bluuebunny/crossref_metadata_2025_split huggingface dataset:
Radial Distribution Function of Hard Spheres
Authors: Ree Francis H. , Keeler R. Norris , McCarthy Shaun L. 
Published: January 2005

The third-order density correction term g3(r) in the density series for the radical distribution function g(r) is evaluated for a system of hard spheres over all distances. Both the Monte Carlo method (r&lt;2σ, σ=sphere diameter) and the analytic method (r≥2σ) are used to calculate the graph integrals appearing in g3(r). In carrying out the Monte Carlo integrations, calculations are simplified if gn(r) is represented by a sum of modified doubly rooted graph integrals instead of the Mayer—Montroll doubly rooted graphs. The modified doubly rooted graphs contain both Mayer f functions and f̃ functions (f̃=f+1). Advantages of this representation are twofold; (a) reduction in the number of graph integrals appearing in gn(r), and (b) the strong dependence of the graph integrals both on distance and dimension for the hard-core potentials. The analytic expression of g2(r) is obtained for r≤σ, by calculating the first-order density correction term of the triplet distribution function.
The above results are compared with the corresponding expressions derived by using three approximate integral equations for g(r): the Percus—Yevick equation, the convolution-hypernetted-chain equation, and the Born—Green—Yvon equation.
The fifth virial coefficient B5 for hard spheres is calculated from the g3(r) data. Use of the virial theorem and the Ornstein—Zernike relation gives the following values of B5: B5/(B2)4 (virial)=0.1105±0.0004,B5/(B2)4 (Ornstein−Zernike)=0.1106±0.0011.
We also compare the truncated density series of g(r) with the molecular-dynamics data of Alder and Wainwright and the g(r) obtained from the Percus—Yevick, the convolution-hypernetted-chain, and the Born—Green—Yvon integral equations at one-half the close-packed density.
Multicenter Integrals in Quantum Mechanics. II. Evaluation of Electron-Repulsion Integrals for Slater-Type Orbitals
Authors: Harris F. E. , Michels H. H. 
Published: January 2005

A unified method for the evaluation of electron-repulsion integrals for Slater-type orbitals is described. This method applies to every electron-repulsion integral needed for polyatomic molecule calculations, and is sufficiently general to handle integrals over orbitals with higher quantum numbers, located at arbitrary spatial points with arbitrary relative orientations.
Computation programs have been prepared to implement this analysis with emphasis on both the requirements of speed and accuracy in evaluating the large number of electron-repulsion integrals required for a polyatomic calculation. Comparisons with other methods are given which indicate that this unified approach can result in at least an order-of-magnitude saving in computation time for large molecular systems.
Change in the Thermionic Emission Current of Palladium Due to Chemisorption of Atomic and Molecular Hydrogen
Authors: Eisenstadt Melvin , Hoenig Stuart A. 
Published: January 2005

The thermionic emission current from a palladium wire at 1000°C was measured while the wire was exposed to molecular- and atomic-hydrogen beams. The molecular-beam source was at 300°K; the atomic-beam source was at 2400°K. Ultrahigh-vacuum techniques were used, and background pressures were 10−9 torr.
The average sticking coefficient, for chemisorption, was found to be larger for molecular hydrogen than for atomic hydrogen. This may be understood in terms of the energy-exchange phenomena between the gas and the surface. The slow moving molecules (300°K) transfer enough kinetic energy to the lattice, during collision, to be adsorbed. The energetic atoms (2400°K) are not so successful in this energy transfer, and a considerable fraction of them are reflected from the surface.
Based upon heat of adsorption considerations, one would expect atomic hydrogen to have a higher sticking coefficient than molecular hydrogen. The data show the opposite, and it is concluded that the kinetic energy of the incoming particle affects the sticking coefficient more strongly than the heat of adsorption, for the conditions studied here.
Theoretical Rate Constant for Thermal Unimolecular Reactions in a Multilevel System
Authors: Valance W. G. , Schlag E. W. 
Published: January 2005

