Volume 34, Issue 1, 01 January 1961

Nuclear Hyperfine Interactions in Orbitally Degenerate States of Aromatic Ions
View Description Hide DescriptionThe dynamical Jahn‐Teller effect in the benzene negative ion is investigated by estimating the vibronic eigenfunctions and energies for the lowest energy degenerate and lowest energy nondegenerate vibronic states using Hückel molecular orbital theory and the normal coordinates for the 606 cm^{—1} and 1595 cm^{—1} E _{2g } vibrations of benzene given by Whiffen. It is concluded that the lowest energy vibronic state is doubly degenerate, and that this degeneracy is removed by interactions with a polar solvent when this ion is in solution. The solventinteraction produces a time‐dependent oscillation or switching of the electronic spin distribution relative to the nuclear framework, which in turn leads to an enhanced broadening of the hyperfine structure through a corresponding fluctuation in the isotropic hyperfineinteraction. The calculated linewidths are the same as those reported by Townsend and Weissman if the switching spin distribution is described by a correlation time of the order of 10^{—9} sec. A similar effect is probably responsible for the anomalously broad protonhyperfine structure reported by Weissman and Townsend in the negative ions of coronene and triphenylene. This effect must also contribute to the linewidth of the hyperfine structure of the negative ion of cyclooctatetraene observed by Katz and Strauss. It is suggested that the enhanced spin‐lattice relaxation rate reported by Weissman and Townsend for the negative ion of coronene is due to enhanced spin‐orbit interaction, also associated with a degeneracy of the ground vibronic state.

Spin‐Orbit Coupling in Orbitally Degenerate States of Aromatic Ions
View Description Hide DescriptionIt is shown that in the orbitally degenerate ground state of the benzene negative ion there is a first‐order electron spin‐orbit interaction associated with the electronic orbital motion around the ring. This first‐order interaction may be as large as a few cm^{—1} and can give rise to enhanced electron spin‐lattice relaxation in solution even though most of the time the electronic orbital motion is strongly quenched by electrostatic interaction with the solvent.

Diffusion Coefficients of Helium in Fused Quartz
View Description Hide DescriptionThe diffusion of helium through the walls of high‐purity fused quartz hollow cylinders was studied using a mass spectrometer as a detecting device. By surrounding the outside of the hollow cylinder with helium and observing it diffuse through into the mass spectrometer, permeation rates and diffusion coefficients were measured in the temperature range of 24° to 1034°C. The diffusion process appeared to be relatively simple with only small deviations from Fick's laws occurring. The activation energy was found to be different in the temperature range of 24° to 300°C than in the range of 300° to 1034°C. In the low‐temperature range the diffusion coefficients are expressed byand in the high‐temperature range they are expressed byThe solubility was also determined by dividing the permeability by the diffusion coefficients. This was expressed byin the temperature range of 24° to 300°C and byin the range 300° to 1034°C.

Dependence of Calculated and Experimental Propane Mass Spectra upon Electron Voltage
View Description Hide DescriptionExperimental propanemass spectra have been obtained with bombarding electrons ranging in energy from 14 to 500 v. The quasi‐equilibrium theory has been used in calculating the same spectra. The grossly simplified version of the statistical theory that satisfactorily predicts the 70‐v mass spectrum is inadequate at low voltages, but if half the theoretical number of oscillators are assumed to be effective in the parent‐ion and activation energies that bear no simple relation to experimental appearance potentials are employed, a semiquantitative fit of the experimental data is obtained. The description of the decomposition reaction of a molecule‐ion in terms of a collection of harmonic oscillators is clearly unsatisfactory. However, the more general form of the quasi‐equilibrium theory, in which it is assumed only that the reaction coordinate is separable, does appear to be applicable.

