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Volume 45, Issue 11, 01 December 1966

Mass‐Spectrometric Study of Ions at Near‐Atmospheric Pressure. III. The Alpha Radiolysis of Methane
View Description Hide DescriptionThe ion—molecule reactions occurring in the alpha‐particle radiolysis of methane have been studied in a mass spectrometer under near‐conventional radiolysis conditions (1–160 torr pressure and a few milliseconds ion reaction time). Comparison of the observed high intensities of CH_{5} ^{+} and C_{2}H_{5} ^{+} at 1 torr with spectra obtained previously with conventional microsecond reaction times shows that the reactions of CH_{5} ^{+} and C_{2}H_{5} ^{+} with methane are very slow (k<10^{−15} cc molecule^{−1}·sec^{−1}). At higher pressures C_{ n }H^{+} _{2n−1}, C_{ n }H^{+} _{2n+1}, and C_{ n }H^{+} _{2n+3} are observed with . The addition of trace concentrations of normal and deuterated hydrocarbons helps to elucidate some of the reactions involved. The ions observed in the presence of traces of deuterated alkanes present a complete confirmation of reactions proposed earlier by Ausloos whose work was based on neutral product studies in α‐radiolyzed methane and deuterated alkanes. The present work with additives shows that impurities at concentrations of 1 ppm affect the course of the ionic reactions in the radiolysis of methane at near‐atmospheric pressures. The origin of the ions observed in the present work in ``pure'' methane at pressures above 10 torr is therefore uncertain. These ions are probably largely due to impurities.

X‐ and γ‐Ray‐Induced Radiolytic Isomerization of Solutions of Stilbene
View Description Hide DescriptionX‐ray and γ‐ray irradiation of benzene solutions of cis‐ or trans‐stilbene causes interconversion towards a stationary cis→trans mixture. The yield of interconversion is smaller for cis→trans than for trans→cis. Both yields increase with stilbene concentration up to a limiting G(trans→cis) of about 2.5 at 0.1M, which corresponds to G(excited stilbene) of about 5. At low stilbene concentrations the yield is lowered by oxygen and by anthracene and enhanced by naphthalene, triphenylene, phenanthrene, and diphenyl. Diacetyl and p‐terphenyl preferentially enhance the trans→cis conversion. The results are explained on the basis of primary excitation of solvent benzene which forms excited stilbene by energy transfer, as in photosensitized isomerization. Direct excitation and possibly charge recombination may account for the primary solvent excitation. Enhancement by additives is due to energy transfer from excited benzene to form eventually triplet additive, which, owing to its much longer lifetime, has a greatly improved chance to transfer its energy to stilbene, at lower concentrations of the latter. A detailed study was made of the change of G(isomerization) with the concentration of stilbene (5×10^{−5} to 10^{−1} M) and of naphthalene (0–7.8M). For 0.1M trans‐stilbene, G(formation of excited stilbene) is about 5 in benzene and about 6 in molten naphthalene. Cyclohexene, used as a specific scavenger of triplet benzene, retards the isomerization by about one‐third, while nitrous oxide, used as an electron scavenger, has no effect. Isomerization yields in toluene are higher than in benzene, while those in methylcyclohexane are much lower. Addition of naphthalene strongly increases the isomerization yields in both solvents, just as in benzene. No significant temperature dependence was found. X rays at 200 kV have only about 60% of the efficiency of ^{60}Co gamma rays.

Electron Spin Resonance of Fe(CN)_{5}NO^{3−} and Fe(CN)_{5}NOH^{2−}
View Description Hide DescriptionIt has been shown by means of ESR in aqueous, nonaqueous, and aprotic solution as well as in irradiatedsingle crystals in the temperature range of 77°—300°K, that two paramagnetic species are obtained by reduction of pentacyanonitrosoferrate(II) which are in a protonation—deprotonation equilibrium. In support of the ESR data, electronic spectra have been investigated and pK_{a} values have been determined by acidimetry and spectrophotometry. The spin density was calculated from ESR data of ^{ n }Fe(CN)_{5}NO^{3−} for n=56, 57 isotopes and found to be consistent with the lowest antibonding orbital being mainly π^{*}NO.

