Volume 50, Issue 10, 15 May 1969

Measurement of Ion–Molecule Reaction Rate Constants Using Ion Cyclotron Resonance
View Description Hide DescriptionThe theory of ion cyclotron resonance line shapes has been developed for the case where the ion does not suffer any collisions with the neutral gas molecules. Experimental results are in very good agreement with the theoretical line shape. Expressions have been derived for the single resonance signal intensities of both primary and secondary ions at low pressure. Ion–molecule reaction rate constants obtained for the following reactions were and are in good agreement with rate constants obtained by other techniques.

Radiative Lifetime of the State of CO^{+}
View Description Hide DescriptionThe lifetime of the state of CO^{+} was measured by noting the decay time of 11 band heads of the (0, 0), (0, 1), (1, 0), and (1, 2) electronic–vibrational transitions of the Baldet–Johnson system. The lifetime exhibited no pressure dependence and no variation of the lifetime was noted for different rotational or vibrational levels. The lifetimes of the and states are 51.0 ± 0.7 and 52.2 ± 1.8 nsec, respectively. These lifetimes are in agreement with other recent measurements.

Inequalities for Multipole Dispersion Interactions
View Description Hide DescriptionSome theoretical relations are obtained for various multipole dispersion force constants and for the total second‐order dispersion energy in the long‐range interactions between atoms.

Vibronic Coupling. VI. Vibronic Borrowing in Cyclic Polyenes and Porphyrin
View Description Hide DescriptionVibronic borrowing in closed‐shell aromatics is investigated by means of the cyclic‐polyene model with the electrons treated according to simple Hückel theory and the electrons treated as outlined by Longuet‐Higgins and Salem. The basis set for the vibronic wavefunctions consists of single‐product Born–Oppenheimer functions whose electronic factors are LCAO cyclic‐polyene molecular orbitals. The coupling between these Born–Oppenheimer functions is treated by means of perturbation theory. The dependence of the vibronic coupling on the size of the aromatic is given. Intensities of the vibronic transitions in benzene, coronene, triphenylene, 18‐annulene, and porphyrin are calculated. Porphyrin is approximated by a 16‐membered cyclic polyene with 18 electrons, and the absorption spectra,fluorescencepolarization, and Zeemanspectra are interpreted in terms of vibronic interactions. The Jahn–Teller distortion vanishes in these cases, a result shown to be a general phenomenon for one‐electron terms in states arising from two electrons or holes.

Fluorescence Self‐Quenching through Hydrogen Bonding
View Description Hide DescriptionA new process of self‐quenching has been observed which seems to involve the dissipation of excitation energy through the formation of hydrogen bonds or possibly a proton‐transfer mechanism. Special derivatives of the basic chromophore 2‐phenylindole which could not self‐quench by normal processes were shown to have decreasing fluorescence and scintillation yields with increasing concentration in toluene solutions. All of these compounds had in common a hydrogen atom on the N atom of the indole part of the molecule. By replacement of that H atom with a methyl group all self‐quenching was completely eliminated.

Semiempirical Model for Atom–Atom Ionization Rates
View Description Hide DescriptionNumerical calculations are carried out to help interpret ionization rates for rare‐gas atoms (particularly argon) obtained in shock‐heating experiments. A simplified semiempiricalmodel with three adjustable parameters is used for electronic transitions induced by atom–atom collisions. The three parameters are a measure of the absolute excitation rate from the ground state to the first excited state and of the ratios of different excitation and ionization rates. Numerical results are presented for the total ionization rate as a function of temperature and time for different values of the parameters. Present experiments determine one of the parameters, limit the other two parameters, and yield a relation between them. The possibility for determining all three parameters uniquely from future experiments is discussed.

