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Volume 53, Issue 8, 15 October 1970

Photochemistry of Aromatic Olefins. II. Intramolecular Energy Transfer in 5‐Phenyl‐2‐pentene
View Description Hide DescriptionIntramolecular energy transfer in 5‐phenyl‐2‐pentene has been studied monitoring cis–transisomerization of solutions of the compound in cyclohexane. The intersystem crossover yield of the phenyl moiety is calculated to be 0.66 or less. The rate of intramolecular energy transfer is found to be much faster than that of intermolecular energy transfer in the concentration range studied.

Determination of Autoionization Lifetimes by Ion Cyclotron Reonances Linewidths
View Description Hide DescriptionThe half‐width and half‐height for power absorption in the ICR spectrometer is shown to depend upon the time during which an ion absorbs power in the detection region of the instrument. In the case of negative ions, it is shown that autoionization can limit resolution, and conversely that the observed resolution for a given negative ion can be used to determine autoionization lifetimes. The SF_{6} ^{−} ion is observed in the ICR spectrometer, and a lifetime of ∼ 500 μsec is calculated for this ion. The C_{4}F_{8} ^{−} ion is observed, and a lifetime of ∼ 200 μsec is calculated for that ion. The lifetimes are discussed with respect to other measured and calculated values, which show a wide variation, and it is suggested that the autoionization lifetimes may be strongly dependent on the energy of the impacting electrons. In this study, both ions are shown to be produced by electrons which are trapped in the ICR cell as opposed to being produced by beamelectrons.

Theoretical Study of SO_{2} Molecular Properties
View Description Hide DescriptionUsing two contracted Gaussian functions for each atomic orbital, plus functions on both sulfur and oxygen to describe molecular charge distortion, a self‐consistent‐field wavefunction was computed for the ground state of SO_{2}. It is estimated that the calculated SCF energy, − 547.2089 hartree, lies no more than 0.1 hartree above the Hartree–Fock energy for SO_{2}. An additional calculation without functions and population analyses indicate that (a) functions on sulfur are much more important in SO_{2} than was the case in previous work on H_{2}S and (b) in SO_{2}, functions on sulfur are much more important than those on oxygen. Calculated molecular properties are in good agreement with available experimental data. Of particular importance is the fact that the calculated elements of the molecular quadrupole moment tensor are 31%, 30%, and 29% greater than those recently determined experimentally by Pochan, Stone, and Flygare. Values of the third moments, octupole moment tensor,diamagnetic shielding tensor,electric field gradient tensor, and ^{17}O quadrupole coupling constants are predicted. On the basis of ab initioelectric field gradients and experimental ^{33}S quadrupole coupling constants for OCS, H_{2}S, and SO_{2}, we deduce nuclear electric quadrupole moments: and .

Apparent Heat of Formation of HDO in Mixtures of H_{2}O and D_{2}O
View Description Hide DescriptionThe heats of solution of H_{2}O and D_{2}O in mixtures of H_{2}O and D_{2}O at 25°C have been measured. Results are interpreted in terms of the reaction to form HDO, assuming an ideal ternary solution. The possible contributions of nonideality to the standard heat of formation of are considered.

ESR Studies of Deuterated dl‐Tartaric Acid X Irradiated at 195°K
View Description Hide DescriptionUsing electron spin resonance techniques, the free radical produced when single crystals of deuterated dl‐tartaric acid are irradiated at 195°K with either 50 kV x rays or 3 meV x rays was shown to be ·CHODCHODCOOD·D_{2}O. The C–C bond to the carboxyl group is broken and the unpaired electron is primarily in a orbital on the carbon atom with the orbital close to the normal to the carbon plane. This results in a hyperfine coupling to two H atoms with eigenvalues of − 33.4, − 23.0, − 10.7 G for the α‐H hydrogen, and 37.2, 35.8, 30.5 G for the . This radical is the same radical that is observed if deuterated dl‐tartaric acid is irradiated at 77°K and allowed to warm to 195°K. This radical follows the decay of the cation radical produced at 77°K and subsequently decays to the stable room temperature radical. The anion radical which was observed at 77°K is still present at 195°K.

