bluuebunny/crossref_metadata_2025 huggingface dataset:
Perturbed Hartree—Fock Calculations. IV. Second-Order Properties of the Fluorine Molecule
Authors: Stevens Richard M. , Lipscomb William N.
Published: January 2005

The coupled Hartree—Fock method with a limited basis set has yielded values at the F nucleus and at the center of charge C of the F2 molecule for the electric polarizability (α∥=2.15 Å3, α⊥=0.77 Å3), the magnetic susceptibility (extrapolated to —10.2 ppm), the magnetic shielding [σ=—276 at F or —200 at C (preferred value); σexpt1=—210 ppm], rotational magnetic moment (extrapolated to —0.108 nuclear magnetons) and spin rotation constant [CF=169 at F or 152 at C (preferred value); Cexpt1=157±2 kc/sec]. The poor gauge dependence for the shielding and spin rotation constant is associated with the unusually high paramagnetic shielding at F which is due specifically to an interaction of the occupied πu orbital with a low-lying excited σu state. The susceptibility and rotational magnetic moment did not vary extensively with change of gauge.
Paramagnetic Resonance Absorption in Phenanthrene in Its Phosphorescent State
Authors: Brandon Roy W. , Gerkin Roger E. , Hutchison Clyde A.
Published: January 2005

Electron paramagnetic resonance absorption in phenanthrene in its lowest photoexcited triplet state has been investigated at the boiling point of N2. The measurements have been made on phenanthrene molecules, oriented in diphenyl host crystals, at the frequency ∼2.3×1010 cycle sec—1 and also at lower frequencies at almost zero field (76 to 3 G). Taking the long principal magnetic axis in the plane of the phenanthrene molecule to be the x axis, the short axis in the plane to be the y axis, and the normal to the plane to be the z axis, the results have been described by the spin Hamiltonian, H=|β|H·g·S+S·T·S,where S=1,Tzz/hc≡D/hc=±0.100430 cm−1,  σ{D/hc}=0.000010 cm−1,−Tyy/hc=Txx/hc≡E/hc=∓0.046576 cm−1,  σ{E/hc}=0.000009 cm−1,gzz=+2.00209,  σ{gzz}=0.00005,gyy=+2.00279,  σ{gyy}=0.00005,gxx=+2.0041.,A preliminary investigation of the hyperfine structure has been made. These results have been compared with published calculations.
Vibrational Spectra and the Structure of Crystalline Triethylenediamine
Authors: Weiss Gerald S. , Parkes A. S. , Nixon Eugene R. , Hughes R. E.
Published: January 2005

The crystal structure of the symmetric-top molecule, triethylenediamine, is discussed in terms of the analysis of three-dimensional x-ray diffraction data in the space groups P63/m and P63. It was possible in the two cases to refine to slightly different structures with different molecular and site symmetries. The centrosymmetric structure with molecular symmetry D3h—6̄m2 was used as the basis for an analysis of the infrared spectrum of the crystal and the assignment of the prominent bands. The Raman spectrum of the molecule in solution and the infrared spectrum of a crystalline monohydrate are also reported.
Structure of InSb at High Pressures
Authors: Kasper J. S. , Brandhorst H.
Published: January 2005

It has been found by x-ray diffraction studies at high pressure (∼30 kbar) that InSb occurs in a form other than the β-Sn type which has been reported in previous studies. The new modification appears to have a simple orthorhombic structure with two atoms in the unit cell and can be derived from the β-Sn structure by a simple shear process. While this structure may be a metastable one, it cannot be ruled out that it may be more stable than the β-Sn form.

On the other hand, it is confirmed that the β-Sn structure is readily obtained by quenching to 77°K and releasing the pressure, after the transformation has occurred in the vicinity of 30 kbar.
Polyelectrolytes : A Fuzzy Sphere Model
Authors: Fixman Marshall
Published: January 2005

The expansion factor α of polyelectrolytes is calculated on the assumption that at least one member of each interacting pair of charged segments is immersed in a segment cloud having the average sement density, here given by a uniform distribution inside a sphere. The counterion concentration is assumed to be much larger inside the sphere than the byion concentration, and a binding parameter is introduced via an effective dielectric constant. As a consequence α3 is predicted to be linear in the reciprocal square root of ionic strength. The dominant source of expansion is repulsion between segments such that one member of an interacting pair is inside and the other outside the background cloud. This same repulsion makes the free energy a minimum when the polymer shape is spherical.
Electrical Conductivity of Low Dielectric Constant Liquids by dc Measurement
Authors: Gavis J.
Published: January 2005

When conductivities of electrolyte solutions are very low dc measurements may be necessary to determine them. A quantitative criterion for when dc or ac may be used is given. Then a linearized partial differential equation for the transport of electric charge in low-dielectric-constant fluids, developed earlier by the author, is applied to the problem of dc conductivity measurements. In the absence of overpotentials at the low current densities usually employed boundary conditions on the transport equation are formulated in terms of charge densities in the solution near an electrode surface, and are related to potentials at the surface. The equation is solved to give expressions for the formation of the equilibrium double layer at the surface, and for the formation of the nonequilibrium double layer when the surface potential of one electrode is raised to cause current flow. From these the current—applied potential—time expression is derived. This consists of a transient polarization current which decays to a steady-state current. The decay rate of the transient depends primarily upon the relaxation time of the solution. The steady-state current obeys Ohm's law if the electrode spacing is large enough; conductivity may then be determined. If the spacing is too small diffusion enhanced transport occurs giving erroneously high apparent conductivities.
ESR Studies and Covalent Bonding of Cyanide and Fluoride Complexes of Transition Metals
Authors: Kuska H. A. , Rogers Max T.
Published: January 2005

