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Volume 39, Issue 10, 15 November 1963

Interaction Energies and Transport Coefficients of Li+H and O+H Gas Mixtures at High Temperatures
View Description Hide DescriptionAccurate potential energy curves for the X ^{1}Σ_{ g } ^{+}, A ^{1}Σ_{ u } ^{+}, B ^{1}Π_{ u }, and C ^{1}Π_{ u } states of the Li_{2} molecule are calculated from observed spectroscopic data by the method of Rydberg—Klein—Rees (RKR), and compared with previous quantum‐mechanical calculations, Long‐range attractive potentials are estimated by extrapolation of functions fitted to the RKR ground‐state curves of Li_{2}, LiH, and OH. From these, the repulsive potentials derivable from interacting ground‐state atoms are estimated semiempirically. Collision integrals are computed from the potentials, and transport coefficients of the gaseous systems Li+Li, Li+H, and O+H are calculated for temperatures of 1000° to 10 000°K.
A surprising result is the extraordinarily large values of the collision inregrals for Li+Li (and Li+H) interactions, which result in unexpectedly small values of diffusion coefficient, viscosity, and thermal conductivity. For traces of Li in Li+H mixtures at low temperature, the thermal diffusion factor is very large. Various approximate formulas for viscosity and thermal conductivity of mixtures are seen to give poor agreement with exact calculations for the systems considered.

Calculation of London—van der Waals Energies
View Description Hide DescriptionA simple expression for the London—van der Waals interaction energies of like molecules, in the absence of retardation effects, is obtained by a perturbation theory calculation using a new approximate method. The approximate method, which is useful for certain second‐order p.t. sums when the unperturbed wave‐functions can be described as products of determinants, is presented with a discussion of its generally small error. This method enables one to express the London—van der Waals energy (also called ``dispersion energy'') as products of certain expectation values over the unperturbed wavefunctions, involving essentially approximate solutions, to the first‐order perturbation Schrödinger equation in its differential form. In particular, the energy in the inverse sixth power of the intermolecular separation R can be expressed as the product of electric dipole polarizabilities and mean‐square electric dipole moments. For two interacting 1s hydrogen atoms the energy is very easily computed and found to beThe first two terms compare favorably with the results of variational calculations while the third does not. Using the approximate perturbed wavefunction, the expectation values of r ^{2} and 1/r for each electron proportional to R ^{—6} are obtained. These expectation values which contribute to the atomic magnetic susceptibility and to the magnetic shielding of the proton agree well with the variational calculations. Also obtained is the third‐order p.t. energy between three like molecules which for three 1s hydrogen atoms iswhere Ω is an angular factor.

Potential and Effective Diffusion Constant in a Polyelectrolyte Solution
View Description Hide DescriptionNumerical computations of the electrostatic potential and the effective diffusion constant of counterions in a periodic polyelectrolytesolution are reported. Some results for the potentials for various polyion charge densities and polyion sizes are presented graphically. The calculated diffusion constants are compared with experimental data on the diffusion of labeled sodium ions in polyacrylic acid‐sodium hydroxide solutions as well as with the earlier approximate calculations.

Vibrational Energy Levels of Ionic Molecules Bound by Classical Forces
View Description Hide DescriptionTheoretical vibrational energy levels of LiI, NaCl, and InF (chosen as representative diatomic ionic molecules) are computed by means of the first‐order WKB approximation. Two classical vibrational potentials are studied for each molecule. The first consists of a Coulombic attraction and an exponential repulsion term, while the second potential adds a polarizability term to the first. Analysis of the data shows that at very low v a power series in (v+½) adequately represents the energy levels, while at very high v the energy levels approach those of a hydrogenlike atom. Further, the first energy difference curves show positive curvature at all v for all cases. Formulas are presented that accurately yield the vibrational energies at all v.

Truncated Reaction Operators
View Description Hide DescriptionThe reaction operator formulation for the exact solution of the Schrödinger equation is used with a truncated basis set to obtain approximate solutions. The relationship between this truncated reaction operator formalism and the Rayleigh—Ritz variational method is emphasized and shown explicitly. The truncated reaction operator and its matrix elements are discussed in general; computed and discussed for a simple example, the helium atom, using a three‐membered basis set. It is shown that the reaction operator can be replaced by a function which we call the ``effective'' perturbation potential V _{eff}. Approximations to V _{eff} are computed for the ground state of helium. This function has fundamental significance and lends itself to accurate empiricism.

