bluuebunny/crossref_metadata_2025 huggingface dataset:
X-Ray K-Absorption Edges of Three-Planar Nickel Compounds
Authors: Mitchell George R.
Published: January 2005

The low-energy structure of the x-ray K-absorption edge of nickel in nickel dimethylglyoxime, nickel phthalocyanine, and potassium nickel cyanide is re-examined for evidence of the second-order transition, the excitation of a 1s electron to a bound orbital, plus the simultaneous excitation of a plasmon. A perturbation calculation indicates that such a process may be observable. The absorption data are consistent with this interpretation if the electron transition is to a perturbed 3d orbital of the K-excited nickel atom or a molecular orbital which in the LCAO—MO approximation contains some d orbital wave function. The appearance of two strong absorption maxima (2 and 6.5 eV) in nickel dimethylglyoxime is explained by the formation of two distinct molecular species when nickel dimethylglyoxime is precipitated from a basic solution of dimethylglyoxime by a nickel salt.
Dielectric Properties of Glycerol—Water Mixtures
Authors: McDuffie G. E. , Quinn R. G. , Litovitz T. A.
Published: January 2005

The frequency dependence of the complex dielectric constant of glycerol—water mixtures has been measured in the megacycle frequency range at −7.5°, −15.3°, and −19.5°C. for various concentrations between nearly pure glycerol and an equal molar mixture. Cole—Cole plots of the data indicate a single main relaxation with an asymmetric distribution of relaxation times of the Davidson—Cole form. The limiting dielectric relaxation time of the Davidson—Cole distribution was found to be strongly dependent on the water content and to vary exponentially with the molar concentration of water. The width of the distribution of relaxation times is independent of the concentration over the range studied and only slightly temperature dependent. The average dielectric relaxation times of the mixtures were extrapolated to 100% water. The dielectric relaxation time of water obtained by this extrapolation agrees satisfactorily with the measured value, indicating a smooth transistion between the average relaxation time of pure glycerol and pure water, as well as indicating a change in the distribution of times from that of the Davidson—Cole form to a single time. These experimental findings can be explained in terms of the ``group'' concept of Schallamach in which it is assumed that in mixtures of associated—associated liquids, such as glycerol and water, dielectric orientation occurs through a cooperative effect in groups of molecules, these groups containing molecules of both kinds.

The concentration dependence of the dielectric relaxation time is also compared to that of viscosity. The comparison indicates that the variation of dielectric times with water content is similar to, but not exactly the same as, the variation of viscosity.
Effect of Centrifugal Distortion on the Shape of the Hydrogen Sulfide Fundamental Infrared Bands
Authors: Emerson M. T. , Eggers D. F.
Published: January 2005

The fundamental infrared vibration bands of hydrogen sulfide exhibit an interesting intensity anomaly characterized by P branches which are much weaker than the corresponding R branches. This work shows that this anomaly is caused by centrifugal distortion of the nonrigid molecule. A formalism based on a semi-classical approach is used to calculate the vibration—rotational line positions and their intensities. The computed theoretical spectra are in good agreement with the experimental spectra. This formalism also gives a method of determining the relative sign of (∂μ/∂Q) with respect to μ0. The values of (∂μ/∂Q) needed in the calculations were obtained from the experimental integrated band intensities and were found to be (∂μ/∂Q1) = −4.4 esu g−½ and (∂μ/∂Q2) = +8.7 esu g−½.
Magnetic Shielding in Some Diatomic Molecules
Authors: Kern C. William , Lipscomb William N.
Published: January 2005

Magnetic shielding constants calculated for all nuclei in LiH, BH, NH, BF, HF, LiF, CO, H2, Li2, N2, and F2 have yielded good results for lighter nuclei bonded to heavier nuclei. The difficult paramagnetic contribution of Ramsey's theory is reduced to tractable terms involving only the ground-state wave function by a choice of the gauge of the vector potential, and by an approximation involving cancellation of average excitation energies of matrix elements depending upon angular momentum and linear momentum operators. The limitations of this approximation are explored.
Vaporization Behavior of Niobium Carbide
Authors: Fries R. J.
Published: January 2005

The vaporization behavior of niobium carbide was studied over the temperature range from 2260° to 2940°K utilizing the Langmuir method. NbC was observed to lose carbon preferentially down to a composition of NbC0.75, at which composition the vaporization proceeds congruently at a temperature of 2940°K. The vapor pressure of carbon above nearly stoichiometric NbC could be represented by the equation log P (atm) = 5.296–3.276×104/T with a corresponding second law heat of vaporization of 150 kcal/mole of C vaporized. However, third law calculations and heat of formation data indicate a ΔH0298 of from 180 to 189 kcal/mole. Several possible explanations of this disagreement are discussed. The total rate of evaporation from NbCx was found to increase by a factor of two as the value of x decreased from 0.97 to 0.80. Finally, a semi-quantitative evaluation of the diffusion constant of C in NbC was made, resulting in a value of D≅8×10−7 cm2/sec at 2940°K.
Spin-Density Distributions in Conjugated Ligands of Paramagnetic Chelates from NMR Contact Interaction Shifts
Authors: Eaton D. R. , Josey A. D. , Phillips W. D. , Benson R. E.
Published: January 2005