ESR spectra of [Cr(CN)6]3— in dilute solid solution in K3Co(CN)6 single crystals have been obtained and the hyperfine splitting constants measured. These have been interpreted to provide values of the isotropic and anisotropic components As=—9.85±0.1 G and Ap=+0.65±0.2 G. The sigma and pi-bond character of the metal—ligand bonds for [Cr(CN)6]3— and [CrF6]3— have been computed using molecular orbital theory and compared with the corresponding values for some other cyanide and fluoride complexes.
Phase Diagrams of Silicon and Germanium to 200 kbar, 1000°C
Authors: Bundy F. P.
Published: January 2005

The phase diagrams of Si and Ge have been investigated experimentally over a P, T range of about 200 kbar and 1000°C by observing electrical resistance behavior. For Si the boundary between the diamond cubic form and the metallic form extends from about 120 kbar at room temperature to about 150 kbar, 810°C, where melting occurs at the triple point. For Ge the corresponding boundary extends from about 115 kbar at room temperature to about 103 kbar, 600°C. A line drawn through the triple points for Sn, Ge, and Si, and extended, suggests that the diamond—metal—liquid triple point for carbon may be around 500 kbar, 2400°C. When the metallic forms are decompressed at room temperature they transform back to semiconducting forms different and more dense than the original diamond cubic forms. Upon heating these denser forms to a few hundred degrees at room pressure they transform to the usual diamond cubic forms. The absolute resistivity and temperature coefficient of resistance of metallic Ge has been determined.
Gaseous Diffusion in Porous Media. IV. Thermal Diffusion
Authors: Mason E. A. , Malinauskas A. P.
Published: January 2005

The pressure dependence of thermal diffusion is derived on the basis of the ``dusty-gas'' model, in which a porous medium is considered as a collection of giant molecules (dust particles) fixed in space. The results can also be applied to capillaries by suitable substitution for geometric parameters.

Thermal separation is zero at zero pressure and constant at high pressures, but the transition can be quite complex and varied, depending upon the temperature, molecular masses, and intermolecular forces of the gas molecules involved. Representative calculations have been made to illustrate the possibility of maxima and sign reversals of the thermal separation as a function of pressure. Comparison with the scanty available experimental results reveals no discrepancies, but further experiments are desirable, particularly for cases in which unusual transition behavior is expected.
Measurements of Thermal Dissociation of Hydrogen, Using Fast Protons
Authors: Lockwood Grant J. , Helbig Herbert F. , Everhart Edgar
Published: January 2005

Experiments involving study of the angular scattering of kiloelectron-volt protons from atomic and molecular hydrogen targets have been used to measure directly the fraction of hydrogen gas dissociated in equilibrium with hot tungsten. The state of the hydrogen gas in a tungsten furnace is determined by analyzing the scattered incident particles which result from single collisions between the incoming protons and the hydrogen gas in the furnace. In particular, the number of H— ions among the scattered particles is a measure of the molecular hydrogen density, since H— ions cannot be created in single collisions between protons and hydrogen atoms. Under the present experimental conditions it was possible to achieve a fraction dissociated of over 87.5% at a furnace temperature of 2380°K and still higher fractions at higher temperatures. These measurements are made at hydrogen pressures of the order of 10—2 Torr.

The practical conditions under which an atmosphere of highly dissociated hydrogen can be created are described and it is pointed out how the dissociation fraction and also the density of the hydrogen can be directly measured in the otherwise inaccessible interior of the gas. These measurements using a proton beam probe do not require that the pressure or temperature of the hydrogen be known and, in fact, do not require thermal equilibrium conditions.
Mössbauer Effect Measurements of Hyperfine Interactions in Laves Phases Containing Fe Combined with Ti, Zr, Y, and the Lanthanide Metals
Authors: Wallace W. E.
Published: January 2005

57Fe Mössbauer absorption spectra have been obtained for the Laves-phase compounds AFe2 in which A=Ti, Zr, Y, Ce, Sm, Gd, Tb, Dy, Ho, Er, Tm, and Lu. TiFe2 and CeFe2 are paramagnets at room temperature and hence only show quadrupole interactions (0.21 and 0.40 mm/sec, respectively). The others exhibit a magnetic hyperfine interaction at room temperature and all show this at the liquid-nitrogen point. The pattern obtained for TiFe2 at 78°K is complex and has been interpreted as indicating two types of Fe, one of which is magnetically ordered and for which the hyperfine field is 71 kOe, whereas the other type is either not magnetically aligned, or if it is, the field is less than 10 kOe. Fe moments for the other compounds are obtained either directly from experiment or estimated from the experimental results using Bleaney's exchange induction effect. These moments are compared with the measured hyperfine fields. Due to the limited range of variability of the moments and fields their functional interrelationship cannot be unambiguously established. A linear relationship seems to be indicated. This is interpreted to imply that only conduction and core electron polarizations contribute significantly to the hyperfine field in the (cubic) AFe2 compounds, and the latter varies linearly with the localized Fe moment.
Equation of State of Polymer Liquids and Glasses at Elevated Pressures
Authors: Nanda V. S. , Simha Robert
Published: January 2005