Low‐Temperature Chemisorption. I. Flash Desorption of Nitrogen
View Description Hide DescriptionFlash desorption(desorption by continuous temperature displacement) is applied to a study of the low‐temperature interactions of N_{2} with an initially clean tungstensurface. Molecular nitrogen is found to dissociate into atoms on adsorption even at 115°K, at a rate which diminishes with increasing temperature, but is initially independent of surface concentration. Formation of this atomically bound β nitrogen is hindered at low temperatures (T∼115°K) by competitive growth of an additional state γ, in which nitrogen, at ∼2½ times the concentration in the β state, is bound as molecules with an energy of 9 kcal mole^{—1}, resulting in a total surface concentration of 600×10^{12} molecules cm^{—2}. The population in this γ state depends sensitively upon the arrangement of atoms in the β state. Preadsorption at T∼300°K equalizes the populations in β and γ; annealing at T∼1000°K at impingement rates of 7×10^{15} molecules cm^{—2} min^{—1}, further lowers n _{γ}/n _{β} and brings about rearrangement of the tungstensurface as well, without appreciable change in the adatom concentration. A third state α is formed at temperatures up to 400°K, with a binding energy of ∼20 kcal mole^{—1}. Initially its rate of formation, just as that of γ at low temperatures, is dictated by the concentration of the atomically held β state. At 300°K and above the α concentration passes through a maximum, then diminishes; at low temperatures, it remains constant, achieving a maximum value 1/30 that of the γ state.

Low‐Temperature Chemisorption. II. Flash Desorption of Carbon Monoxide
View Description Hide DescriptionFlash desorption studies of the interaction of carbon monoxide with a tungsten surface indicate that this gas forms at an initial rate considerably higher than that for nitrogen (CO sticking coefficient: s∼0.5; N_{2} sticking coefficient: s∼0.25). This rate also remains independent of the amount adsorbed for higher coverages, up to n∼300×10^{12} molecules cm^{—2}. Unlike nitrogen, CO does not dissociate on the surface. It retains its molecular identity in both the primary chemisorbed state β, and the weaker state of 20 kcal mole^{—1} binding energy α, which forms as the rate of β growth diminishes. At T=298°K, the α state reaches a concentration of ∼200×10^{12} molecules cm^{—2}. No additional weak binding is found even at low temperatures, T∼115°K. The β state is itself made up of three subpeaks, arising from different surface structures, and designated β_{1}, β_{2}, and β_{3} in order of increasing binding energy. Only β_{2} and β_{3} form initially, with desorption energies of 75 and 100 kcal mole^{—1}, respectively; β_{1} appears at higher coverages, at which the desorption energy of β_{2} has also diminished.

Criticality Criteria for Various Configurations of a Self‐Heating Chemical as Functions of Activation Energy and Temperature of Assembly
View Description Hide DescriptionIn 1939 D. A. Frank‐Kamenetsky proposed a criticality criterion that is a dimensionless constant that varies only with configuration of the self‐heating chemical. In his studies of the equation equating power production as a function of temperature by the formula of Arrhenius and the power loss by conduction alone, he made a simplifying assumption. A Pace analog computer and an IBM 704 have been used to study the exact equation and it was found that the value of the F‐K criticality criterion is a slowly varying function of E/RT _{0} in the range from infinity to 30 but becomes a sensitive function for values of E/RT _{0} less than 30.

Reactions of Active Nitrogen with Hydrogen Bromide, Bromine, and Ethylene
View Description Hide DescriptionMeasurement of the specific rate constant for the reactionindicates that k is 3.8×10^{—14} sec^{—1} (molecules/cc)^{—1} at 40°C. Attempts to obtain complete turbulence of reactants at a pressure of 0.85 mm were unsuccessful so that diffusion techniques were employed. The homogeneous flamereaction accompanying the above reaction was too weak to define the reaction zone, so calculations were based on the reaction tube diameter and the critical flow rates of reactants at which the orange flame initiated by a wall reaction involving active nitrogen and bromine was prevented. Spectra of flames obtained from the N+Br_{2} and N+HBr reactions in a stirred‐flow reactor indicate that NBr is the source of the orange flame in the latter reaction. The flow rates of atomic nitrogen were calibrated by chemical titration with ethylene. A conventional diffusionflame technique was used to obtain k=1.6×10^{—13} sec^{—1} (molecules/cc)^{—1} at 40°C for the reaction

Quantum‐Mechanical Cell Model of the Liquid State. II. Application to the Zero‐Point Properties of Close‐Packed Crystals
View Description Hide DescriptionThe quantum‐mechanical cell model previously developed for liquids [J. M. H. Levelt and R. P. Hurst, J. Chem. Phys. 32, 96 (1960)] is adapted and used to evaluate zero‐point properties of the noble gases, H_{2} and D_{2}. Specifically, this theory is applied to determine the heats of sublimation, the zero‐point energies and the equation of state for these gases at 0°K. By using the Lennard‐Jones (6–12) intermolecular potential constants from second virial coefficients measurements as the only experimental parameters included in the theory, good agreement with the experimentally determined zero‐point properties is generally obtained.

