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Volume 53, Issue 6, 15 September 1970

Interactions of Hyperthermal Gas Particles with Contaminated Surfaces
View Description Hide DescriptionInteractions of hyperthermal molecules with contaminated surfaces are studied analytically for a simple classical model in which the surface is covered by a monolayer of physisorbed contaminant and the gas particle energy is much greater than that corresponding to the temperature of the solid. Calculations indicate that if the adsorption potential varies periodically along the surface, then the adsorbed particles are sputtered into a multilobular distribution. The positions of the peaks depend on the velocity of the incident particles, the heat of adsorption, the amplitude of the adsorption‐potential variation, and the equilibrium adatom–surface distance. Predictions for argon beams impinging on mica and silversurfaces contaminated with water vapor agree qualitatively with pertinent experimental results. Hence the present model provides a possible explanation for the observed multilobular scattering distributions.

Electron Paramagnetic Resonance in Gamma‐Ray‐Irradiated Niobium‐Doped Calcium Molybdate
View Description Hide DescriptionCalcium molybdate (CaMoO_{4}) doped with niobium impurity ions was studied by electron paramagnetic resonance(EPR).Single crystals were irradiated with ^{60}Co gamma rays at 77°K which caused three paramagnetic species. One of these is associated with the niobium impurity ion substitutional for molybdenum; the major part of its EPR spectrum showed an defect with a 10‐line hyperfine structure for each of four equally probable defect sites. Normally forbidden transitions were also observed. The spectra were fit to a rhombic spin Hamiltonian with parameters: , and where lies approximately along a normal Mo–O bond direction in the lattice. A partially resolved six‐line ligand hyperfine structure appeared on the major resonances with the intensity expected for overlapping ^{95}Mo and ^{97}Mohyperfine interactions. The model proposed for this defect is a hole shared between adjacent niobate and molybdate complexes with a higher probability density on the niobate.

Intensity Perturbations and Breakdown of the Ordinary Selection Rules in the Infrared Spectrum of the Asymmetric Rotor
View Description Hide DescriptionThe influence of first‐order rotation–vibration interaction on line intensities in vibration–rotation fundamental bands of asymmetric‐top molecules is treated here. The method of the preceding paper of Braslawsky and Ben‐Aryeh is generalized. This generalization is attained by means of the group‐theoretic method, using the symmetry properties of the zeroth‐order rotational Hamiltonian. The influence of the interaction on ordinary lines is summarized in a simple formula for the intensities correction factors. In addition, it is proved that the ordinary (zeroth‐order) selection rules are violated due to the first‐order centrifugal interaction. Such violation of selection rules did not obtain for diatomic or symmetric‐top molecules.

Structure of Ammonium Fluoride. IV
View Description Hide DescriptionX‐ray powder diffraction patterns of ammonium fluoride IV have been obtained at about 450°K and 4 kbar in a pressure vessel made of single‐crystal diamond. The unit cell is cubic with , and has a sodium‐chloride‐like structure with the space group . Since ammonium fluoride IV appears to have a configurational entropy of about 3.8 cal deg^{−1}·mole^{−1} and the hydrogen atoms of the ammonium ion cannot fit into an ordered sodium‐chloride‐like structure, the ammonium‐ion orientations are probably disordered. The thermodynamic evidence does not favor free rotation. Ammonium fluoride IV is very plastic, in contrast to phases I of ammonium chloride, bromide, and iodide, which have the same structure.

Optical Properties of Amorphous Polypeptides. I. One State Solutions
View Description Hide DescriptionA model for the optical properties of disordered polymers is presented to describe both flexible polypeptides in solution and disordered regions of films or proteins. The model links current optical theory with configurational statistics. The partition function determining population averaged rotational and dipole strength is constructed with current approximate potential‐energy functions. Oligopeptides are randomly generated and the circular dichroism and optical absorption for the amide transition are reported. This one state calculation can account for both the large negative and small positive circular‐dichroism bands observed experimentally, as well as the unusual noncoincidence of the circular‐dichroism and absorption extrema.

Polarized Single‐Crystal Absorption Spectrum of 1‐Methyluracil
View Description Hide DescriptionThe single‐crystal absorptionspectrum of 1‐methyluracil, polarized along three mutually perpendicular axes, is investigated from 3200 to 2400 Å at room temperature. The spectral measurements were made with a microspectrophotometer, and crystal extinction coefficients were obtained from Lambert's law plots. The spectrum polarized normal to the molecular planes uncovers an transition at 2640 Å. The longest wavelength absorption band at 2755 Å exhibits well‐resolved vibrational structure which broadens considerably on the high‐energy side of the band. It is suggested that this broadening results from a perturbation by the underlying state. The transition moment for the lowest transition is found to be almost parallel to the N_{1}–C_{4} molecular direction. The difference of about 23° between the transition moment directions for 1‐methyluracil and 1‐methylthymine agrees well with π‐electron calculations. The exciton splitting of the 0, 0 band for the lowest transition is in qualitative agreement with dipole–dipole calculations for weakly coupled chromophores. The angular dependence of absorption of plane‐polarized light is investigated.

