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15 Jun 1966

Volume 44, Issue 12, pp. 4367-4654

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General Solution for One‐Center Zero‐Field‐Splitting Integrals

John B. Lounsbury and George W. Barry

J. Chem. Phys. 44, 4367 (1966); http://dx.doi.org/10.1063/1.1726644 (6 pages) | Cited 4 times

Online Publication Date: 18 May 2004

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By 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

Tadamasa Shida and William H. Hamill

J. Chem. Phys. 44, 4372 (1966); http://dx.doi.org/10.1063/1.1726645 (6 pages) | Cited 48 times

Online Publication Date: 18 May 2004

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Aromatic 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

James W. Buchanan and Ffrancon Williams

J. Chem. Phys. 44, 4377 (1966); http://dx.doi.org/10.1063/1.1726646 (8 pages) | Cited 22 times

Online Publication Date: 18 May 2004

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The 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 (C2H5OD) 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

R. L. Clendenen and H. G. Drickamer

J. Chem. Phys. 44, 4385 (1966); http://dx.doi.org/10.1063/1.1726647 (2 pages) | Cited 1 time

Online Publication Date: 18 May 2004

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The effect of high pressure has been measured on a series of alloys, including Fe plus 8 at. % Si, which has a (disordered) bcc structure, Fe3Al and Fe3Si, which have an ordered bcc structure, and FeAl and AgMg, which have the CsCl structure. The compressibilities of all the alloys except Fe3Si decrease with increasing pressure and lie between those of the pure components. For Fe3Si 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

C. W. DeKock and D. M. Gruen

J. Chem. Phys. 44, 4387 (1966); http://dx.doi.org/10.1063/1.1726648 (12 pages) | Cited 63 times

Online Publication Date: 18 May 2004

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Electronic absorption spectra of gaseous VCl2, CrCl2, FeCl2, CoCl2, NiCl2, and CuCl2 have been measured near 1000°C and in the range 4000–50 000 cm−1. With the exception of VCl2, extensive vibronic structure was observed in the spectra of these molecules. The spectra are characterized by low intensity (ϵ=10–120 liter/mole⋅cm) dn←dn 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 dn←dn transitions are reasonably well fitted by A2=±900 cm−1, A4=±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 NiCl2 is assigned to a 1Σ(1D)←3π(3F) transition.

K‐Absorption Fine Structures of Sulfur in Gaseous SF6

Robert E. LaVilla and Richard D. Deslattes

J. Chem. Phys. 44, 4399 (1966); http://dx.doi.org/10.1063/1.1726649 (2 pages) | Cited 38 times

Online Publication Date: 18 May 2004

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Measurements are reported on the K‐absorption fine structure of sulfur in gaseous SF6. The results differ qualitatively from previous measurements on molecular gases of lower coordination. Comparison is also made with preliminary results on H2S.

Structure in the Photoionization Continuum of SF6 below 630 Å

K. Codling

J. Chem. Phys. 44, 4401 (1966); http://dx.doi.org/10.1063/1.1726650 (2 pages) | Cited 22 times

Online Publication Date: 18 May 2004

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The absorption spectrum of neutral SF6 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 SF6 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 SF6 in the Far Ultraviolet by Electron Impact

J. Arol Simpson, C. E. Kuyatt, and S. R. Mielczarek

J. Chem. Phys. 44, 4403 (1966); http://dx.doi.org/10.1063/1.1726651 (2 pages) | Cited 37 times

Online Publication Date: 18 May 2004

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Measurements of forward inelastic scattering of 400‐eV electrons from SF6 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 SF6 in the Wavelength Region 1050 to 600 Å

Vernon H. Dibeler and James A. Walker

J. Chem. Phys. 44, 4405 (1966); http://dx.doi.org/10.1063/1.1726652 (2 pages) | Cited 30 times

Online Publication Date: 18 May 2004

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The threshold energy of SF5+ 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

B. J. Dalton

J. Chem. Phys. 44, 4406 (1966); http://dx.doi.org/10.1063/1.1726653 (10 pages)

Online Publication Date: 18 May 2004

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The 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

P. J. Reucroft, H. K. Kevorkian, and M. M. Labes

J. Chem. Phys. 44, 4416 (1966); http://dx.doi.org/10.1063/1.1726654 (5 pages) | Cited 15 times

Online Publication Date: 18 May 2004

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Self‐diffusion studies at extended diffusion anneal 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 106−107, 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. Diffusion anisotropy is more marked for phenanthrene diffusion, diffusivity perpendicular to the ac plane being greater than that perpendicular to the ab plane.