By a combination of experimental isotherms and making use of theoretical results, we establish the validity of the theorem of corresponding states for chain liquids and derive an explicit expression for the reduced pressure—volume—temperature surface encompassing oligomer and high-polymer liquids. For this purpose empirical Tait isotherms are employed with one adjustable parameter only, by showing that they describe experimental data for high-polymer liquids also. One observes furthermore that the Tait relation remains valid below the glass transition temperature with only one of the parameters changing its functional dependence on temperature in the transition. We are able to conclude that a reduced equation of state describes the isotherms of polymer glasses with the same reducing parameters which characterize the liquid. This permits appropriate predictions at elevated pressure from volume—temperature studies of the glass at atmospheric pressure, combined with equation of state results of the liquid polymer. Our results thus support for both chain liquids and glasses the postulates formulated by others as a basis for a principle of corresponding states. A correction must be made, however, in computing enthalpies or cohesive energy densities for polymers with highly asymmetric units from equation of state properties by means of this principle. Deviations between the reduced experimental and theoretical equations of state at low temperatures are entirely determined by the characteristic failure of cell theory in respect to the internal pressure. At elevated temperatures, the theoretical thermal expansions are also in error. The principle of corresponding states and the general equation of state derived from it are, of course, unaffected and serve as a guide for further theoretical developments. Finally, it turns out that the Tait equation describes the isotherms of partially crystalline branched polyethylene whereas it predicts larger compressibilities than are observed for linear crystalline polymethylene. Above the melting region we interpret the departures from the Tait relation for both polyethylene and polymethylene as due to crystallization effects and compute the variation of crystallinity with pressure.
Nonadiabatic Elastic Scattering. II. The Scattering Process.
Authors: Thorson Walter R.
Published: January 2005

Previous studies on nonadiabatic elastic scattering of high-energy atomic beams have shown that the potentials which produce such scattering exhibit downward shifts (``Coriolis shifts'') due to high angular velocities during collisions. The elastic-scattering cross sections produced by such potentials are studied in the present work, and it is found that the scattering tends to mask the presence of Coriolis shifts, so that the apparent potential which could be deduced from measurements of such scattering differs from the adiabatic potential by only small fractions of the Coriolis shifts.

The 9-eV discrepancy between the potential for He2 at 0.5 Å, calculated in the adiabatic approximation, and the potential deduced from beam experiments cannot be accounted for in terms of Coriolis shifts.
Solvent Effects in Nuclear Magnetic Resonance. II. Critical Examination of the Reaction Field
Authors: Laszlo P. , Musher J. I.
Published: January 2005

The reaction-field concept is examined quantitatively using nuclear magnetic spectroscopy by determining the magnetic shielding constants of three protons within the same molecule as a function of dielectric constant: the results are based on the fact that the magnetic shielding constant of a bonded proton depends linearly on the effective electric field along the bond axis. It is shown that (1) the reaction field must take on different values at different points in the molecule, and (2) the calculated reaction field's dependence on ε for a dipole in a spherical or spheroidal cavity does not adequately describe the experimental reaction field's dependence on ε.
Electronic Structure and Spectra of Biphenyl and Its Related Compound
Authors: Gondo Yasuhiko
Published: January 2005

The Pariser—Parr method has been used to elucidate the electronic structure and the spectrum of biphenyl. The absorptions at 300, 250, 200, and 170 mμ seem to be explained reasonably. Simple forms of linear combinations of the symmetry orbitals constructed from 2pπAO's were used as molecular orbitals. Calculations were made for three conformations, the angle between the planes of two benzene rings being 0°, 45°, or 90°. In each of the conformations 16 singlet and 16 triplet excited configurations were taken into account. An application has been made to 2,2′-bipyridyl, and its absorption spectrum has been explained.
Structural Form of Vibronic Bands in Crystals
Authors: Wagner Max
Published: January 2005

A method is given to calculate the line structure of vibronic bands for a given coupling function p(s), which latter incorporates the frequency and equilibrium change of the oscillator s. The form of the single lines is generally given in terms of their moments. For the important case, where p(s) decomposes into a sum of Gaussian or Lorenzian functions, the line functions are written explicitly. In absorption the lines must appear above the low-energy part of the background. In emission the opposite is true. Other features are also explained. The theory is restricted to T=0, yet can be easily extended to finite, but low temperatures (at higher temperatures there is no vibronic structure).
Van der Waals Forces in Atoms and Molecules
Authors: Karplus M. , Kolker H. J.
Published: January 2005

