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15 Jun 1969

Volume 50, Issue 12, pp. 5049-5430

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Molecular Schrödinger Equation. IX. Square and Rectangular States of H4 and the Molecular Ions H43+ and H42+

Harold Conroy and Gulzari Malli

J. Chem. Phys. 50, 5049 (1969); http://dx.doi.org/10.1063/1.1671019 (17 pages) | Cited 32 times

Online Publication Date: 15 December 2003

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Our method for the solution of the molecular Schrödinger equation has been further developed and extended to the case of the four‐electron system. Ab initio calculations are presented which lead to the electronic wavefunctions and energies of square and rectangular forms of H4. As a preliminary to the four‐electron studies, the energies and wavefunctions for a number of states of the ions H43+ and H42+ are calculated. Complete contour maps for the potential energy surfaces of these systems are reported and the H4 surface is discussed in connection with the bimolecular isotope exchange reaction H2+D2→2HD. Contour maps for the electron density distribution in square and rectangular H4 are presented and discussed.

Vapor Pressure and Crystal Structure of Curium Metal

P. K. Smith, W. H. Hale, and M. C. Thompson

J. Chem. Phys. 50, 5066 (1969); http://dx.doi.org/10.1063/1.1671020 (11 pages) | Cited 6 times

Online Publication Date: 15 December 2003

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The vapor pressure of liquid and solid curium metal between 1179° and 2068°K and between 10−10 atm and 0.1 mm was measured by the Knudsen effusion method to be
math
ΔH°1600°K and ΔS°1600°K for vaporization are 82.6 ± 2.7 kcal/g⋅atm and 21.7 ± 1.7 eu, respectively. A previously unreported fcc close‐packed structure for curium metal was identified with a  =  4.382 ± 0.004Å, and a density of 19.26 g/cm3, corresponding to a +4 metallic valence. The entropy of condensed curium is indicated to be relatively high by the low heat of fusion and by the ΔH°298°K for vaporization calculated by second‐ and third‐law methods. The heat of vaporization of curium may be explained from the opposing effects of a quadrivalent metal and a 5f66d27s2 to 5f76d7s2 transition on vaporization.

ESR Study of the Kinetics of the Reaction of H Atoms with Methane

Michael J. Kurylo and Richard B. Timmons

J. Chem. Phys. 50, 5076 (1969); http://dx.doi.org/10.1063/1.1671021 (7 pages) | Cited 48 times

Online Publication Date: 15 December 2003

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A wide‐temperature‐range study using ESR atom detection has been employed to measure the rate of the reaction H + CH4→H2 + CH3. Over the temperature range 426°–747°K, we obtain a specific rate constant for the above reaction of k1  =  6.9 ± 0.6 × 1013exp[(−11800 ± 200) / RT] expressed in units of cubic centimeters per mole per second. The value obtained in the present work is compared to a number of other results obtained by various workers. The activation energy we observe is considerably higher than previous values obtained in this temperature range. However, our results coupled with the heat of the reaction predict an activation energy for the reverse reaction which agrees well with experimental values. In addition, the pre‐exponential factor we obtain agrees with absolute rate theory predictions as well as with entropy considerations. We do not agree with literature results which give very low pre‐exponential factors suggesting steric factors of the order of 10−3–10−5 for this reaction.

Molecular Freedom of the Ammonium Ion. Heat Capacity and Thermodynamic Properties of Ammonium Perchlorate from 5°–350°K

Edgar F. Westrum and Bruce H. Justice

J. Chem. Phys. 50, 5083 (1969); http://dx.doi.org/10.1063/1.1671022 (5 pages) | Cited 34 times

Online Publication Date: 15 December 2003

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The heat capacity of NH4ClO4 has been determined by adiabatic calorimetry from 5°–350°K and found to be of simple sigmate character without thermal anomalies. The heat capacity (Cp), entropy (S°), enthalpy function (H°−H°0) / T, and Gibbs energy function (G°−G0°) / T evaluated at 298.15°K from these data are 30.61, 44.02, 20.24, and −23.78 cal/(gfm °K). Combination of these values with aqueous NH4ClO4 thermochemical data suggests the absence of zero‐point entropy. Comparison with the heat capacity of isostructural KClO4 permits resolution of the molecular dynamics of the ammonium ions and leads to the conclusion that these ions are restricted rotators, prevented from freely rotating by comparatively low‐energy barriers.