Sign of the 17O Hyperfine Coupling Constant in Fremy's Salt

Z. Luz, Brian L. Silver, and C. Eden

J. Chem. Phys. 44, 4421 (1966); http://dx.doi.org/10.1063/1.1726655 (6 pages) | Cited 5 times

Online Publication Date: 18 May 2004

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The electron spin resonance spectrum of Fremy's salt—17O, [(SO3)2N17O]K2—has been studied in aqueous solution. Twelve out of the expected 18 17O satellites were clearly resolved. The measured hyperfine coupling constant for 17O, aO, is 20.7±0.2 G. Variations in linewidth between the 17O satellites were observed and interpreted quantitatively in terms of relaxation by modulation of the anisotropic dipolar and g tensors. The relaxation rate is mainly determined by interactions involving the magnetic moment of 17O. The terms in the expression for the linewidth that depend on mN are small, except for a cross term EmNmO. Analysis of the results combined with a knowledge of the sign of the g‐tensor anisotropy allowed the determination of the signs of aN and aO, which are positive and negative, respectively.

Effusion from Spherical Orifices. I. Transmission by Molecular Flow

Jimmie G. Edwards and Paul W. Gilles

J. Chem. Phys. 44, 4426 (1966); http://dx.doi.org/10.1063/1.1726656 (5 pages) | Cited 3 times

Online Publication Date: 18 May 2004

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Molecular 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

J. A. R. Coope

J. Chem. Phys. 44, 4431 (1966); http://dx.doi.org/10.1063/1.1726657 (9 pages) | Cited 1 time

Online Publication Date: 18 May 2004

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A 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 n(n−1) in δ2. 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 S≦math, with a second‐order tensor zero‐field term, in a uniform external magnetic field.
A second approach is to construct an operator F={(K1×12−11×K2)2}, in a n(n−1)‐dimensional space of antisymmetric two‐particle states, whose eigenvalues are the squares of the differences of the eigenvalues of the Hamiltonian K. The resonance condition is then det ∣F−δ2I∣=0. A feature of this approach is that transition intensities can be calculated directly from the appropriate eigenvector of F, without knowledge of the individual eigenvectors of K.
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

Raymond Wilson and Daniel Kivelson

J. Chem. Phys. 44, 4440 (1966); http://dx.doi.org/10.1063/1.1726658 (5 pages) | Cited 25 times

Online Publication Date: 18 May 2004

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The ESR linewidths 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 anisotropic g and hyperfine interactions and from spin—rotational effects. The parameter λ⅓=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

Raymond Wilson and Daniel Kivelson

J. Chem. Phys. 44, 4445 (1966); http://dx.doi.org/10.1063/1.1726659 (8 pages) | Cited 36 times

Online Publication Date: 18 May 2004

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The 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 g tensors 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(gi−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

Ian L. McLaughlin and John S. Dahler

J. Chem. Phys. 44, 4453 (1966); http://dx.doi.org/10.1063/1.1726660 (7 pages) | Cited 5 times

Online Publication Date: 18 May 2004

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The 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

M. Godfrey, C. W. Kern, and M. Karplus

J. Chem. Phys. 44, 4459 (1966); http://dx.doi.org/10.1063/1.1726661 (11 pages) | Cited 51 times

Online Publication Date: 18 May 2004

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The 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., CH3) 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?

Stuart A. Rice and Joshua Jortner

J. Chem. Phys. 44, 4470 (1966); http://dx.doi.org/10.1063/1.1726662 (3 pages) | Cited 56 times

Online Publication Date: 18 May 2004

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In 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

R. B. Bernstein and K. H. Kramer

J. Chem. Phys. 44, 4473 (1966); http://dx.doi.org/10.1063/1.1726663 (13 pages) | Cited 103 times

Online Publication Date: 18 May 2004

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The 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 cos3Θ). 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)☒, where S is the total inelastic cross section.

Steady‐State Studies in the Conventional Verneuil Process—the Trajection (Melting) Zone

R. C. Pastor, A. C. Pastor, H. Kimura, and K. Arita

J. Chem. Phys. 44, 4486 (1966); http://dx.doi.org/10.1063/1.1726664 (7 pages) | Cited 6 times

Online Publication Date: 18 May 2004

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In the conventional Verneuil growth of ruby, it is shown that certain parameters pertinent to the final concentration of the additive in the crystal product (solid solution) are: starting concentration, surface distribution of additive in the powder, trajection distance, and growth rate. The effects of these factors are studied at the trajection (or melting) zone.