The time-dependent variation-perturbation method is applied to the estimation of van der Waals forces (—C/R6 term) in atoms and molecules. Use is made of an expression for the coefficient C involving an integral over imaginary frequencies of the dynamic polarizabilities of the interacting species. With an analytic approximation to the dynamic polarizabilities that can be extended into the imaginary frequency range, a simple formula for the van der Waals force is obtained. Applications of the method to the interactions between S-state atoms (H, He, Ne, Ar) are given and the results are compared with available theoretical and experimental values. Also, atom—molecule interactions involving (H, H2) and (He, H2) are examined, and the anisotropies in the van der Waals forces are calculated.
Some Aspects of the Quantal and Semiclassical Calculation of Phase Shifts and Cross Sections for Molecular Scattering and Transport
Authors: Munn R. J. , Mason E. A. , Smith Francis J.
Published: January 2005

A critical study is made of the JWKB approximation for phase shifts by comparison of the approximate phases with those calculated by numerical solution of the radial wave equation. A region of E—l—Λ* space is mapped out for the Lennard-Jones (12–6) potential in which the JWKB approximation is unsatisfactory. Reasons for the failure of the JWKB approximation are noted, and a simple but effective method of predicting the region of E—l—Λ* space where failure occurs is suggested. The study is continued by a comparison of the quantal and semiclassical transport and total cross sections. It is shown that the JWKB transport cross sections are of limited practical value and that the semiclassical total cross sections are useful only at high values of E and low values of Λ*. Particular attention is centered on features associated with classical orbiting and with semiclassical rainbow and glory scattering. An apparent sign change in the quantum corrections for the viscosity cross section found by de Boer and Bird is shown to be an artifact caused by the neglect of the attractive part of the interaction potential. Finally, small-angle quantal differential cross sections for a repulsive r—12 potential are compared with some recent semiclassical calculations. The behavior as exp (—cχ2) at small angles is found to be valid to larger angles than previously thought.
Vibration—Rotation Interaction Factors for Diatomic Molecules Calculated by Numerical Methods
Authors: Cashion J. K.
Published: January 2005

The influence of vibration—rotation interaction on transition probabilities for diatomic molecules has been studied through numerical solution of the Schrödinger radial equation. The numerical method employed is readily applicable to any choice of potential and dipole moment functions for the molecule, its accuracy considerably exceeds the requirements of practical applications, and it is very economical in terms of computer-time requirements. Its use is demonstrated here in two applications. First, it has been used to check the accuracy of the approximate formulas for the F factors of a rotating Morse oscillator with a linear dipole-moment function derived by Herman, Rothery, and Rubin. It was found that their formulas were very accurate for Δv=1 transitions, but that the two formulas given by them for the first and second overtones could introduce errors of several percent at moderate J values. Secondly, quadratic and cubic terms were added to the dipole-moment function in order to estimate the sensitivity of F factors to changes in this function. The results indicate that for all transitions in which Δv>1, the higher terms can have considerable significance. For example, F factors for the lines R(19) and R(20) of the 3–0 band of LiH were changed by factors of more than 3 when the dipole-moment function employed was carried from a linear to a cubic approximation in a Taylor's series expansion.
Analytical Self-Consistent Field Functions. III. Isoelectronic Series with 19 to 30 Electrons
Authors: Clementi Enrico
Published: January 2005

The ground-state Hartree—Fock wavefunctions are reported for the K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn atoms. The basis sets have fully optimized orbital exponents, and each function satisfies accurately the virial theorem. The basis set consists of 11 exponential functions of s symmetry, 6 exponential functions of d symmetry. With basis sets of the same size, the positive ions isoelectronic series have been computed up to Z=30. For the positive ions only the essential features of the computation are reported.
Viscosity—Molecular Weight Dependence for Short Chain Polystyrenes
Authors: Allen Vernon R. , Fox Thomas G
Published: January 2005

Data on the viscosity coefficient η in the limit of zero shear on binary polystyrene mixtures having identical number average chain length Zn (hence identical density) but different weight average Zw establishes that η∼Zw, when Zw<630 chain atoms, confirming the theory of Bueche for the viscosity of short polymer chains. Strong support for Bueche's theoretical equation, η=16N0[(〈s02〉Av/M)(1/v)]Zζ,is provided by the successful quantitative prediction of the observed value of η from the independently measured values of the unperturbed reduced mean-square radius of gyration of the polymer coil 〈s02〉Av/M, of the specific volume v, the friction coefficient per chain atom ζ, and Avogadro's number, N0. Application of this equation now permits ready evaluation of ζ from viscosity measurements on short chain polymers.
Anisotropy of the 19F Chemical Shift in Trapped CH3F Molecules
Authors: Hunt Earle , Meyer Horst
Published: January 2005

We have grown β-quinol clathrates with trapped CH3F and studied the anisotropy of the chemical shift of 19F. It is known that molecules trapped in these compounds become aligned at low temperatures so that effectively single-crystal studies of these molecules become possible. The NMR structure showed that the C–F bond was aligned parallel to the trigonal crystal axis of the clathrates. The resonance was observed at several frequencies with a corresponding constant magnetic field applied successively parallel and perpendicular to the crystal axis. It was found that the frequency of the line center was always highest with the C–F bond parallel to the field. This frequency difference between both directions gave a chemical shift anisotropy σ⊥—σ∥=66±8 ppm. This anisotropy has a different sign from that expected from recent theories for fluorine bonds and the results are discussed in relation to the chemical shifts for certain other fluorine compounds.
Theoretical Interpretation of the Zeeman Effect in the Near-Ultraviolet Bands of CS2
Authors: Hougen Jon T.
Published: January 2005

