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Volume 65, Issue 3, 01 August 1976

Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at −45°C
View Description Hide DescriptionUsing a capillary technique for small samples, the isothermal compressibility κ_{ T } of water has been measured to −26°C. Accelerating increases of κ_{ T } at the lower temperatures can be described by an expression of the form κ_{ T }=Aε^{γ} [where ε= (T−T _{ s })/T _{ s }], which is known to describe anomalies encountered in the vicinity of a thermodynamic singularity located at T _{ s }. The implication that the thermodynamic and certain other properties of water at lower temperatures may be decomposed into a normal component and an anomalous component which diverges at T _{ s }=−45°C is supported by analysis of numerous other thermodynamic and relaxation data which extend into the supercooled regime. The anomalous characteristics are shown to originate primarily in the sensitivity of the volume to temperature changes, suggesting a geometrical basis for the cooperative behavior. The singularity at T _{ s }=−45°C may be a lambda transition associated with the cooperative formation of an open hydrogen‐bonded network, but the near coincidence of T _{ s } with the experimental homogeneous nucleation temperature suggests, as an alternative, that T _{ s } may correspond to the limit of mechanical stability for the supercooled liquid phase.

Teratomic recombination in alkali metal–noble gas vapors
View Description Hide DescriptionThe teratomic recombination rates for the reaction M*+2X→MX* (A ^{2}Π)+X have been studied for Rb–Xe, Na–Ar, Kr, Xe, and Li–Ar, Kr, Xe. This analysis employs data and molecular potential determinations from earlier measurements where free alkali M was optically excited to M* in the presence of noble gas X and the MX* (A ^{2}Π) →MX(X ^{2}Σ) fluorescence resulting from teratomic recombination was measured. Collisional processes compete with radiative decay, so that in the low [X] limit where dissociation collisions are negligible the ratio of bound molecular to atomic photon emission gives the branching ratio between the molecular formation rate and the known atomic radiative rate. The molecular spectrum is observed as a continuum whose intensity profile may be used to infer a bound state vibrational distribution at each [X]. Both bound and quasibound states are included in this distribution, as both contribute to the observed molecular spectra. The low pressure limit of this distribution yields the teratomic recombination rate as a function of binding energy, and the total recombination rate constantk _{ f }. It is generally found that this distribution per quantum state is almost independent of binding energy; i.e., the probability of molecular formation appears to be about the same for all bound states, it does not favor the highest bound levels. When the density of states is considered, weakly bound molecules are formed more frequently, but this weighting depends on the shape of the potential rather than the gas temperature. Comparison with theoretical models is made, and reasons for the discrepancies are discussed.

Semiclassical calculation for collision induced dissociation
View Description Hide DescriptionThe classical S‐matrix theory of Miller and Marcus has been used to compute collision induced dissociation probabilities (P ^{diss}) for particle–oscillator one dimensional collisions. The continuum of dissociation states was discretized in a straightforward way by confining the oscillator to a suitably large box. From this simple discretization an expression for P ^{diss} in the limit of an infinite box is derived. Numerical results for a truncated harmonic oscillator with an exponential repulsive interaction with the colliding particle are presented for several masses and potential parameters. The behavior of P ^{diss} as a function of collision energy, well depth and initial vibrational excitation is studied. The energy profile of P ^{diss} shows a prominent structure which is directly related to the initial vibrational state of the oscillator. The relative dissociation ’’efficiencies’’ of the different vibrational levels of the oscillator depend drastically on the collision energy, with highly excited vibrational states being more ’’efficient’’ dissociation candidates at low (near threshold) energies but with the opposite behavior at higher kinetic energies. The dependence of the dissociation probability on potential parameters and masses is analogous to the trends for a comparable energy transfer process.

