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Volume 65, Issue 8, 15 October 1976

Statistical mechanics of chemical equilibria and intramolecular structures of nonrigid molecules in condensed phases
View Description Hide DescriptionAn exact classical statistical mechanical theory is developed which describes how intermolecular forces alter the average intramolecular structures of nonrigid molecules and how these forces affect the equilibrium constant of chemically reacting species. The theory lends itself to computationally convenient approximations. Three illustrative applications of the theory are given. First, the equilibrium constant for the reaction N_{2}O_{2}?2NO_{2} is studied. Second, the shift in the chemical bond lengths of N_{2} and O_{2} from their gas phase values to those in the liquid are calculated from the theory. Third, the average conformational structure of n‐butane in various dense fluid solvents is predicted. The basic methods used in the derivation of the theory are the techniques of physical cluster series (as opposed to the usual Mayer ’’mathematical’’ cluster expansions), and topological reductions. The formalism gives rise to a renormalization of chemical bonding Boltzmann factors so that the theoretical expressions are not swamped by essentially infinite and unnormalized cluster functions. Along with the results on chemical equilibria and intramolecular structures, the interaction site cluster series for intermolecular correlation functions is rederived in a more general manner than the derivation originally presented by Ladanyi and Chandler.

An ab initio potential‐energy surface study of several electronic states of NO2
View Description Hide DescriptionThe results of abinitio potential‐energy surface calculations are presented for 12 doublet and four quartet states of NO2. In several cases Cs as well as C2v conformations have been studied. The predicted equilibrium conformations and the character of the wavefunctions are discussed. Vertical excitation energies are given for 40 doublet and 12 quartet states. The electronic spectrum of NO2 is discussed, and barriers to photodissociation are estimated for several electronic states. Whether states will be strongly Jahn–Teller coupled by a symmetry‐reducing vibrational interaction depends on their potential surfaces and the character of their wavefunctions. This vibronic interaction in some cases is expected to produce non‐C2v equilibrium conformations.

Vibrational resonance energy transfer and dephasing in liquid nitrogen near its boiling point: Molecular computations
View Description Hide DescriptionOn the basis of current models of oscillator–oscillator and oscillator–anharmonicity–lattice coupling, the band broadening increments leading to the spontaneous width of the (near‐isotropic) Raman stretching fundamental of liquid nitrogen near its boiling point are predicted. Using known constants of the atom–atom Lennard‐Jones potential and known dynamic autocorrelation times of the system, the observed spontaneous bandwidth of 0.067 cm^{−1} and its Lorentzian band contour are satisfactorily reproduced (0.07 cm^{−1}) by a vibrational dephasing mechanism if it is assumed that motional narrowing takes place through a modulation process decaying on the same fast time scale as that of the velocity correlation between two nitrogen molecules. On the other hand, resonanceenergy transfer contributes less than 1% to the band broadening.

Electron scattering by N_{2} at 5 and 10 eV: Rotational–vibrational close‐coupling calculations and crossed beam studies of vibrational excitation
View Description Hide DescriptionThe ratios of differential cross sections for excitation of the first excited vibrational state to differential cross sections for elastic scattering of N_{2} have been measured at scattering angles ranging from 20° to 135° at 5 and 10 eV impact energies. Using previously measured and normalized elastic differential cross sections for N_{2}, the ratios have been converted to inelastic cross sections. Laboratory‐frame close‐coupling calculations using a four‐state vibrational–rotational basis set and an effective interaction potential developed previously are reported at both energies. It is shown that the four‐state treatment of this potential scattering model can account for the approximate magnitude and the qualitative behavior of the cross sections, but there are some significant quantitative differences between theory and experiment.

Molecular motions in liquid. I. Rotation of water and small alcohols studied by deuteron relaxation
View Description Hide DescriptionThe deuteron spin lattice relaxation timeT _{1} of CH_{3}OD, C_{2}H_{5}OD, (CH_{3})_{2}CHOD, and (CH_{3})_{3}CHOD is reported as a function of temperature and frequency. The deuteron T _{1} of the alcohols in dilute benzene solutions was also measured at 25°C. A detailed analysis of the experimental results and other magnetic and dielectric relaxation data from the literature was made. Based upon the analysis, it is suggested that the success of the Debye model in explaining the dielectric and magnetic relation behavior of water and small alcohols may be purely coincidental. It seems that the error in applying Stokes law for the rotation of a macroscopic sphere to small molecules in liquid and the error in assuming that water and alcohols rotate as monomers largely cancel each other, yielding much better apparent agreement between calculated and experimental data than those for nonassociating liquids. The deuteron T _{1}’s for the alcohols are further analyzed in terms of anisotropic rotation.