A macroscopic unimolecular rate constant is given here in terms of the detailed microscopic rates of transport and relaxation in a many-quantum-level system. A rate equation for each quantum level is written considering all input and output processes. The resulting set of equations constitutes a master equation. The conventional unimolecular rate constant is then the lowest eigenvalue to the relaxation problem defined by the master equation. This is then a general prescription for the theoretical treatment of unimolecular behavior based only on the assumed mechanism and explicitly including the multilevel behavior of real systems undergoing chemical reaction.
General methods for solving this eigenvalue problem are discussed. These methods are illustrated with the master equation for a generalized Lindemann mechanism. The lowest eigenvalue for this mechanism is obtained by an iteration procedure. The zero-order result of the iteration is shown to be equivalent to the rate constant derived from a steady-state approximation. Both the zero-order and exact expressions for the lowest eigenvalue are given in terms of a computationally useful many-shot expansion. The lowest eigenvalue result then constitutes an exact and computationally simple version of the unimolecular rate constant which is an unambiguous consequence of the microscopic parameters inserted into the chosen relaxation mechanism.
Since the particular mechanism used here is also the point of departure in the derivation of the well-known RRKM theory of unimolecular reactions, the lowest eigenvalue solution is directly compared with the RRKM rate constant. The additional restrictive conditions for agreement between the two rate constants are enumerated.
Some generalized expressions for mean first passage times in unimolecular rate theory are also derived and expressed in terms of many-shot solutions. These latter expressions are computationally useful for extremely rapid reactions.
Effect of High Pressure on the Lattice Parameters of Cr2O3 and α-Fe2O3
Authors: Lewis G. K. , Drickamer H. G. 
Published: January 2005

The effect of pressure to several hundred kilobars has been measured on Cr2O3 and α-Fe2O3. Both have the corundum structure. Results are compared with previously published data for Al2O3.
Cr2O3 exhibits a compressibility which decreases markedly with increasing pressure; Al2O3 has a compressibility nearly independent of pressure; the compressibility of α-Fe2O3 actually increases with pressure in the low-pressure region. This is probably associated with the unusual behavior observed in Mössbauer studies.
Based on hexagonal indexing, Al2O3 shows the smallest change in aH and the largest change in CH. Cr2O3 is at the opposite extreme with α-Fe2O3 in between. In rhombohedral indexing, Al2O3 exhibits the largest change in aR and Cr2O3 the smallest. Al2O3 shows an increase of ½ deg in α, Cr2O3 a decrease of about 1 deg, while for Fe2O3 α is nearly independent of volume.
NMR Relaxation Times of Adsorbed Ammonia
Authors: Reuben J. , Fiat D. , Folman M. 
Published: January 2005

NMR relaxation times of NH3 adsorbed on modified silica surfaces have been studied using a progressive-saturation method. Measurements have been done for different surface coverages and frequencies. It has been found that the longitudinal and transverse relaxation rates of the adsorbate depend strongly on surface coverage. This has been explained by the existence of distribution of correlation times.
The relaxation rates differed in some respects from those known for liquids and solids, in other respects they showed some similarity. Possible relaxation mechanisms are discussed.
Collisional Energy Transfer. Thermal Unimolecular Systems in the Low-Pressure Region
Authors: Tardy D. C. , Rabinovitch B. S. 
Published: January 2005

Collisional activation—deactivation efficiencies, β, for thermal unimolecular reactions in the second-order region were computed on a stochastic model by use of an iterative procedure. Four assumed collisional transition probability models were used: stepladder, Gaussian, Poisson, and exponential; detailed balance and completeness were observed. The collisional efficiencies increase with increase of average energy removed per collision, 〈ΔE〉, and with decrease in the average excess energy of the molecules, 〈E+〉, above the critical energy for reaction. Efficiency is defined as a product, β=γNγP, and varies with inert gas dilution.
Calculations were made for the nitrous oxide, nitryl chloride, methyl isocyanide, cyclopropane, and 1,2-dimethylcyclopropane systems over a range of temperatures. This provides a large variation in the internal vibrational-energy densities and critical energies in question. For a particular transition probability model, β may be expressed as a quasiuniversal function of the reduced parameter, E′ = 〈ΔE〉/〈E+〉. Experimental data may thus be readily related to a corresponding value of 〈ΔE〉. The relation between the various probability models is discussed. Various deductions made are reminiscent of those previously encountered in work on chemical activation systems. The range of validity of the conventional strong-collision assumption for thermal systems is made explicit.
Nonbonded Potential Parameters Derived from Crystalline Aromatic Hydrocarbons
Authors: Williams Donald E. 
Published: January 2005

