Volume 41, Issue 7, 01 October 1964

Rate of Destruction of Acetylene in Flame Gases
View Description Hide DescriptionThe burnt gas from fuel‐rich acetylene—oxygen flames contains larger than equilibrium amounts of acetylene, but only equilibrium amounts of the species , which are listed in order of decreasing concentrations. The decay of acetylene in this environment at 1700° to 2000°K can be represented bybut cannot be represented by k[X][C_{2}H_{2}] where [X] is [H], [O], or [O_{2}]. Therefore acetylene may be consumed at the rate of its irreversible reaction with OH; and if so, it reacts five to 10 times slower with OH than with an equal concentration of O in flames, the latter rate having been estimated previously in an environment where [O]>[OH].

Equilibrium in the Deuterium Exchange of Acetylene and Water
View Description Hide DescriptionThe isotopic‐exchange equilibrium between acetylene gas and deuterated water vapor has been experimentally studied over a wide range of deuterium content in the temperature range from 5° to 85°. The equilibrium constantK _{7} for the gas‐phase reaction C_{2}H_{2}+D_{2}O=C_{2}D_{2}+H_{2}O is 0.473±0.008 at 25°. The thermodynamic parameters for the reaction are ΔH°=0.29 kcal/mole and ΔS°=—0.56 eu at 25°. The equilibrium constant for the disproportionation reaction C_{2}H_{2}+C_{2}D_{2}=2C_{2}HD has also been measured and is found to have a constant value of 3.95±0.10 for the temperature range 5° to 85°. The exchange constant K _{7} has been calculated from the available spectroscopic data for the relevant acetylene and water species and the theoretical values agree with the experimental values to within 10%. The observed data for both the exchange and disproportionation reactions are consistent with those for similar systems.

ESR Studies and the Electronic Structure of Vanadyl Ion Complexes
View Description Hide DescriptionThe ESR spectra of vanadyl acetylacetonate and tetraphenylporphyrin have been studied in various liquid solvents and frozen glasses. The spectra have been analyzed and the components of the gtensor and of the vanadiumhyperfine interaction tensors have been determined, and for the porphyrin the nitrogen extrahyperfine interaction tensor has been obtained. The unpaired electron is in the b _{2g } ^{*} orbital. The extrahyperfine splitting is very isotropic which indicates that the b _{2g } ^{*} orbital is localized on the vanadium in the porphyrin complex and the ``in‐plane π bonding'' is slight. An explanation of the origin of this extrahyperfine splitting is discussed in terms of configuration interaction. An analysis of the vanadiumhyperfine interaction indicates that the b _{2g } ^{*} orbital is localized on the vanadium in the acetylacetonate also, and that the Fermi contact interaction depends upon a number of excited configurations and varies from complex to complex and with change of solvent. The g‐tensor analysis suggests that the spin—orbit constant λ≥170 cm^{—1}, that the in‐plane σ antibonding and out‐of‐plane π antibonding orbitals are delocalized, the delocalization increasing in the order: VO(H_{2}O)_{5} ^{+ +}, vanadyl acetylacetonate, vanadyl porphyrin.

Theory of Nuclear Hyperfine Broadening of ESR Lines in Liquids
View Description Hide DescriptionThe theory of the broadening of ESR spectral lines arising from fluctuations in the isotropic and anisotropicg factors and hyperfine tensors is discussed. Particular attention is paid to the case where the molecule has several equivalent nuclei and the spectrum, therefore, has degenerate lines, i.e., several transitions of the same frequency corresponding to different nuclear states. A mean linewidthT _{2γ} ^{—1} is calculated for each degenerate set, and the significance of this quantity is discussed. Certain special cases where the relaxation matrix is diagonal in a spin‐state basis are discussed, and the linewidths for each component line of the degenerate set is obtained. The Redfield and the Kubo and Tomita theories are compared, and the limitations of the latter in dealing with degenerate lines is analyzed.

Direct Determination of the Crystal Structure of Cornetite, Cu_{3}PO_{4}(OH)_{3}, by the Monte Carlo Method
View Description Hide DescriptionThe crystal structure of the peacock‐blue mineral cornetite, Cu_{3}PO_{4}(OH)_{3}, orthorhombic, with a _{0}=10.845, b _{0}=14.045, c _{0}=7.081 Å, space group Pbca, has been determined. The phase problem has been solved by the direct determination of the heavy atom positions through the application of the Monte Carlo and optimal shift methods. Subsequent three‐dimensional Fourier synthesis revealed all the light atom positions. The atomic parameters have been refined, using three‐dimensional data, by the method of full‐matrix least squares.
Two of the three independent copper atoms have essentially fivefold tetragonal pyramidal coordination, the coordination plane being curved in a boat shape towards the fifth ligand. The third copper atom has a highly distorted tetragonal bipyramidal coordination. Cornetite contains two sets of dimeric cupric complex ions. The first set [Cu_{2}(OH)_{4}O_{2}] is formed by two different copper coordination planes sharing an edge, and the second [Cu_{2}(OH)_{4}O_{4}] by two tetragonal pyramids, related by a center of symmetry, sharing a pyramidal edge. The [Cu_{2}(OH)_{4}O_{2}] dimers are stacked upon each other along the c axis in a zigzag fashion, so that each dimer has two (OH) groups common with two other dimers above and below it. The dimeric chains thus formed are held together in a three‐dimensional network, through isolated [Cu_{2}(OH)_{4}O_{4}] dimers, PO_{4} groups, and O–H···O bonds.