Douglas and Milton have observed that the rotational lines of certain bands in the spectrum of CS2 are broadened in a magnetic field, the broadening being proportional to the product of the magnetic field strength and the rotational quantum number. This behavior is characteristic of an orbitally nondegenerate singlet electronic state, except that the magnitude of the broadening is about 1000 times larger than usually observed. It is shown that these observations can be satisfactorily explained in terms of a model proposed by Douglas, namely, by assuming that the observed upper electronic state is the B2 multiplet component of a (bent) 3A2 electronic state, whose other two multiplet components, A1 and B1, are nearly degenerate with each other but are separated from the B2 component.
Calculation of the Electron Spin Resonance Line Shape of Randomly Oriented Molecules in a Triplet State. II. Correlation of the Spectrum with the Zero-Field Splittings. Introduction of an Orientation-Dependent Linewidth
Authors: Kottis Philémon , Lefebvre Roland
Published: January 2005

The structure in the electron-spin-resonance spectrum of randomly oriented molecules in a triplet state is due to resonance fields stationary with respect to a change in the molecular orientation. This is the basis for the derivation of the electron spin—spin coupling constants from such spectra. In this paper we investigate this structure with the help of a computer program which generalizes the one described in Part I to deal with the so-called Δm=2 spectra. Some rules are derived for the interpretation of spectra. We then examine the possibility of including in such calculations the anisotropy of the electron g tensor and some dependence on the orientation of the linewidth. For the canonical orientations, the linewidth in a variable-magnetic-field experiment is shown not to depend on the microwave quantum.
Thermodynamic Properties of the Acetyl Radical and Bond Dissociation Energies in Aliphatic Carbonyl Compounds
Authors: Murad Edmond , Inghram Mark G.
Published: January 2005

Photoionization mass spectrometry was used to study the thermodynamic properties of the acetyl radical and to determine bond energies in acetone and biacetyl. From measured appearance potentials of CH3CO+ and by the use of thermodynamic cycles, the following bond energies were determined: D0(CH3–CO)=0.49±0.03 eV, D0(CH3CO–CH3)=3.34±0.06 eV and D0(CH3CO–COCH3)=2.84±0.06 eV. D0(CH3CO–H) is calculated to be 3.69±0.06 eV. ΔHf°(CH3CO) is calculated to be —0.28±0.06 eV.
Effect of Hindered Rotation on the Nuclear Quadrupole Resonance Frequency and the Linewidth in Trans-1,2-Dichloroethane
Authors: Tokuhiro Tadashi
Published: January 2005

The 35Cl and 37Cl nuclear quadrupole resonance frequency, linewidth and line shape have been measured in trans-1,2-dichloroethane at temperatures from 77°K to the melting point. The temperature dependence of the resonance frequency agrees with Bayer's theory. Remarkable increase of the linewidth with rising temperature below the 177°K phase transition is attributed to the slow reorientational motion around the long axis passing through the two chlorine atoms. Fast reorientational motion above the transition is probably accountable in itself for the heat-capacity anomaly.
Anharmonicity in Vibrational State Sums
Authors: Wilde Kenneth A.
Published: January 2005

Refinements have been made in the treatment of vibrational state sums. These modifications are particularly important at energies greater than the dissociation energies. It was not possible to extend the available analytical treatments of harmonic oscillators, and numerical sums were computed for several anharmonic examples and compared with previous work. Values of the empirical correction factor a were given and the previously derived approximate equations involving a extended to the anharmonic case.
Nuclear Quadrupole Resonance of 115In in InI3
Authors: Brooker H. R. , Scott T. A.
Published: January 2005

The three lower-frequency pure quadrupole resonance lines of 115In in InI3 have been studied at several temperatures in the range between 4.2°K and room temperature. The quadrupole coupling constant, the asymmetry parameter, the linewidths, and rough measurements of some of the relaxation times are reported. Pressure-dependence studies at pressures up to 2000 bars were also made. A pressure-induced phase change was detected and investigated. This phase change was found to be extremely sluggish for our samples at low temperatures.
Approximate Series Solutions of Nonseparable Schrödinger Equations. III. B Matrix Method
Authors: Frost Arthur A. , Harriss Donald K. , Scargle Jeffrey D.
Published: January 2005

The series solution B matrix method, developed in Paper I is applied to systems of one and two electrons with wavefunctions expressed in interparticle coordinates. The application to more complicated systems is considered.
Horizontal and Vertical Correlation in Pi-Electron Systems
Authors: Lowe John P.
Published: January 2005

