Volume 38, Issue 1, 01 January 1963
Index of content:
38(1963); http://dx.doi.org/10.1063/1.1733446View Description Hide Description
In order to obtain information regarding disproportionation and recombination reactions of ethyl radicals and iodine atoms we have investigated the photolysis of various mixtures of diethyl ketone and methyl iodide.
Ethyl radicals, produced by photolysis of diethyl ketone, react with iodine atoms, produced by photolysis of methyl iodide, according to reactions (13) and (14) The results indicate k 13/k 14=0.33±0.03. The influence of added gas and the effect of temperature are discussed.
38(1963); http://dx.doi.org/10.1063/1.1733492View Description Hide Description
The recombination and disproportionation reactions of CH2CH2Cl and CCl3 radicals have been investigated. Trichloromethyl radicals and monochloroethyl radicals were produced by photolyzing carbon tetrachloride in the presence of ethylene. The main features of the resulting reaction mechanism are given by reactions (1) to (8) The following rate constants have been determined .
38(1963); http://dx.doi.org/10.1063/1.1733500View Description Hide Description
From the general molecular vibration—rotation Hamiltonian in the Nielsen—Amat—Goldsmith formulation, Hamiltonians for asymmetric‐top molecules of the orthorhombic, monoclinic, and triclinic point group symmetries are deduced. These Hamiltonians are appropriate for the calculation of vibration—rotation energies to the fourth order of approximation.
38(1963); http://dx.doi.org/10.1063/1.1733459View Description Hide Description
An analysis of the recent kinetic isotope effects in the pyrolysis of cyclopropane and cyclopropane‐d 6 is shown to be in excellent agreement with the diradical path for the reaction. This is true at the high‐pressure limit and possibly near the low‐pressure limit for the reaction.
Using the same transition state for the isomerization with a structure about half‐way between trimethylene and propylene and containing a bridged H atom, leads to a frequency factor for the high‐pressure rate constant in excellent agreement with the experimental data. It is also shown, from the examples of the C2H6 and H2O2pyrolyses that ``secondary'' isotope effects may have temperature coefficients as large as or larger than those associated with ``primary'' isotope effects.
Extending the same type of analysis to cyclobutane pyrolysis leads to an excellent a priori calculation of the frequency factor for the high‐pressure rate constant and of the kinetic isotope effects in cyclobutane‐d 8. It is further shown that the apparently discordant kinetic isotope effects reported for[Complex chemical formula]are actually in good agreement with those for cyclo‐C4D8. Finally, the use of group additivity relations in kinetics is explored and shown to lead to excellent predictions in the reactions of isotopically labeled species with different isotopic content. Their application to other types of reactions cannot be evaluated at present because of insufficient data.
Classical Model for Vibrational and Rotational Excitation of Diatomic Molecules by Collision. I. Hard‐Sphere Collision38(1963); http://dx.doi.org/10.1063/1.1733471View Description Hide Description
The details of inelastic energy transfer between a diatomic, classical, harmonic oscillator, A—B, and a hard‐sphere atom C are explored for the simple case of colinear collisions. The influence of the masses M A, M B, and M C on the efficiency of energy transfer is examined in detail. The case of equally matched masses (M B = M C) does not necessarily correspond to high efficiency. It is shown that for colinear collisions not all phase angles of the oscillator can occur at the instant of collision, but that instead certain phase angles are excluded. In the case of a highly excited oscillator in a ``cold'' gas, these excluded phase angles are just those that restrict the energy transfer from the oscillator to small amounts of energy. For a harmonic oscillator, near the dissociation threshold, this implies a small, stepwise deactivation process. It is also shown that even for the hard‐sphere case, 100% efficiency of energy transfer is not possible, i.e., there is an activation energy in excess of the energy transferred. This is required as an ``escape energy'' in order to avoid a double collision whose effect would be to reduce the energy transferred. This escape phenomenon is also shown kinetically to favor stepwise energy transfer for quantized oscillators. Some simple cases of rotational‐energy transfer are examined.
38(1963); http://dx.doi.org/10.1063/1.1733491View Description Hide Description
The radiolysis of (CH3)3CD—I2 and mixtures has been investigated as a function of pressure (0.2 to 75 cm) and temperature (30° to 225°C). Propane, which is the major product, is mostly formed by a hydride transfer reaction such as . From the distribution of the isotopic propanes produced in the radiolysis of (CH3)3CD it can be concluded that hydrogen atoms in the sec‐propyl ion are randomized in various degrees depending on the pressure of isobutane. Ethane is mainly formed by a hydride transfer reaction.Two distinct processes lead to the formation of ethylene, (a) molecular elimination from isobutane and (b) reaction of vinyl ions with isobutane. The effect of xenon, krypton, and argon on the product distribution and the randomization of the sec‐propyl ion is discussed in some detail.