Corrections to the Fuoss–Onsager Theory of Electrolytes
View Description Hide DescriptionMathematical corrections are made to the theory of Fuoss and Onsager for the conductivity of ionic solutions to first order in the concentration. The theory is extended to cover the case of asymmetric binary electrolytes; it is found that in this case the results are strongly affected by deviations of the equilibrium ion pair distribution function from that predicted by the Debye–Hückel theory. The results of the conductivity theory are compared to corresponding results of the equilibrium theory.

Magnetic Renner Effect: Direct Orbital and Spin Interaction with “Vibrational” Rotation in Linear Triatomic Molecules
View Description Hide DescriptionDetailed and explicit expressions are derived for a new type of vibronic effect that involves the direct magnetic interaction of the electron's orbit and spin motion with “vibrational” rotation; the latter occurs in a linear triatomic molecule executing the doubly degenerate mode of vibration. Such magnetic vibronic interaction (Sec. III) is compared with the corresponding electrostaticvibronic interaction which is the conventional Renner effect (Sec. II). The expansion of the magnetic interaction, which is proportional to an irregular solid spherical harmonic, in terms of electronic and nuclear coordinates is shown in detail (Appendix A). The interaction Hamiltonian is expressed in terms of the eigenvalue, creation, and annihilation operators of the two‐dimensional isotropic harmonic oscillator. The Lie algebraic treatment of such a system of operators and the derivation of diagonal as well as off‐diagonal matrix elements, which are needed for higher‐order perturbations, are shown (Appendix B). Effective Hamiltonian for first‐order perturbation and its application in molecule, in which the conventional Renner effect is absent, are given (Sec. IV).

Electronic Energies and Electronic Structures of the Fluoromethanes
View Description Hide DescriptionThe high‐resolution He i and He iiphotoelectron spectra of all fluoromethanes in the series CH_{4} to CF_{4} and their deuterated analogs have been recorded and are compared with the Koopmans' theorem results of near‐Hartree–Fock calculations performed in a Gaussian basis. The agreement is very good in general and offers an unambiguous assignment of almost all of the bands observed. In particular, repeated correlations are demonstrated between the compositions of the orbitals from which the electrons are ejected and the characters of the resulting photoelectron bands. Identifiable trends throughout the series are stressed and an anomalous feature in the CF_{4} spectrum is noted. Jahn–Teller effects in CH_{4} and CH_{3}F are clearly evident, but as expected, they are not observed in CHF_{3} and CF_{4}. Comparison of the photoelectron spectra excited with He i and He ii radiation shows wide variations in the relative intensities of various bands in certain of the more symmetric molecules, suggesting that relative intensities can be a poor measure of relative orbital degeneracies. Mass‐spectrometric appearance‐potential data are briefly discussed in the light of the photoelectron results. The carbon and fluorine binding energies as measured with 1254‐eV x rays are shown to be electronically adiabatic. The accurate determination of the lower ionization potentials of these molecules leads readily to the assignment of several of their electronic transitions as lower members of and Rydberg series.

Ionic Conductivity of NaCl: SrCl_{2} Crystals
View Description Hide DescriptionThe ionic conductivity of NaCl crystals highly doped with SrCl_{2}(, expressed in molar fraction) has been measured from room temperature to the melting point. In this wide range of concentration a unique value for the migration energy for the cation vacancy has been found: 0.75 ± 0.02 eV. With this value all the parameters for the creation and motion of lattice defects have been determined. Simple association theory could not explain the observed results. The Debye–Hückel approach was used to account for the observed absence of association at high temperature. Quenching experiments from high temperatures were performed on these doped crystals and a saturation limit of 8 × 10^{−4} was found for the dilution of dipoles in the matrix. The effect of clustering of these dipoles was followed by quenching from different annealingtemperatures.

Exclusion Problem for Mobile Atoms of Any Size in One Dimension
View Description Hide DescriptionSuccessive random desorption and random readsorption of atoms of any size leads to Fermi–Dirac statistics, in which all possible nonoverlapping patterns become equally probable. This equivalent characterization of the adsorption process of individual mobile atoms, discussed in greater detail in previous papers, lends itself to a stochastic pattern generating process, yielding the required Fermi–Dirac statistics, at any required adsorption density and atom size. For the discrete case where all potential adsorption sites are equally spaced, the process reduces asymptotically to the continuous case where all sites of the continuum are potential adsorption sites, by letting the diameter of the atom become large relative to the spacings. The parameters of the process are readily expressible in terms of the adsorption density and atom size. The proportion of “excluded sites,” usually obtainable only by simulation, is here derived exactly as a function of the adsorption density, for both the discrete and the continuous case.

