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Volume 48, Issue 6, 15 March 1968
48(1968); http://dx.doi.org/10.1063/1.1669456View Description Hide Description
Dynamic polarization experiments have been carried out in dilute solutions of sodium in liquid ammonia (mole ratio ) at room temperature in a magnetic field of 3.3 kG. A positive Overhauser enhancement corresponding to a leakage factor of 0.5 was measured for 14N, showing an important relaxation process due to the hyperfine interaction with electrons. The paramegnetic shift of 14N was measured in a direct way, and the results are in agreement with those of other authors. Overhauser shift measurements were performed for 14N and H; an experimental proof of a negative spin density at the proton was thus obtained.
48(1968); http://dx.doi.org/10.1063/1.1669457View Description Hide Description
The structure of liquidcarbon tetrachloride has been studied by neutron diffraction. The theoretical basis of neutron diffraction from multiatomic liquids is discussed in terms of polyatomic and molecular assemblages. The data is analyzed using these models. The parameters obtained in this study agree with those obtained from x‐ray and electron diffraction.
48(1968); http://dx.doi.org/10.1063/1.1669458View Description Hide Description
The transfer of electronic excitation energy between naphthalene, acting as donor, and anthranilic acid, acting as acceptor, in a variety of alcohols, was investigated. The efficiency of energy transfer in all of the solvents used was different from the value to be expected according to the theory of Förster. The transfer efficiency was considerably higher in alcohols of low viscosity than in alcohols of high viscosity. This was attributed to the variation of intermolecular distance between donor and acceptor, as a result of Brownian motion, during the lifetime of the excited donor. Fair agreement was found between the experimental data and the values calculated according to theoretical treatments of nonradiative energy transfer in which diffusion has been taken into consideration.
Theoretical Analysis of the Role of Diffusion in Chemical Reactions, Fluorescence Quenching, and Nonradiative Energy Transfer48(1968); http://dx.doi.org/10.1063/1.1669460View Description Hide Description
The kinetics of diffusion‐controlled chemical reactions in solution are analyzed by a statistical treatment. To start with, the probability of interaction of two molecules A and B, separated by a given distance at zero time and undergoing Brownian motion subsequently, is determined. The probability of interaction of an A molecule with one of many surrounding B molecules is then deduced. Finally, the course of reaction between A and B molecules distributed at random at zero time in a system containing a large number of molecules of both species, is calculated. The treatment outlined is readily extended to systems in which factors other than random diffusion are operative, as well as to systems in which the distribution of A and B molecules is not random at zero time. A few examples are discussed in detail. The theoretical treatment presented is applied to the kinetics of quenching of electronically excited molecules by collision with quencher molecules in solution, and to the calculation of the extent of nonradiative transfer of electronic excitation energy between molecules which are free to undergo Brownian motion.
48(1968); http://dx.doi.org/10.1063/1.1669461View Description Hide Description
The effect of the complete restriction of rotatory Brownian motion of donor and acceptor molecules on the extent of nonradiative energy transfer in systems containing many donors and acceptors has been investigated. It is assumed that the molecules under discussion are randomly distributed and randomly oriented in space at the moment of excitation. The number of donor molecules which retain their excitation energy at time after excitation is found to decrease exponentially with the sum of two terms: one proportional to and the other proportional to . This time dependence is similar in form to that found by Förster for systems in which donor and acceptor molecules undergo rapid rotatory diffusion. While the coefficient of in the exponent is the same in both cases, the coefficient of is smaller for systems in which molecular rotation is frozen than for systems in which rotatory Brownian motion is rapid.
48(1968); http://dx.doi.org/10.1063/1.1669462View Description Hide Description
The thermal conductivities of ammonia, methylamine and binary mixtures of these polar gases have been measured in the temperature range 66° − 258°C, using a “potential‐leads” hot‐wire apparatus. For the pure gases, the Mason‐Monchick theory is found to give reasonably good agreement with experiment when the average rotational collision number in the temperature range is treated as a disposable parameter. For the mixtures, good agreement is obtained between the experimental data and the values calculated from the Hirshfelder‐Eucken formula, provided that the pure component heat conductivities are replaced by the corresponding experimental values.