38(1963); http://dx.doi.org/10.1063/1.1733493View Description Hide Description
A simple approach for supplementing the usual variational energy criterion for molecular wavefunctions is described. With the requirement that integrals of selected operators agree with the known experimental or theoretical values for the corresponding properties, a constrained variation method is formulated. For an appropriate choice of one‐electron operators, the resulting charge distribution can be of greater accuracy than that obtained from an unrestricted variation treatment with the same basis set. Since the method is of most interest for simple wavefunctions, it is illustrated in terms of a modification of the best‐limited LCAO—MO hydrogen fluoride function of Ransil. A comparison of the two functions shows that the constrained variation treatment leads to improved results for certain one‐electron properties. The calculations also demonstrate the sensitivity of the one‐electron expectation values to small changes in the orbital coefficients and the total energy.
38(1963); http://dx.doi.org/10.1063/1.1733494View Description Hide Description
Fundamental infrared absorption bands of NOCl and NOBr solids at liquid‐nitrogen temperature exhibit remarkable frequency shifts compared to the gas‐phase spectra. Peak frequencies, band shapes, and band multiplicities of the solid spectra are strongly influenced by the nature of the solid matrix. Studies of the reactions of nitric oxide with chlorine and with bromine in the solid state suggest that the observed band multiplicities may be due to the formation of molecular complexes between the nitrosyl halide and the halogen.
38(1963); http://dx.doi.org/10.1063/1.1733495View Description Hide Description
The determination of precise structural information about solids by means of NMR fine‐structure measurements is investigated theoretically. Attention is directed to the interpretation of broadening effects resulting from subsidiary dipolar interactions. Consideration is limited primarily to systems in which the fine structure is that produced by a strongly interacting pair of spin ½ nuclei, of which the water molecule in hydrate crystals is the prototype. It is shown that the fine‐structure lines are expected to broaden asymmetrically and that the asymmetry is a measure of the anisotropy in the pair distribution. The nature of the asymmetry can often be interpreted in terms of the relative angular position of nearby interacting pairs in the crystal. It is further proved that, within the validity of a first‐order perturbation theory approach, the center of gravity of a broadened fine‐structure line is the correct measure of the interaction responsible for the main splitting. This result is independent of the number or relative positions of the interacting pairs.
The breakdown of the first‐order theory with increasing interpair interaction strength is discussed. Using a simple two‐pair model, calculations are made which show typical interpair distances at which one may expect a significant shift of the center‐of‐gravity position from that determined only by the intrapair interaction. Extension of the center‐of‐gravity theorem to other systems in which fine structure produced by a dominant interaction is asymmetrically broadened by subsidiary nuclear magnetic dipolar interactions is discussed briefly.
38(1963); http://dx.doi.org/10.1063/1.1733496View Description Hide Description
The effects of interpair broadening upon the NMRspectra of proton pairs in hydrate crystals are explored experimentally. The shape of a fine‐structure line is generally found to be asymmetric. The importance of using the position of the center of gravity of a fine‐structure line rather than the position of maximum absorption in determining structural parameters is emphasized by several experimental illustrations. In a coupled pair framework the former quantity is independent of interpair broadening to first order, the latter only to zero order (isolated pairs), but the position of maximum absorption is the quantity most commonly used in the literature. Data for a crystal not previously investigated with NMR, K2C2O4·H2O, illustrates the importance of the use of centers of gravity for a case in which the interpair interactions are relatively weak. It also demonstrates how the nature of the line asymmetry may be interpreted to give information about relative positions of neighboring water molecules.
The protonspectra of CaSO4·2H2O and Li2SO4·H2O have been remeasured and are reinterpreted. For these crystals short interpair distances suggest large modifications of the zero‐order treatment given in the literature. It is demonstrated that in CASO4·2H2O a first‐order treatment gives consistent results, with minor changes in the previously derived structural parameters. Second‐order effects on the position of the center of gravity of the NMR line are largely suppressed by the relatively large number of interacting pairs.
In Li2SO4·H2O it is concluded that strong interpair couplings along a chain of water molecules cast grave doubts on any interpretation of the spectra based on an analytical treatment using a coupled pair framework.