Statistical‐Mechanical Study of Stability of Folded‐Chain Polymer Crystals with Irregular Fold Surfaces
View Description Hide DescriptionA model of folded‐chain crystals of polymers is considered, in which the length of crystalline sequences between folds is assumed to be uniform, while the number of segments comprising the folds is allowed to vary. The partition function is formulated by the generating function technique, with the fixed crystalline layer thickness introduced as an additional parameter of the system. The random‐walk problem in the presence of a barrier, as the representation of folds, is solved for simple and body‐centered cubic lattices. As variants of the basic model, the two ends of the fold are either assumed constrained in adjacent positions in the adjacent re‐entry model, or are allowed at an arbitrary separation in the random re‐entry model. The free energy of the system as a function of crystalline layer thickness exhibits no minimum, confirming the extend‐chain crystals as the thermodynamically most stable. As the temperature is raised toward the melting point, the number of segments in folds increases beyond bound in the random re‐entry model; while they remain about 10 in the adjacent re‐entry model. In both models the size of the amorphous chain ends grows much faster than that of folds with increasing temperature. The frequency distribution of fold sizes is very broad. Even when the majority of folds consists of tight loops of a small number of segments, the fraction of very large folds is small but still significant. The entropy term of the surface free energy, calculated for the random and adjacent re‐entry models, differs by as much as 50 erg/cm^{2}.

Calculation of Cartesian Coordinates and Their Derivatives from Internal Molecular Coordinates. II. Second and Higher Derivatives and Derivatives of Vectors
View Description Hide DescriptionA process is given to extend a previously described algorithm so as to calculate analytically second and higher partial derivatives of Cartesian with respect to internal molecular coordinates within molecules. Each derivative calculation requires at most a single vector multiplication per order and is thus much faster than calculation of the original coordinates. An algorithm is also presented to calculate derivatives of a variety of vectors within molecules with respect to internal coordinates.

Anisotropic Chemical Shifts in Trigonal Cobalt Carbonyls Containing Metal–Metal Bonds
View Description Hide DescriptionThe ^{59}Co NMR was studied in a number of single crystals and solutions of cobalt carbonyl complexes X_{3}MCo(CO)_{4} (M=Si, Ge, Sn, Pb; X=Cl, Br, I, C_{6}H_{5}) containing metal–metal bonds. The component of the chemical shift as determined by single crystal measurements in I_{3}GeCo(CO)_{4}, Br_{3}SnCo(CO)_{4}, and (C_{6}H_{5})_{3}SnCo(CO)_{4} was found to be constant within the series and showed a paramagnetic contribution of at least 3.6‰. As ligand field theory predicts no paramagnetic shift in this case, the data showed that for low oxidation state complexes the chemical shift can only be explained using MO theory. Good agreement with experiment was obtained using MO coefficients for the isoelectronic Fe(CO)_{5}. The paramagnetic contributions to the and components of the shift vary considerably within the series (3.3‰–5.0‰). These variations were attributed to differences in the metal–metal bonds. It was found that for a given X the shifts do not vary linearly as the atomic weight of M is changed. This was attributed to differences in the importance of π‐bonding effects for the metal–metal bonds. The data suggest that in this series π‐bonding effects are strongest for the Co–Sn bond.

Trajectory Studies of Hot‐Atom Reactions. I. Tritium and Methane
View Description Hide DescriptionWe have studied the reactions of T+CH_{4} and T+CD_{4}, treating these as six distinct particles, using a variety of potential energy surfaces subject to the restriction that only one methane hydrogen at a time is reactive. Our principal findings are: (1) This trial assumption about the potential is unjustified. Substitution (products CH_{3}T+H and CD_{3}T+D) involves strong interactions between at least four atoms. (2) There were no inertial isotope effects of any kind when CH_{4} was replaced by CD_{4}. (3) From (2) and the details of the trajectories, there is suggestive but not conclusive evidence that substitution in CH_{4} proceeds by Walden inversion. (4) Abstraction (products CH_{3}+HT and CD_{3}+DT) is direct and concerted and occurs at relatively low energy. In our calculations it had a maximum cross section of 3.5 Å^{2} for a reactant translation energy of 65 kcal. At sufficiently high energy it is a stripping reaction. (5) About half the abstraction product energy is translational; the remainder appears as internal energy of both HT and CH_{3}. When substitution occurs as a three‐centered process, it deposits about 70 kcal in CH_{3}T. Fragmentation is an important process above 100‐kcal reactant energy.

Boundary Layer Effects on Chemical Kinetics Studies in a Shock Tube
View Description Hide DescriptionThe effect of the cold boundary layer on kinetic parameters was studied behind reflected shocks in a single pulse shock tube. By inserting hollow cylinders into the test section, parallel to the tube walls, the surface relative to the volume was increased, and the lowering of the chemical conversion was determined as a function of the surface per unit volume. The test reaction studied was the unimolecular decomposition of perfluorocyclobutane (C_{4}F_{8}→2C_{2}F_{4}). It was shown that the lowering of the chemical conversion was proportional to the surface‐to‐volume ratio in the test section. A hypothetical cold layer in which no conversion occurred was found to be around 0.2 mm. It was concluded that in a shock tube of ∼ 2‐in. i.d., at an initial pressure of torr the cold boundary layer has very little effect on kinetic parameters obtained in a single‐pulse shock tube. At lower pressures and in smaller diameters shock tubes these effects should be considered when interpreting kinetics results.