Configurational Correlations in Chain Molecules
View Description Hide DescriptionAlthough the potentials affecting the rotation about a skeletal bond in a chain molecule such as polymethylene (PM) usually depend only on rotations of immediately adjoining bonds, the interdependence of rotational states may be transmitted over greater distances. In the case of PM or of polyoxymethylene(POM) the effective range of correlation is only four or five bonds. This has been established by calculating a priori probabilities for rotational states of a bond as a function of its location relative to the chain termini and of the total chain length. The range of directional correlations between bonds is much greater owing to the further effects of the geometrical constraints imposed by bond angles and hindrance potentials. The correlation between bond directions is reflected in the average sum of the projection on bond of all bonds to . Convergence of this quantity calculated for PM occurs for sequences exceeding about 25 bonds in length. Effects of chain ends are perceptible only for . In confirmation of these observations, the characteristic ratio of the mean‐square distance between chain atoms and converges only for sequences , but for it differs inappreciably from the value for a finite chain of length , i.e., for and .

Moments of Chain Vectors for Models of Polymer Chains
View Description Hide DescriptionFour model chains, namely, the freely jointed chain (1), the freely rotating chain (2), the Porod–Kratky wormlike chain (3), and the model with independent bond rotations hindered by a symmetrical potential (4), are compared with a realistic isomeric‐state representation (5) of the polymethylene chain through calculations of various properties of their distributions. Parameters used for Models 1–4 were adjusted to secure agreement with 5 at the infinite chain limit. Properties treated are the mean‐square end‐to‐end distance, its temperature derivative, the mean‐square radius of gyration, and higher even moments of the end‐to‐end distance. Convergences to asymptotic ratios with chain length are examined. None of the simpler models 1–4 adequately represents these properties of the realistic chain 5 at all chain lengths. The success of any one of the models 1–4 in accounting for the dependence of a given property on chain length varies considerably from one property to another.

Distribution Functions for Chain Molecules
View Description Hide DescriptionDistribution functions of the end‐to‐end vectors r of chain molecules are calculated according to: (i) the exact expression of Rayleigh for a freely jointed chain, (ii) the Kuhn and Grün approximate function, (iii) a revised form of the KG function which amends a basic error in its traditional derivation, and (iv) the Gaussian function . For chains of 4–20 freely jointed bonds, (iii) is a considerable improvement over (ii). Except at higher extensions, in the vicinity of , the Gaussian expression (iv) offers the most satisfactory approximation to (i). Series expansion of in Hermite polynomials in the even moments , , etc., readily yields results previously obtained by a more lengthy Fourier transformation method due to Nagai. For chains of short or moderate length the convergence of Nagai's series is slow, many higher moments being required for significant refinement of beyond its approximation by . Analysis of the moment ratios and and their trends with chain length suggests that the Rayleigh (exact) distribution functions for freely jointed chains may afford very good approximations for real chains, provided, however, that the number of equivalent bonds for the freely jointed model is properly scaled in relation to the actual number of bonds in the real chain. About 20 bonds of a polymethylene chain are equivalent to one of the freely jointed model chain.

Studies of Chemical Shift Anisotropy in Liquid‐Crystal Solvents. II. Theoretical Calculations for the Methyl Halides
View Description Hide DescriptionExperimentally determined values of the proton chemical‐shift anisotropy for the methyl halides have been used to test simple phenomenological theories which have been proposed to account for protonmagnetic shielding. It is shown that the frequently used magnetic dipole model predicts that the long‐range contribution to the proton shielding anisotropy should largely depend on the average neighbor magnetic susceptibility.Anisotropies calculated from this model are much larger than those measured. Expressions have also been derived relating the proton shielding anisotropy to the electric dipole moment and charge densities of polar substituents. Results of these calculations are not as conclusive as in the magnetic dipole case.

Magnetothermodynamics of MnCl_{2}·4H_{2}O. I. Heat Capacity, Entropy, Magnetic Moment, from 0.4° to 4.2°K with Fields to 90 kG along the Crystallographic Axis
View Description Hide DescriptionThe heat capacity and magnetic moment of a 3.934‐cm‐diam spherical single crystal of MnCl_{2}·4H_{2}O have been measured over the range 0.4°–4.2°K, with stabilized magnetic fields of 0, 5, 7.5, 10, 14, 18, 25, 40, 65, and 90 kG, along the crystallographic axis. At the lower temperatures, magnetic saturation was attained at 90 and 65 kG. The temperature‐dependent saturation value was found to be 28 076 G·cm^{3}/mole, corresponding to a . At 90 kG the several nuclear spins were found to contribute a heat‐capacity term equal to . The amount of energy required to remove a quantum of angular momentum from the saturated condition at 90 kG was found to be 22.9 cal/mole. This is less than , the equivalent required magnetic work at 90 kG, by 1.3 cal/mole, which is the amount of stored internal energy contributed by the saturated condition for this limiting process and indicates antiferromagnetic interactions. Using magnetic saturation at 90 kG to locate a zero entropy reference for the electronic and lattice systems, the entropy was evaluated over the above range of field and temperature. Temperature–field observations on a large number of isentropes were used to correlate the entropies along the various isoerstedic heat‐capacity curves. The upper limit of the electronic entropy was found to be 3.559 gibbs/mole, compared to the amount expected for an system. Smoothed values of the heat capacity,entropy, enthalpy, internal energy, magnetic moment, and the magnetic work have been tabulated.