Dynamic Mechanical Properties of Polystyrene Solutions from 23 to 300 MHz

R. S. Moore, H. J. McSkimin, C. Gieniewski, and P. Andreatch

J. Chem. Phys. 50, 5088 (1969); http://dx.doi.org/10.1063/1.1671023 (13 pages) | Cited 7 times

Online Publication Date: 15 December 2003

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Measurements of dynamic shear impedance at five frequencies from 23 to 300 MHz and at 25°C are reported for a monodisperse polystyrene as a function of concentration. The concentrations ranged from 3% to 20% polymer in di‐n‐butyl phthalate, a near‐theta solvent, and covered the region from the start of coil overlap to well beyond entanglement. Results are reported in terms of the in‐phase, G′−ν1Gs′, and quadrature, G″−υ1ωηs′, components of the dynamic shear modulus of the polymer, where Gs′ is the solvent contribution to the in‐phase modulus, ω is the angular frequency, ηs′ is the dynamic solvent viscosity, and υ1 is the volume fraction of solvent. The use of dynamic values for the solvent follows from observation of relaxation and non‐Newtonian behavior in the solvent beyond 100 MHz. The usual reduced variables method, even in this modified form, could not be successfully applied to superimpose data at different concentrations, indicating the need for further modification to account for finite concentration effects. The dynamic solution viscosity η′ is found to increase with increasing concentration at fixed frequency. At any one concentration, it decreases with increasing frequency above 200 MHz. This is in contrast to the nearly constant values attained at lower frequencies at concentrations to 15% polymer; the decrease is too large to be accounted for by only solvent viscosity effects. Results are also reported in terms of the reduced dynamic viscosity (η′ − υ1ηs′) / (η − υ1ηs), where η and ηs are the steady‐flow values for the solution and the solvent, respectively. A high‐frequency limiting value of the reduced viscosity is found to obtain for the lower concentrations at the three lowest frequencies. However, for the highest concentration the limiting value is believed to occur at frequencies lower than those measured, so that a further decrease is, in fact, being observed above 100 MHz. An estimate of 10−1.04 was obtained for the reduced high‐frequency limiting viscosity in the limit of infinite dilution. From an estimate of the number of statistical segments (259) based on intrinsic viscosity measurements and on the results of Thurston, and an estimate of the extent of hydrodynamic interaction per segment, h*, of 0.2, a value of 1.97 was obtained for ϕ/f, the ratio of the internal to segmental friction coefficients. The concentration dependence of ϕ was determined assuming little or no change in h* with concentration, and an appropriate dependence of f on concentration and viscosity. It ranged from c0.26 below entanglement to c0.07 above it, approximately the one‐fourth and zeroth powers, respectively. The concentration dependence of (η′ − υ1ηs′) increased by about c1 while that of (η − υ1ηs) increased by c2 on going from concentrations below to those above entanglement. Plots of the dynamic impedance against frequency indicate that departure from Newtonian behavior occurs sooner for the quadrature component than for the in‐phase part. Solvent relaxation was evaluated in terms of Lamb's semiempirical theory for low‐molecular‐weight liquids. From a comparison of the observed frequency dependence and the reference plots of Lamb, values for G∞′ and τ, the high‐frequency limiting dynamic shear modulus and the average relaxation time, were obtained of 1.97×1010 dyn/cm2 and 8.5×10−12 sec, respectively. The magnitude of the latter is discussed and is shown to be in reasonable agreement with estimates of Pinnow, Candau, and Litovitz for n‐alkyl bromides. Based on values of the reduced dynamic viscosity obtained by Ferry, Holmes, Lamb, and Matheson at 73 kHz and upon the present results, it appears that the high‐frequency limiting viscosity of polystyrene in a near‐theta solvent persists for about 3½ decades before it decreases further at a frequency in the vicinity of that for the onset of solvent relaxation. Extension of optical techniques (e.g., Brillouin scattering) to studies of polymer solutions is briefly noted.

