Index of content:
Volume 71, Issue 1, 01 July 1979

Crystalline vanadium (II) fluoride, VF_{2}. Preparation, structure, heat capacity from 5 to 300 °K and magnetic ordering
View Description Hide DescriptionCrystalline VF_{2} was prepared by the reduction of VF_{3} in an atmosphere of 3 H_{2}:1 HF at 1100°C. The VF_{2} formed deep blue crystalline needles. The crystal structure is of the rutile type, space group P4_{2}/m n m. Parameters determined by x‐ray diffraction are a=4.804±0.005 Å, c=3.237±0.005 Å, u=0.306±0.005. The low temperature heat capacity of VF_{2} is reported from 5 to 300 °K. A sharp peak in heat capacity associated with the development of long‐range magnetic order is observed at 7 °K. Smoothed values of the total heat capacity,entropy,enthalpy, and Gibbs energy are tabulated between 5 and 300 °K. Values at 298.15 °K are: C °_{ P }=15.10 cal °K^{−1} mole^{−1}, S °=18.217 cal °K^{−1} mole^{−1}, H°−H°_{0}=2661.0 cal mole^{−1}. By a corresponding states approximation the magnetic contributions to the heat capacity and entropy are calculated. The magnetic heat capacity has a gradual maximum at 26.8±1 °K. The heat capacity curve agrees with that calculated for a one‐dimensional chain with antiferromagnetic Heisenberg interactions. A value of the exchange constant, J/k=−9.4±0.4 °K is obtained.

Heat capacity and entropy of CuF_{2} and CrF_{2} from 10 to 300 °K. Anomalies associated with magnetic ordering and evaluation of magnetic contributions to the heat capacity
View Description Hide DescriptionThe low temperature heat capacity of CuF_{2} and of CrF_{2} is reported from 10 to 300 °K. Peaks in heat capacity associated with the onset of long‐range magnetic order are observed at 70.90±0.05 °K for CuF_{2} and 49.26±0.01 °K for CrF_{2}. Magnetic contributions to the heat capacity and entropy are evaluated and tabulated. Smoothed values of the total heat capacity,entropy,enthalpy, and Gibbs energy are tabulated between 10 and 300 °K. Values at 298.15 °K are: CuF_{2}, C °_{ P }=15.65 cal °K^{−1} mole^{−1}, S °=18.506 cal °K^{−1} mole^{−1}, H°_{ T }−H°_{0}=2891.8 cal mole^{−1}; CrF_{2}, C °_{ P }=15.48 cal °K^{−1} mole^{−1}, S°=20.762 cal °K^{−1} mole^{−1}, H°_{ T }−H°_{0}−2911.5 cal mole^{−1}.

Comparison of dielectric and refractive virial coefficients and collision induced absorption bands
View Description Hide DescriptionThe second dielectric virial coefficient minus the second refractive virial coefficient is equal to the Kramers–Kroning contributions arising from the far‐infrared and infrared pressure induced absorption bands due to bimolecular interactions. The usefulness in comparing such results is illustrated for CO_{2}, C_{2}H_{4}, CH_{4}, and SF_{6}. It is shown that for SF_{6} there may be as yet unmeasured collision induced bands and for C_{2}H_{4} the far‐infrared collision induced absorption is anomalously large.

Electron impact study of the 50 000 cm^{−1} band of benzene
View Description Hide DescriptionThe 5.7–6.7 eV energy loss region of the electron scatteringspectrum of benzene which contains the 50 000 cm^{−1} (2100 Å) optical absorption band has been studied with incident energies from 10 to 42 eV, scattering angles from 0° to 15°, and energy resolution from 25 to 35 meV. Three different inelastic processes have been detected including the S _{2} ^{1} B _{1u }←S _{ o } transition whose diffuse vibronic bands extend from 6.0 to 6.7 eV, a process at 6.31 eV which occurs strongly at incident energies above 20 eV and increases in intensity relative to the rest of the spectrum with increasing scattering angle and a weak, featureless process below the onset of the S _{2}←S _{ o } transition starting at 5.67 eV. Aside from the weak process below the onset of the S _{2} state and a singlet–triplet transition observed at very low impact energy, the electron impact spectrum at incident energies below 20 eV and scattering angles to 15° agrees completely with the optical absorptionspectrum. The 6.31 eV process arises from a second electronic state at this energy which causes the apparent shift in vibronic band intensities with scattering angle of the S _{2}←S _{ o } transition first observed by Lassettre e t a l. The state responsible for this effect is shown to be the same state observed in two photon absorption by Johnson and assigned as ^{1} E _{1g } or ^{1} E _{2g }. Neither the 6.31 eV process nor any energy‐shifted analog of it is observed in toluene—providing additional evidence that the 6.31 eV state is a Rydberg state.