Photoconduction Activation Energies in cis‐trans Isomers of β‐Carotene
View Description Hide DescriptionThe activation energies for photoconduction have been measured in all trans and 15–15′ cis β‐carotene powders and in β‐carotene glass consisting of a mixture of isomers. The average values of a number of measurements of each are all trans, 0.37 ev; 15–15′ cis, 0.20 ev; isomerized glass, 0.19 ev. The values predicted by the triplet state theory of photoconduction are 0.35 (or 0.53), 0.18, and 0.18 ev, respectively. The larger activation energy (two or three vibrational quanta) of the all trans is attributed to the thermal energy necessary to allow an intersystem crossing from the first singlet excited state (about 2.6 ev) to the triplet state (about 3.0 ev). The activation energy of the cis‐trans forms of the molecule (1 vibrational quanta) correspond to intersystem crossing from the ``cis peak'' state (about 3.5 ev) to the triplet state. The excitation spectrum of photoconduction in 15–15′ cis β‐carotene and isomerized glass, peaks in the ``cis peak'' region, in agreement with this assignment. These results, that intersystem crossing occurs more readily from the cis peak state than the first singlet excited state, provide an explanation for the shape of the photocurrent excitation spectra in β‐carotene and for the lack of phosphorescence in all trans lycopene as reported by Lewis and Kasha.

Proton Magnetic Resonance Study of Crystalline Potassium Trisoxalatorhodium(III) Hydrate
View Description Hide DescriptionThe broad‐line protonmagnetic resonancespectrum of crystalline potassium trisoxalatorhodium(III) hydrate, K_{3}Rh(C_{2}O_{4})_{3}4½H_{2}O, has been investigated in the temperature range 77°K—330°K. The spectrum at 77°K indicates that some of the protons in the crystal are not present in water of crystallization and an analysis of this same spectrum indicates that the compound should be formulated asThis formula is not inconsistent with the chemical reactions that the compound undergoes, and it explains some properties which are not satisfactorily accounted for by the previously accepted formulaThe absorptionspectrum at 318°K substantiates the analysis of the spectrum at 77°K and it also indicates that the water of crystallization can be grouped into at least three sets, the water molecules in different sets having different degrees of mobility. The protonmagnetic resonance data also indicate that the ``monohydrate,'' K_{3}Rh(C_{2}O_{4})_{3}H_{2}O, is probably .

Method of Alternant Orbitals for Allyl
View Description Hide DescriptionThe π‐electron correlation energy and ground‐state wave function for allyl are calculated by the method of alternant orbitals. This method accounts for 98.8% of the correlation energy given by the configuration interaction treatment. The atomic orbital spin density matrix obtained with this approximation is also included.

Density Expansions of Correlation Functions for Equilibrium Systems
View Description Hide DescriptionA method of deriving density expansions of correlation functions from density expansions of the excess free energy is based on certain thermodynamic relations between derivatives of the grand partition function and derivatives of the excess free energy. The method also depends on using the most general expansion of the interaction energy into components; it is not assumed that this energy is limited to pairwise components. Expansions are obtained for the correlation functions in multicomponent gases and for the correlation functions for solute species in solutions. The method is also applicable to ionic solutions. A mathematical difficulty limits the systems for which these equations are proved to those in which there is a certain flexibility in treating the model.

Molecular Statistics of Vinyl Polymers
View Description Hide DescriptionA formula is proposed to describe the end‐to‐end distance and the total dipole moment of the vinyl polymer (CH_{2}CHX)_{ n }. The interaction of neighboring X's is taken into account. The formula treats the general atactic polymer and includes the isotactic polymer and the syndiotactic polymer as special cases.

On the Luminescence Minimum in Certain Scintillator Solutions
View Description Hide DescriptionSeveral scintillator solutions have been examined for the luminescence minimum previously reported for the case of Co^{60} gamma irradiated cyclohexane+benzene+p‐terphenyl with oxygen present. The minimum is shown to be dependent on the nature of the solvents and of the quencher. A satisfactory interpretation of the data involves the notion of energy transfer from molecules of the less‐efficient (``common'') solvent to the molecules of the more efficient (``better'') solvent and thence to the scintillator. The latter transfer appears to involve more than one molecule of the solvent. A suggested model of the quenching process explains the existence of two classes of quenchers, one of which does not give a minimum.