Matrix Infrared Spectrum and Bonding in the Dibromomethyl Radical
View Description Hide DescriptionSimultaneous condensation of bromoform and lithium atoms at high dilution in argon on a CsI window at 15°K produces new infrared absorptions which are assigned to lithium bromide and the dibromomethyl radical. The identity of dibromomethyl is confirmed by comparison of spectra obtained from HCBr_{3}, DCBr_{3}, and HCBr_{2}Cl precursors reacting with lithium and sodium. These new absorptions are assigned to the antisymmetric H–C–Br bending and C–Br stretching modes and the symmetric C–Br vibration. The antisymmetric vibrational assignments are supported by product‐rule and normal‐coordinate calculations which give the potential constants , , and , while the symmetric C–Br mode yields an approximate force constant . The C–Br valence force constants for bromomethyl radicals exceed normal C–Br values, while electronic stabilization for these radicals is indicated by bond dissociation energies. Similar results for chloromethyl radicals, in contrast to fluoromethyl radicals, suggest that bonding between the free‐radical carbon orbital and the orbitals on chlorine and bromine might account for the stabilization of chloromethyl and bromomethyl radicals, which cannot occur for fluoromethyl radicals or molecules with completely satisfied valence.

Matrix Infrared Spectrum and Bonding in the Dichloromethyl Radical
View Description Hide DescriptionSimultaneous deposition of chloroform and lithium atoms at high dilution in argon on a CsI window at 15°K produces new infrared absorptions which are attributed to lithium chloride and the dichloromethyl radical. The identity of dichloromethyl is provided by comparison of spectra recorded after reactions of HCCl_{3}, DCCl_{3}, and HCCl_{2}Br with lithium and sodium and the detection of (HCCl_{2})_{2} following diffusion and the decrease in HCCl_{2} absorptions. The new absorptions are assigned to the antisymmetric H–C–Cl bending and C–Cl stretching vibrations. These vibrational assignments are supported by product‐rule and normal‐coordinate calculations which give the potential constants , , and . The carbon–chlorine valence force constant deduced here exceeds normal C–Cl values, while bond dissociation energies indicate that HCCl_{2} is electronically stabilized. Similar results for bromomethyl radicals, in contrast to fluoromethyl radicals, suggest that bonding between the free‐radical carbon orbital and the orbitals on chlorine and bromine may account for the stabilization of chloromethyl and bromomethyl radicals, which cannot occur for fluoromethyl radicals or molecules with completely satisfied valence.

Photoionization of High‐Temperature Vapors. VI. S_{2}, Se_{2}, and Te_{2}
View Description Hide DescriptionFrom the photoionization‐efficiency curves of S_{2}, Se_{2}, and Te_{2}, the thresholds for formation of parent and fragment ions have been determined. The ionization potentials of Se_{2} and Te_{2} obtained from these measurements are 8.88 ± 0.03 and 8.29 ± 0.03 eV, respectively. For , the value 101.0 ± 0.2 kcal/mole is deduced, in general agreement with other techniques. The result distinctly favors one of two proposed thermochemical values. The experimental result has considerable uncertainty but tends to favor the highest of three spectroscopic possibilities. Evidence is presented for a 0.35 ± 0.04‐eV splitting between the ground state of Te_{2} and the state.