Observation of Rotational De‐Excitation of D_{2} Using Crossed Molecular Beams
View Description Hide DescriptionThe collision‐induced transition j=2→0 in ortho‐D_{2} has been observed using a direct kinematic technique. A velocity‐selected atomic beam of K was crossed with a cooled, modulated beam of o‐D_{2} molecules. Velocity analysis of the K beamscattered through known center‐of‐mass angles (near 110°) gave direct evidence of recoil arising from inelastic collisions in which the rotational de‐excitation j=2→0 had occurred.

Nuclear Magnetic Relaxation in Camphor
View Description Hide DescriptionSolid solutions containing d‐ and l‐camphor have been investigated by nuclear magnetic resonance and x‐ray powder diffraction between 77° and 473°K. Striking differences are observed among the various solutions in the vicinity of the second‐order phase transition. The transition temperature is found to vary with composition, passing through a minimum at the 3:1 d:l solution. The width of the λ transition, reflected in the NMR second moment, increases going from the pure isomer to the racemic mixture. Methyl group reorientation persists at 100°K, although molecular tumbling has been arrested at this temperature in all samples. The x‐ray powder patterns of the pure isomer, the 1:1, and 3:1 mole ratio solids differ at 77°K, but are identical at 298°K. Plots of the NMR spin—lattice relaxation time versus reciprocal absolute temperature yield an activation energy of 2.35 kcal/mole for methyl‐group reorientation in d‐camphor below the λ point. Above the rotational transition, the x‐ray and NMR data are independent of concentration. Activation energies of 2.8 and 14.6 kcal/mole are calculated for the processes of molecular tumbling and self‐diffusion, respectively. The T _{1} data are quantitatively examined in terms of the BPP theory.

Initiation of Lead Azide by High‐Intensity Light
View Description Hide DescriptionRadiation from an argon flash‐bomb is used to initiate detonation in lead azide aggregates. Optical methods are employed to measure initiation delay as a function of energy absorbed by the azide. It is found that the product of the rate of energy absorption and the initiation delay is constant. This is interpreted in terms of a thermal initiation mechanism as follows: Absorption of flash‐bomb radiation causes a continuing increase in azide surface temperature; above a critical temperature T_{c}, exothermic decomposition of the azide becomes very rapid and leads to thermal explosion and detonation in very short times. Typical initiation delays are of the order of 1 μsec and T_{c} ∼900°K. Reaction‐rate parameters calculated on the basis of this model, using measured initiation delays, are in good agreement with those obtained from thermal decomposition studies without explosion. It is shown that, for the experimental conditions used, purely photochemical reactions are unimportant.

Pair‐Correlation Effects in a System of Coupled Rotators
View Description Hide DescriptionOrientational transitions in systems of coupled molecular rotators have previously been treated by methods that take account of pair‐correlation effects, but only in the case of molecules with axial symmetry coupled by forces that do not depend on the direction of the line of centers between molecules. The theory is here generalized to the case of direction‐dependent couplings. The resulting integral equations are treated by expanding in powers of T_{b}/T and 1/z, where T_{b} is the branching temperature of the ordered solution under consideration, and z is the number of next neighbors to which a molecule is coupled. The zero‐order solution of the problem is related to the solution in the internal‐field approximation. The first‐order correction for pair‐correlation effects is determined by an integral equation. The theory is applied to the James—Keenan model of solidmethane, for which the integral equation is easily solved. Inclusion of the first‐order pair‐correlation correction increases the estimated octopole moment of methane by some 10% over that derived by the internal field method, to 0.55×10^{—24} electron·cm^{3}. The effect of pair correlations on the orientational distribution of the molecules is discussed on the basis of this theory. The calculations on solidmethane are of illustrative value only, since the small moment of inertia of even CD_{4} makes quantum effects important, whereas the present theory is based on classical statistical mechanics.