Mobility of Solvated Electrons in 2‐MTHF
View Description Hide DescriptionSolvated electrons in 2‐methyltetrahydrofuran prove to have much higher mobilities than alkali ions. This confirms our conclusion drawn in a previous paper that the solvated electrons behave very similarly in MTHF and liquid ammonia.

LCAO Description of Symmetric Molecules by Unified Theory of Finite Graphs
View Description Hide DescriptionLCAO MO descriptions of symmetric molecules have topological and energetic aspects. Topological effects include the point symmetry of the nuclear configuration and the various connections between these points (connectedness). An appropriate mathematical tool for a discussion of molecular topoligies is given by the general theory of graphs. This theory anticipates various properties connected with the topological matrix. Special graphs and their matrix representations which reflect all topological properties of symmetric molecules serve to determine the molecular‐orbital‐term scheme and the symmetry orbitals for various sorts of molecules. In particular, tetrahedral, square planar, trigonal prismatic, and octahedral molecules are investigated. Finally some remarks are made on the relative choice of parameters in the semiempiricaltheory as suggested by the consideration of the virial theorem.

Single‐Center Calculations on the Lowest‐Lying Π_{ u } and Π_{ g } Excited States of H_{2}
View Description Hide DescriptionSingle‐center wavefunctions are constructed for the lowest‐lying singlet and triplet Π_{ u }(1sσ2pπ) and Π_{ g }(1sσ3dπ) excited states of the hydrogen molecule using a basis set of integral Slater‐type orbitals centered at the molecular midpoint. It is found that the convergence is more rapid than for a corresponding single‐center calculation on the ground state. The error in the binding energy is about 0.065 eV for the Π_{ u } states and 0.033 eV for the Π_{ g } states if a 19‐term configuration‐interaction wavefunction is used for the description of each.

Photolysis of cis‐Hexene−2 and cis‐Butene−2 at 2026 and 2062 Å
View Description Hide Descriptioncis‐Hexene−2 and cis‐butene−2 were photolyzed directly using 2026‐ and 2062‐Å radiation at varying methane pressures up to 52 cm and olefin pressures of 2 cm. Collisional stabilization of the trans isomer in each case competes with the first‐order decomposition reactions:From the observed pressure dependencies, the values of the first‐order rate constants are k _{1}=8.2×10^{7} sec^{−1}, k _{2}=5.0×10^{8} sec^{−1}, k _{3}=3.5×10^{8} sec^{−1}. Quantum yields for the total of trans olefin and cleavage Reaction (2) are of the order of unity for both butene−2 and hexene−2 photolyses. It is concluded that the cleavage reactions occur after rapid internal conversion to the ground electronic states. The cis—transisomerization and an isomerization to the 1‐olefin (5% of total reaction) occur in a time short compared to the time between deactivating collisions at the highest pressures.

Molecular Self‐Consistent‐Field Calculations on B_{4}H_{4}
View Description Hide DescriptionThe wavefunction and Hamiltonian matrix for tetrahedral B_{4}H_{4} have been obtained from an SCF calculation based upon accurate integrals over a minimum basis set of Slater orbitals (H exponent of 1.2). The molecule is bound by 0.43 a.u. relative to 4 BH, the overlap populations are 0.837 for BH and 0.451 for BB, and charges are −0.08 on B and +0.08 on H.

Optimized Minimum‐Basis‐Set SCF Calculations on BH_{3} and B_{2}H_{6}
View Description Hide DescriptionWavefunctions and energies, optimized for BH_{3} and very nearly optimized for B_{2}H_{6}, have yielded a charge of −0.034 on H in BH_{3}, and charges of −0.032 on H (terminal) and −0.001 on H (bridge) in B_{2}H_{6} where the BB overlap population is 0.288.

Temperature Dependence of the Total Intensity of Difference‐Band Systems: The 10‐μ Band System of CO_{2}
View Description Hide DescriptionThe temperature dependence of the total intensity of difference‐band systems is discussed and a general expression is given in the harmonic‐oscillator approximation for difference transitions between two nondegenerate vibrations. The results are compared with experimental measurements of the sum of the total intensities of the (ν_{3}—ν_{1}) and (ν_{3}−2ν_{2}) difference bands of CO_{2} (the 10‐μ band system). New data are presented at temperatures higher than previously investigated (up to 2300°K). In the temperature range studied, the main contribution to the temperature dependence comes from the Boltzmann term.