It is of interest to know the relative importance of horizontal and vertical correlation in pi-electron systems. A method has been developed for including both kinds of correlation simultaneously. Vertically correlated atomic orbitals are formed by combining 2pπ and 3dσ orbitals. These are then used as a basis for alternant molecular orbitals. Calculations to minimize the ground-state energy of ethylene indicate that horizontal correlation accounts for almost all of the energy improvement. This is due to the fact that the increase in kinetic energy associated with vertical correlation is greater than that for horizontal correlation.
Significant Structure Theory of Surface Tension
Authors: Ree Teresa S. , Ree Taikyue , Eyring Henry
Published: January 2005

The approximation is made that the dividing surface between a liquid and its vapor phase is a monomolecular layer, in which a molecule has a free volume larger than for an interior molecule and a potential energy less than for the latter. By introducing the approximation into the significant structure theory of liquids, a partition function fN is derived which involves the terms belonging to the surface as well as to the bulk liquid. The surface tension is calculated by γ = (∂A/∂Ω)N,V,T, where A is the Helmholtz free energy which equals —kTlnfN, Ω is the surface area, N the total number of molecules in the system, V the volume of the liquid, and T the absolute temperature. The surface tensions of nonpolar substances at various temperatures are calculated with good results. Our theory is compared with other theories, and it is found that the present theory most satisfactorily predicts the surface tensions at various temperatures.
Kinetics of the Gas-Phase Addition of HI to Butene-2
Authors: Nangia Prakash S. , Benson Sidney W.
Published: January 2005

The kinetics of the gas-phase reaction 2HI+butene-2→n-C4H10+I2 have been studied from 292° to 333°C using a spectrophotometer to follow I2 production. Except for the first few minutes of each run d[I2]/dt is a constant for up to 25% reaction. On the basis of two coupled sets of reactions: HI+butene−25⇋6sec−C4H9Isec−C4H9I+HI→n−C4H10+I2it is shown that the reaction path 5 consists of two separate steps, one a direct molecular addition of HI and the other an I-atom-catalyzed addition.

Using estimates of the equilibrium constant K5·6 it is shown that the rate constants for molecular and I-atom-catalyzed paths are consistent with data of Ogg and Polanyi on the pyrolysis of sec-C4H9I. The Arrhenius parameters for the two addition paths are examined in terms of recent proposed theories of the transition states for four-center reactions and shown to be compatible with similar data in other systems.

Some complexities of the present system are examined involving the butene-1, butene-2 isomerizations catalyzed by I2. The pyrolysis studies on the iodides are shown to be complicated by butadiene+HI production.
Direct Correlation Functions and Their Derivatives with Respect to Particle Density
Authors: Baxter R. J.
Published: January 2005

An equation relating the many-body distribution functions of a classical statistical mechanical system and their derivatives with respect to the particle density is stated and proved. It is found possible to define a heirarchy of symmetric functions of 2, 3, 4, etc. variables, of which the two-variable function is the Ornstein— Zernike correlation function. These functions, termed the direct correlation functions, and their derivatives with respect to density satisfy a strikingly simple relation. The possibility of a closure of the equations is discussed and a superposition approximation suggested. The resulting equation for the two-particle direct correlation function has the advantage that a knowledge of the function at one density predicts its values at another, thereby differing from most approximations, which require the solution of an integral equation in each case.
Variational Methods for Solving the Boltzmann Equation
Authors: Snider R. F.
Published: January 2005

Known variational methods are reviewed and their applicability to the Boltzmann equation when detailed balance does not hold is discussed. The relation between these variational methods and time-reversal and space-inversion symmetry is indicated.
Statistical Thermodynamics of Incompletely Specified Systems
Authors: Leff Harvey S.
Published: January 2005

A formal theory of incompletely specified systems based on reasonable physical assumptions is presented. It is shown that the free energy for such systems involves the average of the logarithm of the partition function, rather than the average of the partition function itself. It is further shown that one cannot always replace the logarithm of the partition function by its average in all of the equations of statistical thermodynamics. The method differs from that of Mazo. We do not obtain a term corresponding to an entropy of mixing due to random elements. Finally, fluctuations as calculated here differ from those implied by Mazo's method. Due to the formal nature of the problem, a strict right—wrong distinction between the two methods cannot be made.
Lack of Charge Transfer in Aromatic Charge—Transfer Complexes
Authors: Hooper H. O.
Published: January 2005

Halogen pure electrical quadrupole resonance frequencies have been measured in the three 1:1 complexes, CBr4·p-xylene, CCl4·p-xylene, and Br2·benzene. From an examination of the measured frequencies of the complexes and the halogen-containing compounds (CBr, CCl4, and Br2) together with information from the x-ray structure determinations for two of the complexes, it has been concluded that little if any charge transfer exists in the ground state of these complexes.
Crystal Field for Yb3+ in Garnets
Authors: Hutchings M. T. , Wolf W. P.
Published: January 2005

