bluuebunny/crossref_metadata_2025 huggingface dataset:
Shock-Tube Study of Chain Branching during the Induction Period of the Hydrogen—Oxygen Reaction
Authors: Gutman David , Schott Garry L.
Published: January 2005

The growth of ``blue continuum'' emission has been measured during the induction period of the reaction of H2 (0.5%, 1.5%, and 5%)–CO (3.3% and 33%)–O2 (0.5%)–Ar mixtures between 1100° and 1700°K. For sensitivity, the reacting gas behind reflected shock waves was viewed axially through a large end plate window and lens. The observed intensity I, representing the integral of I′ (x)dx between reflected shock front and end plate, exhibited 2 to 3 decades of exponential growth, I = I0 exp(αt). α is related to the branching chain kinetics of H2–O2 combustion through the proportionality of I′ (x) to the product [CO][O]. α was found to be satisfactorily proportional to density and independent of [CO], and its dependence upon [O2] and [H2] was analyzed to yield rate coefficients for H+O2→ lim k1OH+Oand O+H2→ lim k2OH+Hbetween 1290° and 1667°K. These are represented by k1=1010.89 exp (−14.45 kcal/RT) liter mole−1·sec−1(±10%) over our range, and k2=1010.51 exp (−10.0 kcal/RT) liter mole−1·sec−1from combination of our mean result with literature data at 400°K.
Experimental Investigations of Ion—Molecule Reactions of D2+ with D2 and H2
Authors: Doverspike L. D. , Champion R. L.
Published: January 2005

The reactions D2++D2→D3++D and D2++H2→(D2H+, H2D+)+(H, D) have been studied using an angular ion-scattering apparatus in which the kinetic-energy distributions of the various product ions have been measured for collision energies in the range 2–15 eV. The angular distributions of the D3+ and D2H+ product ions have also been determined, at primary beam energies in the interval 7–11 eV. The observed product-ion kinetic-energy distributions show that several endothermic reaction channels exist for these reactions. The most probable channels for D3+ and D2H+ formation are those in which the product ions are formed by a pickup process, in which very little momentum is transferred to the H or D atom. By comparing the results of these isotopic reactions, it is inferred that D3+ is formed not only by D atom transfer to D2+, but also by D+ ion transfer to the target D2 molecule. Furthermore, at low collision energies, reaction channels corresponding to completely inelastic reactions in which all the center-of-mass collision energy appears as excitation energy of the product ions were observed for all three product ions.
Study of the Electronic Structure of Molecules. IV. All-Electron SCF Wavefunction for the Ground State of Pyridine
Authors: Clementi Enrico
Published: January 2005

An all-electron SCF LCAO MO wavefunction is presented for the ground state of the pyridine molecule. The basis set is built with Gaussian functions and all many-center integrals are accurately computed in this work. The lowest π orbital is below the second-lowest σ orbital; the lone pair on nitrogen is partly delocalized on the neighboring carbon atoms, but retains 1.41 electrons in the sp hybrid on the nitrogen nucleus.
Viscosity of Three Binary Gaseous Mixtures
Authors: DiPippo R. , Kestin J. , Oguchi K.
Published: January 2005

This paper reports relative measurements of the viscosity of three binary mixtures: Ne–N2, He–CO2, N2–Ar. Measurements were made at 20° and 30°C at pressures from 1–25 atm.
Structure of the Alkali Hydroxides. I. Microwave Spectrum of Gaseous CsOH
Authors: Lide David R. , Kuczkowski Robert L.
Published: January 2005

The microwave spectra of gaseous CsOH and CsOD have been studied in a high-temperature spectrometer. The spectrum indicates a linear or near-linear molecule with a large-amplitude, low-frequency bending vibration. A large number of excited states involving the bending mode and the Cs–O stretching mode have been identified. The rotational constant Bv shows an unusual variation as the bending mode is excited; the cause is not yet understood. The Cs–O bond length is found to be 2.40±0.01 Å and the O–H distance is probably about 0.97 Å. The electric dipole moment is 7.1±0.5 D. Relative intensity measurements indicate a Cs–O stretching frequency of 400±80 cm−1 and a bending frequency in the neighborhood of 300 cm−1. All of the evidence supports a highly ionic cesium—oxygen bond.
Some Reactions of Oxygen Atoms. III. Cyclopropane, Cyclobutane, Cyclopentane, and Cyclohexane
Authors: Stuckey Wayne K. , Heicklen Julian
Published: January 2005

The rate that oxygen atoms react with certain cycloalkanes was determined at 25°, 70°, and 125°C by the competition for oxygen atoms between a cycloalkane and hexafluoropropene. Oxygen atoms were generated by the mercury-sensitized decomposition of N2O. Then, the known rate-constant expression for C3F6 was used to calculate the rate constant for the oxygen atom—cycloalkane reaction. The Arrhenius parameters A and E are as follows: CycloalkaneA×10−9 (liter mole−1·sec−1)E (kcal/mole)cyclo−C3H60.313.8cyclo−C4H86.13.9cyclo−C5H104.82.6cyclo−C6H127.62.8
Vibrational Spectra and Structure of Four-Membered Ring Molecules. II. Chlorocyclobutane, Chlorocyclobutane-d1, and Chlorocyclobutane-d4
Authors: Durig J. R. , Morrissey A. C.
Published: January 2005