Reaction Kinetics of Powdered Uranium and Deuteroammonia
View Description Hide DescriptionA rate law for the nitridation of pyrophoric uranium with deuteroammonia was established for the entire course of the reaction. The rate of reaction between powdered uranium and deuteroammonia was determined to be a linear function of the initial Brunauer, Emmett, and Teller (BET) surface area and the fraction of unreacted uranium.Sintering of powdered uranium to a stable surface area was found to be a prerequisite to reproducible experiments. The fractional composition of the products UN and U_{2}N_{3}–UN_{2}solid solution was found to be constant for the entire course of the reaction. An interpretation of the results was done in terms of a diffusion mechanism involving diffusion of uranium ions to the surface as the rate‐determining step. The temperature coefficient in the range 265°—385°C was described by the Arrhenius law and the activation energy was measured to be 25±3 kcal/mole of uranium reacted.

Intrinsic Photoconduction in Anthracene Crystals
View Description Hide DescriptionThe dc photoconductance of ``pure'' anthracene crystals, anthracene crystals doped with tetracene and acridine, and ``pure'' anthracene melts in the uv region (2500–4000 Å) has been investigated. A novel conduction cell allowed crystals to be grownin situ between electrically conducting, semitransparent electrodes, and photocurrent measurements to be carried out at temperatures up to and above the anthracene melting point (>220°C). A photocurrent peak at ∼2800 Å, which was first reported by Castro and Hornig in pulsed‐light experiments, has been confirmed. The photocurrent spectral‐response data and the change in the spectral response, produced by adding the fluorescence quenchers tetracene or acridine to the anthracene, or by melting the crystals, demonstrate that 2800‐Å light generates carriers by a direct optical transition to a conducting state of the crystal. The threshold for this direct ionization process (i.e., a band‐to‐band transition) occurs at ∼3100 Å or ∼4.0 eV. The quantum yield for carrier generation at 2800 Å is on the order of 10^{−4} or greater. Excitation in the 4000–3100‐Å region generates carriers by a mechanism which involves singlet exciton states as intermediates, and the interaction of these excitons with surface or near‐surface impurity sites. Some preliminary data on intrinsic photoconduction in pyrene crystals are also reported.

Dielectric Properties of Ice VII. Ice VIII: A New Phase of Ice
View Description Hide DescriptionThe dielectric properties of ice have been studied up to 107 kbar using opposed circular anvils. Ice VII undergoes orientational polarization, and consequently its molecules are orientationally disordered. The volume of activation for the relaxation of the orientational polarization is ∼3 cm^{3} mole^{−1}, which suggests that the reorientation occurs by the migration of Bjerrum defects, as it appears to do in ice I, III, V, and VI. The energy and entropy of activation at 23 kbar are about 11.6 kcal mole^{−1} and 9.2 cal deg^{−1}·mole^{−1}, which are similar to those for other phases of ice.
At about 0°C, ice VII undergoes a transformation to a phase, here designated ice VIII, whose molecules are orientationally immobile at audio frequencies. This phase had previously been suggested by an analysis of the boundary line between ice VI and VII. The transformation occurs with a hysteresis of about 5.5°C at constant pressure, and the transformation temperature is independent of pressure to within about 0.5° up to 50 kbar. Some measurements previously identified with ice VII must now be identified with ice VIII or perhaps with another phase occurring at much lower temperatures.
The results illustrate the usefulness of dielectricmeasurements in an opposed‐anvil apparatus for the study of phase changes in nonconductors at high pressures.