Attachment of slow electrons to hexafluorobenzene
View Description Hide DescriptionSlow (≲ 3 eV) electrons attach to hexafluorobenzene (C_{6}F_{6}) nondissociatively with large cross sections via two distinct processes, one at ∼0.0 eV and another peaking at 0.73 eV. The absolute rates and cross sections have been determined as a function of electron energy for both processes and are reported. At 0.03 and 0.73 eV the cross sections are 1.23×10^{−14} and 8.04×10^{−16} cm^{2}, respectively; the thermal (T=297°K) value of the attachment rate is 3.3×10^{9} sec^{−1} torr^{−1}(=1.02×10^{−7} sec^{−1} molecule^{−1} cm^{3}). The lifetime τ of C_{6}F_{6} ^{−}* at ∼0.0 eV is ∼12 μsec, but at 0.73 eV it is much shorter, 10^{−8}≲τ<10^{−6} sec. The ∼0.0 eV process is associated with electron capture into the degenerate π_{4} and π_{5} molecular orbitals and is ascribed to the configurations π^{2} _{1}π^{2} _{2}π^{2} _{3}π^{1} _{4} and π^{2} _{1}π^{2} _{2}π^{2} _{3}π^{1} _{5}, while the 0.73 eV process is associated with electron capture into the π_{6} orbital and is ascribed to the configuration π^{2} _{1}π^{2} _{2}π^{2} _{3}π^{1} _{6}. For both C_{6}H_{6} and C_{6}F_{6} a relationship is shown to exist between the ionization energies of the occupied π_{1} and π_{2}, π_{3} orbitals and the position of the negative ion (shape) resonances associated with the unoccupied π_{4}, π_{5}, and π_{6} orbitals. The observed large attachment rates for C_{6}F_{6} extending from thermal energies to ≳3 eV recommend it as a potential ’’additive’’ in high‐voltage multicomponent gaseous insulators.

Density dependence of the ratio of second to first order terms in a perturbation expansion of characteristic thermodynamic properties of dense noble gases
View Description Hide DescriptionThe perturbation theory is applied to the evaluation of the thermodynamic properties of dense noble gases. The numerical results obtained for the ratio of the second to the first order perturbation terms as a function of the density are compared to those proposed by Rosenfeld and Thieberger for model gases, like the square‐well and the triangular‐well potential gases. These authors have remarked that for a given potential range the ratio decreases for increasing density and that this ratio is smaller for the compressibility than for the free energy. They have also pointed out that such ratios increase for a shorter square‐well range. It is shown here that such observations cannot be directly extended to more complicated systems like argon and xenon. The difference obviously stems from the long range attractive tail and the softness of the core of the intermolecular potential for such systems.

Observations of the high vibrational levels of N_{2}(B ^{3}Π_{ g }) in the Lewis–Rayleigh afterglow of nitrogen
View Description Hide DescriptionOptical studies of the first positive system in the nitrogen afterglow were conducted in a conventional discharge ‐flow system. The vibrational level of v′=13 was observed readily at pressures up to 20 torr. For the first time, high‐vibration levels of N_{2}(B ^{3}Π_{ g }) with v′≳13 were observed in the Lewis–Rayleigh afterglow under conditions of sufficiently high [N] and purity of N_{2}. Bands from ΔV=4, 5, and 6 with v′ up to 26 have been identified. Based on the observed effects of pressure, temperature, atom concentration, and gas purity on the intensity of the emission bands, excitation processes responsible for the formation of these high‐vibration levels are briefly discussed.

The transport coefficients for a fluid of square‐well rough spheres: Comparison with methane
View Description Hide DescriptionRecently derived expressions for the transport coefficients of a dense fluid of square‐well rough spheres and corresponding expressions for smooth spheres have been evaluated with structural data generated in computer simulations. The results are used with recommended square‐well potential parameters to calculate the tranport properties of methane for both models. For the shear viscosity and thermal conductivity the rough‐sphere values have the better agreement with experiment, while for the self‐diffusion coefficient they have marginally the worse agreement. No experimental data exist with which to compare the calculated bulk viscosities, which are considerably higher for rough than for smooth spheres.

The density dependence of bulk viscosity in a simple dense gas
View Description Hide DescriptionRadial distribution functions for a hard‐sphere modified Lennard‐Jones (12,6) fluid have been calculated for six reduced densities at a reduced temperature of 2.0 by a standard Monte Carlo procedure. These functions are used to calculate the bulk viscosity of dense gaseous argon according to the Enskog and Rice–Allnatt theories, and the results are compared with the experimental data of Madigosky.

