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Volume 65, Issue 2, 15 July 1976

Charge transfer in electrostatically coupled chains: Effects of the nearest neighbor Coulomb correlations
View Description Hide DescriptionThe effects of the nearest neighbor Coulomb correlations on the character of the charge transfer between donor and acceptor molecular chains are investigated. We use a modified Hubbard model for the individual donor and acceptor chains. In this model the intramolecular Coulomb interactions are taken to be infinitely large, and the transfer integrals are considered to be infinitely small. All the intermolecular interactions except those between the nearest neighbors along the chains are treated within the mean field approximation. The free energy of this model can be calculated for an arbitrary strength of the nearest neighbor interaction and results are given for the temperature dependences of the charge transfer and the zero field paramagnetic spin susceptibility.

Energy transfer and relaxation phenomena in CaF_{2}:Er^{3+}
View Description Hide DescriptionA selective laser excitation technique has been used to study energy transfer between the individual ions of specific crystallographic sites in charge compensated CaF_{2}:Er^{3+}. Unique energy transfer rates have been obtained directly from the fluorescent transients of the selectively excited sites. No energy transfer processes were observed between sites corresponding to single Er^{3+} ions. For those sites composed of Er^{3+} clusters, very efficient and complex intracluster energy transfer was observed despite large energydefects requiring phonon assistance. The ion pair relaxation processes compete efficiently with multiphonon relaxation because smaller contributions from lattice phonons are required. Analogous energy transfer interactions were found to occur between Yb^{3+} and Er^{3+} ions in mixed cluster sites in double‐doped crystals. Detailed relaxation and energy transfer mechanisms are presented. Kinetic expressions describing excited state relaxation are derived from these mechanisms and are used to provide theoretical fits to experimental fluorescence transients confirming the relaxation mechanisms proposed.

Nuclear magnetic relaxation of ^{119}Sn, ^{35}Cl, and ^{127}I in two symmetric top molecules, SnCl_{3}I and SnI_{3}Cl, in liquid mixtures
View Description Hide Description^{119}Sn nuclear magnetic relaxation times were measured for the two symmetric top chloroiodides of tin in the liquid state using pulsed nuclear magnetic resonance. The temperature and magnetic field dependence of T _{1} and T _{2} of ^{119}Sn in SnCl_{3}I and SnI_{3}Cl were studied to identify and separate relaxation mechanisms. The longitudinal relaxation rates were found to arise from competing scalar and spin–rotation interactions, while the transverse rates are completely scalar dominated. T _{1}’s of both SnICl_{3} and SnCl_{3}I show evidence of a maximum in (T _{1})^{−1} _{scalar} when T _{2}(^{127}I) equals the difference of the ^{119}Sn and ^{127}I Larmor frequencies. This behavior is predicted by Abragam’s ’’scalar relaxation of the second kind.’’ The maximum occurs near the melting points in a 5 kG field and was used indirectly to determine ^{127}I relaxation times. A least‐squares analysis of these results permitted direct determination of three tin–halogen scalar coupling constants: J (^{119}Sn–^{127}I) =1638 Hz for SnCl_{3}I, J (^{119}Sn–^{127}I) =1097 Hz for SnI_{3}Cl, and J (^{119}Sn–^{35}Cl) =421 Hz for SnI_{3}Cl. Rotational correlation times and halogen relaxation times were also measured as a function of temperature. The analysis failed to reveal a T _{1} component due to chemical shift anisotropy for any of the compounds at or below 13.3 kG. A comparison of molecular rotational correlation times with those of the unmixed tetrahalides, SnCl_{4} and SnI_{4}, indicates that electric dipole forces and shape effects associated with deviations from tetrahedral symmetry are less important determinants of the rotational diffusion tensor than is intermolecular rotational friction resulting from London dispersion forces. The effect on rotational diffusion constants of varying the composition of the medium was examined and found to be small.