Infrared Spectrum of the Difluoromethyl Radical in Solid Argon

T. Granville Carver and Lester Andrews

J. Chem. Phys. 50, 5100 (1969); http://dx.doi.org/10.1063/1.1671024 (8 pages) | Cited 13 times

Online Publication Date: 15 December 2003

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When HCBrF2 and DCBrF2 at high dilution in argon are codeposited with an atomic beam of lithium on a CsI window at 15°K, lithium bromide absorptions appear along with several new absorptions not present when the precursor was deposited without alkali metal. These new absorptions are assigned to the antisymmetric hydrogen bending and carbon–fluorine stretching modes and the symmetric C☒F vibration of the HCF2 and DCF2 radicals. The antisymmetric vibrational assignments are supported by product rule and normal coordinate calculations which give the potential constants F55  =  5.27 ± 0.1mdyn/Å, F56  =  0.44 ± 0.02mdyn/rad, and F66  =  0.64 ± 0.05mdyn⋅Å/rad2. An approximate force constant F22  =  7.19 ± 0.7mdyn/Å is calculated from the symmetric C☒F vibration. The carbon–fluorine valence force constant for HCF2 is in the range of those for typical fluorocarbons.

Natural Orbital Expansion of Interacting Geminals

David M. Silver

J. Chem. Phys. 50, 5108 (1969); http://dx.doi.org/10.1063/1.1671025 (9 pages) | Cited 27 times

Online Publication Date: 15 December 2003

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An antisymmetrized product of “interacting” geminals is proposed for the form of a many‐electron wavefunction. The interacting geminals are given a natural orbital expansion where the natural orbitals of the geminals are also natural orbitals of the total wavefunction. This ansatz is more general than the strongly and weakly orthogonal geminal and identical geminal models and includes them as particular cases. However, the use of the interacting geminal wavefunction is not significantly more complicated for the purpose of calculations. Different constraints on the geminal occupation coefficients define the various geminal models and more than one model can be incorporated into a single wavefunction. The case of two singlet pairs of electrons is examined in terms of the interacting geminal model—density matrices, energy expressions, and variational equations being given.

Dipole Davydov Splittings in Crystalline Anthracene, Tetracene, Naphthalene, and Phenanthrene

M. R. Philpott

J. Chem. Phys. 50, 5117 (1969); http://dx.doi.org/10.1063/1.1671026 (12 pages) | Cited 58 times

Online Publication Date: 15 December 2003

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The contribution of dipole–dipole interactions to the Davydov splitting (i.e., the dipole Davydov splitting) of the moderately intense 1Ag → 1La transitions of anthracene, tetracene, naphthalene, and phenanthrene has been investigated. Unlike most previous calculations, the Bose character of molecular excitons has been taken fully into account by using the classical theory of exciton states. In the dipole approximation this treatment is equivalent to the second quantized formulation of Agranovitch. Formulas are also derived for coupling of Born–Oppenheimer separable states through the full interaction potential. Dipole sums are calculated for infinite crystals by Ewald's method. High‐energy π–π* transitions are shown to make sizeable contributions to the Davydov splittings and are responsible for increasing polarization ratios of the 0–0 transition. For anthracene these high‐energy states push the splittings of the 3800‐Å system beyond the accepted values, implying that the residual intermolecular interactions due to higher multipole and exchange effects act in the opposite direction, thereby reducing the total splitting. In tetracene the dipole splittings, after including higher states, are in excellent agreement with experiment, thereby relegating multipoles, etc., to a minor role. The 1La states of naphthalene and phenanthrene are subject to a pinching effect, due to the proximity of levels above and below, which inhibits the development of a large dipole splitting.

High‐Order ESR Transitions of Eu2+ in CaF2, SrF2, and BaF2

Sook Lee, T. J. Menne, and E. C. Paxhia

J. Chem. Phys. 50, 5129 (1969); http://dx.doi.org/10.1063/1.1671027 (4 pages) | Cited 1 time

Online Publication Date: 15 December 2003

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The X‐band ESR spectra obtained from single crystals of CaF2, SrF2, and BaF2 containing dilute concentrations of Eu2+ ions show many weak absorption lines at magnetic field values lower than those of the allowed (ΔM  =  ±1) Eu2+ lines. These additional weak lines display a marked angular variation, but for a given crystal orientation, their relative field positions and ESR intensities are qualitatively similar for the three crystals. Calculations were made to determine the exact energy levels and probabilities of all high‐order (ΔM  ≠  ± 2) ESR transitions for various crystal orientations as a function of the magnetic field strength. These calculations were based on the diagonalization of the energy matrix for the 8S7/2 state in a cubic environment without use of the high‐field approximation. The observed field positions and relative ESR intensities of the additional low‐field lines were found to be qualitatively consistent with those calculated for the high‐order ESR transitions corresponding to ΔM  =  ± 2,± 3,⋅⋅⋅± 7 of Eu2+ ions in cubic sites of the crystals.

