Volume 54, Issue 8, 15 April 1971

Classical Trajectory Calculations of the Scattering of TlF on Ar in Thermal Beams
View Description Hide DescriptionWith the method of classical mechanics a statistical number of trajectories is calculated for thermal collisions of TlF on Ar. Two potential models developed in a previous paper have been used. Because of the absence of out‐of‐plane scattering the calculations are restricted to two‐dimensional collisions. Total and differential cross sections are evaluated for initial rotational states and in the range of relative velocities between 150 m/sec and 800 m/sec. Because of the high frequency of inelastic collisions and the important part played by orbiting collisions measurements of the cross sections are incompatible with the determination of potential parameters in the manner customary for atomic scattering. The effects of the various dynamical processes which dominate in the collisions can be followed in differential measurements. Two types of orbiting can be distinguished, one with weak and one with strong coupling between rotational and orbital angular momenta. In both types the attraction by permanent induction forces prevails, because the asymmetric potential favors an approach of argon from the fluorine side of the molecule.

Electrochemical Potential as the Sum of Chemical and Electrical Potentials with a Generalization to a Wider Class of Perturbations
View Description Hide DescriptionIt is shown that the local relation relating the Fermi level, the chemical potential, and an electrostatic potential , does not predict the correct dependence of the electron density, , upon position, , for every choice of . As a consequence, the electrochemical potential, , in the form cannot be used in formulating the equilibrium conditions of the system for every choice of . The restrictions upon are found to be identical with those of the “band‐bending” approximation of semiconductor physics. The simplicity of the above form of can be extended to more general potentials by using instead the form where is that shift in energy of the unperturbed density of states which would give rise to the electron density actually produced in the presence of .

Far‐Infrared Spectra and Zeeman Effect of Rare‐Earth Double Nitrates
View Description Hide DescriptionThe far‐infrared spectra of several rare‐earth double nitrates have been observed over the range 30–170 cm^{−1}. The frequencies of the low lying phonon modes have been determined by comparison of the spectra of the diamagnetic and paramagnetic salts. The absorptions due to the crystal field split ground states of the rare‐earth ions have been positively identified by observations of the Zeeman effect. The experimental energies and values have been compared with the predictions of earlier crystal field calculations based on approximate symmetries. Some of these are in reasonable agreement with the experimental results, but none of them provides a consistent description of the ground state levels for all the ions studied.

Energetics of HeH^{+} Formed in H_{2} ^{+}–He Collisions
View Description Hide DescriptionKinetic‐energy distributions of forward‐scattered HeH^{+} ions resulting from H_{2} ^{+}–He collisions have been experimentally determined for H_{2} ^{+} laboratory kinetic energies in the range 1.7–12.5 eV. These distributions have two main peaks over most of this primary ion energy range. The lower‐energy peak which appears to correspond to completely inelastic collisions is believed to result from enhanced collection efficiency, a conclusion which is supported by energetic considerations. The behavior of the higher‐energy peak, which corresponds to ions formed in the forward direction (center of mass), is consistent with theoretical calculations for the HeH^{+} species.

Group Theoretical Analysis of Vibronic Interactions in Molecules
View Description Hide DescriptionThe canonical transformation methods previously developed for the solution of problems involving dynamical vibronic interactions in molecules are examined by means of group theory. It is found that and the quantum mechanical group (the group generated by the position and momentum operators) afford physical insight into the reasons for the success of the transformation methods. In each method, the Hamiltonian is closely related to and can be written in terms of the elements of the groups. In these methods we use the fact that the basis functions of the representations of the quantum mechanical group are the harmonic oscillator functions, the natural functions for the problem. Products of representation matrices are in fact the matrix elements of the Hamiltonian. We also make use of the fact that the representation matrices are themselves the wavefunctions of the two‐dimensional isotropic harmonic oscillator. In addition to the physical insight, the group theoretic methods simplify the calculations.

Exciton Self‐Trapping in Rare‐Gas Crystals
View Description Hide DescriptionThe problem of exciton self‐trapping in rare‐gas solids is investigated from a dynamical point of view. Experimental ultraviolet emission spectra from rare‐gas solids and liquids have been interpreted as arising from the radiative decay of an excited‐state dimer which becomes localized in the substance. This embedded dimer can arise from electron capture by a self‐trapped hole (R_{2} ^{+}), or by the dynamical trapping of an exciton into an excimer state (R_{2}*). A study of the vibrational relaxation of a molecule embedded in a solid leads to a fast trapping process in which an exciton becomes localized for all the heavy rare‐gas substances. This localization is achieved within 6 × 10^{−12} sec by means of a resonant transfer relaxation process in which two neighboring atoms lose sufficient energy (∼ 0.5 eV) to become stabilized in a lower vibrational state of the excimer.