The description of the smectic A and C phases and the smectic A–C phase transition of TCOOB with a diffuse‐cone model
View Description Hide DescriptionA previous paper demonstrated that the orientational disorder present in all smecticA phases causes most molecules to make fairly large angles with the normal to the smectic plane. Thus, the molecular directions form a diffuse cone around the layer normal. It is now argued that even the p r e f e r r e d directions of the molecules in a smecticA phase will make a nonzero angle with the layer normal, and from the data examined, this angle, ϑ_{ m }, appears to be about 10–15 ° for the compound TCOOB (t r a n s‐1,4‐cyclohexane‐di‐n‐octyloxybenzoate). The smecticA‐to‐Cphase transition is found to have two aspects in the diffuse‐cone model: the distribution of the molecular directions around the layer normal loses its rotational symmetry at the phase transition temperature T _{ A–C }, and the angle ϑ_{ m } starts increasing sharply at a temperature T _{ t }. In most cases these two temperatures are probably equal. The increase of ϑ_{ m } with decreasing temperature in the smecticC phase of TCOOB can be described by a (T _{ t }−T)^{0.35} dependency superimposed on a much smaller linear temperature dependency already present in the smecticA phase.

Relativistic calculation of the electronic structure of UF_{6}
View Description Hide DescriptionUsing a one‐component relativistic theory we have obtained the self‐consistent (SCF) one‐electron levels of UF_{6} via the multiple scattering (MS) Xα method. The calculated ionization energies are found to be in good agreement with the photoionizationspectrum. Our first electronic transition (dipole forbidden) energy at 3.34 eV agrees well with the onset of absorption and the experimentally assigned transition at 3.04 eV. An analysis of the spin–orbit parameters, calculated via perturbation theory, is given. It is found that the contributions from the 6p components are especially important. We conclude that the absorptionspectrum can not be interpreted in terms of the spin–orbit splitting of the highest occupied MO (t _{ l u }). A comparison is made with other relativistic (and nonrelativistic) one‐electron calculations of UF_{6}. This comparison yields reasonable agreement on the relativistic one‐electron structure of this molecule.

Polydisperse systems. I. Scattering function for polydisperse fluids of hard or permeable spheres
View Description Hide DescriptionThe scattering function I (k) for all k is given in the Percus–Yevick approximation for a polydisperse fluid of hard spheres. The extension to a simple model of interpenetrable particles introduced herein, the permeable‐sphere model, is made in order to widen the applicability of our results to colloid and polymer problems.

Raman spectroscopy of the hydrogen bond in crystallized normal and deuterated glycerol: Influence of the anharmonic multiphonon interactions on ν_{OH}, ν_{OD}, and γ_{OH} vibrations
View Description Hide DescriptionThe polarized Raman spectra of oriented single crystals of glycerol (normal and 0‐deuterated) have been recorded from 120 to 273 K; the spectra of super‐cooled and glassy glycerol have been obtained within the same range of temperature. The behavior of the ν_{OH}, ν_{OD} and γ_{OH} bands of the crystal is analyzed according to the theory of anharmonic multiphonon processes. The interactions involving one or two low‐frequency (optical and acoustical) phonons appear to be chiefly responsible for the damping of these modes. The thermal shift of the bands is mainly assigned to the effect of volume variation; the corresponding Gruneisen mode parameters are calculated.

Low energy electron scattering from methane
View Description Hide DescriptionMeasurements of the exponential attenuation of electron currents in a straight line collision chamber are reported using methane gas as the scattering medium. From the transmission spectra obtained at different methane pressure in the scattering chamber, the total cross sections for the energy range 0–16 eV are derived and compared to previous measurements. A small structure in the region of the Ramsauer–Townsend minimum is observed, confirming earlier interpretations of electron swarm experiments. A possible mechanism of excitation is discussed.