48(1968); http://dx.doi.org/10.1063/1.1669463View Description Hide Description
The kinetics of ozone formation have been studied in the pulse radiolysis and flash photolysis of gaseous oxygen by measuring the change in optical absorption following the pulse. The absorptionspectrum of the ozone present immediately after the pulse is considerably broader and the peak is at longer wavelength (∼2860 Å) than that of ground stateozone (∼2560 Å). The initial absorption is attributed to ozone in the upper vibrational levels produced by O + O2⇋O3 ‡. It is clearly shown that the over‐all third‐order reaction O + O2+M→O3 + M occurs by a sequence of steps. The relaxation time for de‐excitation from the upper vibrational levels to the ground state is ≥6 × 10−6 sec in O2 at 740 torr and 24°C. De‐excitation requires at least 4.5 × 104 collisions, and assuming 20 vibrational levels, the average efficiency is about one quantum in 2200 collisions. The third‐order rate constant based on O atom disappearance is several times larger than that based on formation of O3 in the ground vibrational state. Neither rate constant can be evaluated accurately by optical absorptionmeasurements.Measurements at 2800 Å, where all vibrational levels appear to have about the same extinction coefficient, gave a value 2.2 × 108 M −2 sec−1. This value should approximate for which Kaufman and Kelso determined 2.4 × 108 M −2 sec−1 by direct measurement of O atom disappearance. Measurements at wavelengths below 2480 Å gave an upper limit for of 1 × 108 M −2 sec −1.
Field‐Electron‐Microscopy Studies of Cesium Layers on Various Refractory Metals: Work Function Change48(1968); http://dx.doi.org/10.1063/1.1669464View Description Hide Description
The variation of work function with Cs coverage is investigated for W, Mo, Re, and Ni substrates. Single‐crystal‐face studies of the relationship performed on the (100) and (110) planes of W show a greater affinity of the (110) plane for mobilely adsorbed Cs at low values of . Coverage anisotropies are reduced as . An empirical relationship between the maximum work function change and substrate work function, and adsorbateionization potential, of the form , is established. The constants and are independent of the substrate and adsorbate for periodic Group Ia and IIa. Measurement of the temperature variation of the work function for Cs‐coated Mo and W substrates show a negative temperature coefficient of ∼ − 1 × 10−4 eV/deg in the temperature interval 77° − 270°K. The average values of the adsorbatepolarizabilitymeasured for the (110) and (100) planes of W are 23 ± 2 and 13 ± 0.2 Å3, respectively. The presence of oxygen coadsorbed with Cs on W greatly alters the emission distribution and reduces the minimum work function from 1.52 to 1.10 eV; also, the Cs coverage at which occurs is decreased from 1.9 to 0.9 × 1014 atoms/cm2.
48(1968); http://dx.doi.org/10.1063/1.1669465View Description Hide Description
The EPR spectra have been obtained for Mn2+ fourfold coordinated in Cs2ZnCl4, K2ZnCl4, K2HgCl4, K2ZnBr4, and K2ZnI4; sixfold coordinated in NaCl, and KCl; and eightfold coordinated in CsCl. Large distortions from cubic symmetry were observed in CsCl. Variations in the manganese nuclear hyperfine splitting are discussed in terms of the nature of the ligand, changes in the manganese–ligand separation, and changes in the manganese coordination number. The effects of the changes in the coordination number have not been determined previously because concomitant changes in the internuclear distance usually have an opposite, and frequently larger, effect.