Molecular alignment and photofragment spectroscopy
View Description Hide DescriptionBy illumination with polarized light, molecules with a dissociative absorption can be aligned by the selective photodissociation of different M states at different rates, as was first shown by Dehmelt and co‐workers for H^{+} _{2}. We have extended this technique to neutral molecules, demonstrating it for a diatomic, IBr pumped by the second harmonic of a neodymium laser at 18 780 cm^{−1}, by observing the recoiling Br fragments with photofragment spectroscopy. Classical and quantum calculations of the selective photodissociationeffect give equivalent predictions except in the limit in which only a few M states remain populated. Several methods are discussed for experimentally monitoring the degree of alignment as a function of light flux: (i) the change in fragment flux, (ii) the change in relative strength of two transitions of different symmetry as reflected in their joint angular distributions, and (iii) the change in the shape of the angular distribution of the recoiling atomic fragments for a single transition. The first two methods are demonstrated for IBr molecules. In addition, experiments using two sequential light pulses are suggested, the second pulse monitoring the alignment produced by the first either through the photofragment angular distribution or through absorption. Our results show that at achievable light fluxes, molecules with dissociative transitions of moderate strength can be strongly aligned. Molecular populations can be prepared which contain only a few M states for each J, or even only M=±J. This technique can potentially provide a wide variety of aligned molecules for molecular beam or bulb studies of relaxation as well as elastic, energy transfer, and reactive scattering, and can provide further directionality for photon and fragment angular recoil studies.

A measurement of the rate constant for the reaction O + O_{2} + O_{2}→O_{3} + O_{2}
View Description Hide DescriptionThe three‐body heterogeneous and wall recombination coefficients for atomic oxygen were measured using an electron paramagnetic resonancespectrometer to monitor the time dependence of the atomic oxygen concentration. This measurements was made for a pressure range from 0.224 to 1.10 torr using pyrolysis of ozone as a source of oxygen atoms. The three‐body heterogeneous rate constant (with molecular oxygen as the third body), resulting from a computer fit of the data to the usual recombination model, was determined independent of ozone concentration to be (6.26±0.94) ×10^{−34} cc^{2} molecule ^{−2} sec^{−1}. The wall recombination efficiency γ for a fused metaphosphoric acid–sodium metaphosphate mixture (the wall coating) was found to be 9.1×10^{−6}.

Determination of collision induced polarizability in Ar, Kr, and Xe by means of collision induced scattering analysis and empirical pair potentials
View Description Hide DescriptionWe show that for the determination of the collision induced polarizability form in Ar, Kr, and Xe from the moment analysis of collision induced scattering it is of primary importance to choose a correct form for the pair interaction potential. We chose the empirical potentials determined by Barker and co‐workers for our investigation, and we determined the polarizability forms from the available experimental data. We compare our argon results with theoretical many‐body calculation of the polarizability.

Theoretical Compton profile anisotropies in molecules and solids. I. Formulation of the MSC procedure and application to lithium fluoride
View Description Hide DescriptionA theoretical calculation of directional Compton profiles and corresponding anisotropies in a diatomic molecule is presented. The different occupied molecular orbitals (MO) give interesting Compton profiles and anisotropies which are related to their roles in the binding of the molecule. The results are extended to approximate a face‐centered‐cubic (fcc) crystal, using a molecular simulated crystal procedure (MSC) in which the MO are modified to match the symmetry of the crystalline environment. The formalism is applied to LiF at an equilibrium spacing of 3.55 a.u., approximately the crystalline spacing. The results compare favorably with previous anisotropy calculations and with experimental measurements of Compton profile anisotropies in LiF.

Further NMR studies of fluoride ion motion in doped β‐PbF_{2}
View Description Hide DescriptionThe fluoride ion motion in β‐PbF_{2}doped with NaF was studied by measurement of the ^{19}F transverse relaxation time (T _{2}), spin lattice relaxation time (T _{1}), and the spin lattice relaxation time in the rotating frame (T _{1r }). Measurements over the temperature range of −50 to 160°C lead to activation energies for T _{1}, T _{1r }, and T _{2} of 0.205±0.01, 0.29±0.02, and 0.27±0.01 eV/ion, and a T _{1r } minimum at 56°C yields a correlation time of 0.74 μsec. Pressure dependence of T _{1} and T _{2} yields activation volumes of ?0.2 cm^{3}/g‐mole and 1.76±0.05 cm^{3}/g‐mole, respectively. These data along with the measuredmagnetic field independence of T _{1} suggest that the measuredT _{1}’s are not caused by ^{19}F motion, but by thermally excited carriers.

The transition state, the electron propagator, and the equation of of motion method
View Description Hide DescriptionThe transition state idea is extended beyond the independent particle model and applied to the electron propagator theory and the so‐called EOM method for calculation of electron binding energies. Application to the second order propagator equations for the neon atom yields excellent results for ionization energies of 1s, 2s, and 2p electrons.