EPR of Mn^{2+}, Fe^{3+}, and Cu^{2+} in glasses of the systems BaO–B_{2}O_{3}–Al_{2}O_{3} and CaO–B_{2}O_{3}–Al_{2}O_{3}
View Description Hide DescriptionAn electron paramagnetic resonance study was made of Mn^{2+}, Fe^{3+}, and Cu^{2+}doped into the glass systems BaO–B_{2}O_{3}–Al_{2}O_{3} and CaO–B_{2}O_{3}–Al_{2}O_{3}. The spectra of the manganesedoped samples exhibited a barely resolved Mn^{2+} hyperfine pattern at g=2 and in some cases low field lines at g∼3 and g∼5. The concentration dependence of these low field lines is interpreted in terms of the lattice distortion produced by the very large barium and calcium ions and the resulting large zero field (D term) splitting. The 0.1% Mn samples produced better resolved hyperfine patterns than the 1% samples. The spectra of iron and copperdoped glasses were also strongly concentration dependent. The results are discussed in terms of the glassy regions of the phase diagram.

Rotational diffusion studied by passage saturation transfer electron paramagnetic resonance
View Description Hide DescriptionA comprehensive description is given of instrumental and theoretical methods employed to make accurate measurements of rotational correlation times using passage saturation transfer electron paramagnetic resonance (ST–EPR). Saturation transfer methods extend by several orders of magnitude the sensitivity of EPR to very slow motion; for example, for nitroxide spin labels, correlation times as long as 10^{−3} sec become accessible to measurement. Two ST–EPR detection schemes are discussed in detail: dispersion, detected 90° out of phase with respect to the 100 kHz field modulation, and absorption, detected 90° out of phase with respect to the second harmonic of the 50 kHz field modulation. The sensitivities of these configurations are illustrated with experimental spectra obtained from a system obeying isotropic Brownian rotational diffusion; namely, maleimide spin labeled human oxyhemoglobin in aqueous glycerol solutions. Two theoretical approaches, one employing coupled Bloch equations and the other utilizing the stochastic Liouville equation for the density matrix with the orientation variables treated by transition rate matrix or orthogonal eigenfunction expansion methods, are in excellent agreement with each other and with model system spectra. Both experimental and theoretical spectra depend on a number of relaxation processes other than rotational diffusion; consequently, considerable care must be taken to ensure the accuracy of measuredrotational correlation times. Although the absorption method is currently the more sensitive and convenient one to apply with most conventional (commercial) spectrometers, the dispersion ST–EPR method is potentially more powerful, providing strong motivation for future technological efforts to decrease noise levels in dispersion experiments.

Spectroscopic studies of hydrated cyano and cyano–halide complexes of platinum (starting materials for the preparation of one‐dimensional conductors)
View Description Hide DescriptionInfrared studies from 4000–80 cm^{−1} were conducted on various hydrates of cyano and cyano–halide complexes of Pt(II) and Pt(IV). Tentative assignments for the vibrations involving the Pt atom, and for the water modes, were made. The latter assignments were based on a comparison with deuterated salts. Comparisons of the results obtained for these starting materials used in the preparation of one‐dimensional electrical conductors, with those of the conductors themselves are given.

Cumulant expansion of a Fokker–Planck equation: Rotational and translational motion in dense fluids
View Description Hide DescriptionA frequency generalized cumulant method is applied to the rotational (R) and translational (T) Fokker–Planck equation derived by Hwang and Freed. The lowest order nonvanishing cumulant is second order in the streaming part of the Liouville operator and generates the R–T coupled Smoluchowski equation. The structure of the fourth and sixth order cumulants for uncoupled R–T motion of a spherical top allows an approximate summation of the cumulant series which is accuate for dense fluids. The orientational time correlation functions for lth rank spherical harmonics calculated using the summed cumulants are in agreement with the high density Fixman and Rider solutions to the rotational Fokker–Planck equation. The zero frequency part of the orientational correlation functions gives an improved Hubbard relation relating the orientational and angular momentumcorrelation times. For the translational case, the summed cumulants lead to a wave vector and frequency dependent single partice diffusion constant. The effects of R–T coupling on the single particle orientational correlation functions are calculated using the Happel and Brenner model for the hydrodynamic part of the torque–force correlation functions. The effects are concluded to be small for a Brownian particle, even if the particle has strongly coupled orientational and translational modes.