Reactions of 2.8‐eV Tritium Atoms with Methane

C. C. Chou and F. S. Rowland

J. Chem. Phys. 50, 5133 (1969); http://dx.doi.org/10.1063/1.1671028 (8 pages) | Cited 20 times

Online Publication Date: 15 December 2003

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Tritium atoms with 2.8‐eV kinetic energy have been formed by 1849‐Å photolysis of TBr, and have been reacted with CH4 in the presence of Br2. In addition to HT from the abstraction reaction known in thermal systems, the direct substitution of T for H to form CH3T has been observed. The ratio of HT/CH3T is 3.6 to 4.0 in low Br2 mole fraction. In Br2 mole fractions exceeding 0.5, this ratio is reduced to 3.0, and the absolute yields of both HT and CH3T are greatly reduced. The formation of HT and CH3T from hot reactions of T with CH4 competes with the hot reaction of T with BR2 to form TBr.

Local Permutational Symmetry and the Separated‐Atom Limit

D. J. Klein

J. Chem. Phys. 50, 5140 (1969); http://dx.doi.org/10.1063/1.1671029 (11 pages) | Cited 6 times

Online Publication Date: 15 December 2003

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Local permutational symmetries are shown to supply approximate quantum numbers for a system composed of approximately localized subsystems. Local permutational symmetries associated with simple valence‐bond wavefunctions in the separated‐atom limit are studied and in certain cases are found to yield a nonphysical combination of local permutational symmetries. This nonphysical behavior can be avoided by use of a certain suitable form of configuration interaction or by a projection with either an appropriate chemically canonical matric basis element or a generalized structure projector.

Interaction of Two Metastable Triplet Helium Atoms

D. J. Klein

J. Chem. Phys. 50, 5151 (1969); http://dx.doi.org/10.1063/1.1671030 (7 pages) | Cited 9 times

Online Publication Date: 15 December 2003

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Ab initio quantum‐mechanical calculations have been performed for the 5Σg+, 3Σu+, and 1Σg+ states arising from the interaction of two 1s2s3S helium atoms. A rigorous upper bound to the quintet potential was found by use of the variational principle. Crude estimates of the autoionizing singlet and triplet states were obtained by the “stabilization” method. The quintet‐state potentials exhibit a van der Waals minimum, and the triplet and singlet potentials exhibit more substantial minima. The behavior of the wavefunctions in the separated‐atom limit was studied, and the range of applicability of the effective Heisenberg spin Hamiltonian was tested on the calculated potentials.

4f–5dExcitation Energy of Tb3+ in Solids

Teruhiko Hoshina

J. Chem. Phys. 50, 5158 (1969); http://dx.doi.org/10.1063/1.1671031 (5 pages) | Cited 14 times

Online Publication Date: 15 December 2003

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Excitation spectra of the 5D4 → 7F emission of Tb3+ were measured in Sc(or In) BO3, and Y (or Gd) BO3, Y3Ga5O12, Sc (or Y) PO4, and Sc2 (or Y2) O3 at room temperature. The 4f–5d excitation band is discriminated from the host lattice excitation band by inspecting the concentration dependences of the excitation spectra. The energy and the shape of the 4f–5d excitation band are almost the same in the lattices with the same structure. The band splittings are related to the symmetry of the crystalline field acting on Tb3+. The 4f–5d excitation band is extremely enhanced by lowering temperature to 77°K.