48(1968); http://dx.doi.org/10.1063/1.1669466View Description Hide Description
The nature of the atomic arrangement in the phase of AgI existing at pressures between 3 and 4 kbar has been deduced from x‐ray diffraction studies with a diamond‐anvil apparatus. The unit cell is either tetragonal or pseudotetragonal and contains a total of 4 atoms at with . The calculated density is 6.19 g/cm3. While it is not possible to determine directly the site preferences of Ag and I, certain distributions are suggested by a simple displacive mechanism of producing the 3‐kbar phase from the zincblende structure existing at room temperature and 1 atm pressure. The relationship of the new structure to that of the rock‐salt structure existing between 4 and 100 kbar is also discussed.
48(1968); http://dx.doi.org/10.1063/1.1669467View Description Hide Description
The electron gasmodel for the lattice dynamics of cubic metals propounded by one of us earlier has been used to test Lindemann's melting criterion by calculating the ratio of the mean‐square amplitude of thermal vibrations to the square of the interatomic spacing at the melting point for a number of cubic metals belonging to different groups of the periodic table. The calculated has roughly the same value for elements belonging to one particular group, but the spread in values is quite large from one group to another. It is concluded that Lindemann's hypothesis of constant for all solids is inadequate.
ESR Study of Intramolecular Spin Exchange Effects on the Hyperfine Interaction in 2,2′‐Dinitrobiphenyl Ether and Sulfide Radical Anions48(1968); http://dx.doi.org/10.1063/1.1669468View Description Hide Description
Studies have been made on the intramolecular spin exchange effects in the ESR spectra of the radical anions of 2,2′‐dinitrobiphenyl ether and sulfide obtained by alkali‐metal reduction in tetrahydrofuran (THF) solution which was later diluted with dimethylformamide (DMF) to eliminate metal coupling effects. The spectra obtained show evidence for rapid spin exchange in the sulfide case whereas the exchange frequency in the ether case is of the order of the hyperfine splittings.
48(1968); http://dx.doi.org/10.1063/1.1669469View Description Hide Description
High‐temperature gaseous equilibria in the Mg–Cu–F system were studied by mass spectrometry and the results were used to derive the dissociation energy of CuF. For the reaction MgF(g) + Cu(g) = Mg(g) + CuF(g), , leading to . This result differs from those obtained on many other mono‐ and difluoride combinations in that . It can be shown, however, that this reversal of bond strengths in the Cu–F system is consistent with the valence‐state concept of bonding.
48(1968); http://dx.doi.org/10.1063/1.1669470View Description Hide Description
A gas‐phase electron‐diffraction investigation of xenon hexafluoride has been carried out in an effort to obtain structural information which might shed light on the curious properties of the compound. Elaborate precautions were taken to prevent decomposition or contamination of the sample (99.8 mole % pure). Several innovations were introduced into the structure analysis to minimize difficulties encountered in conventional analyses of molecules containing both heavy and light atoms. Two different sets of analyses (I and II) employing two different levels of approximation in electron scatteringtheory were conducted to test the adequacy of the expressions usually adopted. Analysis I was based on Hartree–Fock x‐ray elasticscattering factors, Heisenberg–Bewilogua inelastic scattering factors, and (modified) Born phase‐shift corrections for Thomas–Fermi atomic fields. Improvements in Analysis II included the new electron elasticscattering factors and Born phase‐shift corrections calculated by the partial wave method by Cox and Bonham, and Hartree–Fock inelastic scattering factors. The Hartree–Fock phase‐shift correction was not in complete agreement with experiment but was markedly better than the Thomas–Fermi correction. The effect of ionic character on phase shift was investigated theoretically and shown to be significant. A mean Xe–F bond length of 1.890 ± 0.005 Å was found, but the radial distribution function for Xe–F bonds corresponded to that of a composite for nonequivalent bonds. Amplitudes of bending oscillations are notably large. The diffraction data are not compatible with a regular octahedral XeF6 molecule vibrating in independent normal modes. A more detailed exposition of alternative structures and internal motion is presented in Paper II.