Electronic spectroscopy in condensed media: The lowest n‐π* transition of the solvated nitrite anion
View Description Hide DescriptionA general formalism developed in earlier publications for treating the electronic spectra of solvated anions is found to successfully described the spectra of the nitrite anion in solvents of differing polarity (H_{2}O, EtOH, CH_{3}CN, DMF). The analysis presented supports the conclusions that the first excited state (^{1} B _{1}) of the solvated nitrite anion is a bound state. The entire width of the spectra can be accounted for via a Frank‐Condon progression alone. The predicted vibrational frequencies of the participating bending mode in the aqueous solution are found to be 1074 and 827 cm^{−1} in the ground (X ^{1} A _{1}) and the excited (^{1} B _{1}) states, respectively. These predicted frequencies have been further verified by a b i n i t i o calculations which simulate the gas‐phase and solvated ion. The force constant for the ground state bending mode is found to be 9.8×10^{−11} dyne cm. in aqueous solution. The fitting procedure allows us to calculate an inhomogeneous broadening of 383 cm^{−1} for NO_{2} ^{−} in water. These properties have been also calculated for the other solvents (EtOH, CH_{3}CN, and DMF) and trends in the changes of these quantities have been established.

Mode‐to‐mode vibrational energy flow in S _{1} benzene. V–V resonant energy transfer, microscopic reversibility, and the role of level degeneracies
View Description Hide DescriptionThe pattern of mode‐to‐mode vibrational energy flow from the level ν_{6}′=522 cm^{−1} in the S _{1} state of benzene has been studied with OCS as a collision partner. OCS has a near resonant bending vibration ν_{2} ^{″}=520 cm^{−1}. V–V transfer to this bend of OCS is efficient, requiring only ten collisions. However, a T,R→V transfer from OCS adding ν_{16}′=237 cm^{−1} to the ν_{6}′ benzene fundamental is even more efficient. Since other V–T,R transfers are also fast, the V–Vresonance does not dominate vibrational energy flow pattern from the initially excited benzene level. As with other added gases energy flow is governed by strong propensity rules which can be expressed simply in terms of final level degeneracies, vibration quantum changes, and energy exchange between V and T,R degrees of freedom. Measurements of V–T,R transfer rates from other S _{1} benzene levels with added CO have been used to demonstrate microscopic reversibility and to show the control of transfer rates by the degeneracies of the final level. OCS also quenches the S _{1} electronic state of benzene with a rate constant k= (1.1±0.1) ×10^{6} Torr^{−1} s ^{−1} for destruction of the S _{1} state with a 300 K Boltzmann distribution of vibronic levels.

Unification of the methods of Onsager and Monchick for calculating the probabilities of various fates in diffusion‐controlled reactions, with applications to diffusion in space and in a plane
View Description Hide DescriptionWe have unified the methods of Onsager and Monchick for calculating the probabilities for the various fates (reaction, escape, re‐encounter, etc.) of a particle undergoing a diffusion‐controlled reaction in three dimensions; the unified treatment applies also to diffusion in a plane and leads easily to some results which have either not been derived before or have required considerable labor. Finally, explicit solutions for a specific force field representing both attraction and repulsion are given.

Laser magnetic resonance spectroscopy of the ν_{2} fundamental band of DO_{2} at 9.8 μm
View Description Hide DescriptionThe ν_{2} fundamental band (bending vibration, ν_{0}=1020.162 cm^{−1}) of the deuteroperoxyl radical DO_{2} has been studied using the technique of laser magnetic resonance, in which molecular transitions are tuned into resonance with fixed laser lines by means of the Zeeman effect. The DO_{2} was produced in a flow system by reacting the products of a discharge in O_{2} with methanol (CH_{3}OD or CD_{3}OD) or ethanol (C_{2}H_{5}OD). About 150 resonances, observed using 19 different CO_{2} laser lines in the 1009–1038 cm^{−1} region, were assigned to DO_{2} transitions with 1⩽N⩽9 and 1⩽K _{ a }⩽6. Their analysis yielded the ν_{2} band origin as well as rotation, spin–rotation, and centrifugal distortion parameters for the ground and ν_{2} excited vibrational states. It was necessary to include in the analysis the effects of Coriolis interaction between ν_{2} and ν_{3}, which lies about 100 cm^{−1} higher in energy. Thus the Coriolis coupling constant and some effective ν_{3} band parameters were also determined, though ν_{3} was not observed directly.