Resonance Theory of Termolecular Recombination Kinetics: H+H+M→H2M

Robert E. Roberts, R. B. Bernstein, and C. F. Curtiss

J. Chem. Phys. 50, 5163 (1969); http://dx.doi.org/10.1063/1.1671032 (14 pages) | Cited 97 times

Online Publication Date: 15 December 2003

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A theory is formulated for atomic recombination reactions which is based upon the identification of the set of transition complexes, X2i, as specific quasibound states or orbiting resonances. The conventional “energy‐transfer mechanism” is assumed, since it has been justified under many experimental situations. Calculations, based on a modified distorted‐wave approximation, demonstrate that the main contribution to the rate is that arising from rotational (rather than vibrational) transitions downwards from the quasibound to the bound states. Computations were carried out for the reaction H+H+M→H2+M for M = He, H2, and Ar making use of detailed ab initio knowledge of the spectrum of quasibound states and their wave‐functions. Good agreement was found between the experimental rate constant and that calculated by the present resonance theory. The theory predicts a maximum in the rate in the temperature range between 65° and 100°K, attributed mainly to one particular quasibound state: υ  =  14,j  =  5. This suggests a promising region for further experimental investigation which could provide a critical check of the present theory.

Absolute Far‐Infrared Absorption Intensities of α‐Nitrogen

Robert V. St. Louis and O. Schnepp

J. Chem. Phys. 50, 5177 (1969); http://dx.doi.org/10.1063/1.1671033 (7 pages) | Cited 37 times

Online Publication Date: 15 December 2003

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The absolute intensities of the translational lattice mode absorptions of α‐N2 in the far infrared have been measured. The experimental values are smaller by a factor of 5 than the calculated intensities obtained from a quadrupole‐induced mechanism theory. This discrepancy is discussed in terms of the model on which the theory was based. The intensity of the 50‐cm−1 line was found to be temperature dependent and decreased gradually between 15°K and 35°K. No discrete absorption was observed for the β phase above 36°K. The 50‐cm−1 line has a width smaller than 0.5 cm−1 and the 70‐cm−1 line has a width of 6 cm−1. Evidence was found for a decrease of the frequency of the 50‐cm−1 line as the phase transition temperature is approached.

Natural Orbitals, Divergences, and Variational Principles

Donald H. Kobe

J. Chem. Phys. 50, 5183 (1969); http://dx.doi.org/10.1063/1.1671034 (12 pages) | Cited 17 times

Online Publication Date: 15 December 2003

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Bogoliubov's principle of compensation of dangerous diagrams (PCDD) is extended to finite fermion systems and is shown to give Löwdin's natural spin–orbitals (NSO) which diagonalize the single‐particle reduced density matrix. Hartree–Fock theory corresponds to the compensation of the lowest‐order dangerous diagrams, which cause divergences in the perturbation expansion of the ground‐state energy. The PCDD is then derived from a variational principle that the number of particle–hole excitations in the true ground state is a minimum. The sense in which the NSO give the most rapid rate of convergence of the configuration‐interaction expansion of the true wavefunction is also discussed.

Rydberg States of Benzene in Rare‐Gas Matrices

Benjamin Katz, Malka Brith, Benjamin Sharf, and Joshua Jortner

J. Chem. Phys. 50, 5195 (1969); http://dx.doi.org/10.1063/1.1671035 (9 pages) | Cited 31 times

Online Publication Date: 15 December 2003

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In this paper we present experimental evidence for the observation of Rydberg states of benzene in solid Ar, Kr, and Xe. On the basis of semiquantitative theoretical evidence we argue that molecular Rydberg‐type states of a guest molecule are amenable to experimental observation in rare‐gas solids. These host matrices are characterized by a free electronlike conduction band, leading to a manifold of Wannier‐type states. The electron–atom interaction in rare‐gas solids is relatively weak so that the line broadening of these Rydberg‐type states will not be excessive. The identification of these “Rydberg‐type” states in a rare‐gas solid is based on matrix shifts, vibrational structure, isotope effects, linewidths, and site splittings. Two Rydberg‐type transitions of the benzene molecule were identified. From our analysis we conclude that: (a) The lowest (n  =  1) molecular Rydberg state in the rare‐gas matrix can be correlated with the lowest Rydberg state in the gas phase, but is appreciably blue‐shifted. The blue shifts are: 6000 cm−1 for Ar, 3150 cm−1 for Kr, and 1610 cm−1 for Xe. (b) The benzene Rydberg levels in the rare‐gas matrix reveal some evidence for Jahn–Teller coupling effects, as is evident from the appearance of a nontotally symmetric vibrational component. (c) The linewidths observed for the Rydberg levels in the rare‐gas matrix are qualitatively consistent with theory. (d) The second Rydberg transition in the rare‐gas matrix is tentatively identified as corresponding to a n  =  2 Wannier state, which has no relation to the molecular levels of the isolated molecule. This assignment makes possible an estimate of the ionization potential of the molecule in rare‐gas solids. (e) Our results provide evidence that the lowest molecular Rydberg state and molecular impurity Wannier states are amenable to experimental observation in rare‐gas solids.