Coriolis coupling and the Raman spectra of SF_{6} and CF_{4} in the liquid and plastic phases
View Description Hide DescriptionIt is shown how to correct the J model to take account of first order Coriolis coupling on triply degenerate lines of spherical tops. The Debye limit of the J model is examined. Corrected Jspectra are then compared to the experimental Raman lines of SF_{6} and CF_{4} in their condensed phases.

Characterization of γ‐ray induced paramagnetic centers in bayerite by means of EPR and ENDOR spectroscopies
View Description Hide DescriptionFour different paramagnetic centers, induced in bayerite samples by irradiation, have been characterized by EPR and ENDOR spectroscopies. Two of them, respectively, of V‐ and F‐types, have been found to be mobile at room temperature and frozen at lower temperature. The first one, with g _{1}= 2.021±0.002, g _{2}=2.010±0.005, and g _{3}=2.005±0.002, is identified with an O^{−} species stemming from the ionization of OH^{−} groups present in the structural cavity walls of the bayerite. The second one, with g _{∥}=1.9970±0.0005 and g _{⊥}=2.0020±0.0005, corresponds to solvated electrons. A third center, with g _{∥}=2.035±0.002 and g _{⊥}=2.0025±0.0005, with strongly hindered motion even at room temperature, is assigned to an O^{−} _{2} species located at the center of the structural cavity, U. The last center is a doublet with a 502.5±0.5 Oe hyperfine splitting and g _{iso}= 2.0022±0.0001; it is due to H atoms located in U. Particular attention has been paid to the ’’matrix’’ ENDOR line at the free proton nuclear frequency and to the nature of the nuclear and electronic relaxation mechanisms that govern its shape and intensity. ENDOR spectra were simulated considering various possibilities for the proton distribution and the relaxation mechanisms. The best agreement is obtained with: (i) a nuclear relaxation time that is angular independent, (ii) a discrete lattice proton distribution in agreement with literature data; (iii) a lower limit for the distance between the paramagnetic center and the different lattice protons that results in the matrix ENDOR line (R≳3.4 Å=0.34 nm). This lower limit excludes all nearby protons that experience direct contact hyperfine interaction; (iv) an upper limit for the distance R. It corresponds to the most distant protons that are involved in the ENDOR mechanism via electron–nuclear dipolar interaction. This limit is shown to increase when microwave power is increased; (v) spin–packet linewidths that are shown to be dependent on the electron spin–lattice relaxation time.

Many‐body perturbation theory applied to Be^{+} ion
View Description Hide DescriptionThe Bruecner–Goldstone many‐body perturbation theory has been applied to the study of the electron correlation problem of atomic beryllium ion in its ground‐state ^{2} S. An orthonormal complete set is generated from V ^{ N–1} potential. In the present calculation, the final correlation energy is −0.0510 a.u., as compared with −0.0477 a.u. from the estimate made by Weiss. The l dependence of the factors, a and b, appearing in the geometric sum approximation is also investigated, and is found to be independent of it in present calculation.

Orientational order parameters and conformation of nematic p‐ethoxybenzylidene‐p‐n‐butylaniline
View Description Hide DescriptionOrientational order parameters for nematic liquid crystalline compound p‐ethoxybenzylidene‐p‐n‐butylaniline (EBBA) have been estimated by studying the dipole–dipole splitings in the wide line NMRabsorption spectra. An attempt has been made to determine the conformation of the same by the NMR studies of one specifically deuterated derivative of the compound.

Saturation effects on collision broadened rotational lines
View Description Hide DescriptionSaturation effects on a three‐dimensional rigid rotator are studied as an extension to several previous works by Gross and the author. The solutions which are obtained for the Karplus–Schwinger (K–S) and the Gross–Lebowitz (G–L) models exhibit a further broadening of the absorption lines.

A dimer model with angular forces: Equation of state
View Description Hide DescriptionA dimer model with angular forces on the square lattice is analyzed. On the basis of low and high density expansions with their Padé approximants it is concluded that it is likely the system exhibits a first order phase transition if the angular forces are fundamentally attractive and do not counteract each other.

