Volume 44, Issue 12, 15 June 1966

General Solution for One‐Center Zero‐Field‐Splitting Integrals
View Description Hide DescriptionBy use of Fourier integral transforms, a general and exact solution is derived for all possible one‐center zero‐field‐splitting (zfs) integrals using Slater‐type orbitals. This solution may be used for development of tables of functions or programmed directly for computer calculations. Direct computer calculation of one‐center zfs integrals using the analysis developed is discussed.

Molecular Ions in Radiation Chemistry. III. Absorption Spectra of Aromatic‐Hydrocarbon Cations and Anions in Organic Glasses
View Description Hide DescriptionAromatic hydrocarbons (ArH) in γ‐irradiated, glassy butyl chloride at 77°K are efficient traps for migrating positive holes, forming the radical cations of 40 compounds in good yield. No ArH^{−} ions appeared to form. Photobleaching is very inefficient, or nil. Resonance charge transfer and simple competition for holes by ArH, solvent, and anions are consistent with observation. In glassy methyltetrahydrofuran, ArH gave ArH^{−} in good yields with very little ArH^{+}. In 3‐methylpentane, both ArH^{+} and ArH^{−} were formed. Addition of propyl chloride enhanced ArH^{+} and suppressed ArH^{−}. Addition of ethanol had the reverse effect.

Kinetics of Ionic Processes in the Radiolysis of Liquids. II. Proton Transfer from Cyclohexane Ions to Ethanol
View Description Hide DescriptionThe extent to which positive ions produced by the radiolysis of cyclohexane undergo proton transfer to a dissolved scavenger before geminate recombination has been studied by an isotopic method. Ethanol‐d (C_{2}H_{5}OD) has been used, and the yield of HD is related to the yield of scavengable ions. The yield is strongly dependent on ethanol concentration over most of the range but at high concentration (>1M) a limiting value is reached corresponding to an estimated total yield of 2.6 ion/100 eV. The dependence of the yield on scavenger concentration suggests that the distribution of recombination times for ion pairs lies in the range between 10^{−7} and 3×10^{−11} sec corresponding to initial separation distances between 280 and 19 Å, respectively. A median separation distance of 50 Å is indicated. The results are consistent with the earlier supposition that the electron is trapped as a negative entity with molecular dimensions. Some implications of this model are examined.

Effect of High Pressure on the Compressibilities of Five Alloys
View Description Hide DescriptionThe effect of high pressure has been measured on a series of alloys, including Fe plus 8 at. % Si, which has a (disordered) bcc structure, Fe_{3}Al and Fe_{3}Si, which have an ordered bcc structure, and FeAl and AgMg, which have the CsCl structure. The compressibilities of all the alloys except Fe_{3}Si decrease with increasing pressure and lie between those of the pure components. For Fe_{3}Si the compressibility increases slightly with increasing pressure and is less than that either of pure iron or pure silicon.

Electronic Absorption Spectra of the Gaseous 3d Transition‐Metal Dichlorides
View Description Hide DescriptionElectronic absorption spectra of gaseous VCl_{2}, CrCl_{2}, FeCl_{2}, CoCl_{2}, NiCl_{2}, and CuCl_{2} have been measured near 1000°C and in the range 4000–50 000 cm^{−1}. With the exception of VCl_{2}, extensive vibronic structure was observed in the spectra of these molecules. The spectra are characterized by low intensity (ε=10–120 liter/mole·cm) d^{n} ←d^{n} transitions in the 4000–22 000‐cm^{−1} region and by higher intensity (ε=2500–24 000 liter/mole·cm), transitions in the 19 000–50 000‐cm^{−1} region.
The d^{n} ←d^{n} transitions are reasonably well fitted by A _{2}=±900 cm^{−1}, A _{4}=±100 cm^{−1}, the two ligand‐field parameters appropriate for a molecule of symmetry D _{∞h }. The narrow band (half‐width ∼120 cm^{−1}) at 11 727 cm^{−1} in NiCl_{2} is assigned to a ^{1}Σ(^{1} D)←^{3}π(^{3} F) transition.