Evolution of Molecular Systems and the Separation of Electronic and Nuclear Motions
View Description Hide DescriptionA time‐dependent approach to the study of molecular systems is used to analyze the interaction between the electronic and nuclear motions. The set of coupled evolution equations for the nuclei, resulting from this treatment, is solved in a first‐order perturbation approximation to obtain the decoupling of electronic and nuclear motions and to give conditions for its validity. A comparison is made with an adiabatic approximation treatment of the evolution equations and with the Born—Oppenheimer approximation, paying attention to the initial suppositions and to the restrictions in the different cases.

Absorption, Fluorescence, and Energy Levels of Ho^{3+} in Hexagonal LaCl_{3}
View Description Hide DescriptionThe absorption and fluorescencespectrum of Ho^{3+} in LaCl_{3} has been obtained between 2600 and 12 000 Å and the energy levels established. The Stark components are virtually complete, except for the high‐lying levels where, because of crowding and weak absorption, the interpretation becomes uncertain. The observed crystal field splittings for the low‐lying levels agree reasonably well with calculated ones if B _{2} ^{0}=122, B _{4} ^{0}=—45, B _{6} ^{0}=—28, B _{6} ^{6}=280 cm^{—1}. Zeeman effects for fields parallel and perpendicular to the axis have been obtained and used for the classification. Approximately 180 absorption and 380 fluorescence lines have been obtained. A considerable number of the former show resolved nuclear hyperfine structure. The mechanism for energy transfer between excited states has been cleared up.

Paramagnetic Resonance of Rare‐Earth Ions in YCl_{3} and LuCl_{3}
View Description Hide DescriptionThe principal g values of the ground‐state doublets of Dy^{3+}, Er^{3+}, and Yb^{3+} in monoclinic YCl_{3} and LuCl_{3} have been measured using EPR at 9.6 kMc/sec and 4.2°K. The results show little variation between the two host lattices, indicating their use for the interpretation of the bulk properties of the concentrated trichlorides. The principal g values of Ce^{3+} and Nd^{3+} in YCl_{3} have also been measured. It is found that the g values may be accounted for to a first approximation by a distorted octahedral cubic crystal field.

Correlation of Activation Energies and Bond Energies in CF_{3} Reactions
View Description Hide DescriptionRate constants and activation energies have been measured for deuterium abstraction from CD_{4}, (CH_{3})_{3}CD, and Cl_{3}CD, to give, respectively: 10^{—12.6} exp(—12.1/RT), 10^{—11.3} exp(—7.4/RT), 10^{—12.0}×exp(—9.0/RT) cc/molecules·sec with activation energies in kilocalories. By means of the London—Polanyi—Eyring—Sato LPES method of evaluating potential energy surfaces (with the one adjustable parameter fitted to the activation energy of the reaction CF_{3}+CH_{4}) and by means of activated complex theory, the predicted kinetic quantities (Arrhenius A, k _{H}/k _{D}, and other activation energies) were calculated for the two series involving both H and D: H_{3}C–H, C_{2}H_{5}–H, (CH_{3})_{2}CH–H, (CH_{3})_{3}–H; H_{3}C–H, H_{2}ClC–H, HCl_{2}C–H, Cl_{3}C–H. The results are compared with observed values from the literature and from this study. The observed trend of E with bond energy for the series was compared with that predicted by the LPES method and that predicted by the one‐parameter Polanyi—Semenov rule. For the general family of reactions of CF_{3} on substituted hydrocarbons RH, the following evaluation of the predictive value of the LPES method is made: Arrhenius E, not predicted but used to select the one adjustable parameter; Arrhenius A, predicted within a factor of 10 when full N‐atom model is used and predicted very poorly when simple three‐atom model is used; k _{H}/k _{D}, excellent prediction over wide range of temperature if large tunneling correction is made; E trend with —ΔH, good prediction, but no better than the vastly simpler Polanyi—Semenov rule.

Hyperfine Structure in the EPR Spectrum of the Manganous Ion in Frozen Solutions
View Description Hide DescriptionEPR spectra of 10^{—3} M MnCl_{2} were studied in various solutions at —180°C, and in 12M HCl or methanol the hyperfine structure was very similar. This hyperfine structure was then studied with respect to a changing Cl^{—}/Mn^{++} ratio by addition of LiCl or HCl to the MnCl_{2} solution. These spectra may be explained in terms of a spin Hamiltonian by considering only the M = ½↔M = —½ transitions, and the occurrence of forbidden Δm = ±1 transitions.