The infrared spectra of chlorocyclobutane, α-chlorocyclobutane-d1, and β,β,β′,β′-chlorocyclobutane-d4 in both the gaseous and liquid states have been recorded from 4000 to 250 cm−1. The far-infrared spectrum of β,β,β′,β′-chlorocyclobutane-d4 in the vapor state has been recorded down to 33 cm−1. The Raman spectra of the three isotopic species of chlorocyclobutane have also been recorded of the liquid phases and depolarization values measured. The spectra have been interpreted by considering the molecule to have a plane of symmetry and belonging to point group Cs. Assignment of the frequencies of the fundamental vibrations is based on position, isotopic shift, band type, and depolarization values. The ring-puckering vibration in chlorocyclobutane was observed in the Raman spectrum at 165 cm−1, and found at 159 cm−1 in the far-infrared spectrum of the vapor. The data shows that the first upper-state transition of the ring-puckering vibration is centered at 142 cm−1. For the tetradeuterated molecule the ring-puckering vibration was found at 144 cm−1 in the far-infrared spectrum of the vapor. The nature of the potential energy function governing the ring-puckering vibration is discussed.
Antiferromagnetic Structure of Anhydrous Cupric Sulfate CuSO4
Authors: Uryû Norikiyo
Published: January 2005

The antiferromagnetic structure of anhydrous cupric sulfate is considered theoretically. The collinear magnetic structure determined from neutron-diffraction data is explained by the isotropic exchange and the dipole interactions, and the effect of the antisymmetric-exchange interaction is discussed.
Oxygen−17 Hyperfine Splitting Constants in the ESR Spectra of p-Semiquinones—17O
Authors: Broze M. , Luz Z. , Silver B. L.
Published: January 2005

Oxygen−17 hyperfine splitting constants have been determined for a number of semiquinones—17O. The results were correlated with the spin density distribution in the radicals. It was found that the splitting constants aO can be very well fitted to an expression of the form, aO=QOC O ρO+QCO O  ρC, where ρO and ρC are pπ spin densities on the oxygen and carbon atoms of the carbonyl group, and the Q's are sigma—pi interaction constants. QOC O is about −40 G, but the analysis does not allow the value of QCOO to be determined, although its magnitude is certainly much less than that of QOC O. These interaction constants are discussed in terms of the general theory of Karplus and Fraenkel. Solvent effects on aO were observed, especially in going from apropic to hydrogen-bonding solvents and are discussed in terms of radical—solvent interaction at the carbonyl oxygen. In the Appendixes molecular orbital parameters for oxygen and chlorine are derived from the analysis of proton hyperfine splitting constants in simple and chloro-substituted semiquinones.
Calculated Spectrum of Quasibound States for H2(1Σg+) and Resonances in H + H Scattering
Authors: Waech Theodore G. , Bernstein Richard B.
Published: January 2005

The Born—Oppenheimer potential of Koℏos and Wolniewicz for H2(1Σg+) was fitted (±0.7 cm−1) by a polynomial, and the complete spectrum of bound and quasibound states was computed by direct numerical integration of the radial Schrödinger equation. The short-lived virtual states were studied via the energy dependence of the resonant phase shifts, following Buckingham, Fox, and Gal. Of the total of 301 bound states, the 108 levels observed by Herzberg and Howe were reproduced by the computations with an average deviation of ∼3.6 cm−1 (maximum deviation of 5.3 cm−1). Of the two observed quasibound states, the lower was satisfactorily reproduced, but for the upper one, the computed value deviated by 5.3 cm−1; in addition the calculated width was inconsistent with the sharpness of the observed level. Thus it is inferred that a small change in the potential (e.g., a drop of ∼5 cm−1 near R=3 a.u.) is required. Of the shortest-lived quasibound states, 10 have fractional widths Γ/E in the range 0.01–0.1, and are thus possibly suitable for observation as resonances in singlet atom—atom scattering. Collision energies for these range from 0.011 to 0.93 eV.
Optical Rotation of Oriented Helices. III. Calculation of the Rotatory Dispersion and Circular Dichroism of the Alpha- and 310-Helix
Authors: Woody Robert W. , Tinoco Ignacio
Published: January 2005

We have carried out a calculation of the optical rotatory dispersion (ORD) of α-and 310-helices which is essentially complete within the limitations of the Kirkwood approximation and its extensions. This treatment predicts that right-handed helices will exhibit three rotatory bands at wavelengths greater than 190 mμ. The sign and position of these predicted bands are in good agreement with experiment. The predicted rotational strengths do not agree so well, but are in sufficiently good accord to provide strong support to the assignment of the longest-wavelength band to the amide nπ* transition, and the shortest-wavelength band thus far observed to a composite band due both to the perpendicular-polarized exciton component and to the intrinsic rotational strength of the NV1 transition. Calculation of the ORD and CD (circular dichroism) of the α-helix from the calculated rotational strengths gives results in fair agreement with experiment, especially when the nπ* rotational strength is adjusted to agree with that observed in CD experiments. An analysis of the calculated ORD curves according to the Moffitt—Yang and Shechter—Blout procedures leads to values for the parameters in these equations which agree well with experiment in the case of the α-helix. A similar treatment of the 310-helix indicates that this helix can be distinguished from the α-helix by: (a) appreciably more positive rotations in the visible region, (b) appreciably larger absolute values of b0, A(α, ρ)225 and A(α, ρ)193. The dependence of various rotatory parameters on the length of the helix has been studied. The dispersion parameters b0, A(α, ρ)225 and A(α, ρ)193, as well as the depth of the 233 mμ trough appear to be the least sensitive to chain length. The magnitude of the maximum at 198 mμ, however, seems quite chain-length dependent, and therefore is probably not suitable as a measure of helix content.
Reaction of Hydrogen Atoms with Acetylene
Authors: Michael J. V. , Niki H.
Published: January 2005