Herzberg–Teller Vibronic Coupling and the Duschinsky Effect
View Description Hide DescriptionThe assumption that the difference in composition, in terms of symmetry coordinates, between the normal vibrational motions of the ground and first excited state (Duschinsky effect) can be neglected in the Herzberg–Teller theory of absorption and fluorescence vibronic intensities is critically examined. A theory of the Duschinsky effect is described which involves expansion of the potential energy of the fluorescent state in terms of the ground state normal coordinate displacements. Off‐diagonal quadratic contributions arise in the expansion whenever there is a coupling between the crude Born–Oppenheimer electronic wavefunctions of the fluorescent and other excited states through two or more ground state normal motions of the same symmetry. The importance of the Duschinsky effect depends on the magnitudes of the Herzberg–Teller vibronic matrix elements and the frequency differences between the fundamentals which effect vibronic perturbations. Inclusion of the Duschinsky effect in the Herzberg–Teller theory for two or more nontotally symmetric perturbing vibrations introduces a constructive–destructive interference problem, involving the “forbidden” transition moments similar to the one that arises in the theory of Craig and Small on totally symmetric vibrational perturbations. The interferences can lead to a breakdown in mirror symmetry between the absorption and fluorescence spectra. The theory presented for a two vibrational model enables the relative signs of the two forbidden moments to be determined by comparison of the relative intensities of the two vibronic bands in absorption and fluorescence. In the case of naphthalene the forbidden moments associated with the 509 and 938 cm^{−1} modes are shown to be antiparallel. Calculations for phenanthrene suggest that, although the Duschinsky effect should be included in any attempt at accurate vibronic intensity calculations, the constructive–destructive interference effects described by Craig and Small are primarily responsible for the gross deviations from mirror symmetry experimentally observed. Illustrative calculations show that the Duschinsky effect should not be neglected in the Herzberg–Teller theory of both fluorescence and absorption vibronic intensities.

Reverse Electrodialysis in Charged Capillary Membranes
View Description Hide DescriptionA detailed study of the transport properties of charged capillary membranes in the reverse electro‐dialysis mode of operation is presented. The compromising assumptions of linearized Poisson–Boltzmann equation, large radius to Debye length ratio, and small concentration difference made by some investigators are relaxed. For various tube sizes, wall charge densities, and solutes, results are presented for the operating characteristics of the membrane as functions of transmembrane concentration ratio.

Correlation Effect in the Rotation Barrier of Ethane
View Description Hide DescriptionAn ab initio calculation of the barrier to internal rotation in ethane using a minimum basis of Slater‐type atomic orbitals is reported. Electron correlation is partly taken into account by a second‐order perturbation method. It decreases the barrier by 0.13 kcal/mol with respect to the SCF value of Pitzer or 0.17 kcal/mol with respect to another set of bond orbitals. These small lowerings are discussed in terms of localized orbitals.

Dielectric Relaxation of Dihalobenzenes. III. Pure Liquids
View Description Hide DescriptionThe real and imaginary components of the complex relative dielectricpermittivity have been measured at 100 kHz and at several microwave frequencies for pure liquidortho‐ and meta‐dihalobenzenes at several temperatures in the range 0–80°C. The data for the difluorobenzenes, for the dichlorobenzenes and for the dibromobenzenes essentially obey the simple Debye theory while the data for the diiodobenzenes lead to the Cole–Cole arc plots. The derived values of the macroscopic relaxation times decrease as the temperature increases in all cases and the value for the ortho isomer is always greater than that for the meta isomer at the same temperature except for diiodobenzene. In addition, the relaxation times increase as the mass of the halogen substituent increases. However, the microscopic relaxation times calculated from the dielectric data are not consistent with the corresponding values calculated from the molecular volumes, temperatures, and viscosities. In all cases, the extrapolated value is significantly greater than the square of the index of refraction and the difference is approximately proportional to the square of the electric dipole moment. Use of the Onsager relation allows the calculation of the dipole moment from either or . The calculated values increase as the temperature increases but the ratio of the value calculated from to that calculated from varies inappreciably with temperature. Also the ratio of the dipole moment for the meta isomer to that for the corresponding ortho isomer is almost independent of temperature.

Temperature Dependence of the ESR Spectrum of CO_{2} ^{−}CF_{2}CFCO_{2} ^{−} in Irradiated Sodium Perfluorosuccinate
View Description Hide DescriptionIrradiated single crystals of sodium perfluorosuccinate show ESR spectra at 300°K characteristic of a single CO_{2} ^{−}CF_{2}CFCO_{2} ^{−} radical, but on cooling below 130°K the spectra show that motion has been frozen out and that the radicals occupy two crystallographically nonequivalent positions. The hyperfineinteractiontensors for one α‐ and two β‐fluorine atoms of each radical have been determined at 77°K and compared with those of the 300°K radical. The average of the hyperfinetensors for the two radicals at 77°K is shown to be close to the observed tensor for the single radical at 300°K. Motional averaging by oscillation about the central C–C bond is indicated. Crystals of sodium perfluorosuccinate irradiated and observed at 77°K without warming up show the presence of a single radical with a somewhat different orientation in the crystal lattice than the room temperature radical or either of the radicals obtained on cooling the room temperature radical to 77°K.