ESR and Electronic Relaxation of Cr^{3+} and Fe^{3+} in Water and Water–Glycerol Mixtures
View Description Hide DescriptionESR intensities and linewidths at X band and linewidths at Q band of [Cr(H_{2}O)_{6}]^{3+} and [Fe(H_{2}O)_{6}]^{3+} in water‐glycerol mixtures are reported. At X band the linewidth increases with glycerol concentration and there is a concommitant decrease in the integrated intensity of the ESR line. The linewidth at Q band is independent of the glycerol content of the solvent. The results are interpreted in terms of the general theory of electronic relaxation. It is shown that the dominant electronic relaxation in solutions of Cr^{3+} and Fe^{3+} hydrates is due to modulation of the zero‐field splitting interaction. This interaction and its time dependence result from collisions of the hydrated complex with solvent molecules. Using equations derived for relaxation by rotational tumbling, a correlation time of about 5 × 10^{−12} sec in water is found for both complexes. The decrease in the integrated intensity with increasing viscosity at X band is due to the smearing out of all but the transitions. At Q band the Cr^{3+} resonance is essentially the transition even in the aqueous solution. Linewidths for a number of other Cr^{3+} complexes are reported and discussed.

Exclusion of Disallowed States from State Density and Its Effect on Unimolecular Rate
View Description Hide DescriptionStatistical rate theory requires the knowledge of the density of allowed states of the decomposing molecule. States may be disallowed if they are unbound, or if they are excluded by angular‐momentum conservation requirements. To investigate such exclusion, the generalized method of steepest descents, as recently formulated by the authors [J. Chem. Phys. 51, 3006 (1969)], is used to compute the density and sum of states for a molecular species represented by a system of independent quantum oscillators and independent classical free rotors under the restriction that (1) all oscillators (harmonic or anharmonic) are subject to vibrational cutoff; or (2) one anharmonic oscillator is coupled with a two‐dimensional rotor whose rotational energy is restricted by angular‐momentum conservation, while its vibrational energy is not allowed to exceed its effective dissociation energy, all other oscillators being subject to Restriction (1). The molecular model used is a “small molecule” where the two restrictions produce an easily noticeable effect. It turns out that Restriction (1) has an appreciable effect on the sum of states and on the unimolecular rate constant when the oscillators are assumed to be harmonic, but the sum of states and rate constant calculated for Morse oscillators does not differ from the strictly harmonic (no cutoff) case by more than an order of magnitude at energies below the total dissociation energy. Restriction (2), applied to the weakest oscillator (bond) in the molecule, has an effect on the rate constant that depends on symmetry. If molecule and complex are of the same symmetry (angular momentum strictly conserved), the rotations are “adiabatic” and the unimolecular rate constant increases with increasing rotational quantum number . If molecule and complex are of different symmetries (angular momentum not strictly conserved), the rotations are “inactive” and the unimolecular rate constant decreases at first with and then goes through a minimum, at constant excitation energy in the complex. Experimental data on this point would be most desirable. Such checks as were feasible show the method of calculation to be accurate within better than 10%.

Kinetics of Vaporization of Zinc Single Crystals
View Description Hide DescriptionThe rates of vaporization from (0001) and (101̄0) surfaces of zincsingle crystals have been measured by the torsion–Langmuir method and have been compared to rates of vaporization of zinc from torsion effusion cells. A small concentration of impurities lowers the vaporization coefficient for the (0001) surface to 0.7, but for the (101̄0) surface of the same material and for the (0001) surface of high purity crystals are unity. The concentration of dislocations that were active in causing thermal etching of the (0001) surfaces was of the order of 10^{5}/cm^{3} for the samples tested. These experimental results are not in accord with the prediction of the Hirth and Pound model for metalvaporization that for low index, low defect surfaces.

Magnetic Susceptibility of Molten Sodium–Sodium Chloride Solutions
View Description Hide DescriptionThe magnetic properties of dilute solutions of sodium metal in molten sodium chloride may be described by a free‐electron gas model, whose spin degeneracy conforms to Fermi–Dirac statistics. Measurements are reported for the magnetic susceptibility in the temperature interval, 800–970°C, for solutions containing 0.00813–0.05347 mole fraction sodium. Correction of the observed susceptibility due to sodium and chloride ions leaves a residual paramagnetism which is ascribed to conduction electrons having rest mass and Landau diamagnetism. Exclusion of the cations and anions from the volume accessible to electrons leads to good agreement between the free‐electron theory and experiment.

