Volume 57, Issue 10, 15 November 1972

Asymptotic Behavior of Pair Correlations in One‐Dimensional Systems
View Description Hide DescriptionAsymptotic decay of the pair correlation functionG(r) is investigated for general square‐well and triangle‐well model intermolecular potentials. For all systems investigated loci are found in the (p, T) plane across which the asymptotic decay changes discontinuously from damped oscillatory to monotonic exponential behavior.

Hyperfine Structure of Indium Fluoride
View Description Hide DescriptionThe radiofrequencyspectrum of the indium fluoride molecule, ^{115}In^{19}F, has been measured with a high resolution molecular beam electric resonance spectrometer. We determined the hyperfine structure in the J=1 and the J=2 rotational states of several vibrational levels under conditions of very weak external electric and magnetic fields. The ∼700 MHz electric quadrupole interaction constant of the indium nucleus changes by 0.010(1) MHz between adjacent rotational states. We looked for, but did not find, an electric hexadecapole interaction of the indium nucleus; the upper limit for the (hexadecapole) interaction constant is 2 kHz.

Lower Bounds on Solutions of the Poisson‐Boltzmann Equation near the Limit of Infinite Dilution
View Description Hide DescriptionRigorous existence, uniqueness and lower bound results for solutions of the nonlinear Poisson‐Boltzmann equation are obtained. The relationship of these bounds with certain assumptions in Manning's limiting law theory for polyelectrolytes is discussed.

Bounds on Solutions of the Poisson‐Boltzmann Equation near Infinite Dilution‐The Moderately Charged Case
View Description Hide DescriptionUpper and lower bounds on solutions of the nonlinear Poisson‐Boltzmann equation are obtained for the case where the so‐called surface charge parameter is less than unity (the moderately charged case). The relationship of these bounds with Manning's limiting law theory for polyelectrolytes is discussed. In particular, we are able to provide rigorous justification (different from Manning's own justification which is based on cluster theory) for Manning's use of the Debye‐Hückel approximation.

Thermal and Near‐Thermal Electron Transport Coefficients in O_{2} Determined with a Time‐of‐Flight Swarm Experiment Using a Drift‐Dwell‐Drift Technique
View Description Hide DescriptionThe drift‐dwell‐drift (DDD) or pulsing technique has been successfully applied to the study of low‐energy electron transport coefficients in oxygen in spite of significant attachment at these energies. A thermal value of the electron diffusion coefficient times pressure was determined. This DP value corresponds to a momentum‐transfer cross section at an energy ε=0.0258 eV if it is assumed that Q_{m} ∞ ε^{1/2}. This thermal value of Q_{m} is ∼40% lower than the lowest values reported from other techniques.

Raman Spectra and Structure of Solid AgNO_{3} and TlNO_{3} at High Temperatures
View Description Hide DescriptionThe laser Raman spectra of AgNO_{3} and TlNO_{3} have been investigated from the room temperature to an upper limit of about 25°C above their respective melting points (AgNO_{3}, mp 210°C; TlNO_{3}, mp 208°C). Striking results are the observation of the asymmetric shape in the totally symmetric N–O stretching mode (∼1046 cm^{−1}) and the spectral changes accompanying the phase transitions in these solids. While various reasons can be advanced for the asymmetry of the 1046‐cm^{−1} band, the explanation based on the coupling of vibrational modes of adjacent NO_{3} ^{−} groups seems most reasonable.

Molten Mixtures of AgNO_{3} and TlNO_{3}: Raman Spectra and Structure
View Description Hide DescriptionThe laser‐Raman spectra of the molten mixtures of AgNO_{3}–TINO_{3} have been investigated from about 20°C above their respective melting temperatures to an upper limit of about 250°C. While the frequencies in the mixtures are nearly the same as in the pure molten AgNO_{3} and TlNO_{3}, the shape of the bands in the 700–750‐cm^{−1} region changes with the composition of the mixtures, and the relative molar intensities of the NO_{3} ^{−} bands are markedly less than in the parent compounds. The results are understood if the ``backdonation'' of electrons to the NO_{3} ^{−} from the cations is inhibited in the molten mixtures relative to this effect for the parent compounds as single‐salt melts.

Surface Structure of a Square‐Well Fluid
View Description Hide DescriptionThe perturbation expansion for fluids is formulated as an expansion of the chemical potential. The interface density profile between the uniform bulk phases of a square‐well fluid is obtained by requiring that the chemical potential is constant in the interface. The profile is compared with the profile obtained from the Born‐Green‐Yvon‐Bogolyubov integrodifferential equation in the density and with the profile obtained by minimizing the excess free energy of the interface. The density profiles obtained from the three different approaches are all in mutual agreement and show that the interface density decreases monotonically and rapidly for temperatures far from the critical point.