Nonbonded (exp−6) potential parameters for C···C, C···H, and H···H interactions were derived from the crystal structures and properties of aromatic hydrocarbons. The exponent of the C···C repulsion term was taken from a calculation based on the interplanar spacing and compressibility of graphite. The exponent of the H···H repulsion was taken from a quantum-mechanical calculation of the repulsion between two hydrogen molecules. The coefficients of the attractive and repulsive terms were fitted by weighted least squares to 77 observational equations involving the geometrical crystal structures, elastic constants, and sublimation energies of nine aromatic hydrocarbons. It was found necessary to externally estimate the H···H repulsion coefficient to obtain an appropriate partition between the C···C, C···H, and H···H energy terms. The geometrical mean combining law was applied for the attractive and repulsive coefficients.
The resulting nonbonded potential parameters, when used to minimize the lattice energy by a steepest descent procedure, were found to reproduce the crystal structures of benzene, napthalene, and anthracene to within about 0.05 Å in the carbon-atom positions and within about 1% in the lattice constants. No assumption of anisotropic forces based on π-electron polarizabilities was necessary to reproduce herringbone-type packing. The position of the minimum in the best C···H nonbonded potential was less than expected, while the minimum in the H···H potential was larger than expected. The minima positions were found to be sensitive to the H···H repulsion coefficient. The correlation coefficients between the potential parameters found by this method were found to be large.
Dielectric Properties of Ice VII. Ice VIII: A New Phase of Ice
Authors: Whalley E. , Davidson D. W. , Heath J. B. R. 
Published: January 2005

The dielectric properties of ice have been studied up to 107 kbar using opposed circular anvils. Ice VII undergoes orientational polarization, and consequently its molecules are orientationally disordered. The volume of activation for the relaxation of the orientational polarization is ∼3 cm3 mole−1, which suggests that the reorientation occurs by the migration of Bjerrum defects, as it appears to do in ice I, III, V, and VI. The energy and entropy of activation at 23 kbar are about 11.6 kcal mole−1 and 9.2 cal deg−1·mole−1, which are similar to those for other phases of ice.
At about 0°C, ice VII undergoes a transformation to a phase, here designated ice VIII, whose molecules are orientationally immobile at audio frequencies. This phase had previously been suggested by an analysis of the boundary line between ice VI and VII. The transformation occurs with a hysteresis of about 5.5°C at constant pressure, and the transformation temperature is independent of pressure to within about 0.5° up to 50 kbar. Some measurements previously identified with ice VII must now be identified with ice VIII or perhaps with another phase occurring at much lower temperatures.
The results illustrate the usefulness of dielectric measurements in an opposed-anvil apparatus for the study of phase changes in nonconductors at high pressures.
Electron Spin Resonance Studies of a Reaction Intermediate in Vacuum-Sublimed NaCl and KCl
Authors: Harrison L. G. , Adams R. J. , Catton R. C. 
Published: January 2005

In accordance with predictions from kinetic studies, electron spin resonance has shown that treatment of vacuum-sublimed NaCl with F2 at room temperature produces a defect containing an unpaired electron, and that the decay of this defect is retarded by Cl2. The ESR spectrum indicates an anisotropic g factor and unresolved hyperfine structure. In KCl, a spectrum is obtained which is closely similar except that the hyperfine structure is partly resolved. The spectra appear consistent with interaction of the unpaired electron with Cl atoms, rather than with F or such impurities as O or Br, and can be accounted for well by a model of the defect as linear Cl43−, i.e., an H center or something very similar. For NaCl, the spectra indicate that the vacuum-sublimed material is sometimes partly oriented.
It is suggested that centers with a one-electron deficiency are observable at such high temperatures in vacuum-sublimed material because this consists of essentially perfect crystals devoid of sites which could accept a second electron from the centers.
Gaseous Reaction Rates at High Temperatures. II. The Dissociation of Hydrogen Chloride
Authors: Fishburne E. Stokes 
Published: January 2005