The reaction of hydrogen atoms with acetylene has been investigated in a fast discharge-flow system coupled to a time-of-flight mass spectrometer. Isotopic studies confirm the following reaction mechanism: H+C2H2→C2H3*,C2H3*→C2H2+H,C2H3*+M→C2H3+M*,C2H3+H→C2H2+H2,where M is a third-body molecule and the asterisk represents chemically activated states. The pressure effect on the apparent over-all bimolecular constant confirms that the system undergoes a unimolecular reaction according to the Rice—Ramsperger—Kassel—Marcus theory, but not to the Lindemann theory. An attempt was made to obtain the rate constants of the elementary reactions for several isotopic modifications of this system.
Quantum Dynamics of Anharmonic Oscillators. III. The Morse Oscillator
Authors: Endres Paul F. , Wilson David J.
Published: January 2005

Quantum calculations of the dynamics of a Morse oscillator with a Gaussian initial wave packet have been performed. As previously observed in other simple oscillators the classical and quantum expectation values for the coordinate exhibit significantly different behaviors, especially after the first few cycles. Some theories of chemical kinetics require the classical-mechanical calculation of lifetimes which may be quite long compared to vibrational periods. These theories deserve re-examination in view of the dynamical behavior observed in the present work.
On the Pressure Broadening of Molecular Multiplet Spectra
Authors: Gordon R. G.
Published: January 2005

Gas-phase line shapes and band contours are calculated for microwave spectra involving fine structure levels due to electron spin and/or orbital angular momentum, or vibrational angular momentum. We use the impact approximation, and a semiclassical treatment of the molecular rotation. The line shapes are expressed in terms of a set of cross sections which depend on the transfer of angular momentum by collisions. Different results are found, depending on whether the spin and rotation are coupled together strongly [Case (a)] or weakly [Case (b)]. Good agreement is obtained with microwave measurements on NO [Case (a)] and O2 [Case (b)]. The results may be applied to study the angle-dependent shape of intermolecular forces.
Paramagnetism of Carbazyl and Hydrazyl Free Radicals
Authors: Duffy W. , Strandburg D. L.
Published: January 2005

Static magnetic-susceptibility measurements in the temperature range 1.4°—300°K are reported on powder samples of the stable aromatic free radicals N-picryl−9-aminocarbazyl (PAC), 2,2-diphenyl−1-picrylhydrazyl in the 106°C mp [DPPH(I)] and 137°C mp [DPPH(II)] crystal modifications, 2-phenyl−2-p-nitrophenyl−1-picrylhydrazyl (DHNO2·) and 2,2-bis(p-nitrophenyl)−1-picrylhydrazyl [D(NO2)2·]. Radical concentrations in the range from 0.81 to 0.99 and Weiss constants in the range −36° to −5.2°K are determined. The measurements are interpreted assuming that the magnetic behavior is due to alternating antiferromagnetic exchange-coupled linear chains. Exchange integrals are inferred from fitting theoretical curves to the susceptibility maxima. Evidence is presented for the presence of random dilution by diamagnetic sites in PAC.
Extended-Average-Energy Method for Perturbation Problems
Authors: Kirtman Bernard , Benston Margaret Lowe
Published: January 2005

An extended-average-energy (eae) method for approximating the first-order perturbation wavefunction ψ1 is presented. This method gives the best ψ1 of the form f(q)ψ0, where f is a function of a single variable q occuring in the perturbation. In the case of a one-dimensional problem our ψ1 is exact. A procedure is suggested for extending this treatment even further to obtain the exact ψ1 for multidimensional problems. Application is made to the polarizability of atomic hydrogen and electron correlation in the helium isoelectronic sequence.
Atom—Molecule Kinetics at High Temperature Using ESR Detection. Technique and Results for O +H2, O +CH4, and O +C2H6
Authors: Westenberg A. A. , de Haas N.
Published: January 2005

A technique is described for the measurement of atom—molecule rate constants over the temperature range 300°—1000°K. It combines a heated fast-flow reactor with ESR atom detection, the ESR cavity being located at a fixed position outside the heated reactor. The system should be useful with a wide variety of reactions, and yields rate constants having ±10% precision independent of temperature. This is also the absolute accuracy when the reaction stoichiometry is known or can be determined by auxiliary mass-spectrometric analysis. Results on some O-atom reactions are (in cubic centimeters per mole·second units): O+H2→H+OH,    k1=4.0±0.4×1013 exp (−10 200/RT),O+CH4→CH3+OH,    k3=1.7±0.2×1013 exp (−8700/RT),O+C2H6→C2H5+OH,  k10=1.8±0.2×1013 exp (−6100/RT).In the O+CH4 case, the stoichiometry determined both in this work and by others indicates that the mechanism subsequent to the initial step may be O+OH→O2+H,O+CH3→CH+H2O,O+CH→CO+H,although [8] and [9] are not definitely established, and other mechanisms are discussed. Little can be said about the O+C2H6 mechanism at present. It is shown that the pre-exponential factors and activation energies for these three hydrogen abstraction reactions are in reasonable relation to each other.
Studies of Ion—Neutral Reactions by a Photoionization Mass-Spectrometer Technique. I
Authors: Warneck Peter
Published: January 2005