Electron Affinities of the Heavy Elements
View Description Hide DescriptionHorizontal analysis has been employed to obtain quantitative estimates for the electron affinities of the elements of the three long periods of the Mendeleev periodic table. Values for the A subgroup were normalized to published experimental values for bromine and iodine and an estimate for astatine, while those for the B subgroup were based on experimental values for the alkali and noble metals. The results are consistent with most of the published experimental values and with those negative ions detected. The near agreement between the electron affinities of the alkali metals and those of the excited rare gases with similar outer‐shell configurations suggests that most of the polarization contribution arises from the outer shell.

Pi‐Electron Charge Densities and Chemical Shifts in Nitrogen Heterocyclics
View Description Hide DescriptionThe relation is examined in some detail, where is the chemical shift between a proton in an aromatic nitrogen heterocyclic and the corresponding proton in its aromatic polycyclic analog, and is the excess π‐electron charge density on the carbon to which the proton is bonded in the heterocyclic. It is found that the relation is quite satisfactory for positions ortho to a nitrogen, as long as only one nitrogen appears in that particular cycle.

Mechanisms of Energy Transport in Ruby
View Description Hide DescriptionThe experimental results of Imbusch on energy transfer between single ions and pairs in 0.003%–1% Cr^{3+}:Al_{2}O_{3} are re‐examined. It is shown that the energy transfer can only be plausibly explained on the basis of orbitally dependent exchange rather than the electric quadrupole–quadrupole interaction as has been postulated. This result, besides being of intrinsic interest, also has important consequences for other energy‐transfer experiments. In particular, the experimental concentration dependence of the intensities seems to imply an law for the interaction operative in the energy transfer rather than the much more rapid falloff characteristic of exchange. It is suggested that this discrepancy arises from the propagating nature of the single ion excitation which tends to enhance the importance of short‐range interactions. This same anomaly should be present in many other systems in which energy transfer has been studied.

Infrared Spectrum, Structure, Vibrational Potential Function, and Bonding in the Lithium Superoxide Molecule LiO_{2}
View Description Hide DescriptionLithium superoxide has been synthesized by reacting lithium atoms and oxygen molecules at high dilution in inert and oxygen matrices. Isotopic substitution at all atomic positions and use of isotopic mixtures verify the molecular identity and indicate an isosceles triangular structure. Eighteen frequencies from six isotopic molecules determine the potential constants , , and . The oxygen–oxygen force constant for LiO_{2} coincides with that calculated for O_{2} ^{−}, which suggests that the LiO_{2} molecule is highly ionic and may be considered as a lithium cation bonded to a superoxide anion by Coulombic forces.

Argon–Methane Phase Diagram
View Description Hide DescriptionThe argon–methane solid phase diagram has been determined between 15° and 65°K by x‐ray diffraction techniques. The diagram shows a miscibility gap with a critical point for unmixing at 35% methane and 63°K, whereas published liquidus and solidus lines indicate a eutectic point at 39% methane and 71°K. Calculation of the interaction energy of the mixture from the properties of the constituents using the simplest forms of solution theory yields values which deviate by an order of magnitude from those derived from the experimental data. The discrepancy is in part due to an appreciable contribution to the excess free energy from strain energy and otherwise due to inadequacies of the methods of calculating both interaction and strain energies and due to imprecision in the experimental parameters required for these calculations.

Improved Variational Bounds on Some Bulk Properties of a Two‐Phase Random Medium
View Description Hide DescriptionThe Hashin–Shtrikman bounds on the bulk magnetic permeability (or dielectric constant, thermal and electric conductivity, solute diffusion coefficient) for a random two‐phase material can be considerably improved by the inclusion of experimentally accessible information, such as the bulk permeability of the material at a different temperature [the main results are expressed in the inequalities (27), (45), and (51)]. These inequalities can also be written as bounds on the rate at which the bulk permeability changes with changing permeabilities of the individual phases [(29) and (30)]. In particular, application of (30) yields the upper and lower bounds (59) on the observed energy of activation for diffusion through a two‐phase medium. The inequalities (27), (45), and (51) can be expressed in a mixed form to bound, for example, the bulk permeability through use of data on the thermal conductivities of the mixed material and the individual phases. Bounds on the viscosity and elastic moduli of a two‐phase medium are also discussed briefly.