Chemical Effects of Isomeric Transitions: The Separation of Tellurium Isomers in Different Chemical Media
View Description Hide DescriptionThe chemical separation of the nuclear isomers of ^{127}Te and ^{129}Te in different media has been studied. The variation of f_{j} (^{127}Te) with pH in aqueous solutions of HCl, HNO_{3}, HClO_{4}, and NaOH has been measured; f_{j} is the probability that, if the parent metastable‐state activity is in the telluric acid form, the daughter ground‐state activity will be found as tellurous acid as a result of chemical interactions in a medium of substance j. The f_{j} 's for the different acids behave very similarly as the pH changes. In 6Nacidsolutions,f_{j} is close to unity; it decreases monotonically with increasing pH and approaches the value for H_{2}O, at pH of 6.0, of 0.760±0.017. In NaOH, f_{j} increases with decreasing pH, and also approaches the value for H_{2}O. The variation of f_{j} with pH may be expressed by the relation, , with ; m_{j} and b_{j} are parameters which are obtained from the data. Also, relative f_{j} values for ^{127}Te and ^{129}Te have been determined in solid telluric acid, H_{2}O, and 6Nsolutions of HCl, HClO_{4}, and NaOH. Although the absolute f_{j} values for these nuclides change from substance to substance, the ratios of the f_{j} 's remain fairly constant, approximately equal to unity. Thus, f_{j} appears to be mainly a function of the chemical, and not the nuclear, properties of the isomer separation process.

Conditions for Optimal Choice of Approximate Wavefunctions and the Hypervirial Theorem
View Description Hide DescriptionThe hypervirial theorem for the operator L does not guarantee the independence of the expectation value L from all essential errors of the approximate wavefunction. The more complete system of conditions includes the matrix elements of higher commutators (and anticommutators) L with the Hamiltonian. These conditions prevent the effect of approximate wavefunction errors and may be useful for evaluations of expectation values and transition probabilities. The problem is considered in terms of dynamics or statics. These treatments are shown to be equivalent only for the exact solution.

Electron Paramagnetic Resonance of Some Sulfur and Selenium Compounds
View Description Hide DescriptionA number of organic compounds containing sulfur or selenium are known to be useful as antioxidants or radio‐protective agents because of their reactivity with free radicals. We have studied the electron paramagnetic resonance(EPR) of some aliphatic and aromatic sulfide and disulfide compounds and their selenium analogs uv‐irradiated at λ=2537 Å in order to characterize and compare the free radicals produced. The irradiation and the EPR measurements were carried out at liquid nitrogen temperature. The EPR spectra obtained for these compounds fall into four categories characteristic of the four types of radical species found—alkyl radicals, benzyl‐type radicals, sulfur radicals, and selenium radicals. The selenium radical, which has not been previously observed, exhibits an asymmetric spectrum having an axially symmetric g factor, with g⊥=2.08 and g∥=2.12.

Effect of Pressure on the Properties of TCNQ and Its Complexes
View Description Hide DescriptionThe effect of very high pressure has been measured on the properties of TCNQ (tetracyanoquinodimethane) and three complexes. For all three complexes the electrical resistance at 296°K decreased with increasing pressure to about 140–150 kbar, beyond which pressure there was a very large rise accompanied by much drifting upward with time. This transformation was irreversible. At 78°K no rise was noted at high pressure, but if a sample was heated at high pressure the transformation initiated about 180°K.
It was found that the absorption peaks in the visible region had almost completely disappeared in the transformed material although the 280‐mμ peak remained. The resistance of TCNQ was too high to permit electrical studies, but samples taken to high pressure also showed disappearance of absorption peaks in the visible. These and other related observations indicate that the TCNQ molecules are reacting, probably through the C≡N bond. The type of reaction seems in many ways similar to that obtained in pentacene and single‐crystal graphite and discussed in a previous paper.

Interaction Effects on Lifetimes of Atomic Excitations
View Description Hide DescriptionThe apparent lifetime of an excited atom in a p state is investigated when another atom, in an sground state, is present. The dependence of the lifetime on the distance R _{AB} between the two atoms is obtained. It is found that the results for a p _{0} state differ somewhat from those for the p _{±1} states. (The axis of quantization is taken as the line joining the two atoms.)

Angular Momentum Distribution and Emission Spectrum of OH (^{2}Σ^{+}) in the Photodissociation of H_{2}O
View Description Hide DescriptionWhen water vapor absorbs light of wavelength less than 1350 Å, an electronically excited OH fragment may be produced. This process has been observed, using wavelengths 1216, 1236, and 1302 Å, and the rotational and vibrational excitation of the product OH ^{2}Σ^{+} has been determined from its emission spectrum. Most of the energy beyond that necessary to produce electronically excited OH goes into rotation of that molecule. Roughly one‐third of the OH molecules have one quantum of vibrational energy, and in these molecules too, the highest energetically allowed rotational levels are strongly populated.
Knowledge of the energy and rotational angular momentum of the OH allows estimation of the kinetic energy and orbital angular momentum of the H as it flies away from the center of mass. This is interpreted in terms of two‐body forces at large distances, with the most probable dissociation corresponding to an orbiting interaction.