Sequential Adsorption of Large Immobile Atoms on the Continuum and Regular Lattices
View Description Hide DescriptionThe nonoverlapping patterns of atoms which arise after sequential random adsorption of large immobile atoms on the remaining free sites of the continuum or regular lattices are for each adsorption density shown to be equally probable asymptotically. The adsorbed atoms therefore obey restricted Fermi–Dirac statistics in that only a subset of the set of all possible nonoverlapping patterns are equally probable. This characterization of the sequential adsorption process is used to derive the functional form of the equation relating the number of “excluded” sites to the adsorption density as the process proceeds. The functional form obtained contains a small number of constants, mathematically definite once the size of the atoms and the adsorption medium are specified. In the case of one dimension, the constants relate simply to the so‐called filling density already known for special cases. In the case of the square and the triangular lattices in two dimensions, the constants in the functional form are estimated from simulation results for the function itself, published recently.

Electron Diffraction Study of Rhenium Fluorides. I. Heavy‐Atom Corrections and Structure of ReF_{6}
View Description Hide DescriptionTo date, no theoretical models for electron molecular scattering have been developed which bring calculated scattered intensities from heavy atoms into satisfactory agreement with experiment. Preparatory to an electron diffraction study of ReF_{7}, a molecule with an uncertain and possibly complex structure, an investigation of ReF_{6} was undertaken. The simplicity of the hexafluoride's geometry ( symmetry) allows an empirical characterization of the discrepancy between experimental and calculated intensities, a discrepancy which can be attributed chiefly to the behavior of ReF interference terms rather than to uncertainties in structural parameters. After a structure analysis of ReF_{6}, the observed difference signal was used with appropriate scaling to modify ReF_{7} intensities before structural parameters for the heptafluoride were refined. Parameters determined for ReF_{6}, e.g., and , are in excellent agreement with those reported from diffraction studies of other transition‐metal hexafluorides. Results for ReF_{7} are reported in Paper II.

Electron Diffraction Study of Rhenium Fluorides. II. Structure, Pseudorotation, and Anharmonic Coupling of Modes in ReF_{7}
View Description Hide DescriptionSignificant departures from symmetry are indicated by the gas‐phase electron diffraction data for ReF_{7}. Observed scattered intensities, corrected for heavy‐atom effects as discussed in the preceding paper, are adequately represented by structures with static deformations of either or symmetry of the following character. A puckering of the ring of five fluorines (maximum out‐of‐plane displacement ≈ 9°) is accompanied by a movement of each axial fluorine from the reference axis of ≈ 8° in the direction which provides maximum avoidance of fluorines on the rhenium coordination sphere. Equally compatible with the data is the much more reasonable dynamic pseudorotation model in which vibrational displacements carry the molecule from to to configurations. The tenfold character of the hindering potential and modest displacements preclude an appreciable barrier. A pronounced skewing of the envelope of axial–equatorial, , distances reveals a coupling in phase of the axial bend to the ring puckering vibration through the cubic term in the potential‐energy function. The skewing, which moves the maximum of the distribution peak inside the distribution center of gravity, results in an apparent “anharmonic shrinkage” of the nonbonded peak by an amount exceeding the well‐known “Bastiansen–Morino” harmonic shrinkage. It is to be noted that the equatorial pseudorotation problem closely resembles that for cyclopentane in reduced mass, in displacement, and therefore, presumably, in frequency. The structure itself may be understood in terms of bond–bond repulsions thrusting the equatorial atoms out of plane; the out‐of‐plane displacement, in turn, induces an axial bend. The actual structure, however, exhibits too large an axial bend to conform to the simple repelling points‐on‐a‐sphere model of Gillespie and too small a deviation from to correspond to the close packing of hard atoms around the rhenium.

Raman Studies of Molecular Motion in Liquid and Solid HCl
View Description Hide DescriptionThe Raman scattering technique was used to study molecular motion of HCl in its condensed phases. In the liquid and in cubic phases, the depolarization ratio, the spectral shape, and the spectral width of the H–Cl stretching mode were measured as functions of temperature. It was found that the modes of HCl molecular motion are not significantly changed as the liquid–solidphase transition was traversed. The depolarized linewidthmeasurements of the intramolecular stretching vibration also indicate that the energy barrier for HCl molecular reorientation is small, suggesting a nearly free tumbling of the HCl molecule in the cubic solid at temperature higher than 120°K. Below 120°K, satellite peaks develop, suggesting that evolution of the lower symmetry structure other than the cubic has already taken place at temperature higher than . The temperature study of the low‐frequency spectrum in the 0–300‐cm^{−1} region suggests that HCl polymeric fluctuations are responsible for the light scatteringspectrum. Moreover, the libration time of HCl polymers (formed as a result of hydrogen bonding) is short compared with the mean reorientation time of a single molecule. The spectra of the lattice phonons as well as the internal stretching vibrations of HCl molecules below the first‐order phase transition temperature were also studied.