38(1963); http://dx.doi.org/10.1063/1.1733497View Description Hide Description
The dielectric constant of cyanoacetylene has been determined over the normal liquid range: ε (T) = (71 000/T) —170. Analysis of the data in terms of a hydrogen‐bonded linear polymer yields: ΔH = —2.80 kcal; ΔS = —15.8 eu per mole of hydrogen bond. The vapor pressure of solid and liquid HCCCN has been measured. Molar enthalpies and entropies of fusion and vaporization are: 3.38 and 6.72 kcal; 12.1 and 21.3 eu, respectively. Hydrogen bonding in this and similar systems is discussed.
38(1963); http://dx.doi.org/10.1063/1.1733498View Description Hide Description
Molecular orbitals from d, s, p types of valence orbitals and parametric expressions for energy levels in octahedral Ta6Cl12 2+ and Mo6Cl8 4+ were obtained by group theoretical methods. Both cages exhibited electron delocalization and similar bonding energies, even though only the Ta6Cl12 2+structure is electron deficient.
38(1963); http://dx.doi.org/10.1063/1.1733499View Description Hide Description
Nuclear spinrelaxation times have been measured for liquid CHFCl2, the values of T 1H and T 1F between 132° and 298°K at 27, 20 and 17 Mc, and T 2H and T 2F over the same temperature range at 20 Mc. The results of these measurements are discussed, and the following relaxation mechanisms are shown to be important: (a) intermolecular dipole—dipole interactions, including their effect upon the electronic, scalar coupling of the proton and fluorine nucleus, (b) the quadrupolar relaxation of the chlorine nuclei which are coupled to the proton and the fluorine nucleus by scalar couplings, and (c) the spin‐rotation interaction between the fluorine nucleus and the reorientation of the molecule. It is noted that relaxation of the same type as mechanism (b) accounts for the relatively large natural linewidths and poorer resolution often found in spectra of heavier nuclei such as F and P, compared to spectra of protons in the same liquid compound.
The statistical assumptions of rotational Brownian motion of the molecule, in the liquid, when applied to the spin‐rotation interaction, are found to predict the wrong temperature dependence of T 1F at high temperatures. A transient rotation model is proposed in which the molecules ``jump'' from one orientation to another at random times; the spin‐rotation interaction is assumed to operate during these ``jumps'' when the molecule is actually rotating. The statistical properties of such a model are calculated, and it is shown that T 1F is predicted to have the correct temperature dependence. The model is compared with that developed by Johnson and Waugh for nuclear relaxation by the spin‐rotation interaction in gases. The dipole—dipole and quadrupole interactions are discussed in detail, and a treatment of intermolecular dipole—dipole relaxation by Redfield's method is given, with results indicating that the electronic, scalar coupling of nuclei contributes to the inequality T 2<T 1 often found in liquids.
38(1963); http://dx.doi.org/10.1063/1.1733501View Description Hide Description
The infrared absorption spectra of B2O3, B2O2, and BO2 isolated in solid argon matrices have been investigated in the region 350–4000 cm—1. The visible absorptionspectrum of matrix‐isolated BO2 was observed in the region 4000–5500 Å. The gaseous species were generated in a high‐temperature effusion cell and trapped under conditions of moderate to high dilution in solid argon matrices at approximately 4°K. Bands were found at 1955, 1921, 1899, 1323, and 1276 cm—1 in the infrared spectra of B2 10O2, B10B11O2, B2 11O2, and B10O2, and B11O2, respectively. For both B2 10O3 and B2 11O3infrared spectra of the most dilute matrices show seven distinct bands in the region 450–2100 cm—1. Six of these can be readily assigned as fundamentals and their relative intensities explained if the known ``V'' structure of B2O3 is supposed to have a larger apex angle than that determined by electron diffraction, and the correlation of the normal vibrations and selection rules with those for the linear symmetric (D∞h ) model is considered. With additional help from the measured B10–B11isotope shifts and force constant calculations the following complete assignment was obtained (all frequencies in cm—1):where the bracketed frequencies were not observed directly.
Thermal functions have been computed for B2O3 and compared with the available calorimetric data. Structural parameters and a complete vibrational assignment have been estimated for B2O2. The infrared and green bands observed for BO2 are in agreement with the high‐resolution results of Johns. Thermal functions for B2O2 and BO2 have also been computed.
Application of Space‐Group Theory to the Vibrational Problem of di‐Tetramethyl Ammonium Uranium Hexachloride38(1963); http://dx.doi.org/10.1063/1.1733502View Description Hide Description
The absorptionspectrum of [(CH3)4N]2UCl6 (abbr. TMA) is discussed. The spectrum is vibronic in nature, i.e., the electronic transitions between levels belonging to the 5f 2 configuration of the U4+ ion are coupled with the vibrations of the TMA lattice. The number and symmetries of the normal modes of vibration of a unit cell are calculated in the factor group approximation. The Winston—Halford decomposition formula is used to reduce the representation of motions among the irreducible representations of the symmetry group of TMA.