48(1968); http://dx.doi.org/10.1063/1.1669471View Description Hide Description
The distribution of internuclear distances in gaseous XeF6 exhibits unusually diffuse XeF6 bonded and F–F geminal nonbonded peaks, the latter of which is severely skewed. The distribution proves the molecule cannot be a regular octahedron vibrating in independent normal modes. The instantaneous molecular configurations encountered by the incident electrons are predominantly in the broad vicinity of structures conveniently described as distorted octahedra in which the xenon lone pair avoids the bonding pairs. In these distorted structures the XeF bond lengths are distributed over a range of approximately 0.08 Å with the longer bonds tending to be those adjacent to the avoided region of the coordination sphere. Fluorines suffer angular displacements from octahedral sites which range up to 5° or 10° in the vicinity of the avoided region.
Alternative interpretations of the diffraction data are developed in detail, ranging from models of statically deformed molecules to those of dynamically inverting molecules. In all cases it is necessary to assume that bending amplitudes are enormous and correlated in a certain way with substantial deformations. Notwith‐standing the small fraction of time that XeF. spends near symmetry, it is possible to construct a molecular potential‐energy function more or less compatiable with the diffraction data in which the minimum energy occurs at symmerty. The most notable feature of this model is the almost vanishing restoring force for small bending distortions. Indeed, the mean curvature of the potential surface for this model corresponds to a force constant of 10−2 mdyn/Å or less. Various rapidly inverting non‐ structures embodying particular combinations of and deformations from symmetry give slightly better radial distribution functions, however. In the region of molecular configuration where the gas molecules spend most of their time, the form of the potential‐energy function required to represent the data does not distinguish between a Jahn–Teller first‐order term or a cubic term as the agent responsible for introducing the deformation. The Jahn–Teller term is consistent with Goodman's interpretation of the molecule. On the other hand, the cubic term is found to be exactly analogous to that for other molecules with stereochemically active lone pairs (e.g., SF4, ClF3). Therefore, the question as to why the XeF6 molecule is distorted remains open. The reported absence of any observable gas‐phase paramagnetism weighs against the Jahn–Teller interpretation.
The qualitative success but quantitative failure of the valence‐shell–electron‐pair‐repulsion theory is discussed and the relevance of the “pseudo‐Jahn–Teller” formalism of Longuet‐Higgins et al. is pointed out. Brief comparisons are made with isoelectronic ions.
Theory of Excitons in Liquids. IV. A Simplified Treatment of the Shift and Damping of Polarization Waves48(1968); http://dx.doi.org/10.1063/1.1669472View Description Hide Description
A simplified theory of the scattering of polarization waves in a liquid arising from the thermal motion of the atoms is presented. The treatment departs somewhat from the general lines of the formal excitontheory in disordered systems set up in the previous papers of this series. Most important, some additional approximations designed to simplify the analysis are introduced. The frequency‐dependent lifetime of the transitions is calculated using second‐order perturbation theory. From this, an expression is deduced for the damping coefficient of excitation waves, both in the case of an impurity atom in a host liquid and in the case of a pure liquid. In both calculations, the thermal motion of the atoms is represented as a small step diffusion or by using a linear‐trajectory approximation. A rough numerical estimation of the level broadening produces the expected orders of magnitude for the lifetimes of states in Ar. Finally, an alternative approach to the exciton problems is discussed in much the same spirit as the Zwanzig treatment of elementary excitations in classical liquids. In the absence of scattering, we demonstrate that this approach leads to the correct form of the exciton dispersion relation.