The ligand hyperfine interaction with rare earth ions. I. A revised covalent model
View Description Hide DescriptionIt is shown that a reformulation of the covalent model can explain the ^{19}F hyperfine interactions observed for Yb^{3+} and Tm^{2+} in cubic and tetragonal sites of alkaline earth fluorides. The same model does not explain data for Ce^{3+}, Gd^{3+}, or Eu^{2+} indicating that the spin polarizationmodel is the dominant mechanism in the first part of the rare earth series but that the covalent model becomes dominant in the latter half of the series. The analysis shows that the distortion from cubic symmetry in the tetragonal site is not as severe as an earlier NMR analysis suggested but is still large. It further suggests that the interstitial ion is closer to the rare earth ion than most observers have assumed.

The ligand hyperfine interaction with rare earth ions. II. Calculation of the paramagnetic NMR shift
View Description Hide DescriptionThe isotropic and anisotropic^{19}F NMR shifts for Yb^{3+}doped into alkaline earth fluorides is calculated using a covalent model for the spin transfer. The good agreement between theory and experiment is strong evidence for the covalent model being the correct model in the case of Yb^{3+}. The calculations reveal that the main contribution to the isotropic shift does not come from the Fermi contact interaction, as has been generally assumed, but rather from a second order Zeeman term due to a spin–orbit interaction between the nuclear spin and the orbital motion of unpaired electrons in the ligand p orbitals. It has been found that the isotropic shift of Yb^{3+} can be reasonably estimated by calculating the high temperature limit of the shift (k T≫ crystal field splittings) even though k T is about one‐third the crystal field in the sytem studied. A general method of calculating the NMR shift in the high temperature limit is developed which is readily applicable to multispin ions and is applied to the Er^{3+} system.

The predicted infrared spectrum and the structure of the isolated UF_{5} molecule
View Description Hide DescriptionThe infrared absorptionspectrum by the fundamental modes of UF_{5} is calculated using force constants transferred from UF_{6} to predict the wavenumbers and using the F atom polar tensor from CH_{3}F to predict the intensities. Calculations are made for several assumed geometrical configurations of UF_{5}. Comparison of the predicted spectra with the recently observed spectrum, in the UF‐stretching region, of a photolysis product of UF_{6} isolated in an Ar matrix suggests strongly that the structure is square pyramidal (C _{4v }) with the U atom above the F atom equatorial plane. Although the model for the intensities is simple, the calculated spectrum is expected to predict the correct order of magnitude of the intensities of the fundamentals, first overtones, and binary combination bands of UF_{5}, and the approximate wavenumbers for the expected absorption. Some comparisons are given between the calculations for the several structures of UF_{5} and observed spectra of other XF_{5} molecules, including PF_{5}, BrF_{5}, and IF_{5}.

Unified rotational dynamics of molecular crystals with orientational phase transition
View Description Hide DescriptionA unified theory for the rotational dynamics of molecular crystals with orientational phase transitions is given. As basic secular variables one takes symmetry adapted functions, which describe the molecular orientations, and the angular momenta of the molecules. Using Mori’s projection operator technique, one obtains a coupled set of two dynamic matrix equations for the corresponding relaxation functions. The coupling is proportional to the order parameter and accounts for the reactive coefficients. The corresponding collective excitations are librons. The damping of librons is described by two transport coefficients that account for orientational relaxation and angular momentum relaxation, respectively. By approaching the phase transition, both matrix equations decouple, the orientational relaxation describes the critical dynamics. In the disordered phase, this equation describes collective hindered rotations. In the same framework one describes phases of partial order as CD_{4} II. Comparison is made with neutron scattering experiments.

Molecular constants of sulfur dichloride from microwave spectrum analysis
View Description Hide DescriptionThe microwave spectrum of ^{32}S^{35}Cl_{2} has been investigated in the frequency region 9000–36 000 MHz. An analysis of the rotational spectrum and hyperfine structure yields the following molecular constants: rotational constants:A=14 613.36 MHz, B=2920.93 MHz, C=2430.74 MHz; asymmetry parameter: κ=−0.919526; quadrupole coupling constants: χ_{ a a }=−38.98±0.10, χ_{ b b }=−8.87±0.10, χ_{ c c }=47.95±0.10, ‖χ_{ a b }‖=64±10 MHz. The structural parameters obtained from these are d (S–Cl) =2.014±0.005 Å, Cl–S–Cl angle=102.8°±0.2°. The electric dipole moment obtained from the Stark effect of the 0_{0}→1_{0} transition is μ_{ b }=0.36±0.01 D.