K‐Absorption Fine Structures of Sulfur in Gaseous SF_{6}
View Description Hide DescriptionMeasurements are reported on the K‐absorption fine structure of sulfur in gaseous SF_{6}. The results differ qualitatively from previous measurements on molecular gases of lower coordination. Comparison is also made with preliminary results on H_{2}S.

Structure in the Photoionization Continuum of SF_{6} below 630 Å
View Description Hide DescriptionThe absorptionspectrum of neutral SF_{6} has been studied in the far‐ultraviolet spectral region (100 to 630 Å) using the pure continuum radiated by the NBS 180‐MeV electron synchrotron as a background source. A well‐developed vibrational progression was observed in the 550–600‐Å region. A Rydberg series of neutral SF_{6} was observed in the 450–500‐Å region, converging to a limit at 26.83 (±0.04) eV. Additional absorption features were evident with peaks at 435 and 350 Å. Absolute absorption cross‐section measurements were made at 539, 584, and 704 Å. The values obtained were 170, 70 and 100 Mb, respectively; the error in these measurements is thought to be no more than 25%.

Absorption Spectrum of SF_{6} in the Far Ultraviolet by Electron Impact
View Description Hide DescriptionMeasurements of forward inelastic scattering of 400‐eV electrons from SF_{6} were made and used to derive relative ultraviolet‐absorption cross sections. The relative values were normalized to an ultraviolet‐absorption measurement at 23.00 eV. Agreement with additional uv measurements at 21.2 and 17.6 eV was excellent. Oscillator strengths for three absorption bands between 10 and 15 eV, as derived from the electron‐scattering measurements, are in fair agreement with the corresponding values measured by uv absorption. The total oscillator strength for excitations up to 32 eV is found to be 15.3.

Photoionization Efficiency Curve for SF_{6} in the Wavelength Region 1050 to 600 Å
View Description Hide DescriptionThe threshold energy of SF_{5} ^{+} at 811 Å (15.29 eV) has been determined by photoionization. An electronically excited state with a threshold at 750 Å (16.53 eV) resulting from partially resolved autoionizing Rydberg levels in the region of 775 Å has been observed also.

Classification of Rotational Energy Levels for Linear Molecules
View Description Hide DescriptionThe classification of the rovibronic energy levels according to the symmetry species of the molecular point group, previously presented only for nonlinear molecules, is extended to linear molecules, within the approximation that the interaction between rotational and vibronic motions can be neglected. Selection rules in terms of these species are obtained for the rovibronic transitions. The effect of the rotation—vibronic interaction on the classification scheme and the selection rules is considered.

Diffusion in Organic Crystals. II. Lattice and Subgrain‐Boundary Diffusion
View Description Hide DescriptionSelf‐diffusion studies at extended diffusionanneal times and impurity (phenanthrene) diffusion studies in melt‐grown anthracene crystals have shown evidence for a fast subgrain‐boundary‐diffusion process in addition to a much slower lattice diffusion. Subgrain boundary diffusion is faster by a factor of 10^{6}−10^{7}, the activation energy being 25% to 66% the value for lattice diffusion.
Phenanthrene diffusion is very similar to self‐diffusion in terms of diffusivity magnitude and activation energy.Diffusionanisotropy is more marked for phenanthrene diffusion, diffusivity perpendicular to the ac plane being greater than that perpendicular to the ab plane.

