} react with N_{2}O_{5} to produce NO_{2} ^{+}, while H_{3}O^{+} reacts with N_{2}O_{5} to form NO_{2} ^{+} and H_{2}NO_{3} ^{+}. NO_{2} ^{+} was observed not to react readily with N_{2}O_{5}.

On the Stokes problem for a suspension of spheres at finite concentrations
View Description Hide DescriptionWe consider the problem of the evaluation of the ensemble averaged translational friction coefficient of, and the velocity field produced by, a single nonrotating sphere, moving with uniform velocity through a stationary suspension of similar spheres at finite concentrations, where the average is performed over the spatial distribution of the remaining spheres. The coupled equations for the forces exerted by the spheres on the fluid are iterated to provide a multiple scattering representation of the friction coefficient and velocity field. This expansion can be viewed as an expansion in powers of the concentration, and all terms beyond the trivial leading one are shown to involve divergent integrals because of the long range nature of hydrodynamic disturbances. However, the integrands are shown to form simple geometric series which produce absolutely convergent integrals after the summation. The result displays the phenomenon of hydrodynamic screening (providing a derivation of Darcy’s law) that has been utilized to explain the concentration dependence of the hydrodynamics of polymer solutions. An effective medium approach is presented which incorporates the hydrodynamic screening in lowest order, leading to a theory which is free of divergent integrals.

Low temperature heat capacity and magnetic susceptibility of the DPPH–benzene complex
View Description Hide DescriptionAn experimental study of the heat capacity in fields of 0 and 50 kOe from 0.55 to 20 K and the powdermagnetic susceptibility from 0.4 K to room temperature of the D P P H–b e n z e n e c o m p l e x is reported. Magnetic and lattice contributions to the heat capacity are well resolved. The susceptibility and magnetic heat capacity are compared with p a i r, c h a i n, and q u a d r a t i c n e tHeisenberg model predictions, none of which give satisfactory agreement with experiment. Calculations based on McConnell’s spin density Hamiltonian indicate the likelihood that dominant intermolecular exchange coupling is of comparable magnitude to s i x near neighbors, in layers separated from adjacent layers by benzene solvent molecules.

Photodissociation of molecular beams of arsenic tri‐iodide
View Description Hide DescriptionA molecular beam of AsI_{3} was photodissociated at 280 and 300 nm and the time of flight distribution of the AsI_{2} fragments was measured. From the broad distributions observed, average total fragment kinetic energies of 13.5 and 10.5 kcal/mole were calculated. If the iodine atom dissociates along the As–I bond direction, the rotational energy of the AsI_{2} fragment is shown to be nearly equal to the total translational energy. Arguments are given to show that there is little vibrational excitation of the AsI_{2} fragment and that the iodine atom leaves in the ^{2} P _{1/2} state. The bondenergyD _{0}(AsI_{2}–I) is 55.9±3.0 kcal/mole.

Electronic to vibrational energy transfer, from Br(4^{2}P_{1/2}) to H_{2}O
View Description Hide DescriptionA pulsed dye laser has been used to photolytically produce excited bromine atoms in the 4 ^{2} P _{1/2} state in a flowing gas mixture containing Br_{2}, H_{2}O, and Ar. By monitoring the time resolvedmolecular fluorescence from the stretching vibrations of H_{2}O, it was possible to determine (1) the rate coefficient for the quenching of Br* by H_{2}O, (2) the fraction of the quenching collisions which result in excitation of the (001) and/or (100) state, and (3) various V–V, R, T energy transfer rate coefficients for H_{2}O. Our results indicate that energy transfer from Br* to H_{2}O is a fast and mode specific process. A comparison to other Br*–hydride systems is made.

The potential energy curve for the X ^{1}Σ_{ g } ^{+} state of Mg_{2} calculated with many‐body perturbation theory
View Description Hide DescriptionThe ground state potential curve for the van der waals molecule, Mg_{2}, is calculated by adding to the Hartree–Fock potential curve those many‐body perturbation theory (MBPT) correlation corrections which arise from double excitation type diagrams through fourth order (DE–MBPT). The fourth‐order binding energy is shown to be unaffected by higher order double excitation diagrams. The DE–MBPT potential curve is compared to the fourth‐order Rayleigh–Schrödinger perturbation theory (RSPT) approximation of the double excitation configuration interaction (DECI) potential curve. The DE–MBPT curve is found to be in much better agreement with experiment. Since the only difference between the MBPT equation and the RSPT equation is the size‐inconsistent E _{2}Δ renormalization term contained in the double CI and its fourth‐order RSPT approximation, the importance of having a size‐consistent model for molecular binding is demonstrated. The inclusion of additional correlation effects, due to the fourth‐order EPV rearrangement diagrams, are found to further improve the computed binding energy. Unlike the terms in the DE–MBPT method, these EPV terms are not invariant to a unitary transformation of degenerate orbitals, and this lack of invariance causes an incorrect dissociation limit. A breakdown of the correlationenergy into pair contributions is made and discussed with particular emphasis on the origin of the molecular binding energy.