Diffuse Reflectance Spectra of Some Rare Earth β‐Diketonates and Esters in the Ultraviolet Region
View Description Hide DescriptionThe diffuse reflectance spectra of dibenzoylmethane and acetylacetonates, dibenzoylmethides, ethylacetoacetates, and ethyl‐1‐methylacetoacetates of La^{3+}, Ce^{3+}, Pr^{3+}, Nd^{3+}, and Sm^{3+} and the absorption spectra of acetylacetone, dibenzoylmethane, ethylacetoacetate, and ethyl‐1‐methylacetoacetate in ethanol in the ultraviolet region (195–400 nm) have been reported. The observed bands have been assigned to π→π* transitions.

Velocity of Sound in Lithium–ND_{3} Solutions
View Description Hide DescriptionThe velocity of 10 MHz compressional waves in solutions of lithium in liquid ND_{3} are reported. These data are quite similar to the earlier data in Li–NH_{3} solutions with the Li–ND_{3} sound velocity being lower than that in the Li–NH_{3} solutions. Data for pure liquid ND_{3} is also reported.

Reactions of H_{2}O^{+} and D_{2}O^{+} with Molecular Hydrogen. I. Proton Affinity of Hydrogen
View Description Hide DescriptionThe cross section of the ion molecule reaction and its deuterium counterpart was studied over an energy range 2–100 eV using a tandem mass spectrometer. The measurements permitted a determination of the proton affinity of H_{2} of and for D_{2}. The energy threshold values indicate that the reaction is proceeding by complex formation at low energies.

Ionization Cross Sections of F_{2} and Cl_{2} by Electron Impact
View Description Hide DescriptionA measurement has been made of the electron impact ionization cross section of F_{2} and Cl_{2} over the energy range 15–100 V. Both species exhibit a maximum cross section at electron energies near 100 eV, the maximum values being approximately and for F_{2} and Cl_{2}, respectively. The measurement in Cl_{2} fits an observed correlation between the maximum cross section and the square root of the polarizability. This correlation seems to apply to a wide variety of atomic and molecular species. Based on this correlation we estimate the polarizability of F_{2} to be approximately

Density and Viscosity of Liquid ND_{3}
View Description Hide DescriptionThe density and viscosity of liquid ND_{3} have been measured over the temperature range from to and compared with the density and viscosity of liquid NH_{3}. At any given temperature, the ratio of densities ρND_{3}/ρNH_{3} is and the ratio of viscosities ηND_{3}/ηNH_{3} is . The fact that both ratios are independent of temperature suggests that the strengths of intermolecular interactions are essentially the same in the two liquids and that the density and viscosity differences are to be attributed to differences in molecular size and mass. The density ratio indicates that the molecular volume of NH_{3} in the liquid is larger than that of ND_{3} while the viscosity ratio indicates that the viscosity varies directly as M/V_{m} (V_{m} =molar volume) for these two liquids.

Product Internal State Distributions from Interactions of Metastable Ar with N_{2}
View Description Hide DescriptionInternal energy state distributions of the products from reactions of metastable Ar(^{3} P _{2.0}) atoms with molecules have been computed from a statistical phase space treatment of the interactions. Calculated rotational and vibrational distributions have been compared with those measured in recent spectroscopic experiments involving metastable Ar atoms. For strongly exothermic reactions producing molecules, the computed vibrational distribution is significantly broader than that measured experimentally. The corresponding vibrational and rotational distributions calculated for slightly exothermic channels are in qualitative accord with experimental distributions; however, some features present in the experimental product distributions are not reproduced by the statistical model.

ESR and Optical Spectroscopy of the RhC Molecule at 4°K
View Description Hide DescriptionRhC molecules produced by the vaporization of a mixture of Rh and C powder from a graphite cell have been trapped in the ^{2}Σ^{+}ground state in neon and argon matrices at 4°K. ESRspectra exhibit hyperfine structure arising from the electron interaction with the ^{103}Rh (100% natural abundance) and ^{13}C (by isotopic enrichment) nuclei, yielding the following parameters in a neon matrix: . The ground state configuration is determined to be largely with some mixing of 4dσ with 5sσ. The relatively large positive value of is in agreement with the spin‐doubling constant, , determined earlier in the gas phase and indicates that there is strong coupling between the ground state and an unknown ^{2}Π_{ i } state, possibly observed in the ultraviolet in the matrix spectra.Spectra of Rh atoms in a neon matrix observed between 2295 and 3540 Å are compared with known gas‐phase transitions.