A shock tube has been employed to study the dissociation of HCl in an argon diluent in the temperature range 3300°—5400°K and at total gas concentrations of 0.21, 0.42, and 0.84×10−5 moles/cc. The rate constant was determined to be k1=1.92×1011T12exp(−69 700/RT) cc/mole·sec.Experiments were conducted employing gas mixtures containing 1% HCl and 99% Ar; 2% HCl and 98% Ar; and 1% H2, 2% HCl, and 97% Ar. The inclusion of H2 did not noticeably affect the rate of dissociation of HCl.
The dissociation of HCl is compared to that of H2, which possesses a similar dissociation energy. It is shown that the rate constant for the dissociation of HCl has a much lower activation energy than that of H2. The possible reasons for this lower activation energy are presented and discussed.
Theory of the Dissociative Recombination and Associative Ionization of Hydrogen
Authors: Nielsen Svend E. , Dahler John S. 
Published: January 2005

A brief survey is given of the experimental information which is presently available on dissociative recombination and the dynamically inverse process of associative ionization. The mechanisms by which the reactions can occur are described in terms of adiabatic potential-energy curves of the ion and of the quasi-molecule formed from the union of ion and electron. The paucity of detailed information about the relevant potential-energy curves suggests that one focus attention upon hydrogen, the system about which the most is known.
A mathematical theory is then constructed which takes as its basis ingredients a Coulomb—Born description of the scattering of ion and electron and an adiabatic, or perturbed-stationary-state, treatment of atom—atom collisions. A very general approach is abandoned in favor of one based upon an approximate wave-function and which includes coupling of only a few entrance and final-state channels. Equations are derived for the scattering amplitudes in the two sets of channels and formulas are given for the relevant cross sections.
Measurement of Enthalpies of Evaporation of Bi and Bi2 by an Optical Absorption Technique
Authors: Rice Philip A. , Ragone David V. 
Published: January 2005

The enthalpies of evaporation of Bi and Bi2 were determined by the second-law method using an optical absorption technique to measure the change of vapor density with temperature for each species. The 3067-Å line was used for Bi and the band head at 2731 Å was used for Bi2. The enthalpy of dissociation of Bi2 is the difference between the two enthalpies of evaporation. The evaporation values obtained were   Bi(l)=Bi(g)ΔH298∘=49 600±1100 cal,  Bi(l)=12Bi2(g)ΔH298∘=24 700±1000 cal,12Bi2(g)=Bi(g)ΔH298∘=24 900±2100 cal.
The optical absorption technique was checked on lead, using the 2833-Å line. For lead, the ΔH°v,298 measured was 47 240±850 cal, as compared with an accepted value of 46 600±300 cal.
Barrier Heights and the Separation of Torsional Motion from Frame Vibrations in Electron Diffraction
Authors: Karle J. 
Published: January 2005

A method is presented for determining the barrier height hindering internal rotation from electron-diffraction data. The method is based on simple assumptions regarding the variation of the contribution of the frame vibrations as a function of the equilibrium positions on the circle of rotation. These assumptions, combined with the occurrence of two or more different interatomic distances which are affected by the torsional motion, permit a separation of the contribution of the torsional motion from that of the frame vibrations.
The assumed form for the functional variation of the squared amplitude of the contribution from the frame vibrations is α{1+βexp[−(π−|φe|)2]}, where α and β are constants and φe is the equilibrium angle for an interatomic distance on the circle of rotation, where φe=0 corresponds to the trans distance. When the variation is assumed to be constant, β=0, some typical values obtained from electron-diffraction data are 12.8 kcal mole−1 for Cl3CCCl3, 4.3 kcal mole−1 for F3CCF3, and 1.1 kcal mole−1 for Cl3SiSiCl3. It was found that a value of β=3.76 and a barrier height of 3.4 kcal mole−1 afforded a very good fit to the diffraction data for Cl3CNO2. Errors in the barrier heights are estimated to extend to 30% above and 20% below the given values. Further studies on Cl3CNO2 indicated that the barrier height is relatively insensitive to the assumptions made concerning the variation of the contribution of the frame vibrations, but strongly dependent on the assumed form for the potential barrier. Comparisons are made with the results of other methods for computing the barrier heights, and quite satisfactory agreement is obtained.
NMR Studies of Aqueous Electrolyte Solutions. I. Hydration Number of NaCl Determined from Temperature Effects on Proton Shift
Authors: Malinowski Edmund R. , Knapp Paul S. , Feuer Bernice 
Published: January 2005