Calculations are compared with the experimental results. The gross features of the spectrum are found to be in agreement with the theoretical predictions.
The method of obtaining the character tables for finite symmorphic space groups is presented in summary form. A general vibrational problem in crystals is discussed.
38(1963); http://dx.doi.org/10.1063/1.1733447View Description Hide Description
In an attempt to fix the value of the vertical electron affinity of the iodine molecule E I2 v the potential curve for I2 — has been constructed from semiempirical considerations. From this curve the value of E I2 v is estimated to be 1.7±0.5 eV, in apparent contradiction to the value around 0 eV indicated by the electron‐capture experiments. It is suggested that the electron‐capture experiment may measure the vertical energy for capture to give an excited state of the I2 — ion, thus explaining the discrepancy.
Having fixed the value for E I2 v , the relationship predicting the charge transfer frequency for iodine complexes is reexamined critically. By fitting curves to the data for three different types of complexes (π donors with I2, amine donors with I2, and complexes with I atoms), three sets of empirical constants required to force the fit are determined. An attempt is then made to calculate these sets of constants from a priori considerations. The success of this treatment supports the general theory, indicating especially that no major terms have been omitted from the estimation of the energy difference, W 1—W 0. Furthermore, the general argument supports the value of E I2 v obtained in the earlier part of the paper as well as the reliability of the estimation of the other parameters. The analysis supports the perpendicular model for the geometry of the complexes between I2 and π donors.
Finally, similar analyses are presented for other halogens; Br2, Cl2, and ICl. Estimates of the vertical electron affinity for these halogens from the empirical potential curves agree reasonably well with estimates from the charge transfer frequency, in support of the results for I2.
38(1963); http://dx.doi.org/10.1063/1.1733448View Description Hide Description
Solid nitrogen, which consists of 99.6% N14 (I=1) at natural abundance has previously been observed to exhibit a single, strong pure quadrupole resonance line in the α phase below 35.5°K. This has been discussed by Scott in the first of this series of papers. When the sample is enriched with N15 (I=½) the N14 resonance is split into two distinct lines. For an approximately equal isotopic mixture, the splitting is 8.2 kc at 4.2°K and decreases with increasing temperature. Using the Bayer—Kushida theory as a basis, the two resonance frequencies may be attributed to the presence of two types of molecules N14–N14 and N14–N15. The former molecule has a resonance frequency close to that of pure N2 14 whereas the latter molecule, being heavier and thus vibrating with a smaller amplitude, has the higher frequency. The data are discussed on the basis of present theoretical and experimental understanding.
38(1963); http://dx.doi.org/10.1063/1.1733449View Description Hide Description
Urey—Bradley force constants of methanol have been calculated by a least‐squares technique using vibrational‐frequency data from CH3OH, CH3OD, CD3OH, and CD3OD. The results show that the vibrational assignment recently proposed by Margottin—Marclou is consistent with the Urey—Bradley field, whereas that of Falk and Whalley is not.
Normal Coordinates of the Planar Vibrations of Pyridine and Its Deuteroisomers with a Modified Urey—Bradley Force Field38(1963); http://dx.doi.org/10.1063/1.1733450View Description Hide Description
A Urey—Bradley potential function has been fitted to the observed vibrational frequencies of pyridine, pyridine‐2,6‐d 2, pyridine‐3,5‐d 2, pyridine‐4‐d 1, and pyridine‐d 5.
As in the case of benzene, it was necessary to include an additional non‐Urey—Bradley force constant ρ to describe the aromatic character of the molecule. Our results suggest several minor changes in the vibrational assignment of some of these molecules.
38(1963); http://dx.doi.org/10.1063/1.1733451View Description Hide Description
The electrical conductivity of near‐stoichiometric α‐Nb2O5 was measured in the temperature range 900° to 1400°C and at oxygen pressures between 1 and 0.005 atm. Over this entire range the change in conductivity with oxygen pressure is in accord with the relation σ∝P o2 —¼. From the exponential temperature dependence of conductivity in the range 1400° to 700°C an activation energy of 1.65 eV can be calculated. These results are in excellent agreement with previous investigators who obtained the same relationships in the temperature range 600° to 900°C. Therefore, it is felt that the conduction process is controlled by a single mechanism over the temperature range 700° to 1400°C at oxygen pressures between 1 atm to 0.005. From mass‐action considerations it is postulated that the mechanism responsible is probably the excitation of the first electron from an oxygen ion vacancy which has trapped two electrons.