Valence Electron Studies with Gaussian‐Based Model Potentials and Gaussian Basis Functions. I. General Discussion and Applications to the Lowest s and p States of Li and Na
View Description Hide DescriptionA new model potential for one‐valence‐electron atoms is introduced. It consists [Eq. (6)] of a core Coulomb potential modified by the addition of a Gaussian screened Coulomb potential. This potential has the desired features outlined for a model potential, and it has particularly convenient and simple mathematical properties when used with Gaussian basis functions. Since the smooth valence orbitals are sought, Gaussian functions are a good basis set because their deficiencies in nuclear regions do not enter the problem. The potential is calibrated to experimental energies for the 2s and 2p states of Li and 3s and 3p states of Na, using extended basis sets. The model Hamiltonians so defined are used with a variety of more modest basis sets to determine pseudowavefunctions. Based on comparisons with ab initio orbitals, energy analyses, radial density calculations, and overlap and expectation value calculations, the conclusion is that good valence pseudowavefunctions can be obtained by this approach with relatively small basis sets. The approach looks promising for valence‐only molecular studies.

Valence Electron Studies with Gaussian‐Based Model Potentials and Gaussian Basis Functions. II. Discussion of the One‐Valence‐Electron Molecular Theory and Applications to , and LiH^{+}
View Description Hide DescriptionA one‐electron theory for one‐valence‐electron molecules is developed. It assumes nuclear‐nuclear repulsions to be between net core atomic charges, and that the potential seen by the valence electron is a superposition of atomic model potentials. The atomic model potentials are the core Coulomb potentials modified by Gaussian screened Coulomb potentials, as found in earlier atomic studies. Such model potentials are quite convenient for the use of Gaussian basis functions, which are also taken from the atomic studies, and for which potential energy matrix elements are simply calculated from physically based rules. The theory is applied to the ground states of , and LiH^{+}, using a variety of basis sets. Increasing the basis set flexibility lowers the energy, as in ordinary all‐electron variational calculations. Binding energies and internuclear distances from the most extended basis calculations are: , R_{e} = 5.8 a.u.; R_{e} = 6.7 a.u.; LiH^{+}: D_{e} = 0.090 eV, R_{e} = 4.5 a.u. These are in excellent agreement with results from more elaborate all‐electron quantum mechanical studies, and we thus conclude that our simple, convenient theory simulates the true problem accurately.

Infrared Spectra in Polarized Light of Crystalline Chloroform
View Description Hide DescriptionHigh resolution spectra in polarized light of oriented crystalline films of chloroform at 77°K were obtained. The ratio of intensities of Davydov components for different angles of polarization were also determined. Comparison with the oriented gas model approximation allowed the assignment of components to the proper representations of the D _{2h } factor group: all bands were assigned to the infrared active factor group symmetry species B _{1u }, B _{2u }, and B _{3u } corresponding to vibrations along a, b, and c crystallographic axes. Comparison with results of measurements in solid solutions in argon made by King allowed the distinction between crystallographic effect and isotopic shifts.

Theoretical Approach to Potential Energy Functions for Linear AB_{2} and ABC and Bent AB_{2} Triatomic Molecules
View Description Hide DescriptionLet the coordinate system for a linear AB_{2} triatomic molecule have its origin on the A nucleus with R _{1} the distance to one B nucleus, R _{2} the distance to the other, and θ the apex angle. Then a working formula for the Born‐Oppenheimer potential energy near equilibrium, W(R _{1}, R _{2}, θ), is,where W _{ D }(R _{1}) and W _{ D }(R _{2}) are potential functions for the ground state diatomic molecule AB, R _{3} is the vector sum , A and B are constants and N is an integer. The potential energy for linear ABC tri‐atomic molecules is given by Eq. (i) with R _{2} [or R _{1}] scaled: . Equation (i) is tested for CO_{2}, CS_{2}, OCS, HCN, and N_{2}O by predicting all force constants up to fourth order except for the harmonic bending constant which is used in the parameterization. For bent AB_{2} molecules the working formula for the potential energy is,where θ_{e} is the equilibrium angle. Equation (ii) is tested for H_{2}O, SO_{2}, and O_{3} by predicting all force constants up to fourth order except for the harmonic bending and stretch‐bend interaction constants which are used in the parameterization. A theory is presented for the presence of the W _{ D }(R) components in Eqs. (i) and (ii). It is suggested that the inverse terms partially represent averaged multipole interaction energies while the inverse terms and angular term in Eq. (ii) partially represent valence orbital effects. The formulas for the parameters in Eqs. (i) and (ii) are given. Suggestions for writing down potential functions for larger molecules are included.

Relaxation of Excess Populations in the Lower Laser Level CO_{2}(100)
View Description Hide DescriptionThe rate of relaxation of excess population in the lower laser level, CO_{2} (100), has been measured by an electrical perturbation method. Gases studied included: CO_{2}, CO_{2}/Xe, CO_{2}/H_{2}O, CO_{2}/He, and CO_{2}/N_{2}. In all cases, the measured rates of relaxation of CO_{2} (100) differ markedly from the accepted rates of relaxation of CO_{2} (010). The difference indicates that the levels (100) and (010) are not strongly coupled.