Dependence of the Time‐Correlation Functions of Molecular Random Motions on the Intermolecular Potential48(1968); http://dx.doi.org/10.1063/1.1669473View Description Hide Description
A general theory on the time‐correlation function and the spectral density for the random motion in molecular system is presented. We study the dependence of these functions on the intermolecular potential and on the rate of fluctuation of the potential. It is shown that the fluctuatingintermolecular interactions or potentials not only introduce the randomness to molecular motion but also characterize important details of the randomness. Here we assume that the fluctuation can be regarded as a Gaussian random process contributed from the perturbers around the molecule. Therefore, the theory may be applied to the molecular motions in the liquid state. As an example of application of the present theory we discuss the collapse of multiplet structure in magnetic resonancespectrum of two‐spin system; Anderson's results for the exchange narrowing of spectrum is derived as a special case of our formulation. The correlation functions and the spectral densities for the random reorientation of diatomic molecules are studied quantum mechanically as second example of application. Graphical presentations are given for the dependence of these functions on the intermolecular potential. The shape of vibrational spectra of molecules can be thus analyzed quantitatively by using the present theory.
48(1968); http://dx.doi.org/10.1063/1.1669475View Description Hide Description
The high‐resolution phosphorescencespectrum of pyrazine crystals has been recorded and analyzed. The fact that the crystal structure of pyrazine crystal is known and that the ground‐state molecular and lattice vibrations are assigned, made it possible to accurately analyze and assign the observed spectrum. The comparison of the observed spectrum obtained from pyrazine crystals with that obtained from pyrazine in cyclohexane matrix at 4.2°K leaves no doubt that the observed emission from the crystals results from the transition of the pyrazine molecule. The 0,0,0 band in emission is found to be 102 cm−1 lower in energy than the 0,0,0 band in absorption. This might suggest that the emission centers have slightly different environment and thus lower energy than those absorbing the radiation. This difference in environment also leads to the trapping of triplet excitons by pyrazine molecules located at physical defects. The different types of trapping mechanisms are briefly discussed in the light of the observed spectrum. There is a strong coupling between the electronic motion and the lattice modes of symmetry (the most prominent ones have frequencies of 57 and 82 cm−1). The intensity of the emission of the phononic and phonon‐vibronic bands is greater than that of the vibronic bands. This observation suggests that either the lattice parameters are different in the excited triplet state from those in the ground state or else there is a lattice‐induced emission resulting from the coupling of the different molecular electronic states of pyrazine with lattice vibrations. These two mechanisms of phonon enhancement of the emission are discussed in terms of the site symmetry of the emitting pyrazine molecules at the trapping sites. Spectral evidence is given showing the coupling between the intramolecular C–H in‐plane bending vibrations and the lattice modes. The lattice modes are found to have lower frequencies when coupled to the C–H in‐plane bending vibration than when it is coupled to the other vibrations. This observed phonon‐vibronic coupling as well as the phonon‐electronic coupling is consistent with the form of the force field proposed for the pyrazine crystal which consists of one term representing an intermolecular hydrogen bonding (C–H···:N) and two intermolecular hydrogen‐hydrogen repulsion terms. A change in the distribution of the hydrogen atoms (as produced by C–H vibrations) or the lone‐pair electron density (as produced in transition) can give rise to observed effects on lattice parameters and vice versa.
48(1968); http://dx.doi.org/10.1063/1.1669476View Description Hide Description
Variational methods based upon a multiconfiguration representation of the lithium eigenfunction are used to calculate a model dipole spectrum of lithium. From the model spectrum, values are obtained of the refractive index of lithium at wavelengths longer than 6600 Å, the mean excitation energy controlling the absorption of fast particles, and the van der Waals interactions of lithium with various gases.
48(1968); http://dx.doi.org/10.1063/1.1669477View Description Hide Description
The radiative lifetimes of seventeen excited states in H2, N2, N2 +, CO, CO+, NO, NO+, BF, CF, BCl, and CO2 + have been measured by the phase‐shift technique of Lawrence. The measured lifetimes were derived from transitions in the 960‐4500‐Å region and range from 0.6 nsec in H2 to 118 nsec in CO2 +. Particular attention has been paid to the understanding and elimination of possible sources of systematic errors in the absolute phase shift measurements. The lifetimes have been combined with measured and calculated emission intensities to derive electric dipole transition moments and absorption oscillator strengths for the diatomic band systems.