Use of the Nuclear Overhauser Effect in the Analysis of High‐Resolution Nuclear Magnetic Resonance Spectra
View Description Hide DescriptionRelative intensity changes may be observed in a high‐resolution protonmagnetic resonance spectrum when one of the lines is partially saturated by irradiation with a radio‐frequency field. This is a manifestation of the general Overhauser effect since the intensity changes result from changes in the populations of the eigenstates of the spin Hamiltonian. A simple theory is based on the approximation that population changes are negligible for energy levels not connected by the irradiated transition. This theory appears to be adequate for applications in the analysis of high‐resolution spectra. Examples are given for systems with spin couplings of low or moderate strength to show how the Overhauser effect may be used to determine the relative signs of spin coupling constants, and to assign spectral lines to transitions between energy levels. The experimental techniques are discussed. Previously reported results for trans‐crotonaldehyde and m‐dinitrobenzene are confirmed, and all coupling constants in m‐dinitrobenzene are found to have the same sign.

Theory for Zero‐Field Splittings in Aromatic Hydrocarbons. III
View Description Hide DescriptionThe assumptions underlying a calculation of the zero‐field splitting parameters D and E are stated in order of increasing severity. Under these assumptions, a number of molecules are calculated and the results compared with experiment. The sensitivity of the calculations to changes in some of the assumptions is examined. The present theory is shown to be in excellent agreement with experiment for the molecules benzene, naphthalene, and anthracene; in fair agreement for phenanthrene; and in poor agreement for triphenylene and coronene.

Magnetic Resonance of Mn^{2+}‐Doped LiF Crystals
View Description Hide DescriptionThe electron paramagnetic resonance of Mn^{2+} in powdered LiF was observed at X‐band and room temperatures for various impurity concentrations. The highest concentration was examined at K‐band and low temperatures to obtain additional information regarding the distribution of Mn^{2+} ions which were introduced chemically into the lattice in small amounts. In the highest concentration, the K‐band spectra indicate that part of the Mn^{2+} goes into the powder in the form of clusters of Mn and F which are antiferromagnetic at helium temperatures. NMRlinewidthmeasurements on the lithium nuclei at low temperatures are qualitatively explained by the antiferromagnetism.
The room‐temperature data from the more dilute samples exhibit not only the expected hyperfine splitting but also a superhyperfine splitting. The hyperfine interaction of the Mn^{2+} ion was determined to be A ^{55}=90±2×10^{—4} cm^{—1}, and the isotropic part of the superhyperfine interaction with each of the six fluorine nearest‐neighbor nuclei was measured to be A_{s} =17.1±0.5×10^{—4} cm^{—1}.
Comparisons between K‐band spectra from chemically prepared powdered samples and single crystals grown from the melt indicate that the melt method is unsuitable for obtaining the solid solution required to examine the superhyperfine spectra.

Satellite Bands in the Spectra of Gaseous Mixtures and the Shape of Potential Curves for Neutral Atoms and Molecules in the State of Collision
View Description Hide DescriptionAn analysis of the experimental data on Cs satellite bands in the spectra of gaseous mixtures suggests the existence of auxiliary minima and relative maxima in the excited‐state potential curves representing binary interactions between colliding atoms and molecules. The auxiliary minima are indicated for interactions of the radiating atoms with the foreign‐gas molecules which produce a red shift of the atomic spectral lines (exhibit the Ramsauer—Townsend effect). The relative maxima are indicated for interactions of the radiating atoms with the foreign‐gas molecules which produce a violet shift of the atomic spectral lines (do not exhibit the Ramsauer—Townsend effect). The depth of the auxiliary minima and the height of the relative maxima are determined primarily by the effective cross sections of the foreign‐gas molecules for collisions with the valence electrons of the radiating atoms. The assumption of such minima and maxima leads to a plausible explanation of most experimentally determined properties of the alkali—foreign‐gas satellite bands.