The use of a photoionization mass spectrometer for ion—molecule reaction studies is described. Ion-source pressures up to 200 μ are employed, measured directly with a McLeod gauge. A method is described for determining ion residence times in the ion source at constant repeller field, using a pulsed-light source. Drift velocities, diffusion coefficients, and ion temperatures are given for N2+ ions in air as derived from an analysis of ion pulse shapes. Reaction studies are reported for nitrogen ions in air and nitrogen, and for hydrogen ions in hydrogen. The associated rate constants are derived.
Studies of Ion—Neutral Reactions by a Photoionization Mass-Spectrometer Technique. II. Charge-Transfer Reactions of Argon Ions at Near-Thermal Energies
Authors: Warneck Peter
Published: January 2005

A photoionization mass spectrometer has been employed to study charge transfer involving 2P3/2 argon ions at ion-source pressures 15 to 60 μ and with a source acceleration potential of 0.5 eV. The average energy of the reacting ions are calculated and are found to be less than 0.17 eV. The following rate constants were obtained: A++NO→A+NO+, k=3.9×10−10 cc/molecule·sec; A++O2→A+O2+, k=1.1×10−10 cc/molecule·sec; A++CO2→A+CO2+, k=7.0×10−10 cc/molecule·sec; A++CO→A+CO+, k=1.25×10−10 cc/molecule·sec; A++N2→A+N2+, k=0.66×10−10 cc/molecule·sec. The theoretical implications are discussed.
Hellmann—Feynman Theorem in Curvilinear Coordinate Systems
Authors: Epstein Saul T.
Published: January 2005

The generalized Hellmann—Feynman theorem in curvilinear coordinates is discussed both for exact and for ``floating'' variational wavefunctions. Particular attention is given to the possibility that the volume element in curvilinear coordinates may depend on the parameter with respect to which one wishes to differentiate the energy.
Intensity Enhancement of Forbidden Electronic Transitions by Weak Intermolecular Interactions
Authors: Robinson G. Wilse
Published: January 2005

This paper discusses the phenomenon where an originally ``forbidden'' electronic transition in a molecule (M) becomes strikingly enhanced through weak interactions with a neighboring perturber (P). The purpose of the paper is to present a general mechanism by which both symmetry-forbidden and multiplicity-forbidden transitions of a molecule in a perturbing environment can gain intensity. The mechanism for intensity enhancement is based on perturbation theory, diagrams being introduced in order to simplify the discussion. The paper emphasizes the fact that the enhanced transition moment may be gained not only from strong transitions in the molecule itself, but also from transitions in the perturbing environment. A number of examples of intensity enhancement are presented and analyzed. The so-called Ham bands of benzene in carbon tetrachloride, for example, are shown to arise from intensity borrowed from the solvent. In spin-forbidden transitions a requirement for enhancement is that either P is paramagnetic (O2 effect) or that strong spin—orbit coupling in the excited states of P exists (external heavy-atom effect). Besides spin-forbidden and symmetry-forbidden transitions, double and multiple transitions made allowed through weak intermolecular interactions are discussed. Double transitions in molecular oxygen are analyzed, and it is concluded that intensity is borrowed from the Schuman—Runge band system. In this case an intermolecular interaction energy of only 5 cm−1 is required to give the observed intensity, so the transition can hardly be thought of as being due to the ``O4 molecule.'' A study of these weak interactions allows knowledge to be gained about molecular eigenfunctions in the important but often neglected regions of intermolecular space.
Vacuum-Ultraviolet Photochemistry. VII. Photolysis of Hydrazine at 1236 and 1470 Å
Authors: Stief L. J. , DeCarlo V. J. , Mataloni R. J.
Published: January 2005

The photolysis of hydrazine vapor has been investigated at 1236 and 1470 Å. At 1236 Å, fluorescence is observed at 3360 Å and is attributed to the NH(A3π→X3Σ−) transition. The emission has been studied as a function of pressure and photolysis time. No emissions were observed at 1470 Å. The products of the photolysis of hydrazine are nitrogen, hydrogen, and ammonia. The pressure dependence of these products has been determined at 1236 and 1470 Å. Formation of the parent ion N2H4+ probably occurs at 1236 Å but not at 1470 Å. At the latter wavelength, reduction of the hydrogen yield upon addition of C2D4 is explained by the reactions: N2H4+hv→N2H3+H,H+N2H4→H2+N2H3.Nitrogen production is not reduced in the presence of C2D4 and the quantum yields of hydrogen and nitrogen are equal under these conditions. These products arise mainly from decomposition of N2H2 (di-imide). The latter may be formed directly from hydrazine, from decomposition of N2H3 or in the disproportionation of N2H3 radicals. Contributions from radical—radical combination reactions are minor based on the relative H2/N2 yields observed in this study and on the lack of mixing of isotopic nitrogen previously reported.
Oscillator Strengths of CF and Comments on Heats of Formation of CF and CF2
Authors: Wentink Tunis , Isaacson Louis
Published: January 2005

Oscillator strengths (f numbers) and Franck—Condon factors for the A—X and B—X band systems of CF are presented. Separate results for CF(A—X) based on directly measured radiative lifetimes and shock-tube intensities are compared. These data indicate that the heat of formation for CF2 and especially CF may be significantly different from the accepted JANAF table values.
Classical Small-Angle Scattering from Anisotropic Potentials
Authors: Cross R. J.
Published: January 2005

A simple, direct method of calculating the small-angle scattering from an arbitrary anisotropic potential is derived. The approximations are valid for large energies or large impact parameters. Two methods are used, both yielding identical results. The first, an impulse approximation, involves integrating the force over the trajectory which would be followed if there were no interaction. The second method involves a perturbation solution of Hamilton's equations of motion. The first method is conceptually simpler, but the second yields a solution of the trajectory and is more easily generalized to include second-order effects.