Mixtures of Hard Spheres with Nonadditive Diameters: Some Exact Results and Solution of PY Equation
View Description Hide DescriptionWe investigate the properties of binary mixtures of hard‐sphere fluids with nonadditive diameters: calling the distance of closest approach between particles of species and we assume with . We find the exact correlation functions as well as the solution of the Percus–Yevick integral equation for this system with , in one dimension. For the three‐dimensional case the Percus–Yevick equation is solved partially.

Primary Processes in the Photolysis of Nitrous Oxide
View Description Hide DescriptionFrom measurements of the isotopic composition of the product nitrogen arising from the photolysis at 2288, 2139, and 1849 Å of gaseous N_{2}O containing ∼ 1% ^{15}NO, it is shown that at all three wavelengths the primary production of N atoms is unimportant, representing less than 1% of the primary production of molecular N_{2}. Taken in conjunction with other observations made in this laboratory these results indicate that at 2139 Å, and perhaps at all wavelengths in the region 1800–2300 Å, the decomposition to is the sole primary photolytic step of importance in the photolysis of N_{2}O.

Energy Distribution in Field Emission from Krypton Covered Tungsten
View Description Hide DescriptionWork functions and energy distributions as functions of relative coverage have been obtained for Kr adsorbed on the (110), (100), (111), and (112) planes of a tungstenfield emitter, from zero coverage to several monolayers.Work function results agree with previous measurements where overlap exists. The data could be fitted by the Topping equation for depolarization, yielding polarizabilities in reasonable agreement with the atomic value if HCP monolayer densities were used, on all but the (110) plane where a higher value resulted. Energy distribution in the submonolayer range show no deviations from free‐electron‐like behavior, except possibly on the (110) plane where a strong antiresonance seems to occur. On the (100) surface the Swanson anomaly found in the distribution from the clean surface decreases monotonically with Kr coverage, indicating that it is probably due to surface states.Work function values in the multilayer range can be interpreted to mean that the conduction band of Kr lies ∼ 1.4 eV below the vacuum. Energy distributions for multilayers deviate from free‐electron‐like behavior; both electric and inelastic scattering processes could explain this result.

Quenching of Naphthalene Luminescence by Oxygen and Nitric Oxide
View Description Hide DescriptionThe quenching of naphthalene‐h _{8} and naphthalene‐d _{8}luminescence by O_{2} and NO in the absence of molecular diffusion is investigated. By measurement of the dependence of fluorescence and phosphorescence yields and lifetimes on quencher concentration, it is possible to separate the effects of singlet and triplet electronic state quenching and to determine the critical quenching radii . No static quenching of naphthalene fluorescence is observed for O_{2} concentrations of up to 0.25M. Thus, the corresponding value in the Perrin formula is less than or equal to 7.1 Å. Conversely, the concentration dependence of naphthalene‐h _{8} and naphthalene‐d _{8} triplet state quenching by O_{2} is in excellent agreement with the Perrin formula, and the corresponding values are 9.9 ± 0.3 and 9.8 ± 0.3 Å, respectively. Contrary to the Perrin model, but in agreement with the theory for quenching by an exchange interaction, the quenching process is competitive with the normal decay rate, and the phosphorescence decay curves become nonexponential with increasing O_{2} concentration. The rate constant for naphthalene triplet‐state quenching by O_{2} decreases upon the deuteration of naphthalene. This suggests that enhanced intersystem crossing, and not energy transfer, is the dominant triplet‐state quenching mechanism, at least for naphthalene‐O_{2} separations ≈ 10 Å. The concentration dependence of naphthalene‐h _{8} and naphthalene‐d _{8}fluorescence quenching by NO is in excellent agreement with the Perrin formula, and the corresponding values are 12.3 ± 0.3 Å and 13.0 ± 0.3 Å, respectively. Fluorescence quenching by NO (80% decrease at 0.3M NO) has no effect on the fluorescence lifetime of naphthalene, which indicates that quenching occurs in less than 5 nsec. Possible causes for the greater efficiency of fluorescence quenching by NO than by O_{2} are discussed. The value of for naphthalene triplet‐state static quenching by NO cannot be determined with certainty because of the possibility that the excited singlet state is quenched directly to the ground state. But the value of for naphthalene triplet‐state quenching must be less than or equal to that for fluorescent singlet‐state quenching.