Infrared Spectra and the Structures and Thermodynamics of Gaseous LiO, Li_{2}O, and Li_{2}O_{2}
View Description Hide DescriptionThe vapor above heated lithium oxide (Li_{2}O) has been investigated mass spectrometrically and by infrared matrix‐isolation spectroscopy. The vapor composition and Knudsen effusion rates were measured as functions of temperature, and the matrix spectra of the principal lithium oxide species—Li_{2}O, LiO, Li_{2}O_{2}—identified and analyzed for different isotopic abundances. The predominant vapor species Li^{7} _{2}O is probably linear with r(Li–O) = 1.59 Å, and has fundamentals ν_{1}, ν_{2}, ν_{3} at [760], [140], and 987 cm^{—1}, respectively. Its heat of formation ΔH _{0}°(f) = —43.7±2.5 kcal/mole. The diatomic molecule Li^{7}O has ν = 745 cm^{—1}, an estimated bond length r = 1.62 Å, and ΔH _{0}°(f) = +16.0±5 kcal/mole. The previously undetected molecule Li^{7} _{2}O_{2} is shown to resemble the alkali halide dimers in having a planar rhombic (V_{h} ) structure for which the O–Li–O angle and Li–O bond length are estimated to be 116° and 1.90 Å, respectively. Its B _{2u } and B _{3u } frequencies are found at 324 and 522 cm^{—1}, respectively, in a krypton matrix. The remaining unobserved modes are estimated in cm^{—1} as follows: ν_{1}(A_{g} ) = 400, ν_{2}(A_{g} ^{t} ) = 250, ν_{3}(B _{1g }) = 300, ν_{4}(B _{1u }) = 270. Its ΔH _{0}°(f) = +27.5+6 kcal/mole.

Time‐Dependent Perturbation—Variation Method
View Description Hide DescriptionThrough the use of the time‐ordered perturbation expansion, an operator equation for the time‐dependent perturbation problem, of the same form as occurs in the time‐independent problem, is generated. Thus, a variational method can be used to study the time‐dependent case as well as the time‐independent case. This variational method is used to recover the Dirac expansion as an example of a solution in series form, and it is also used to develop a simple (approximate) analytic solution as an example of a solution in closed form.

Vibrational Spectra and the Inversion Phenomenon in Cyanamide and Deuterated Cyanamide
View Description Hide DescriptionThe infrared and Raman spectra of H_{2}NCN and D_{2}NCN have been examined in the liquid state in the region of 2.5 to 35 μ. Polarization data imply a planar configuration, but the experimental data for the region beyond 12 μ are inconsistent with this. The observed product rule ratio for the symmetric N–H stretch, NH_{2} deformation, N–C and C≡N stretches are also inconsistent with a planar molecule. The observations do fit a nonplanar molecule with an inversion barrier described by a Manning potential. The barrier height is found to be 660 cm^{—1}, with q _{0} = 0.17_{6} Å. Every distinct feature of the infrared and Raman spectra of the liquid state for both isotopic species may be given a satisfactory assignment with this model.

Neon—Hydrogen Ion—Molecule Reactions
View Description Hide DescriptionIon—molecule reactions producing NeH^{+} in a Ne–H_{2} mixture subjected to electron bombardment in the ion source of a mass spectrometer have been studied. Ionization‐efficiency curves show that NeH^{+} is primarily formed by reaction of H_{2} ^{+} and Ne. The calculated rate constant is in good agreement with theory when only H_{2} ^{+} ions in the second or higher vibrational levels are considered as reactant. The energetic requirements of reaction appear to be satisfied exclusively by internal energy of H_{2} ^{+}. At higher ion‐source pressures NeH^{+} is formed in a third‐order process which was found to be first order in hydrogen and second order in neon pressure. The ionization‐efficiency curve of the third‐order NeH^{+} closely resembles a Ne^{*} metastable excitation curve. Results suggest a Ne^{*}–H_{2}interaction producing a highly excited hydrogen molecule which subsequently ionizes to H_{2} ^{+} and then reacts with Ne producing NeH^{+}. The H_{2} ^{+}–He ion molecule reaction served as a sensitive probe to show that Ne^{*}–H_{2} collisions produce H_{2} ^{+} in vibrationally excited states with v≥5. A momentum‐transfer cross section calculated for the metastable atom—molecule interaction is in reasonable agreement with the measured cross section.

Computation of Unique NMR Parameters for ABC Systems with the Aid of C^{13}–H Satellite Spectra
View Description Hide DescriptionTheoreticalanalyses of protonmagnetic resonance spectra of ABC systems have on occasion resulted in more than one set of acceptable parameters. It is proposed that such ambiguities can be eliminated by requiring the parameters to satisfactorily predict not only the normal spectral patterns but also those of the C^{13}–H satellite spectra. This procedure has been successfully applied to tetravinylsilane and acrylonitrile.

X‐Ray Study of Critical Opalescence in Argon
View Description Hide DescriptionThe small‐angle x‐ray scattering from argon has been investigated at the critical pressure and at four other pressures over a range of temperatures above and below the liquid—vapor transition temperature for each pressure. For three of these pressures the angular distribution of the scattering was analyzed in terms of the Ornstein—Zernike theory of critical opalescence and found to be in good agreement with this theory. Values of the short‐range correlation length and relative values of the isothermal compressibility were determined for each condition of pressure and temperature. For the conditions for which compressibilities can be found by numerical differentiation of the isotherms of Michels, Levelt, and De Graff, the compressibility values calculated by numerical differentiation are in good agreement with those obtained from the scattering curves.