For scattering of ions and fast neutrals, molecular rotation can be neglected, and a simple expression is obtained for the differential cross section at small angles. This is applied to ion—dipole scattering where the potential is completely anisotropic, being repulsive for half the orientations and attractive for the other half. It is found that the differential cross section behaves exactly like that for a spherically symmetric potential given by μe/2r2. However, when the ion—dipole potential is combined with a repulsive term in the potential, deviations from the behavior of spherically symmetric potentials are found. For scattering at thermal energies, the molecular rotation averages out the anisotropic terms in the potential, introducing further deviations from the behavior of spherically symmetric potentials.
Partial Molal Volumes in Regular Solutions
Authors: Hildebrand J. H. , Dymond John
Published: January 2005

When liquids that form regular solutions are mixed, there occur, simultaneously, absorption of energy, increases in activity coefficients of the components, and expansion in volume. We consider the partial molal expansion and energy of transfer from pure liquid to solution at high dilution, where these quantities are maximum and v2—v2° is easily measured. The subscript 2 denotes the highly dilute component. We write for the energy absorbed in expansion against the internal pressure of the solvent, E2−E2∘=(V2−V2∘)(∂E1/∂v). We confine our attention to systems for which we may expect the energy to be calculable from solubility parameters as in regular solution theory, E2−E2∘=V2∘(δ2−δ1)2. (The square of the volume fractions usually present in the right-hand member is virtually 1 under these conditions.) These equations agree within experimental errors in 19 cases for energies up to 2.5 kcal and expansions up to 20%. An earlier equation in which the expansion is dependent upon the compressibility of the solvent fails badly.
Chemisorbed β Phase of Nitrogen on Tungsten
Authors: Robins J. L. , Warburton W. K. , Rhodin T. N.
Published: January 2005

The pertinent experimental information now available on the chemisorption of nitrogen in the β phase on tungsten is reviewed. The concept of two distinct, unrelated types of absorption site being responsible for the β1- and β2- desorption peaks is considered to be inadequate to explain many recently published experimental observations. A new model for the chemisorbed state is proposed based on the existence of a single type of site for β-phase adsorption and with emphasis on the role of surface diffusion on different types of planes. The model is then applied to the interpretation of a range of published observations on nitrogen adsorption on tungsten including desorption effects, isotopic mixing, contact potential changes, and field electron emission microscopy observations.
Energy Balance in the Photochemistry of Benzene
Authors: Noyes W. Albert , Harter D. A.
Published: January 2005

Quantum yields of triplet-state formation in benzene vapor have been determined at several wavelengths by the method of Cundall. From 2520 to 2668 Å, values average about 0.63 if one excludes those at a single wavelength of 2535.5 Å. At this wavelength a higher value is obtained, and its possible significance is briefly discussed. At 2420 Å the triplet-state yield is small and may be zero. Fluorescent yields have been scanned for ranges of a few Angstrom units from 2400 to 2600 Å. Above 2520 Å there is no significant change with wavelength. The trends in these results are briefly discussed, and it is pointed out that a detailed discussion of the theory of the photochemistry of benzene has little value because data now available are not sufficient to test any theory.
Excitation of Molecular Vibration on Collision: Role of the High-Order Angular Momenta
Authors: Shin Hyung Kyu
Published: January 2005

Excitation of molecular vibration in the collision between two diatomic molecules is studied. The specific aims are to calculate the partial cross sections for general values of the collision angular momentum l and to show the important role of the high-order partial waves in the calculation of total cross sections. It is shown that the partial cross section becomes largest at lmax=12[(2/L)12−1], where L is dependent on the collision parameters and is of the order of 10−3−10−4; in H2–H2 values of l up to about 30, 55, 90, and 125 must be considered for the relative energy of 0.5, 1, 2, and 3 eV, respectively, for the calculation of total cross sections. In O2–O2 the corresponding l values are 125, 200, 340, and 450. It is also shown that the modified wavenumber approximation underestimates the average total cross section by a factor of 1.7 at 300°K and 1.3 at 4000°K for H2–H2 and for O2–O2 by 1.8 and 1.4 at the corresponding temperatures. The connection between the cross section for inverse power potentials and those for exponential potentials is discussed analytically.
Thermomolecular Pressure Difference Measurements for Precision Helium−3 and Helium−4 Vapor-Pressure Thermometry
Authors: Watkins Reed A. , Taylor William L. , Haubach Walter J.
Published: January 2005

Thermolecular pressure differences due to thermal transpiration were measured to find the corrections for low-temperature vapor-pressure thermometry using helium−3. The experimental apparatus consisted basically of several stainless-steel, pressure-sensing tubes, each connected to the same pressure container inside a cryostat. The upper, or warm, ends of the tubes were connected to differential pressure gauges outside the cryostat. The gauges measured the differences in warm end pressures between a 0.29-cm radius reference tube and tubes of 0.14-, 0.055-, and 0.0271-cm radii for a variety of cold end temperatures and pressures.