Laser‐Induced Luminescence and Dissociation in Biphenyl

K. B. Eisenthal, W. L. Peticolas, and K. E. Rieckhoff

J. Chem. Phys. 44, 4492 (1966); http://dx.doi.org/10.1063/1.1726665 (6 pages) | Cited 14 times

Online Publication Date: 18 May 2004

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The interaction of the radiation field of an unfocused ruby laser with molecules containing a phenyl—phenyl or benzyl—benzyl single bond is found to give rise to a new luminescence. This luminescence is linearly dependent on the molecular concentration and proportional to either the second or the third power of the laser intensity. Thus it appears that a multiphoton absorption is occurring. The absorption does not appear to involve the electronic states of the molecules. This luminescence occurs throughout the visible region and bears no resemblance whatever to either the normal fluorescence or phosphorescence. Because of the exceedingly high laser intensities or electric fields necessary for electronic dielectric breakdown it appears that this mechanism is not of importance. It is suggested that multiphoton vibrational excitation to a dissociative state of the molecule may occur which leads to molecular fragmentation. This process is followed by a chemiluminescent emission. A quantitative comparison of the experimental results with a theoretical treatment of multiphoton vibrational dissociation is made.

Neutron‐Diffraction Study of the Structures of Ferroelectric and Paraelectric Ammonium Sulfate

Elmer O. Schlemper and Walter C. Hamilton

J. Chem. Phys. 44, 4498 (1966); http://dx.doi.org/10.1063/1.1726666 (12 pages) | Cited 121 times

Online Publication Date: 18 May 2004

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Three‐dimensional neutron‐diffraction data have been collected for both the room‐temperature (paraelectric) and the low‐temperature (ferroelectric) phases of ammonium sulfate. Both phases are ordered. The transition, occurring at 223°K and involving a change from Space Group Pnam at room temperature to Space Group Pna21 in the ferroelectric phase, results in somewhat stronger hydrogen bonds in the ferroelectric phase, although there is no dramatic change in the barrier to rotation of the ammonium ions as a result of the transition. In both phases the two crystallographically independent ammonium ions have quite similar rotational barriers and hydrogen‐bond strengths. The transition also results in less distorted ammonium ions in the ferroelectric phase. At room temperature, there are only two hydrogen bonds with O⋅⋅⋅H distances less than 2.0 Å. In the ferroelectric phase there are six. The mean distance is decreased by 0.1 Å in the ferroelectric phase, although the range of distances remains the same. The principal effect is thus a strengthening of the hydrogen bonds of intermediate length; this is accomplished by a reorientation of the ammonium groups. The shortest bonds at room temperature are not necessarily the shortest at low temperature.

Measurement of the Relative Abundances and Recoil‐Energy Spectra of Fragment Ions Produced as the Initial Consequences of X‐Ray Interaction with CH3I, HI, and DI

Thomas A. Carlson and R. Milford White

J. Chem. Phys. 44, 4510 (1966); http://dx.doi.org/10.1063/1.1726667 (11 pages) | Cited 53 times

Online Publication Date: 18 May 2004

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Methyl iodide, hydrogen iodide, and deuterium iodide have been irradiated with x rays, whose energies are such that the most probable event is the formation of a vacancy in the L shell of iodine. The readjustment to this vacancy, principally by a series of Auger processes, gives rise to extensive ionization and decomposition; and the relative abundances of the fragment ions and their recoil‐energy spectra have been measured with a specially designed mass spectrometer. As the result of the inner‐shell vacancy, CH3I decomposed primarily into hydrogen, carbon, and iodine ions, having, respectively, the average charges of 1+, 2+, and 5+. Very few molecular ions were observed. The recoil energies were quite large with values in some cases above 100 eV. A calculation, based on a simple model for a Coulombic ``explosion,'' is shown to be consistent with the data. In the studies made with HI and DI the recoil spectra of H+ and D+ are compared with calculations of the kinetic energies expected from multiple ionization. From this comparison there appears to be evidence that the multiply charged molecular ions separate slightly during the time the Auger processes are taking place. Finally, a brief discussion is given concerning the importance of the initial consequence of x‐ray interaction in radiation damage.

Rotational States of a Tetrahedron in a Cubic Crystal Field

Harry F. King and Donald F. Hornig

J. Chem. Phys. 44, 4520 (1966); http://dx.doi.org/10.1063/1.1726668 (12 pages) | Cited 73 times

Online Publication Date: 18 May 2004

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The Schrödinger equation is solved for the rotational states of a rigid cube whose center of mass is fixed at a point of symmetry in an external field. This is shown to be equivalent to the equation of motion for a regular tetrahedron in a field with symmetry Oh. The quantum states are classified under the direct product group Ō×O, where Ō is an octahedral group of rotations about body‐fixed axes and O is a similar but distinct group of rotations about space‐fixed axes. The wavefunctions are obtained by an expansion in a series of symmetry‐adapted linear combinations of spherical‐top functions. Projection operators are defined which generate the various linear combinations. Closed‐form expressions are obtained for the matrix elements of the Hamiltonian and of the projection operators. Upper and lower bounds are computed for representative energy levels. The results demonstrate that using basis sets of practical size, high accuracy can be obtained. This analysis forms the basis of a more general theory of rotation of small molecules and polyatomic ions in crystals.
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