Radiative Lifetime of the State of K_{2}
View Description Hide DescriptionUsing the phase‐shift method, a radiative lifetime study has been made of the K_{2} molecule excited by the 632.8‐nm line of an He–Ne laser. The radiative lifetime extrapolated to zero pressure is found to be nsec where the error represents three standard deviations of the statistical uncertainty. A simple valence‐bond model for the molecular transition is proposed which predicts that the radiative lifetime of the state of the dialkalis will be shorter, by about a factor of 2 or more, than the lifetime of the parent atomic state into which the excited alkali dimer separates. The results of these calculations are compared with the experimentally observed lifetimes for several vibrational states of Na_{2} and K_{2}.

Three‐Body Correlations in Simple Dense Fluids
View Description Hide DescriptionCorrelations between triples of molecules in simple fluids at thermodynamic equilibrium are studied through their contribution to the isothermal density derivative of the pair probability density. Explicit computations are performed to indicate the role of the triplet function in accounting for the structure of the density derivative of the radial distribution function. The results imply that contributions from triplet correlations are in general quite appreciable. Various consequences of the results are disscussed, and the procedure is examined in general as a method for studying correlations between triples of molecules in simple fluids.

Nonradiative Decay of Individual Vibronic Levels in Large Molecules
View Description Hide DescriptionThe nonradiative decay of particular vibronic levels in large molecules has been investigated by use of a simple model system involving identical surfaces shifted in energy and normal coordinates. A general expression for the nonradiative decay probability of individual vibronic levels is derived in the weak coupling statistical limit and the energy gap law is obtained. Our expression for the nonradiative transition reveals the explicit dependence on the vibrational quantum numbers of the decaying vibronic level, in contrast with previous treatments.

Equation of State of Dense Fluids. VIII. Comparison of the Internal Pressure from the PY Theory and the Lennard‐Jones (6–12) Potential with Experiment
View Description Hide DescriptionThe internal pressures are calculated from the PY theory with the Lennard‐Jones (6–12) potential in a density range from to and from temperatures to . In the region of overlap with the krypton and xenon PVT data, a comparison is made with the experimental internal pressure and suitable scaling constants for this comparison are obtained. A comparison is made with the molecular dynamics calculations of Verlet in a limited range.

EPR and Mössbauer Spectra of Iron (III) N, N‐Dimethyldithiocarbamate
View Description Hide DescriptionThe EPR and Mössbauer spectra have been measured at 4.2°K for samples of iron (III) N, N‐dimethyldithiocarbamate diluted in cobalt (III) N, N‐dimethyldithiocarbamate. values close to 2 and an isotropic hyperfine interaction were observed. The results indicate that the ferric atom occupies a site of almost cubic symmetry. The orbital ground state consists of approximately equal amounts of and holes with slightly less of . The value of the observed magnetic hyperfine field at the nucleus (300 ± 5 kG) is in agreement with that predicted.

Effects of Ring Geometry on Triplet and Singlet Energies of the Metal Mesoporphyrins
View Description Hide DescriptionCorrelations were found between the hole size of 10 metalloporphyrins, determined by x‐ray crystallography, and the ionic radius of the central metal atom, derived from a new compilation of ionic radii as a function of coordination number, spin state, and valence. These correlations were used to define representative porphyrin geometries for each of three different hole sizes. We recommend the use of these geometries for future molecular‐orbital calculations. Molecular orbital calculations based on these porphyrin geometries predict a decrease in the phosphorescence energy as the hole size increases, a prediction in agreement with data in the literature on metal mesoporphyrins. Experimental excitation energy of the singlet Soret (but not the visible) band also decreases with increasing hole size, a result not given by calculations using either four‐orbital or extensive configuration‐interaction models. Electronegativity has a statistically significant effect on the lowest excited singlet and, to a lesser extent, the lowest triplet energy. Changes in hole size produce little change in calculated bond order, indicating that structural changes induced by increased hole size are due to strain induced in sigma bonds. There is no correlation between either singlet or triplet energy and the charge density of the central metal atom as determined by previous molecular‐orbital calculations. Thus, the primary effect of changing metals on the lowest triplet state of metal porphyrins is due to effects on the pi electrons of the geometric distortion of the porphyrin ring imposed by the steric requirements of the central metal atom. The effect of the central metal on the singlet energies remains to be fully explained.