The results for saturated and unsaturated helium−3 and unsaturated helium−4 are identical but greater at the maxima than the values computed from the semiempirical Weber—Schmidt equation, which was based on measurements with unsaturated helium−4. However, experimental data for saturated helium−4 in the low-pressure region were much higher than the Weber—Schmidt equation and the other data. This disagreement was attributed to superfluid film flow. An outline of the derivation of the differential equation describing thermal transpiration is given in this report. Theoretical predictions for the high-pressure region of saturated helium−4 are in agreement with the experimental data. It is concluded that a revision of the Weber—Schmidt equation is needed for precision thermometry.
Vibronic Coupling. IV. Trimers and Trigonal Molecules
Authors: Perrin Marilyn H. , Gouterman Martin
Published: January 2005

The mathematical treatment of vibronic coupling in trimers and in benzene is presented. The vibronic matrix is diagonalized by computer methods for weak, intermediate, and strong coupling limits. Perturbation solutions in the two cases, ε≫1≫λ2 and ε≪1≪λ2 are presented. The first case is shown to be analogous to the Jahn—Teller case. Calculated spectra and vibronic probability densities are presented. The values of ε and λ for the real systems, barrelene, triquinacene, and benzene are estimated, and the systems are classified as strong, weak, and intermediate coupling, respectively. This method gives qualitative agreement with the observed benzene spectrum.
Extended Hückel Theory and the Shape of Molecules
Authors: Allen Leland C. , Russell J. Dennis
Published: January 2005

Ab initio MO SCF wavefunctions and one-electron energies are compared with extended-Hückel-theory values for the polyatomic molecules BeH2, BH2+, BH2−, NH2+, H2O, BeH3−, BH3, CH3+, Li2O, F2O, LiOH, and FOH. A remarkable similarity in the nodal structure, order of the energy levels, prediction of molecular shape, and changes in hybridization and ionization potential with angle is observed. The origin of this correspondence for molecular shape is found to be a general theorem relating changes in the sum of one-electron energies to the total energy and implying a low information content to the angular dependence of molecular energetics. Analysis of the Hückel molecular orbitals also shows that quantitative evaluation of many other chemically interesting quantities is not to be expected. These investigations help give a quantum-mechanical underpinning to extended Hückel theory, elucidate its a priori capabilities, and lead to proposals for realizing more quantitative predictions from this model.
Energy Distribution of Energetic Atoms in a Gaseous Medium. I. Elastic Scattering of Particles by Spherical Potentials of the Form V(r) = (A1/r
S1) + (A2/r
S2)
Authors: Baer Michael , Amiel Saadia
Published: January 2005

The energy distribution function n(E) for energetic particles in a gaseous medium is treated (classically) assuming elastic scattering governed by a two-term spherical potential of the form V(r) = (A1/rS1) + (A2/rS2). It is found that in the energy interval from 1 MeV to 1 keV, n(E) differs from that computed for a single-term potential, but it makes almost no difference whether the second (long-range) component is of an attractive or repulsive nature. In the low energy range (<1 keV), if the long-range component is repulsive it almost completely screens the short-range one (which is always assumed to be repulsive). If it is attractive it lowers the values of n(E) in comparison with those obtained with a repulsive long-range term. The calculations also show that n(E) is almost independent of the initial energy of the incoming particles.

The results can be applied to the calculation of the yields of chemical reactions caused by energetic atoms such as fission fragments. One of the implications which emerges is that the yields of the reactions would not be influenced by the initial spectrum of the energetic atoms, since this has practically no effect on n(E) provided that the atoms behave like material points.
Ionization Cross Sections, Charge-Transfer Cross Sections, and Ionic Fragmentation Patterns of Some Paraffins, Olefins, Acetylenes, Chloroalkanes, and Benzene with 40–100-keV Protons
Authors: Collins J. G. , Kebarle P.
Published: January 2005

The simple and charge-transfer ionization cross sections for Kr, Ne, N2, CH4, C2H4, and n-C4H10 were measured with 40–100-keV protons. The simple ionization cross sections are almost constant in this range, while the charge-transfer cross sections are roughly 40% of the total ionization at 40 keV and decrease to about 10% at 100 keV. The relative ionization cross sections (both simple and charge transfer) of a variety of molecular compounds (see title) were measured with 100-keV protons and found to be linearly related to the polarizabilities.

The mass spectra of a number of hydrocarbons were measured with 50- and 100-keV protons. The mass spectra are qualitatively very similar to spectra obtained with electrons of the same velocity (55 eV for 100-keV protons). This is to be expected from a qualitative extension of the Bethe—Born equation to ionization of molecular electrons. Since the mass spectra change little with velocity the American Petroleum Institute (A.P.I.) fragmentation patterns with 50–75-V electrons are a good guide to ionization by any (singly) charged particle with velocity higher than 108 cm/sec.

Fragments of high appearance potentials and doubly charged ions are considerably more abundant in the 40–100-keV proton spectra than at higher proton energies or in the electron-impact spectra. Conclusions can be made as to the charge-exchange mass spectra produced by particles with velocities in the range 108 cm/sec. These mass spectra are very different from charge-transfer spectra obtained at low primary ion energies. Thus there is little dependence on the recombination energy of the primary ion. The charge-transfer spectra seem not very different from the spectra produced by simple ionization. This means that the distribution of internal energies imparted to the new ion cannot be very different from that in pure ionization.
Line Profiles in Nuclear Magnetic Double Resonance
Authors: Freeman R. , Ernst R. R. , Anderson W. A.
Published: January 2005