Optical Properties of Polymers: Model Calculations for Dinucleoside Phosphates

Allan S. Schneider and Robert A. Harris

J. Chem. Phys. 50, 5204 (1969); http://dx.doi.org/10.1063/1.1671036 (12 pages) | Cited 23 times

Online Publication Date: 15 December 2003

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The optical properties (absorption, polarizability, circular dichroism, and optical rotatory dispersion) are calculated for models of dinucleoside phosphates using the time‐dependent Hartree theory with a simple free‐electron monomer model. Detailed results over the entire frequency spectrum have been obtained for a variety of dimer and polymer structures. The relation between the following conformational effects and the resulting polymer optical properties were determined: base stacking and unstacking, helical winding and unwinding, and changes in distance between monomer planes. In addition, several other optical effects were calculated: the relative contributions of nearest and nonnearest neighbors along an infinite helical polymer; the effect of band half‐width on the observable splitting; and the relation between monomer and polymer line shape. The calculated results predict reasonable quantitative values as well as the main qualitative features of the experimental dinucleoside phosphate and polyribonucleotide spectra. The stacking–unstacking calculations are consistent with the experimental temperature dependencies of the hypochromism and optical rotation of ApA, and the right‐handed‐stacked conformation of this dimer is confirmed.

Configuration Interaction in the Simple Valence‐Bond Wavefunction for the Potential‐Energy Surfaces of Sigma‐Bonded Four‐Center Exchange‐Reaction Complexes

R. N. Porter and L. M. Raff

J. Chem. Phys. 50, 5216 (1969); http://dx.doi.org/10.1063/1.1671037 (7 pages) | Cited 17 times

Online Publication Date: 15 December 2003

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The two closed‐shell and nine open‐shell symmetry‐adapted MO electron configurations contained in the simple nonionic VB wavefunction for H4 in the limit of 2H2 with D2h symmetry and in a D4h complex are identified and their coefficients are obtained in terms of overlap integrals. Numerical comparison of the configuration coefficients obtained from the nonionic VB wavefunction with those obtained by the full CI calculation of Wilson and Goddard show that the ionic contribution to the D4hH4 complex of side 2.54a0 is small in the ground state but significant in the upper state. The implications of a VB or CI treatment of four‐center potential‐energy surfaces regarding a recent extension of the Woodward–Hoffmann rules (conservation of orbital symmetry) to the reactions H2 + D2→2HD and H2 + I2→2HI are discussed.

Determination of Electrolyte Apparent Molal Compressibilities at Infinite Dilution Using a High‐Precision Ultrasonic Velocimeter

R. Garnsey, R. J. Boe, R. Mahoney, and T. A. Litovitz

J. Chem. Phys. 50, 5222 (1969); http://dx.doi.org/10.1063/1.1671038 (7 pages) | Cited 58 times

Online Publication Date: 15 December 2003

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Using a newly designed high‐stability sing‐around circuit ultrasonic velocities in aqueous salt solutions down to concentrations of 2 × 10−4mole/liter have been measured. Adiabatic apparent molal compressibilities at infinite dilution, and where possible standard molal compressibilities, have been determined for some aqueous solutions of tetra‐alkylammonium bromides, alkali‐metal chlorides and sulfates, and MgSO4. The determination of these quantities from precise sound velocity, volumetric, and calorimetric measurements is discussed. The practice of obtaining ϕKs0 from empirical extrapolation of ϕKs data is shown to be unreliable and unnecessary.

Many‐Body Corrections to Isotopic Volume Differences in Solid Neon

J. S. Brown

J. Chem. Phys. 50, 5229 (1969); http://dx.doi.org/10.1063/1.1671039 (3 pages)

Online Publication Date: 15 December 2003

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A calculation is presented of the effect of triple‐dipole forces on the differences of volume of 20Ne and 22Ne lattices at 0°K in the quasiharmonic approximation.