Phase Transition of a Hard‐Core Lattice Gas. The Square Lattice with Nearest‐Neighbor Exclusion
View Description Hide DescriptionWe consider an M×N periodic system of hard squares each of which prohibits the occupation of its nearest‐neighbor sites by the other squares. An appropriate unitary transformation factors the matrix required in evaluating the grand canonical partition function into a direct sum of submatrices. Each submatrix belongs to a distinct irreducible representation of the dihedral group of order 2M. For an M×∞ system, only the submatrix belonging to the one‐dimensional symmetric representation A _{1} must be considered. To investigate the possible existence of an order—disorder transition for a system infinite in both dimensions, detailed calculations are carried out with the M×∞ systems (M=2, 4, 6, ···, 18). All eigenvalues λ_{ i } ^{+} and eigenvectors of the submatrix are evaluated with eight‐digit accuracy, and the various thermodynamic variables are expressed exactly in terms of the eigenvalues and eigenvectors. The result indicates that an order—disorder transition takes place continuously without any sharp break in a density (ρ)‐ vs‐activity (z) plot, or a pressure (P)‐ vs‐ρ plot. The transition point is characterized by the following set of numbers: z_{t} =3.7966±0.0003, ρ_{ t }/ρ_{0}=0.73552±0.00001 (ρ_{0}≡the close‐packed density), and P_{t}/kT=0.7916±0.0001. Within numerical accuracy of the data, P_{t}/kT is equal to z_{t} /(1+z_{t} ). The compressibility ρ^{−1} dρ/dP appears to become infinite at the transition point, while the ratio λ_{1} ^{+}/λ_{2} ^{+} of the two largest eigenvalues of the submatrix becomes unity. For a semi‐infinite system in the neighborhood of z_{t}, these two quantities exhibit, respectively, a maximum and a minimum given for large M by and . We find that the activity z at [λ_{1} ^{+}/λ_{2} ^{+}]_{min} converges rapidly to z_{t}, thus providing a good means of locating the transition point. From the study of the eigenvalue spectrum over all densities, it appears that the transition point z_{t}, the ordered (z>z_{t} ), and the disordered (z<z_{t} ) phases are, respectively, characterized by asymptotic degeneracy of order ∞, 2, and 0 in the modulus of the largest eigenvalue. The ordering of the hard‐square lattice is investigated by introducing a radial distribution functiong(l, ρ) (l is lattice spacing). The calculations of g(l, ρ) are carried out for the 4×4, 8×8, and 8×∞ systems. A long‐range order parameter L(ρ) {≡lim_{ l→∞}[g(l, ρ) −1], l: even} is introduced. For a two‐dimensionally infinite system, all coefficients in the low‐density expansion of L(ρ) vanish identically, while the first five terms of the high‐density expansion of L(ρ) are computed. Therefore, the transition to an ordered state presumably takes place at density between 0 and ρ_{0}.

Magnetic‐Resonance Studies on Copper(II) Complex Ions in Solution. II. Oxygen−17 NMR and Copper(II) EPR in Aqueous Solutions of Cu(en)(H_{2}O)_{4} ^{2+} and Cu(en)_{2}(H_{2}O)_{2} ^{2+}
View Description Hide DescriptionThe temperature dependences of the ^{17}O NMR and Cu(II) EPR spectra of solutions of the ethylenedi‐amine complex ions Cu(en)(H_{2}O)_{4} ^{2+} and Cu(en)_{2}(H_{2}O)_{2} ^{2+} are analyzed in terms of an octahedrally coordinated structure with tetragonal distortion. It is found that the ^{17}O NMR spectrum is broadened and shifted by Cu(en)(H_{2}O)_{4} ^{2+} through scalar hyperfine interaction with the copper (II) electron spin, while Cu(en)_{2}(H_{2}O)_{2} ^{2+} has no effect. The Cu(II) EPR spectra of both species have linewidth contributions from spin—rotational relaxation, from tumbling of an ionic complex having an anisotropicg factor and an anisotropichyperfine coupling constant, and from ^{63}Cu isotropic hyperfine and ^{14}N isotropic extrahyperfine splitting. The results are discussed in terms of the antibonding molecular‐orbital model for the B _{1g }ground state of Cu(II) and compared with the previous study on Cu(H_{2}O)_{6} ^{2+}.