In nuclear magnetic double-resonance experiments where the irradiated resonance has an appreciable linewidth due to spin—spin relaxation, some broadening may be transferred to the observed resonance line. The expected line profiles have been calculated by the density-operator method for double irradiation in the ``spin-tickling'' and ``spin-decoupling'' modes, and are found to be in good agreement with the experimental results. In the ``spin-tickling'' approximation, where only two energy levels are appreciably perturbed by the second radio-frequency field, the observed line shapes are also obtainable by a simple convolution integral, but this method is not generally valid for ``spin decoupling.'' One application is the measurement of the width of a line that is not directly observable in the spectrometer, either through low inherent sensitivity or because of overlying resonances. As a practical example, the line profiles of the 13C satellites of the proton spectrum of chloroform during heteronuclear double irradiation indicate that the 13C resonance is 1.8 cps wide. This broadening is attributed to spin coupling to the chlorine nuclei which are rapidly relaxed through quadrupolar interaction with the environment, permitting an estimate of the magnitude of this spin coupling constant J(13C35Cl)≈49 cps.
Debye-Hückel Potential of Mean Force and Activity Coefficient for Point Defects in Ionic Crystals
Authors: Allnatt A. R. , Hoines P. C.
Published: January 2005

The solid-state analogs of the Debye—Hückel potential of mean force and activity coefficient have been calculated numerically for defects interacting with Coulomb forces in sodium chloride. An approximate formula for this potential of mean force derived previously is accurate to 1% for κ≤1.4×107 cm−1, where κ is the Debye—Hückel shielding parameter.
Franck—Condon Factors in Ionization: Experimental Measurement Using Molecular Photoelectron Spectroscopy. II
Authors: Turner D. W. , May D. P.
Published: January 2005

A 180° magnetic-field electron velocity analyzer described in an earlier paper has been used to clarify the vibrational fine structure in the molecular photoelectron spectra which helium resonance line photons (hv=21.21 eV) excite in carbon dioxide, carbon oxysulfide, carbon disulfide, and nitrous oxide. Experimental Franck—Condon factors for ionization from the levels of CO2 and N2O lying just above 21.21 eV have been determined and compared in the case of two of the CO2+ states (X, A) with calculated values. For COS only one state (C) could be analyzed and in CS2 no detailed structure could be resolved. Vertical I.P. values have however now been recorded for all these levels.
Dielectric Relaxation and Hindered Internal Rotation
Authors: Provder Theodore , Vaughan Worth E.
Published: January 2005

The effect of hindered internal rotation on the dielectric relaxation in a liquid whose molecules contain two polar groups of equal size with a common rotation axis is calculated for twofold symmetric cosine and parabolic potential barriers. The dielectric properties are calculated from the configuration space distribution function which is obtained by a perturbation expansion of a differential equation resulting from a rotational Brownian motion argument. The results are combined with a similar calculation involving an asymmetric potential to interpret the effects of symmetry, barrier height, and barrier shape on the relaxation process.
Electron Recombination in Hydrocarbon—Oxygen Reactions behind Shock Waves
Authors: Wilson L. N. , Evans E. W.
Published: January 2005

The rate of recombination of electrons with ions behind shock waves in argon containing dilute lean mixtures of hydrocarbons and oxygen has been measured with a microwave system. The recombination reaction was found to be two body, as evidenced by insensitivity of the recombination coefficient α to changes in pressure and concentration; and the recombination coefficient for acetylene—oxygen and methane—oxygen mixtures was found to depend upon temperature as T−1.98 between 2500° and 5000°K. Extrapolating to room temperature gives a value of α=1.3×10−5 cm3/sec, consistent with the electron removal process being a dissociative recombination involving a complex ion. In the case of acetylene, the reaction is probably a previously proposed scheme: H3O++e−→neutral products. Measurements made at a temperature of about 3800°K, using ethane, ethylene, propane, and benzene, gave recombination coefficients similar in magnitude to those obtained for the acetylene and methane, consistent with the recombining ion being the same for all these hydrocarbon—oxygen reactions.
Comparison of Valence-Bond and Molecular-Orbital Results for Some Ion-Radicals
Authors: Brown Thomas H. , Karplus Martin
Published: January 2005

The results of valence-bond spin-density calculations for a number of positive (+) and negative (—) aromatic ion radicals are given. For naphthalene, it is found that the α and β position spin densities in the positive ions do not equal those in the negative ion; that is (ρα(+)/ρα(−)) = 1.01 and (ρβ(+)/ρβ(−)) = 0.933. This result, which contrasts with that of molecular-orbital calculations, may provide a partial explanation of the small hyperfine splitting differences found in (+/—) ion pairs. It is noted that for a number of ion radicals, predominantly positive ions, the symmetries of the ground state, as predicted by the valence-bond and molecular-orbital methods, are not the same. Although these symmetry disagreements introduce only small changes in the spin densities of most of the molecules studied, the azulene positive-ion results may be sufficiently different to permit an ESR test of the theories. Other experiments and calculations which would also be important for evaluating the valence-bond method for ion radicals are discussed.
Significant-Structure Theory of Liquids. Heat Capacities, Compressibilities, and Thermal-Expansion Coefficients of Some Molten Alkali Halides
Authors: Vilcu R. , Misdolea C.
Published: January 2005

By means of the significant-structure theory of liquids, heat capacities at constant volume and pressure were computed, as well as thermal-expansion and compressibility coefficients of the ionic melts: KCl, KBr, NaCl, and NaBr at 1073°, 1173°, and 1273°K. Some aspects of significant-structure theory are analyzed in the light of the computations.
Field Ionization near Nonuniform Metal Surfaces
Authors: Alferieff M. E. , Duke C. B.
Published: January 2005