Viscosity of Polymer Solutions
View Description Hide DescriptionIn the expression for the viscosity of polymer solutions, the Huggins constant K is calculated for hard spheres and for interpenetrable spheres of uniform segment density. For hard spheres K = 0.6909, and for soft spheres where K is larger, the dependence of K on the segment—segment interaction constant is given. Difficulties in the basic theory caused by the long range of hydrodynamic perturbations are resolved. The theory is approximate, in that the velocity field arising from Sphere 1 is assumed to vary slowly in the vicinity of 2, but within this approximation all orders of ``reflections'' are correctly summed.

Electrostatic Contribution to the Energy of the Hydrogen Bond in Hydrogen Fluoride Dimer. I. Utilizing Approximate Evaluation of Multicenter Integrals
View Description Hide DescriptionThe electrostaticenergy of the hydrogen bond has been calculated for a pair of hydrogen fluoride molecules using the Ballinger wavefunction for the isolated molecules, and the approximations of Mulliken and Löwdin for estimating the overlap population between two centers of charge distributions. The calculations were carried out for variable angle between the axes of the two molecules, keeping the hydrogen bond distance fixed at 3.086 a.u., and taking the bonding hydrogen atom in line between the two fluorine centers. It is concluded that the electrostaticenergy terms arising from the penetration of the charge clouds are very important. These terms are dominated by the penetration of the nuclear and electronic charges associated with the fluorine atom into the charge cloud of the hydrogen atom.

Preparation and Properties of Monomolecular Films of Chlorophyll a and Pheophytin a
View Description Hide DescriptionMonomolecular films of chlorophyll a and pheophytin a on aqueous subphases have been prepared and studied. The preparation and preservation of these pigments in a state of high purity has required procedural refinements which are described. Chemical degradation in solution and in the monolayer can be prevented by appropriate precautions. At surface pressures below 22 dyn/cm for chlorophyll and 10 dyn/cm for pheophytin, the films on pH 8.0 buffer are mechanically stable in the dark at 20°C. At these pressures, there is little difference in the force—area curves of chlorophyll and pheophytin, although the surface potentials and surfacedipole moments of the two pigments are markedly different. The visible absorptionspectrum of the pigment monolayers on the aqueous subphase is rapidly altered by illumination, although under optimum conditions it shows little change in the dark over periods of several hours. These experiments were performed with a monolayer spectrometer, which permits measurements of the absorption spectra of monolayersin situ. This instrument is briefly described. The unified set of quantitative measurements of this study, together with previous observations in the literature, provide evidence for a monolayer structure in which the pigment molecules, with a folded configuration (both porphyrin plane and phytol sidechain rising above the water surface), are closely packed but randomly oriented in the two‐dimensional array. There is no evidence for any marked rearrangement on compression under our conditions. Anomalies in the absorption spectra are observed when pheophytin monolayers are compressed beyond the stable limit.

Dissociative Charge‐Exchange Reactions of Rare‐Gas Ions with Propane
View Description Hide DescriptionDissociative charge‐exchange reactions of rare‐gas ions with propane and with partially deuterated propanes have been investigated using a modified commercial mass spectrometer. The experimental results for propane are in good agreement with data previously obtained using much more sophisticated instrumentation. Charge‐exchange spectra obtained with 2,2‐dideuteropropane and with 1,1,1,3,3,3‐hexadeuteropropane permit the determination of details of the fragmentation mechanism. The data suggest that both s‐propyl and n‐propyl ions are formed by charge exchange, but that the latter is a relatively unimportant process. Ethylene is formed chiefly by 1,3 elimination of methane from the molecule ion, but 1,2 elimination becomes relatively more important with increasing recombination energy of the rare‐gas ion. In contrast to observations on the vacuum uvphotolysis of deuterated propanes, the present data indicate that elimination of molecular hydrogen as HD is of substantial importance in the over‐all ionic decomposition of both compounds.

Infrared Spectra of Molten Salts
View Description Hide DescriptionAn emission technique for the study of the infrared absorption spectra of high‐temperature liquids is described, and absorption spectra obtained by this technique for silver chloride and sodium nitrate, using two possible sampling arrangements, are compared with those obtained from reflectivity data. Absorption spectra derived from infrared reflectivity data are presented for the systems LiF–KF, LiF–KF–ZrF_{4}, and NaF–KF–ZrF_{4}. Interpretation of these spectra is consistent with the assumption of a complex zirconium species in the latter systems.