Argon–helium mixture viscosities from independent intermolecular potentials
View Description Hide DescriptionThe viscosity of gaseous argon–helium mixtures at 298 K is calculated in terms of quantum collision integrals for many‐parameter potentials that were previously obtained without the use of measured values of nonequilibrium bulk properties. The Chapman–Enskog first approximation expression and the Sutherland expression are used to evaluate the viscosity, with the Chapman–Enskog expression proving superior, in fact fitting experiment to within the uncertainty of the potential parameters for all but the most helium‐rich compositions. To confirm this result, the collision integrals are obtained by least‐squares fits of the two viscosity expressions to the data itself. The Chapman–Enskog expression accommodates the data within the experimental tolerance of ±0.1%, while the Sutherland fit deviates from the data as much as ±0.5% and does so with an argon–helium collision integral significantly different from that of the a b i n i t i o calculation.

Mössbauer spectroscopic studies of frozen aqueous solutions of Fe^{3+} salts
View Description Hide DescriptionFrozen aqueous solutions (FAS) of Fe^{3+} salts have been investigated by use of Mössbauer spectroscopy in order to study the conditions for formation of glasses. A general discussion of spin–spin relaxation in glasses is given, and we discuss how changes in the spin–spin relaxation time can be attributed to changes in the average separation between the ironions. In the FeCl_{3}–H_{2}O system, it was found that homogeneous glasses are easily formed when the salt concentration is larger than 3.5 moles FeCl_{3} per 100 moles H_{2}O. In more dilute samples, icecrystallizes during cooling, while the salt concentration of the solution increases. At low temperatures the crystallization terminates and the remaining liquidsolidifies into a glass. During exposure at 200 K, the dilute samples change irreversibly. This is discussed in terms of a metastable phase diagram. The properties of frozen solutions with other glass forming agents such as NO_{3} ^{−}, ClO_{4} ^{−}, and glycerol are also discussed. In some systems it was found that the states obtained after cooling depend critically on the cooling rate.

Elastic and rotationally inelastic diffraction of hydrogen molecular beams from the (001) face of LiF at 80°K
View Description Hide DescriptionThe in‐plane scattering of H_{2} molecules at thermal energies from the (001) face of LiF was studied at low temperatures, by means of nozzle beam techniques. Both elastic and rotationally inelastic diffraction peaks were resolved over a wide range of incident and final angles. Taking into account the properties of the supersonic beam,diffraction probabilities were derived for the observed peaks. A discussion of the results in light of the present theories is given. The large probability of occurrence of rotational transitions in the presence of the surface is pointed out.

Rotational relaxation in HD–inert gas mixtures
View Description Hide DescriptionAn expression for the inelastic collision cross section σ (l m→l′m′) has been derived for the rotational transition in the HD molecule caused by a collision with an inert gas atom. The interaction potentials for the HD systems have been derived from the theoretical potentials for the H_{2} systems by shifting the center of mass of the molecule. The rotational relaxation number values have been calculated for HD–He, HD–Ne, and HD–Ar systems in the temperature range from 10 to 100 °K. A good agreement has been obtained between theory and experiment. Temperature dependence and the effect of replacement of an isotope in a homonuclear molecule have been discussed in detail.

Thermal expansion and Grüneisen parameters of a polyoxymethylene crystal
View Description Hide DescriptionThe linear thermal expansion coefficient α of polyoxymethylene has been measured parallel (_{∥}) and normal (_{⊥}) to the symmetry axis, from 2 to 32 K, 55 to 90 K, and at 283 K. Below 100 K, α_{∥} is small and negative, while α_{⊥} is relatively large and positive. The heat capacity has been measured from 2 to 18 K and values have been calculated for the principal Grüneisen parameters γ, γ_{⊥}, and γ_{∥}. The first two are nearly constant at ∼+1.3 from 3 to 80 K, while γ_{∥} has a value of ∼−1.1 at helium temperatures but becomes positive at higher temperatures.

Metric geometry of equilibrium thermodynamics. V. Aspects of heterogeneous equilibrium
View Description Hide DescriptionThe general analysis of phase equilibrium in heterogeneous systems is considered from an abstract geometric point of view. Particular attention is drawn to the thermodynamic ’’invariants’’ (or ’’symmetries’’), which arise as null eigenvectors of the thermodynamic metric matrix and can be associated with variations which leave the thermodynamic state unchanged. The analysis of these invariants leads to conditions connecting the thermodynamic field vectors, including Gibbs–Duhem relations, Clausius–Clapeyron equations, Gibbs–Konowalow laws, and systematic generalizations thereof.