Correlated hopping conductivity in a general two sublattice structure
View Description Hide DescriptionWe show for a general ordered two sublattice model with inequivalent A and B sites that the classical hoppingconductivity is anomalously low at stoichiometry (total number of mobile ions equal to total number of A sites). The activation energy increases from its value V _{ A } for a mobile ion concentration well off stoichiometry to V _{ A }+1/2(V _{ A }−V _{ B }) at stoichiometry, where V _{ A } and V _{ B } (V _{ A }≳V _{ B }) are depths of the potential wells at A sites and B sites. This is a generalization to arbitrary dimensions and coordination number of similar results obtained by Sato and Kikuchi for the two dimensional β‐alumina structure and by the author for a linear chain. As an example, the relevance of recent experiments on the alkali zirconium phosphates is discussed.

Direct determination of the imperfect gas contribution to the refractive index of ethylene and a discussion of the quadrupole moment
View Description Hide DescriptionThe experimental value of the second refractivity virial coefficient of ethylene obtained directly is higher than the classically calculated theoretical value. The quadrupole moment of ethylene determined by combining the results of the second dielectric virial coefficient and the second refractivity virial coefficient compares very favorably with the one derived from the microwave absorption as well as the value obtained directly by the method of induced birefringence.

Monte Carlo study of a hard‐sphere fluid near a hard wall
View Description Hide DescriptionMonte Carlo value of the density profile and pair distribution function of a hard‐sphere fluid near a hard wall are reported for four densities. The density profile is found to be extremely high near the wall, in agreement with earlier simulation and integral equation studies. However, the number of molecules near the wall is no higher than in a comparable volume of the bulk fluid. The high density near the wall is caused by the fact that the molecules near the wall are generally constrained to remain near the wall and undergo a quasi‐two‐dimensional random walk. A layering is also observed in the pair distribution function.

Statistical mechanics of helical wormlike chains. VI. Approximations
View Description Hide DescriptionTwo methods of evaluating approximately the distribution functions and related averages for the helical wormlike chain are presented. One, called the weighting function method, is a modification of the Laguerre series approximations developed in Paper V and also a generalization of the procedure of Fixman and Skolnick. The other, called the ε method, is a simple one leading to expansions in terms of the relative deviation of the squared end‐to‐end distance near the rod limit. After an examination of the convergence of the two methods, they are applied to a derivation of approximate expressions for the mean reciprocal distance required in the calculation of the transport coefficients of helical wormlike cylinders, and also to a re‐evaluation of the scattering functions at large magnitudes of the scattering vector. Relations between the characteristics of the average chain configuration and the model parameters are also examined to serve as criteria for the selection of test codes.

Raman phonon spectra of partially‐deuterated crystalline ethylenes
View Description Hide DescriptionThe Raman phononspectra of C_{2}H_{3}D, c i s‐C_{2}H_{2}D_{2}, t r a n s‐C_{2}H_{2}D_{2}, 1,1‐C_{2}H_{2}D_{2}, and C_{2}HD_{3} have been obtained, and various sets of atom–atom interaction potentials were used to calculate the lattice frequencies of the C_{2}H_{4} crystal using recent single crystal x‐ray data. The ’’best’’ interaction potential was used to calculate the librational frequencies of the partially‐deuterated ethylenes, assuming that the crystal structure and symmetry is unchanged by deuteration. From a comparison of the observed and calculated frequencies, it was determined that the lattice modes of these crystals are amalgamated, and can be described in the virtual crystal limit. Consistent with the virtual crystal theory, mutual exclusion was retained for the lattice modes of these disordered solids, illustrating the ’’effective’’ C _{ i } site symmetry. Slight changes in the relative intensities of the observed librations were noted, and the experimentally determined perturbation strengths were found to be in agreement with those calculated using the virtual crystal approximation. An attempt to observe the ’’missing’’ optically active translation of C_{2}H_{4} in the far infrared is described; it is suggested to be at ∼35 cm^{−1}.

Clusters of alkali halide molecules
View Description Hide DescriptionThe equilibrium geometry and formation energy of clusters (MX)_{ n } with n=1 to 44 and the vibrational spectrum of clusters with n=1 to 6 for a variety of alkali halides have been calculated using a simple shell model for the interionic forces. As n increases, the deviation of the binding energy and atomic volume from that of bulk crystals approaches that given by the macroscopic surface energy and tension. The rate of convergence to this asymptotic limit will be discussed. Although the vibrational spectrum converges slowly, the first moment of the spectrum converges rapidly to the bulk crystal value. Approximate analytical formulas have been derived which aid in understanding the competing roles of electrostatic, repulsive, and polarization interactions in determining the equilibriuim surface energy and distortions in ionic clusters and microcrystals.