Sign of the ^{17}O Hyperfine Coupling Constant in Fremy's Salt
View Description Hide DescriptionThe electron spin resonance spectrum of Fremy's salt—^{17}O, [(SO_{3})_{2}N^{17}O]K_{2}—has been studied in aqueous solution. Twelve out of the expected 18 ^{17}O satellites were clearly resolved. The measured hyperfine coupling constant for ^{17}O, a _{O}, is 20.7±0.2 G. Variations in linewidth between the ^{17}O satellites were observed and interpreted quantitatively in terms of relaxation by modulation of the anisotropic dipolar and gtensors. The relaxation rate is mainly determined by interactions involving the magnetic moment of ^{17}O. The terms in the expression for the linewidth that depend on m _{N} are small, except for a cross term Em _{N} m _{O}. Analysis of the results combined with a knowledge of the sign of the g‐tensor anisotropy allowed the determination of the signs of a _{N} and a _{O}, which are positive and negative, respectively.

Effusion from Spherical Orifices. I. Transmission by Molecular Flow
View Description Hide DescriptionMolecular flow through orifices which are spherical segments is treated by a method analogous to that which previously has been applied to cylindrical and conical orifices. The integral equation which expresses the rate at which molecules impinge on a unit area is shown to possess a simple, closed‐form solution for spherical orifices, and the transmission probability for such orifices is derived in closed form. Transmission probabilities are presented for several spherical orifices and are shown to be always larger than those for conical or cylindrical orifices of the same dimensions. For very short and very long divergent spherical orifices the transmission probability approaches unity, and at intermediate lengths it passes through a minimum. For very short spherical orifices with equal and parallel plane entrance and exit, the transmission probability approaches unity, and it decreases to a limiting value of one‐half for very great length.

Formulation of Resonance Conditions
View Description Hide DescriptionA resonance condition is a condition on the variables of a system (external field, orientation, etc.) such that two energy levels differ by a fixed energy δ. This paper discusses the formulation of exact theoretical resonance conditions by methods which do not require knowledge of the energy levels themselves. An exact resonance condition for an n‐level system can be written as an algebraic equation of degree ½n(n−1) in δ^{2}. The determination of this equation from the characteristic equation for the energies is an old algebraic problem discussed by Lagrange and by Cayley, the formulation of the equation of differences. Relevant properties are reviewed, and polynomial and determinantal formulas are given. Application is made to a particle of spin , with a second‐order tensor zero‐field term, in a uniform external magnetic field.
A second approach is to construct an operator , in a ½n(n−1)‐dimensional space of antisymmetric two‐particle states, whose eigenvalues are the squares of the differences of the eigenvalues of the Hamiltonian . The resonance condition is then det . A feature of this approach is that transition intensities can be calculated directly from the appropriate eigenvector of , without knowledge of the individual eigenvectors of .
For a system of many levels the exact resonance condition may be very complicated, and knowledge of the resonance condition is by no means equivalent to knowledge of the resonance fields.

ESR Linewidths in Solution. III. Experimental Study of the Solvent Dependence of Anisotropic and Spin—Rotational Effects
View Description Hide DescriptionThe ESRlinewidths of vanadyl acetylacetonate in diphenylmethane have been studied as a function of temperature. The results confirm the analysis made previously for the linewidths of vanadyl acetylacetonate in toluene. The major contributions arise from anisotropicg and hyperfine interactions and from spin—rotational effects. The parameter λ^{⅓}=r/3.045 Å, where r, the hydrodynamic spherical radius of the radical, is introduced as an adjustable parameter. This one parameter is sufficient to enable the theory to explain the linewidth results in a number of solvents, but a slightly different value of λ is required for each solvent. This variation may be due to solvation effects.
Studies of deuterated vanadyl acetylacetonate in carbon disulfide indicate that neither intermolecular dipolar interactions nor unresolved proton extrahyperfine splittings contribute appreciably to the linewidth.