Negative ions from phosphorus halides due to cesium charge exchange
View Description Hide DescriptionAn experiment has been conducted in which cesium atoms in the kinetic energy range 2–350 eV collide with phosphorus halides. Parent anions and fragments are formed. Molecular energies are obtained from threshold measurements. The electron affinites for PCl_{3}, POCl_{3}, PBr_{3}, PCl_{2}Br, PBr_{2}Cl, and POCl_{2} are found to be 0.8, 1.4, 1.6, 1.5, 1.6, and 3.8 eV, respectively. The P–X bond energies for PCl_{3}, POCl_{3}, and PBr_{3} are 3.3, 3.5, and 2.6 eV, respectively.

The structure of the liquid–vapor interface
View Description Hide DescriptionA formal derivation is presented for the equilibrium relation between the singlet density in a fluid and the direct correlation function and for the equivalent relation involving the pair number density. It is shown that this relation is equivalent to the macroscopic condition for hydrostatic equilibrium when the singlet density varies sufficiently slowly to permit the introduction of local thermodynamics. Some aspects of the usage of this in the determination of the singlet density in the liquid–vapor transition region are discussed.

Liquid carbon tetrachloride: Atom pair correlation functions from neutron and x‐ray diffraction
View Description Hide DescriptionNeutron and x‐ray diffraction data for liquid CCl_{4} at 20 °C are presented and analyzed to yield structure and correlation functions for C–Cl and Cl–Cl atom pairs in different molecules. In the liquid, a central molecule is interlocked with four of its nearest neighbors and this arrangement explains the strong orientational correlations that exist over short radial distances. The data are sufficiently accurate to provide a sensitive test for molecular theories of the liquid state and for intermolecular forcemodels in computer experiments.

Tunneling rotation of the methyl radical in solids
View Description Hide DescriptionHyperfine coupling elements, energy levels, and ESR transition frequencies have been computed for the methyl radical taking into account the large anisotropy of the proton hyperfine couplings. The interpretation of low‐temperature ESR and ENDOR spectra of methyl radical is discussed with particular attention to the tunneling rotation about the threefold axis.

Molecular motions in compressed liquid water
View Description Hide DescriptionProton and deuteron NMR spin–lattice relaxation times in liquid water and heavy water were measured as a function of pressure and temperature in the range 10–90°C and 1 bar–9 kbar. D_{2}O was also studied at 150 and 200°C. Availability of density and viscosity data under these experimental conditions enabled us to separate the effects of temperature and density on the spin–lattice relaxation times,T _{1}, and viscosities. Under the assumption that the intermolecular dipolar contribution to the protonT _{1} follows the changes in shear viscosity with temperature and density, we separated the intramolecular and intermolecular dipolar contributions to the protonT _{1}. We found that at a temperature of 10°C the initial increase in density leads to faster reorientation of the water molecules. The effect was much smaller at 30°C. Analysis of the experimental data on H_{2}O and D_{2}O leads to the conclusion that compression diminishes the coupling between the rotational and translational motions of water molecules. The change in the nature of the rotation–translation coupling with increasing density is mainly responsible for the failure of the Debye equation to describe the density effects on the reorientation of water molecules. In the case of D_{2}O we find a relatively small variation in the deuteron quadrupole coupling constant with increasing density. Its average value is approximately 230 kHz over the range of our experimental conditions. Another experimental finding of this study is the decrease in the activation energies for relaxation and shear viscosity with increasing density. All the experimental evidence indicates that compression of water leads to significant distortion and/or disruption of the hydrogen bond network with the important consequence that the dynamic behavior of water under high compression resembles more that of a ’’normal’’ molecular liquid of comparable molecular size. At high densities the hard core repulsive interactions begin to dominate over the directional interactions which are mainly responsible for the open structure of liquid water at low temperatures and pressures.