On the Solution of the Hartree‐Fock Equation in Terms of Localized Orbitals
View Description Hide DescriptionThe Hartree‐Fock method is discussed with emphasis placed on the transformation properties of the Hartree‐Fock equation. It is emphasized that the Hartree‐Fock equation may be solved in terms of non‐orthogonal one‐electron functions, and that in some cases it may be more convenient to choose such solutions. Equations are developed which define the localized one‐electron functions and it is shown how these equations may be solved. For a system of closed shell atoms or ions, it is suggested that the localized orbitals of each atom or ion can be expanded in terms of functions centered on its nucleus. This suggestion is based on the success of the ionic theory of crystals. Due to the symmetry of a crystal, it is suggested that use of the localized orbitals could lead to expressions for the first order, Hartree‐Fock density matrix and the Hartree‐Fock energy of a crystal, i.e., one could obtain the solution of the Hartree‐Fock equation for a crystal.

Electron Spin Resonance and Optical Absorption of K_{3}[Cr(CN)_{5} NO]· H_{2}O
View Description Hide DescriptionElectron spin resonance of a water solution and of the pure powder of K_{3}[Cr(CN)_{5}NO]·H_{2}O reveal a single sharp resonance line at room temperature. The water solution resonance gives a Cr^{53}hyperfine structure which is further split by a ``superhyperfine'' structure due to the nitrogen in the NO ligand. From the electron spin resonance the Cr^{1+} ion appears to be in a spin quenched (dε^{5}) orbital singlet ground state. The optical absorption data allows the determination of the splittings of the d levels in concordance with the ESRspectrum.

Spin‐Spin Interactions in Nuclear Magnetic Resonance. Contact Contribution
View Description Hide DescriptionA method for calculating the contact contribution to spin‐spin interactions between nuclei in nonaromatic molecules is described. The method is based on the valence bondmodel. The equivalent Hamiltonian of the Dirac vector model is used for a perturbation calculation in a representation where the total spin of the two electrons in each bond in the molecule is a good quantum number. The Ramsey‐Purcell contact term in the interaction is calculated by a double perturbation method where only terms linear in the electron‐nuclear interactions are considered but the perturbation is carried to higher order in the exchange integrals. In this way the interaction constants can be obtained explicitly in terms of the exchange integrals, and the calculation of the valence bondwave functions is avoided. It is then possible to see how the signs and magnitudes of the interaction constants depend on these integrals and what the dominant interaction mechanisms are. The perturbation series is evaluated explicitly with the electron nuclear contact interaction and the results are compared with the results of a similar calculation based on Ramsey's closure formula. In this way the objections against the closure procedure can be avoided. It is shown that Ramsey's formula can be used when different average energy separations are used for terms of different order in the expansion. The results of Ramsey for H_{2} and of Karplus et al. for hydrogen atoms separated by two and three bonds and the justification of the method of calculation used by them are discussed in detail. It is found that only perturbation terms of one type are important in each of the cases discussed by these authors and therefore their procedure can be justified. The results previously obtained by the author for spin‐spin interactions in the allyl group are also discussed.

Moment Analysis of Magnetic Resonance Signals
View Description Hide DescriptionA relation is given between the moments of a generalized convolution transform of a function, and the moments of the function itself. This relation is applied to the signal obtained with a field‐modulated EPR spectrometer, a consequence being that the integrated intensity of an absorption line may be obtained from first moment measurements at any modulation amplitude, regardless of line shape or various instrumental nonidealities. This result has been verified experimentally to within a few percent with a Varian EPR spectrometer. Extension to measurement of higher moments is discussed.

Free‐Volume Model of the Amorphous Phase: Glass Transition
View Description Hide DescriptionFree volume v_{f} is defined as that part of the thermal expansion, or excess volume Δv̄ which can be redistributed without energy change. Assuming a Lennard‐Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv̄ considerable energy is required to redistribute the excess volume; however, at Δv̄ considerably greater than some value δv̄_{g} (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass‐forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.