ESR Linewidths in Solution. IV. Experimental Studies of Anisotropic and Spin—Rotational Effects in Copper Complexes
View Description Hide DescriptionThe linewidths of copper acetylacetonate in toluene and in chloroform have been measured as a function of temperature (T), viscosity (η), and magnetic field. The contributions arising from motional modulation of the anisotropic dipolar and gtensors have been calculated in terms of independently determined magnetic parameters and a single adjustable parameter, the hydrodynamic radius r (r=3.857 Å in chloroform and 3.357 Å in toluene). The remaining or residual linewidth is independent of nuclear quantum number M and only slightly dependent on the applied magnetic field; it is linear in T/η. A theory of spin relaxation through spin—rotational interaction has been discussed in Article II of this series; the predicted linewidth arising from this spin—rotational interaction accounts very well for the residual linewidth in terms of the single adjustable parameter r already determined. The spin—rotational linewidth is proportional to Σ(g_{i} −2.0023)^{2}, which, in turn, is proportional to the spin—orbit coupling constant squared; the comparison of the residual linewidths of vanadyl and copper acetylacetonate indicate that this dependence is in fact satisfied by the residual linewidths.

Transport Properties of Polyatomic Fluids. III. The Transport—Relaxation Equations for a Dilute Gas of Rough Spheres
View Description Hide DescriptionThe Boltzmann equation for a dilute gas of rough spheres is linearized and its solution expanded in irreducible tensors constructed from the linear and spin velocities of the spheres. This procedure is patterned closely after Waldmann's development of the kinetic theory for a Lorentz gas of rough spheres. Transport—relaxation equations are derived for the expansion coefficients, i.e., for the moments of the nonequilibrium distribution function. By examining selected subsets of these equations we are able to construct estimates for the transport coefficients and characteristic relaxation times. Relationships are established between these results and the transport coefficients generated by the method of Chapman and Enskog.

Studies of Zero‐Field Splittings in Aromatic Molecules
View Description Hide DescriptionThe zero‐field splitting parameters corresponding to exponential‐orbital wavefunctions for benzene and naphthalene have been evaluated by the Gaussian transform technique. Comparison of the results obtained with and without multicenter integrals shows significant differences; in particular, an erroneous value for E in naphthalene is found if only two‐center integrals are included. For the lowest triplet in benzene, the use of accurate integrals with the wavefunction of van der Waals and de Groot for the quinoid structure improves the agreement with the experimental D ^{*} value. In naphthalene, Pariser's wavefunction and accurate integrals give a D that is close to the measured result; however, the E determined from the same wavefunction is considerably too small in magnitude.
A qualitative examination of the effect of D on substitution in benzene and naphthalene is made. For benzene it is found that most substituents should decrease D or D ^{*}; only if a weak mesomeric interaction is involved (e.g., CH_{3}) is an increase in D ^{*} expected. In naphthalene, the effect of substituents is expected to be considerably smaller than in benzene. Comparisons with the limited available data show agreement with these conclusions.

Do Exciton States Exist in the Liquid Phase?
View Description Hide DescriptionIn this note we conjecture that a sufficient condition for the existence of Wannier exciton states in a dense liquid is that an excess electron be accurately describable as a plane wave. Scattering processes then lead to a broadening of the exciton level. A theory of electron scattering in simple liquids is used to estimate linewidths, and the predictions are consistent with the data available. A number of predictions resulting from, and implications of, the proposed mechanism are considered.

Sudden Approximation Applied to Rotational Excitation of Molecules by Atoms. II. Scattering of Polar Diatomics
View Description Hide DescriptionThe sudden approximation is applied to the computation of rotational transition probabilities and inelastic total cross sections for the scattering of polar and nonpolar diatomic molecules (rigid rotors) by atoms. The calculations are based upon an interaction potential which includes both short‐ and long‐range anisotropies. At thermal energies the long‐range attractive parts of the potential are of principal importance in determining the inelasticity, with a significant contribution arising from the quadrupole interaction term (varying as R ^{−7} cos^{3}Θ). The computations show the rapid onset of ``dominant‐coupling'' behavior (randomization of transition probability among all close‐coupled states) for impact parameters below about (S/π)^{½}, where S is the total inelastic cross section.