Fourier Transform Study of NMR Spin–Lattice Relaxation by “Progressive Saturation”
View Description Hide DescriptionWhen a nuclear spin system is subjected to a repetitive sequence of strong radiofrequency pulses, a steady state is established where there is a dynamic balance between the effect of the pulses and spin relaxation. Under certain readily satisfied pulse conditions, the deviation of the intensity of the free induction signal from its thermal equilibrium value is an exponential function of the pulse interval with time constant equal to the spin–lattice relaxation time. The determination is unaffected by spin–spin relaxation provided that the interval between pulses is long enough to permit all transverse components of magnetization to be eliminated, and provided precautions are taken to inhibit spin‐echo formation. Through Fourier transformation of the transient response, high resolution spectra with many component resonances may be studied, and the spin–lattice relaxation times of the individual lines determined. The technique lends itself particularly well to repeated accumulation of the transient signal for the purpose of improving sensitivity. It has been applied to the problem of determining the spin–lattice relaxation rates of the eight different carbon‐13 resonances in 3,5‐dimethylcyclohex‐2‐ene‐1‐one. The results span a range from 2.6 to 39 sec, and are in good agreement with those obtained by applying 180°–t–90° sequences to the same sample.

Electron Spin Resonance of Pd(I). II. γ‐Irradiated Single Crystals of K_{2}PdCl_{4} and (NH_{4})_{2}PdCl_{4}
View Description Hide DescriptionWith the use of the electron spin resonance technique, it is confirmed that the Pd(I) complex ion (PdCl_{4})^{3−} is formed in γ‐irradiated K_{2}PDCl_{4} and (NH_{4})_{2}PdCl_{4}. The chlorine superhyperfine coupling constants and the values for the Pd(I) complex ion are used to obtain the fractional unpaired spin density in the chlorine and orbitals and the crystal field splittings, respectively.

Mass Spectrometric Determination of the Heats of Atomization of NdO_{2}, NdBO, and NdBO_{2} and Upper Values for the Dissociation Energies of NdAg and Nd_{2}
View Description Hide DescriptionDuring evaporation of Nd and Ag from a boron nitride Knudsen cell the new molecules NdO_{2(g)}, NdBO_{(g)}, and NdBO_{2(g)} were detected by mass spectrometric analysis. The enthalpies of the following reactions were determined by a third‐law method: From these reactionenthalpies the heats of atomization of NdO_{2}, NdBO, and NdBO_{2} were calculated: . A discussion of the possible geometric arrangement of these molecules on the basis of thermochemical data is given. Upper limits for the bond energies of Nd_{2(g)} and NdAg_{(g)} are given as 39 and 50 kcal mol^{−1}, respectively.

Mass Spectrometric Studies of Ion–Neutral Reactions in Perfluoroethane
View Description Hide DescriptionIon–molecule reactions in perfluoroethane have been investigated using mass spectrometric techniques. Reaction trends observed in the high‐pressure mass spectrum of C_{2}F_{6} are not consistent with kinetic data for the elementary fragment ion reactions determined in a tandem mass spectrometer. At very low kinetic energies (∼ 0.3 eV), C_{2}F_{5} ^{+} undergoes collision‐induced dissociation while CF_{3} ^{+} reacts principally by a F^{−} transfer process, both reactions being endothermic for ground state reactants. Charge transfer experiments with CF_{3} ^{+} and C_{2}F_{5} ^{+} indicate that these ions have excess internal energies up to 2.9 and 2.4 eV, respectively, which can account for their endothermic reactions. Apparently, at higher pressures, some of the internal energy is degraded by nonreactive collisions, leading to unexpected differences in the reactivity of the fragments. Other reactions observed in the perfluoroethane system are F‐atom transfer and F_{2} transfer. The generally small rate constants (∼ 10^{−11} cm^{3}/molecule·sec) determined for ion‐molecule reactions in C_{2}F_{6} suggest that these reactions involve sizable activation energies. The breakdown patterns from dissociativecharge transferreactions of rare gas ions with C_{2}F_{6} have been re‐examined. The results strongly indicate that some fragment ion formation occurs by direct elimination from repulsive electronic states of C_{2}F_{6} ^{+}.

Ion‐Pair Theory of Concentrated Electrolytes. III. Variational Principle
View Description Hide DescriptionTwo major contributions are devised for that theory of concentrated electrolytes which by convention regards the ions as completely paired into uncharged dipolar “molecules.” First, a more satisfactory expression is obtained for the wavelength‐dependent static dielectric “constant” . Second, a variational principle for Helmholtz free energy is displayed whose minimization with respect to the ion‐pair size distribution serves to determine both and . In anticipation of future numerical applications, a binary collision approximation is specified for the short‐range interaction aspect of the functional .