An attempt has been made to determine the nine parameters required to define the crystal field acting on an Yb3+ ion in yttrium gallium garnet. Even for this most favorable case, there are at present insufficient data to determine the parameters from experiment alone, and we have therefore carried out an analysis combining seven independent and reliable experimental measurements with theoretical estimates based on an accurate point-charge calculation. The results of the point-charge calculations, made also for several other garnet lattices, indicate that distortions from a cubic potential are generally large, and that the second-degree terms are poorly determined by the model. In fitting to the experimental data, the parameters V20, V22, V40, and V60 (Vnm = Anm〈rn〉) were treated as adjustable, and the remaining parameters given the values expected from the point-charge ratios. The set of parameters thus obtained fit the six experimental g values to within 0.2 and the two fitted energy splittings to within 2 cm—1, and they also predict further energy levels in agreement with less definite experimental evidence. The remaining discrepancies reflect the inadequacies of the point-charge model. The apparent success of previous analyses of data for Yb garnets in terms of a near-cubic approximation is discussed, and it is shown how an insufficient number of parameters may incorrectly account for a limited set of experimental data.
Rotation—Vibration Interaction and Other Corrections to the Spin Doublet Separation in 2Π Diatomic Molecules
Authors: James Thomas C.
Published: January 2005

The effect of rotation—vibration interaction on the spin doublet separation in 2Π states of diatomic molecules is treated. Almy and Horsfall's refinement of Hill and Van Vleck's treatment is questioned and an alternative approach making use of Dunham's treatment of 1Σ diatomic molecules is used. The J dependence of the spin-orbit coupling constants is included in the discussion. Vibrational wavefunctions (including rotation—vibration interaction) and matrix elements are discussed. Additional corrections arising from the Λ doubling and from the spin—rotation interaction ΓN·S are briefly considered. A comparison of the results of this work with experimental spin doublet separation leads to better agreement between theory and experiment for the examples treated.
On the Continuous Absorption, Photoionization, and Fluorescence of H2O, NH3, CH4, C2H2, C2H4, and C2H6 in the 600-to-1000-Å Region
Authors: Metzger P. H. , Cook G. R.
Published: January 2005

The hydrogen-containing molecules H2O, NH3, CH4, C2H2, C2H4, and C2H6 have strong continuous absorption spectra in the 12 to 21 eV (600-to-1000-Å) region. Photoionization and absorption coefficients and cross sections have been computed from absorption and ionization spectra using the Hopfield He continuum as a continuous background-radiation source. A parallel plate combination absorption and ionization chamber was used behind the exit slit of a Seya scanning vacuum monochromator arranged for 0.5 Å bandwidth. Data were obtained with a windowless system using rare-gas calibration to measure the absolute photon flux from which photoionization efficiencies were determined. In general, the cross sections increased with increasing number of hydrogen atoms, and for the process corresponding to electron loss by photoionization, the cross section was found to be proportional to the number of bonding electrons, varying from 17.5 Mb for H2O to over 76 Mb for C2H6 (1 Mb=10—18 cm2). Inflections in the cross-section curves indicate processes other than simple electron loss by photoionization. Preliminary results of the fluorescence from these gases indicate that NH3, CH4, and C2H2 show measurable fluorescence. Maxima in the relative fluorescence yield curves are shown to be correlated with minima in the ionization efficiency curves, suggesting that the long-wavelength photon emitted may be associated with ion removal, either by a molecular recombination process or by reaction leading to molecular products.
Influence of Resonance Transfer on Luminescence Decay
Authors: Eisenthal K. B. , Siegel S.
Published: January 2005

The effects of dipole—dipole resonance transfer on the population and decay of excited donor molecules are discussed. The limitation of the previous treatments of this problem to flash excitation is demonstrated. The present treatment is applicable to systems which have achieved a steady state or have been flashed. Expressions are given for the donor quantum yields, the decay of excited donor molecules for flashed and steady-state systems, and the steady-state population of excited donor molecules.
Single-Configuration Calculations on Excited States of Helium
Authors: Davidson Ernest R.
Published: January 2005

The best one-configuration wavefunctions for several excited states of helium have been found. The error in the energy obtained varies from 0.5% to 1.0% of the binding energy of the outer electron. The method used is shown to give a rigorous upper bound to the excited-state energy.
Primary Photochemical Processes in Glyoxal at 4358 Å
Authors: Parmenter C. S.
Published: January 2005

Quantum yields of CO and of H2 have been measured in the gas-phase photolysis with 4358-Å radiation at temperatures between 37° and 207°C. φCO is generally about 0.6; φH2 is about 0.01. The data suggest that about 70% of the excited molecules cross to the triplet state by a first-order process, and the remaining excited singlet molecules return to the ground state with fluorescence. The principal reaction of triplet molecules is a dissociation into CO and HCHO, while a small fraction of triplet molecules are destroyed by collision with ground-state glyoxal molecules. About 3% of the triplet molecules undergo a first-order intersystem crossing to the ground state, forming molecules with about 55 kcal of vibrational energy. These either dissociate into H2 and CO or relax to vibrational equilibrium by collision with heat-bath molecules. At pressures near 100 Torr, where higher concentrations of triplet molecules are formed because of increased absorption, reactions of free radicals produced in collisions between triplet molecules also contribute significantly to φH2. The data suggest that temperature variation has little effect on the reactions destroying the triplet state, but that the rate of vibrational relaxation in the ground state increases markedly at higher temperatures.
Hard-Sphere Model for the Dissociation of Diatomic Molecules
Authors: Nielsen Svend Erik , Bak Thor A.
Published: January 2005