Four one-dimensional, solvable pseudopotential models are employed to calculate the field-ionization energy distributions outside of (a) step-function clean metal surfaces (b) step-function metal surfaces with a monolayer or less of adsorbed metallic or neutral impurities, and (c) clean metal surfaces with finite thickness and various shapes. All models lead to resonances for low-energy ions. For the step-function clean metal surface these resonances occur near the Bohr quantization energies for an inverted, infinite triangular potential. Both adsorbates and changes in the shape of the surface potential alter the intensity pattern of the resonances. A model in which the surface region is described by a linear potential leads to a two-slit intensity pattern. Potentials with a finite discontinuity in the zeroth, first, or second derivatives all lead to slowly damped interference effects explicitly associated with the nonanalytic dependence of the potential on the position coordinate.
Light Scattering from Solutions of Polymers in Mixed Solvents
Authors: Yamakawa Hiromi
Published: January 2005

A distribution-function theory of light scattering in multicomponent systems is presented, taking into account the angular distribution of the scattered light. The general theory is applied to solutions of one flexible homopolymer in two solvents. An apparent polymer molecular weight M2,ap and an apparent second virial coefficient are expressed as functions of the concentration of a second solvent, which is assumed to be poor for the polymer, in terms of molecular distribution functions to discuss the procedure of determining the true second virial coefficient and the molecular dimension in the mixed-solvent system. In the absence of angular dissymmetry, the result is equivalent to the fluctuation theory of Kirkwood, Goldberg, and Stockmayer. It is pointed out that the second virial coefficient can be determined at low concentrations of the second solvent without applying the dialysis technique of Casassa and Eisenberg. Further, it is shown that, even if the refractive-index increment with respect to the second solvent does not vanish completely, the molecular dimension can be determined under the condition, 0.8<M2,ap/M2<1.2, where M2 is the true polymer molecular weight. The determination of the theta point in the ternary system at which the unperturbed dimension is measured is also discussed.
Glass Transition in o-Terphenyl
Authors: Greet R. J. , Turnbull D.
Published: January 2005

Volumetric and thermal measurements on its undercooled liquid indicate that o-terphenyl undergoes a glass transition in the vicinity of −30°C. This glass temperature is about 60°C higher than that predicted by correlations applicable to simple molecular glass formers. The viscosity of the undercooled liquid was measured over the temperature range 20° to −16°C. These data and the higher-temperature data of other investigators are described approximately (between 250° and −16°C) by the equation η=4.65×10−4exp[689/(T−231)] P.The apparent activation energy for viscous flow increases from about ¼ of the heat of vaporization ΔHv at the highest part to about 5 ΔHv at the lowest part of the temperature range. The rates of volume relaxation in the vicinity of the glass transition temperature were measured. Each relaxation isotherm could be described with a single time constant over volume changes ranging up to 0.2%. In a cylindrical dilatometer, with a large length-to-diameter ratio, the relaxation rates apparently were limited by a flow process reflecting the adhesion of terphenyl to the dilatometer walls. Approximate values of the shear viscosity were inferred from a model for this process. Apparently, the homogeneous nucleation frequency of crystals in amorphous o-terphenyl does not reach a measurable level. The undercooling dependence of the rate of advance of the crystallization front was measured.
Optical Spectra of Orientationally Disordered Crystals. II. Infrared Spectrum of Ice Ih and Ice Ic from 360 to 50 cm−1
Authors: Bertie J. E. , Whalley E.
Published: January 2005

The far-infrared spectra in the range 360–50 cm−1 of ice Ih and ice Ic made from H2O and from D2O, and of vitreous ice made made from H2O have been investigated. The spectra are due to essentially purely translational vibrations, and have been interpreted using the theory of the spectra of orientationally disordered phases developed in the preceding paper. There are peaks at 229.2 and 164 cm−1 that are due (in ice Ic) to maxima in the density of vibrational states due to the transverse optic and longitudinal acoustic vibrations, respectively, and a shoulder at 190 cm−1 due to the maximum in the longitudinal optic vibrations. There is also a peak just below 50 cm−1 in the spectrum of optical density divided by the square of the frequency that is due to the maximum in the transverse acoustic vibrations. Corresponding assignments are proposed for ice Ih. The Raman spectrum can in principle yield similar information, and agrees with the infrared spectrum in so far as the measurements can be compared.

Some of the observed frequencies can be fitted reasonably well with a simple nearest-neighbor bond-stretching and angle-bending potential field, but there is absorption at sufficiently high frequencies to indicate that long-range forces are important in determining the translational lattice vibrations of ice. The effects of temperature and of deuterium substitution on the spectrum are discussed.
Relaxation of a Gas of Harmonic Oscillators
Authors: Rankin C. C. , Light J. C.
Published: January 2005

The temporal evolution of the vibrational distribution function for a gas of harmonic oscillators undergoing binary collisions, in which they can exchange vibrational quanta among themselves as well as transfer energy between the vibrational and translational degrees of freedom, is determined exactly. The solution, given in terms of a generating function, involves only a double integral and is valid for transition probabilities due to an interaction potential linear in the oscillator coordinate. The relaxation toward ``local equilibrium'' of the vibrational distribution is found to be at least twice as fast as the relaxation of the average vibrational energy to the final equilibrium value. The solution is valid for an arbitrary initial vibrational distribution and for arbitrary ``dilution'' of the oscillators by inert collision partners.