Influence of the Distorted Wave Approximation in Calculations of Chemical Reaction Cross Sections; Ar^{+}+HD
View Description Hide DescriptionTwo different approximations to the formal quantum theory of rearrangement collisions are applied to the same reactive system. The comparison enables some conclusions to be drawn concerning the effects of approximations to perturbed translational motion on predicted product energy distributions. In both schemes, the exact wavefunction is approximated by a product of a translational and a molecular wavefunction, where the molecular wavefunction is treated in the perturbed‐stationary‐state approximation. In one scheme (DWBA PSS) the translational wavefunction is expressed as a WKB solution to the appropriate elastic scattering problem, while in the other (BA PSS), free translational motion is assumed. Calculations are performed for the system Ar^{+}+HD using an assumed potential surface. Significant differences are noted in predicted distributions of translational exoergicity and product vibrational and rotational energy. In particular, the behavior of the most probable translational exoergicity with respect to incident energy predicted by the DWBA PSS is in substantial agreement with experiment, whereas the BA PSS consistently overestimates product excitation. Isotope effects predicted by both schemes are in serious disagreement with experiment; it is concluded that the source of this discrepancy lies largely in the neglect of the noncentral nature of the forces in this system.

Collision‐Induced Singlet→Triplet Intersystem Crossing of Methylene and Methylene‐d _{2}
View Description Hide DescriptionThe photolysis of ketene or ketene‐d _{2} in the presence of propane, oxygen, and inert gas was studied at 300°K at each of the four wavelengths 2600, 3130, 3340, and 3500 Å. Inert gases used were He, Ar, Xe, N_{2}, and CF_{4}. The inert gases cause the transition of methylene from the first singlet state to the triplet ground state to occur. The observed kinetics of the intersystem crossing process, being first order in methylene and first order in inert gas, are second order. The second‐order rate constants, relative to the rate constant for reaction of singlet methylene with propane, are independent of wavelength, and increase in the order He<Ar<CF_{4}≤Xe. The rate‐constant ratios for methylene‐d _{2} show the same trend with inert gas but are 2–3 times larger. The results are consistent with a bimolecular intersystem‐crossing mechanism where the role of the collision partner is to cause the transition to occur by sufficiently perturbing the singlet methylene stationary states.

Torques in Sheared Nematic Liquid Crystals: A Simple Model in Terms of the Theory of Dense Fluids
View Description Hide DescriptionA fluid of equally and rigidly oriented molecules interacting through a smooth ellipsoidal two‐body potential is considered. We derive the ratio of the shear‐torque coefficients and the ratio of the shear‐viscosity coefficients for two orientations of the unique axis, one parallel to the flow and the other parallel to the velocity gradient. In addition, we confirm the validity of an Onsager relation. Given one of the four coefficients, the other three can be calculated if the axial ratio of the prolate ellipsoids of revolution is known. In accordance with the theory of dense fluids, it is assumed that intermolecular forces rather than molecular motion dominate momentum transfer.

Orientational Freedom of Molecules in Crystals. II. Higher‐Order Transition by Progressive Decorrelation of Orientations. A Monte Carlo Calculation
View Description Hide DescriptionA clear‐cut example of a higher‐order transition involving orientational disordering in some molecular crystals is presented. In these crystals, which are polar chloromethyl hexasubstituted benzenes, the molecules exhibit a one‐axis sixfold disorder at high temperatures. On cooling, the static dielectric constant decreases, indicating the cooperative setting in of orientational order. This is confirmed by x‐ray studies which indicate that the superstructure at low temperature is an antiferroelectric arrangement. A quantitative interpretation of the phenomenon is given. The energy which governs the ordering is shown to be essentially electrostatic in origin: Among 288 envisaged ordered arrangements, the electrostatic energy is the lowest for the observed (antiferroelectric) one. These calculations have been made using Coulomb interactions between charges located on the atoms since the point dipole model has been found to be too crude. A Monte Carlo calculation, which is partly dynamic and partly stochastic in nature, has been carried out for the transition region; this yields a semiquantitative agreement for the observed static polarization, and a fairly good reproduction of the shape of the experimental relaxation spectrum at different temperatures.

Quantum Mechanical Basis for the Cubes Models in Gas–Surface Scattering Theory, and an Experimental Test
View Description Hide DescriptionIt is suggested that there is a quantum mechanical basis for the classical flat surface (cubes) models of gas–surface scattering, the important characteristic of which is the assumption of conservation of tangential momentum of a scattering gas molecule. The theory is applied to the diffractive system He–LiF, and it is shown that existing experimental data confirm some predictions of the theory.