Effect of Intra‐atomic Correlation on London Dispersion Interactions: Use of Double‐Perturbation Theory
View Description Hide DescriptionA simple double‐perturbation‐theory method is outlined for the calculation of the first‐order effects of intra‐atomic electron correlation on the dipole polarizability at imaginary frequencies, and on the London coefficient for interactions between two‐electron systems. Both single‐parameter Slater and Hartree—Fock orbitals are used as zero‐order wavefunctions. The static polarizability of helium and the London coefficient for helium—helium interactions found with the Hartree—Fock wavefunction are (in atomic units) 1.3346 and 1.382, respectively; accepted values are 1.384 and 1.47. The extensions of this method to larger systems, higher multipole interactions, and more complicated zero‐order wavefunctions are discussed.

Vibration Spectrum and Specific Heat of Lithium
View Description Hide DescriptionThe vibration spectrum and the specific heat of lithium have been calculated by using Sharma and Joshi's model of electron—lattice interaction. The calculated specific heats and the equivalent Debye temperatures are compared with experimental data. Except for temperatures below about 50°K, the theoretical Debye temperatures are in broad agreement with empirical data.

Electron Spin Resonance Studies of a Reaction Intermediate in Vacuum‐Sublimed NaCl and KCl
View Description Hide DescriptionIn accordance with predictions from kinetic studies, electron spin resonance has shown that treatment of vacuum‐sublimed NaCl with F_{2} at room temperature produces a defect containing an unpaired electron, and that the decay of this defect is retarded by Cl_{2}. The ESR spectrum indicates an anisotropicg factor and unresolved hyperfine structure. In KCl, a spectrum is obtained which is closely similar except that the hyperfine structure is partly resolved. The spectra appear consistent with interaction of the unpaired electron with Cl atoms, rather than with F or such impurities as O or Br, and can be accounted for well by a model of the defect as linear Cl_{4} ^{3−}, i.e., an H center or something very similar. For NaCl, the spectra indicate that the vacuum‐sublimed material is sometimes partly oriented.
It is suggested that centers with a one‐electron deficiency are observable at such high temperatures in vacuum‐sublimed material because this consists of essentially perfect crystals devoid of sites which could accept a second electron from the centers.

Theory of Fluids and the Fifth Virial Coefficient
View Description Hide DescriptionExpressions for the fifth coefficient are obtained for the Percus—Yevick (PY) theory, the convolution or hypernetted‐chain (CHNC) theory, the self‐consistent approximations of Rowlinson and Hurst (SCA), the PY2 theory and the CHNC2 theory. Numerical values for the fifth virial coefficient are computed using the 6:12 potential. Comparison with Barker's calculations of the exact fifth virial coefficient shows that the PY, CHNC, and SCA results are unsatisfactory. However, the PY2 and CHNC2 fifth virial coefficients are in good agreement with the exact results. The PY2 fifth compressibility virial coefficient is particularly accurate.

Ultrasonic‐Absorption Measurements in Mixed Solvents: Water—Dioxane
View Description Hide DescriptionUltrasonic‐absorption measurements in water—dioxane solutions have been carried out at 25° and 10° over the entire composition range in the frequency region 10 to 200 Mc/sec. The data can be described quantitatively in terms of two relaxation processes. A theory is presented for the absorption of ultrasonic energy in mixed solvents which can be approximated as ideal solutions. Deviations from ideality and excess absorption of ultrasonic energy are attributed to the formation of intermolecular complexes. If only a single relaxation process is observed, the composition at which the amplitude of the relaxational part of the absorption goes through a maximum and the concentration dependence of the relaxation time can be used to determine the stoichiometry of the aggregates, as well as associated kinetic and thermodynamic constants. For a system in which multiple relaxation processes occur, a normal‐mode analysis must be used that yields a spectrum of relaxation times and normal thermodynamic variables. In the case of water—dioxane, all of the ultrasonic data are consistent with the formation of intermolecular hydrogen‐bonded complexes according to the mechanism 2W+D⇌DW_{2}, D+DW_{2}⇌D_{2}W_{2}, where D represents dioxane and W water. Associated thermodynamic and kinetic constants have been evaluated. The standard volume and enthalpy changes for both reactions are quite small (about ±1 cc/mole and ±1 kcal/mole). The thermodynamic stability of the aggregates and their slow rate of breakdown relative to the rate of hydrogen bond breaking in pure water can be attributed to the formation of ``hydrophobic'' clusters of water around the hydrocarbon portion of dioxane.