ReO3 Band Structure in the Tight-Binding Approximation

J. M. Honig, J. O. Dimmock, and W. H. Kleiner

J. Chem. Phys. 50, 5232 (1969); http://dx.doi.org/10.1063/1.1671040 (11 pages) | Cited 3 times

Online Publication Date: 15 December 2003

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Using tight-binding, LCAO methodology, a formal band structure scheme has been specified for the ReO3 structure based on the use of 2s and 2p orbitals for oxygen and of 5d, 6s, and 6p orbitals for rhenium. The scheme should also be useful in the characterization of band structures for perovskites in general. Two sets of sufficient conditions have been found under which the secular determinant reduces to two special cases: one corresponding to a model previously considered by Goodenough and the other to a model considered by Kahn and Leyendecker. The nature of the approximation schemes is discussed in some detail.

ESR Relaxation Studies on Orbitally Degenerate Free Radicals. I. Benzene Anion and Tropenyl

Robert G. Kooser, Walter V. Volland, and Jack H. Freed

J. Chem. Phys. 50, 5243 (1969); http://dx.doi.org/10.1063/1.1671041 (15 pages) | Cited 54 times

Online Publication Date: 15 December 2003

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Careful continuous saturation measurements, which include corrections for nonuniform microwave and modulating fields, have been used to examine, at different temperatures, the ESR linewidths and saturation behavior of the benzene anion in a tetrahydrofuran: dimethoxyethane solvent and the tropenyl radical in molten bitropenyl. It has been found that the ratios of the longitudinal to transverse electron‐spin relaxation times (T1 / T2) for these free radicals in solution are about 1.1 ± 0.1 for the benzene anion below − 60°C and for tropenyl at 165°C. Analysis of the results has shown that at 9.1 GHz, g‐tensor, anisotropic dipolar, and spin–rotational relaxation mechanisms do not contribute appreciably to the observed times. The anomalously small relaxation times associated with these radicals have been attributed to effects involving the degenerate ground states of these radicals. The spin‐relaxation behavior of peroxylamine disulfonate anion in aqueous solution has also been studied.

Direct Enumeration Study of Self‐Avoiding Walks on the Tetrahedral Lattice

Mahadevappa Kumbar and Stanley Windwer

J. Chem. Phys. 50, 5257 (1969); http://dx.doi.org/10.1063/1.1671042 (5 pages) | Cited 15 times

Online Publication Date: 15 December 2003

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See Also: Erratum

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By application of a general procedure devised by Martin, we generated, up to N  =  14, the number of self‐avoiding open chains, and determined their mean‐square end‐to‐end distance, their radius of gyration, the number of returns to the origin, and its corresponding mean‐square end‐to‐end distances. The self‐avoiding chain results were in excellent agreement with Monte Carlo calculations, and the mean‐square radius of gyration of ring systems agreed with our previous Monte Carlo estimates. The number of returns to the origin was used to calculate the order of a phase transition for a tetrahedral model of the helix‐to‐random‐coil system. The higher‐order transition found is the same as that previously obtained by Fisher for other three‐dimensional model systems.

Optical, EPR, and ENDOR Studies of CdF2:V3+, V2+

R. H. Borcherts and L. L. Lohr

J. Chem. Phys. 50, 5262 (1969); http://dx.doi.org/10.1063/1.1671043 (4 pages) | Cited 17 times

Online Publication Date: 15 December 2003

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Single crystals of CdF2 containing either V3+ or V2+ ions have been prepared and studied by optical, EPR, and ENDOR techniques. As expected, the properties of V3+ in the eight‐coordinated (cubal) environment closely resemble those of Ni2+ in octahedral sites. The ENDOR data show that Ms  =  ± 1, confirming the identification of the ion as V3+. The V2+ ions, produced by heating samples containing V3+ in Cd vapor, exhibit evidence for a large trigonal Jahn–Teller distortion of the cubal site. On the basis of the EPR and optical data it is suggested that the environment about the V2+ ions may be more nearly octahedral than cubal, thus reflecting the presence of a static trigonal field comparable in magnitude to the (undistorted) cubic field. Some optical and EPR data are presented for isoelectronic Cr3+ ions, which also display a strong Jahn–Teller effect.
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