On the coupling of the hole–particle and particle–particle (or hole–hole) Green’s functions
View Description Hide DescriptionIt is shown that a ladder vertex function can be related with an approximate particle–particle (or hole–hole) Green’s function in the same way as a screened potential is represented by a hole–particle Green’s function. Then, a screened potential and a ladder vertex function are constructed of solutions of the RPA and the PVA equation, respectivly, and using the ’’static’’ forms of these, we propose the coupled scheme of the RPA and the PVA.

Application of ’’multiple basis set technique’’ to the RPA and PVA equations
View Description Hide DescriptionWe propose the ’’modified’’ RPA (MRPA) and ’’modified’’ PAV (MPVA) equations using the ’’modified’’ Hartree–Fock one‐particle Green’s function. It is shown that when we choose the ’’modified’’ particle states in the vertex which represents a simultaneous creation (or annihilation) of two particle–hole pairs, there are two cases [(i) and (ii)]. Case (i) is what has been discussed by Ishihara and Poe, and case (ii) is an artificial exchange type of case (i). The MRPA including the contribution of particle–hole EPV ladder diagrams is derived by using case (ii). On the other hand, MPVA including the contribution of particle–hole EPV ring or ladder diagrams is derived by using case (i) or case (ii). Also, the application of case (ii) to the correlation‐energy diagram, the self‐energy diagram, and the augmented RPA is discussed.

Thermodynamics of the vaporization processes for potassium sulfate
View Description Hide DescriptionIn the design of MHD systems and components it is necessary to have reliable values for the vaporization of potassium sulfate including thermodynamic values for K_{2}SO_{4}(g), and partly for this reason there are a number of recent experimental studies on the vapor pressure of K_{2}SO_{4}. This paper reviews these data critically, calculates a theoretical heat capacity curve for K_{2}SO_{4}(g), and replaces second law calculations with a third law treatment, obtaining ΔH°_{ f298.15}=−261.2 kcal/mol and S°_{298.15} 90.63 eu for K_{2}SO_{4}(g). Thermodynamic values for K_{2}SO_{4}(g) are computed and tabulated for temperatures in the range from 1000 to 2200 K and are used to calculate the concentrations of various potassium containing species present in seeded combustion gases over the temperature range where liquid and solid K_{2}SO_{4} may form.

Spin–echo diffusion coefficients of water to 2380 bar and −20°C
View Description Hide DescriptionThe self‐diffusion coefficient of water has been measured by the steady‐gradient spin‐echo method at pressures up to 2380 bar and temperatures between 2 and −20°C in the stable liquid range using both strengthened glass and beryllium–copper pressure vessels. At low temperatures and high pressures the diffusion coefficient becomes almost independent of pressure. However, a rapid increase in D _{H} _{ 2 } _{O} with the first kilobar of applied pressure is inferred for the supercooled liquid from the relation of the new data to the 1 atm pressure diffusivity of supercooled water. The observations may be correlated with the high pressure low temperature thermodynamic properties of water in a manner consistent with the Adam–Gibbs entropy theory of liquidtransport processes.

Three‐body effects in the exchange and dissociation encounters for Ar+Ar_{2}
View Description Hide DescriptionMany‐body effects in reactive scattering are studied by investigating Ar+Ar_{2}(v=0, j=0) reactions through the use of quasiclassical dynamics. The Axilrod–Teller triple dipole term is used to describe nonadditive contributions, while Morse and MSV III expressions are employed as pair potentials. Inclusion of the three‐body term is found to modify polar differential cross section, opacity, and total cross section for exchange and dissociation at initial kinetic energies below 0.5 kcal/mole (250°K), although all differences calculated with the Morse lie within statistical uncertainties. The dissociation total cross section calculated with the more accurate MSV III pair potential is shifted beyond statistical uncertainty at an initial kinetic energy of 0.3 kcal/mole (150°K). This suggests that low energy reactive scattering in the Ar_{3} system may be measurably influenced by many‐body forces.

Regular chemisorption of hydrogen on graphite in the crystalline orbital NDO approximation
View Description Hide DescriptionA Hartree–Fock treatment of the regular chemisorption of hydrogen on a graphitemonolayer in a crystalline orbital NOO approximation is presented. The computational problems concerning the full exploitation of the point symmetry of the lattice, as well as the integration procedures are the same as encountered in a corresponding a b i n i t i o treatment. Three different cases have been considered, corresponding to the chemisorption of one hydrogen atom per unit cell: (A) above alternate carbon atoms; (B) above the center of a C–C bond; (C) at the center of a carbon ring. Bound states are found to occur only for cases A and B. The electronic features of the adsorbent–adsorbate system are appreciably differentiated. Such differences are discussed by using energy band structures and total and partial density of states spectra.