A simple classical model for the activation of diatomic molecules interacting with a heat bath of monatomic particles is proposed. The diatomic molecules are considered as hard spheres connected by springs and the monatomic particles as hard spheres. The model permits strongly nonadiabatic interaction, and because of its simplicity it makes possible a detailed calculation, which takes into account the energy transfer to translational, rotational, and vibrational degrees of freedom. The only parameters in the theory are the gas-kinetic hard-sphere radii of the atoms and the experimentally known activation energy. Comparison with experiments on the dissociation of molecules as I2, Br2, O2, and H2 in the inert gases shows an excellent numerical agreement, as well as a satisfactory dependence of the rate constant on the mass and temperature.
Structure of Water and Hydrophobic Bonding in Proteins. IV. The Thermodynamic Properties of Liquid Deuterium Oxide
Authors: Némethy George , Scheraga Harold A.
Published: January 2005

A model, proposed earlier for the theoretical derivation of the thermodynamic parameters of liquid water, is shown to be applicable to liquid deuterium oxide as well. The model, based on the ``flickering cluster'' concept proposed by Frank and Wen, and the partition function were described in a previous publication. In the application to D2O, the intermolecular vibrational frequencies are changed in accord with the theoretical ratios for isotopic substitution. The energy of the hydrogen bond is the only adjustable parameter; its value is 0.24 kcal/mole higher than for H2O. The calculated structural parameters indicate that more structural order exists in D2O than in H2O at a given temperature. The calculated values of the free energy, enthalpy, and entropy of the liquid have an over-all average error of 6%, as compared with experimental data, over the range 0° to 65°C. The deviation of cv is of the same magnitude as for H2O. The temperature dependence of the molar volume is reproduced with an error of less than 0.4%, and the temperature of maximum density is obtained within one degree of the experimental value. Excellent agreement is also obtained between the calculated and observed compressibility. The calculation of the PVT data involved no new assumptions. Calculated first peak areas for the radial distribution functions of H2O and D2O are shown to be almost identical.
Alternating Linewidths and Related Phenomena in the Electron Spin Resonance Spectra of Nitro-Substituted Benzene Anions
Authors: Freed Jack H. , Fraenkel George K.
Published: January 2005

Studies of linewidths in the electron spin resonance spectra of a number of nitro-substituted benzene anions are reported. The radicals were generated electrolytically in N,N-dimethylformamide solutions, and spectra were obtained over a range from above to below room temperature. Pronounced alternations in the linewidths of the nitrogen lines in many of the spectra were observed. If MN is the total z component of the nuclear spin angular momentum in compounds containing two equivalent nitrogen nuclei, the alternating linewidth phenomenon causes a broadening of the lines for which MN=±1 and a reduction in the amplitude of the central line. Large alternating linewidths were observed in the room-temperature spectra of the anions of dinitrodurene, dinitromesitylene, and 2,6-dinitro-3,5-dimethyl-4-acetyl-t-butylbenzene; and also in a spectrum which shows splittings from two equivalent nitrogen nuclei that was obtained from trinitromesitylene. Slight alternating linewidth effects at room temperature that became more marked at low temperatures were found in the spectra of the 2,6-dinitrotoluene and m-dinitrobenzene anions. No linewidth alternations were detectable even at low temperatures in the spectra of the o-dinitrobenzene, p-dinitrobenzene, and 2,6-dinitrophenolate anions. The 2,6-dinitroaniline anion, which was investigated only at room temperature, showed no evidence of an alternating linewidth effect. None of the spectra of the mononitrobenzene anions examined exhibited any anomalous linewidth phenomena. The experimental observations are in general agreement with the recently developed theory of linewidths. The theory attributes the alternation in widths in these radicals to an out-of-phase correlation of a modulation of the isotropic hyperfine splittings of the two equivalent nitrogen nuclei. This out-of-phase modulation probably arises from either fluctuating solvent complexes with the nitro groups, or from internal rotations of these groups relative to the plane of the benzene ring, and both types of motion may occur simultaneously. Steric hindrance of the nitro groups was found to enhance the magnitude of the alternations in width, as did lowering of the temperature.
Molecular Structure and Bonding of InC5H5
Authors: Shibata Shuzo , Bartell L. S. , Gavin R. M.
Published: January 2005

The molecular structure of gaseous indium cyclopentadienyl was investigated by electron diffraction. Diffracted intensities revealed the molecule to be an ``open-faced half-sandwich'' with a symmmetry at least closely approximating C5v. The principal mean distances and vibrational amplitudes found were 2.621±0.005 Å and 0.077±0.007 Å for In–C and 1.427±0.007 Å and 0.040±0.009 Å for C–C. It was observed that the C–H bonds are pushed 4.5°±2° out of the plane of the carbon ring by the indium atom. The failure of the Born approximation significantly lowered the sensitivity of the analysis but did not prevent the deduction of reasonably good structural parameters.

Metal—carbon bonds were 0.4 Å shorter than the sum of the ionic radii but both the In–C and C–C bond lengths agreed well with calculations based on Pauling's theory of covalent bonds of fractional bond order. Moreover, metal—ring overlap integrals were found to be of substantial magnitude. Therefore it is reasonable to conclude that the binding in the complex is essentially covalent, contrary to some previously published conjectures.