Calculations of surface structures for naphthalene crystals
View Description Hide DescriptionModels for surface structures on (001) and (100) planes have been calculated for naphthalene crystals, assuming semiempirical atom–atom potentials. Relaxation of the bulk structure in proximity of surfaces leads to small shifts, with molecular rotations of the order of 0.5–2° and translations of the molecular centers of 0.007–0.1 Å, without appreciable energy variations; on going inside the crystals these effects fall off rapidly. The perfect cleavage of the crystal on (001) is easily explained on grounds of packing energy and of the most likely surface model.

A study of laser‐assisted surface ionization of lithium
View Description Hide DescriptionAn experimental study on the influence of electronic energy in surface ionization has been performed using hot tantalum and rhenium ribbons with electronically excited lithium. Upper limits of quantum yield for this process are 10^{−4} for the tantalum and 4×10^{−2} or less for the rhenium.

A Monte Carlo study of the dense polarizable dipolar hard sphere fluid
View Description Hide DescriptionIn this paper we report Monte Carlo results for a fluid of polarizable dipolar hard spheres. Both isotropic and anisotropic particles are considered. It is shown that the induced forces make a large contribution to the thermodynamic properties and significantly influence the fluid structure. The various approximate treatments of polarizable systems are evaluated and a recent theory proposed by Wertheim is found to be very successful.

Correlation function of an anisotropic fluid of hard rods to first order in the density
View Description Hide DescriptionThe pair correlation function of an anisotropic fluid of hard rods, allowed to point only in three perpendicular directions, is calculated to first order in the density. Using this correlation function, the average of a model isotropic intermolecular attraction is evaluated; the results support a previous suggestion that short range correlations in a liquid crystal affect very significantly the dependence of the internal energy on the liquid crystal orientational order parameter.

Charge overlap effects in dispersion energies
View Description Hide DescriptionCharge overlap effects in dispersion energies are calculated using frequency dependent atomic polarizabilities. The dispersion energy is expanded in the usual multipole interaction series but the dispersion coefficients are found to be given as a product, C (L _{ A },L _{ B }) χ (L _{ A },L _{ B };R) where C (L _{ A },L _{ B }) is the usual coefficient for nonoverlapping fragments and χ is called a damping function which equals one asymptotically. Damping functions have been calculated for He(1^{1} S)–He(1^{1} S), Be(1^{1} S)–Be(1^{1} S), and combination of He(2^{3} S), He(2^{1} S), He(1^{1} S), and H(1^{2} S). The results are used to analyze qualitatively the extent of the dispersion contribution to the energy of interactions at either the equilibrium separation or the critical distance for orbiting collisions.

The variational method and the stochastic‐Liouville equation. II. ESR spectral simulation via finite elements
View Description Hide DescriptionA Galerkin finite element(FE) method, closely related to the variational FE method of Zientara and Freed, is developed for the solution of the stochastic Liouville equation (SLE). The particular illustrative application considered is the ESR spectral simulation of the simple axially symmetric gtensor problem. Both linear and quadratic interpolating functions are considered. It is found for this simple case that the Galerkin FE is almost, but not quite, as efficient as eigenfunction expansions (EE). However, the potential advantages of the Galerkin FE in more complex problems are discussed.

Critical behavior of the refractive index in a binary fluid
View Description Hide DescriptionWe have performed very accurate interferometer measurements of the refractive indexn (precision ±6×10^{−7}) in the critical mixture nitroethane–iso‐octane. n depends on the density ρ and local field effects F. Even though this mixture is expected to show a very small anomaly in Δρ/ρ (exponent α) so that local field effects should have been observed, in fact we never saw a contribution due to F and the critical behavior of n is governed by the density anomaly alone. Using the matching of refractive index components and of thermal derivatives, the regular part of n can be evaluated and the value α=0.10±0.02 is found, in agreement with the group renormalization value 0.110. The corresponding amplitude is compatible with the value obtained from ξ_{0} and (∂T _{ c }/∂_{ p }) _{ V },_{ x c } measurements using universal amplitude relations.