An inverse approach to the theory of fluids
View Description Hide DescriptionWe construct a random process to simulate a model mixture (in any number of dimensions) at equilibrium. The system is exactly soluble but has an underlying potential dependent on macroscopic parameters. We argue that regarded as an approximation to a physical system its behavior can be interpreted as a phase separation. We argue that a general approximate theory of fluids might be built along the lines suggested in this paper.

New values of the light scattering depolarization and anisotropy of water
View Description Hide DescriptionA new value for the depolarization ratio of pure water has been measured at 514.5 nm using an argon ion laser light source and photon counting detection. This depolarization ratio is lower than any previous literature value by a substantial amount. Stray light and photometer geometry are shown to be responsible for overestimated values reported previously. The depolarization ratio is also shown to be a function of the portion of the spectrum being investigated. With no filters we find ρ_{ v }=0.026. The magnitude of error due to finite acceptance angle is calculated and shown to be substantial. Depolarization ratios using 0.46 and 22.5 nm filters (half‐peak bandwidth) are reported.

Pairwise trapping of radicals in single crystals of n‐decane irradiated at 1.5 and 4.2°K
View Description Hide DescriptionThe electron spin resonancespectra of single crystals of n‐decane‐d _{22}, n‐decane‐h _{22}, and their mixtures irradiated and measured at 1.5 and 4.2°K have been studied to shed light on the mechanisms of alkyl radical formation in saturated hydrocarbons. From the analyses of low temperature spectra and of the spectral changes caused by thermal annealing, it is suggested that almost all alkyl radicals are inherently formed in pairs and that the initial radical pair formation is fairly random especially for distant radical pairs, although there is some preference in the short range reactions for forming very close radical pairs with separation shorter than 6 Å. The predominant radical pairs in deuterated crystals irradiated at 1.5 and 4.2°K have separations ranging 6–25 Å. The spatial distribution of the generation of paired radicals depends upon irradiation temperature. Radical site migration takes place even at 35°K. There is a remarkable mass effect on the spatial distribution of the paired radicals. The deuterated crystals give much smaller spatial distribution. Random scission of the C–H bonds at any carbon atom seems to take place at 4.2°K.

A derivation of the cell cluster theory for harmonic solids
View Description Hide DescriptionThe cell cluster algorithm for the calculation of the free energy of harmonic solids is obtained as a resummation of the central moment expansion of the free energy. The nth term in the central moment expansion corresponds to n‐step closed walks on the lattice, whereas the nth correction term in the cell cluster expansion corresponds to closed walks of any number of steps which visit n lattice sites.

An SCF method for hole states
View Description Hide DescriptionAn SCF method is derived for doublet states with one vacancy in an orbital within the occupied manifold (hole states). This method gives an upper bound to an excited state energy. Hence it is a stable procedure which is bounded from below and cannot collapse to a lower energy SCF state. This new procedure is compared with several other open‐shell SCF procedures which have been advocated for the ground doublet state.

Thermochemical studies of the gaseous lower‐valent fluorides of molybdenum
View Description Hide DescriptionEquilibria among the gaseous molybdenum fluorides were studied by high temperature mass spectrometry, and the results were used to derive thermochemical heats of formation and bonddissociation energies for the gaseous species MoF, MoF_{2}, MoF_{3}, MoF_{4}, and MoF_{5}. Effusion beams containing the gaseous fluorides were generated by the reaction of SF_{6} or MoF_{6} with elemental Mo at temperatures of 1100–2200 K, and the thermochemical results were derived from a second‐law analysis of the equilibrium data. Values of the standard heats of formation, ΔH f °_{298}, obtained are as follows: for MoF, 65.0±2.2 kcal/mol; MoF_{2}, −40.2±2.9 kcal/mol; MoF_{3}, −141.5±3.5 kcal/mol; MoF_{4}, −228.0±3.9 kcal/mol; and MoF_{5}, −296.7±8.6 kcal/mol. The value for MoF yields the dissociation energyD ^{0} _{0}(MoF) =110.3±2.2 kcal/mol (4.78±0.10 eV). Estimated spectroscopic and molecular constants are consistent with the gaseous equilibrium data, indicating that assumptions about the derivation of equilibrium constants from ion currents are reasonable. ]