Proton chemical shifts of purified water and of aqueous sodium chloride solutions are measured as a function of temperature and concentration. The shifts are referenced with respect to the resonance signal of gaseous ethane, which does not vary with temperature. An increase in temperature causes an upfield shift. Increasing sodium chloride concentration also causes an upfield shift.
The shift of the single resonance line observed is interpreted as being a time average of the proton in its different envorinments, namely, in the normal water structure and in a form hydrated to the ions. Although water in the secondary layer may be affected by the ions, such effects are neglected. It is argued that the shift of a proton in the hydrated form does not vary with temperature, whereas the shift of a proton in the normal water structure increases with increasing temperature due to the breaking of hydrogen bonds. From this simple interpretation, the total primary, or so-called ``effective'' hydration number of sodium chloride, is determined to be 4.
On the Analytical Mechanics of Chemical Reactions. Quantum Mechanics of Linear Collisions
Authors: Marcus R. A. 
Published: January 2005

The analytical quantum mechanics of chemically reactive linear collisions is treated in the vibrationally near-adiabatic approximation. The ``reaction coordinate'' in this approximation is found to be the curve on which the classical local vibrational and internal centrifugal forces balance. Expressions are obtained for the calculation of transmission coefficients for these nonseparable systems. Some implications for tunneling calculations in the literature are noted. Expressions for nonadiabatic corrections are derived, the latter being associated with vibrational transitions undergone by the transmitted and reflected waves. When the system does not have enough energy to react, the last results refer to the vibration—translation energy-transfer problem in linear collisions.
Two novel features are the introduction of an actual coordinate system which passes smoothly from one suited to reactants to one suited to products and the introduction of an adiabatic-separable method, a method which includes curvilinear effects. Extensions to collisions in higher dimensions are given in later papers.
Temperature Dependence of the Structure and Transport Properties of Liquid Thallium
Authors: Halder N. C. , Wagner C. N. J. 
Published: January 2005

Using a theta—theta diffractometer and quartz-crystal monochromatized MoKα radiation, x-ray scattering from liquid thallium has been measured as a function of temperature ranging from 350° to 700°C. The radial distribution functions (RDF) which have been obtained by Fourier inversion of the normalized intensity do not show any unusual feature and indicate a close-packed structure for the liquid thallium. The modulation-free part of the RDF in the region of small r where r is the radial distance suggests a high degree of reliability in the calculated value of atomic scattering factors of thallium and a considerable accuracy in the measured intensity. The interatomic distance r1=3.30 Å of thallium does not change with temperature, and the coordination numbers change very little from 11.5 atoms at 350°C to 10.9 at 700°C. This decrease may be explained with excess- or free-volume theory.
The resistivity and thermoelectric power have been determined using the x-ray interference functions and theoretically calculated values of the pseudopotential elements. The predicted values of the resistivities Rpred are little lower than the measured values Rexpt1 (e.g., Rpred=63 μΩ·cm, Rexpt1=79 μΩ·cm at 500°C). Further, the temperature coefficient of the predicted resistivities is also smaller than that of the measured resistivities. The observed discrepancy has been attributed to the inadequacy in pseudopotential elements.
Effect of Very High Pressure on the Compressibilities of NH4Cl, TlCl, CdO, and CdS
Authors: Lewis G. K. , Perez-Albuerne E. A. , Drickamer H. G. 
Published: January 2005

The effect of pressure to several hundred kilobars has been measured on the compressibilities of NH4Cl, TlCl, CdO, and CdS. NH4Cl and TlCl have the simple cubic (CsCl) structure at all pressures covered by this study. Our results for these compounds agree quite well with Bridgman's data to 98 kbar. The Born—Mayer equation fits NH4Cl very well at all pressures. TlCl shows a lower compressibility than predicted by the B—M equation above about 150 kbar.
CdO has the face-centered-cubic (NaCl) structure at all pressures. The B—M equation fits well up to 160 kbar, above which pressure CdO is less compressible than is predicted. CdS transforms from wurtzite to NaCl structure at 23 kbar. The compressibility of the high-pressure phase is quite small and does not present a good test for ionicity by the B—M equation.