Electron-spin-density distributions in a variety of π systems have been obtained from proton-contact interaction shifts in paramagnetic nickel II chelates of N,N′-disubstituted aminotroponeimines. The results have furnished a great deal of new information regarding the detailed manner in which π electrons are distributed via conjugative effects. Spin-density distributions in these systems calculated by the valence-bond scheme are shown to be in quite good general agreement with experimental determinations. Effects attributable to hyperconjugation have been observed and the conjugating abilities of linking groups C=C, N=N, NH, O, S, and SO2 have been assessed. It is shown also that metal-ligand π-bond formation results in transfer of 0.1 of an unpaired electron from nickel to the π system of each of the ligands of these bischelates.
Modification of the Rydberg—Klein—Rees Method for Obtaining Potential Curves for Doublet States Intermediate Between Hund's Cases (a) and (b)
Authors: Vanderslice Joseph T.
Published: January 2005

The Rydberg—Klein—Rees method for obtaining potential-energy curves from band-spectroscopic data has been modified in order to handle doublet electronic states intermediate between Hund's cases (a) and (b). In the derivation, the spin-orbit coupling constant has been taken to be independent of distance. The modified equations have been used to recalculate the curves for the X2II state of NO.
Growth of Crystal Whiskers
Authors: Blakely J. M. , Jackson K. A.
Published: January 2005

A solution has been found for the rate of growth of crystal whiskers from the vapor when nucleation on the whisker surfaces does not occur. Expressions have also been derived relating the supersaturation ratio of adsorbed atoms along the whisker to the total length from which certain predictions can be made concerning the probability of nucleation.
Quantum-Mechanical Transition-Complex Theory of Rearrangement Collisions
Authors: Thorson Walter R.
Published: January 2005

The theory of rearrangement collisions is discussed in applications to bimolecular chemical reactions, using the method of stationary-state solutions to the Schrödinger equation to avoid the perplexities associated with the non-orthogonality of initial and final states. The analysis employed is originally due to Gerjuoy [E. Gerjuay Phys. Rev. 109, 1806 (1958); Ann. Phys. (N. Y.) 5, 58 (1958)]. The usual results of the formal theory of scattering, involving the transition matrix element, are derived, and a further explicit development of the theory is given which permits the use of a model Hamiltonian to represent the reacting system. Several alternate expressions are obtained for the transition matrix element, involving the use of the ``transition complex'' eigenfunctions as an approximate basis for expansion of the state vector; and an approximate expansion in ascending orders of ``virtual reactive scatterings'' is introduced as a method for rapidly expanding the state vector.
Absence of a Linewidth Transition for the Protons in KH2PO4-Type Crystals
Authors: Bjorkstam J. L. , Jones E. D. , Silsbee H. B. , Uehling E. A.
Published: January 2005

The linewidth and shape of the proton resonance in KH2PO4 is described, and the nonexistence of a linewidth transition in the range of 77° to 300°K is discussed. The calculated and experimental values of the second moment are about 1.5 G2.
Effect of Pressure on the Resistance of Pyrolytic Graphite
Authors: Samara G. A. , Drickamer H. G.
Published: January 2005

The effect of pressure to several hundred kilobars has been measured on samples of pyrolytic graphite of density 2.18 and 2.20. Measurements along the c axis show a relatively high resistance which decreases with increasing pressure and levels at high pressure, apparently due to strongly decreasing compressibility. Along the a axis the resistance is low, but increases at higher pressures apparently due to recrystallization.
On the Theory of Spin-Orbit and Hyperfine Interactions in Molecules. Application to the Hydrogen Molecule—Ion
Authors: Roberts E. M. , Foster M. R. , Selig F. F.
Published: January 2005

Previously, calculations on molecular systems have employed spin-orbit and hyperfine operators which possess strong singularities at the nuclei of the molecule. The matrix elements of the latter operators may, depending on the symmetries of the wave functions, involve divergent integrals. The spin-orbit and hyperfine interactions are re-examined. The correct operators are derived from a reduction of the Dirac equation. It is shown that the correct forms of the spin-orbit and hyperfine operators have finite and unique matrix elements. The theory is specifically applied to the hydrogen molecule—ion. It is found that the anisotropic part of the spectroscopic splitting factor is very small. The dipole—dipole coupling parameter D is calculated for the ground state of H2+. At the equilibrium internuclear distance, D=−0.1067. The latter result does not agree with the result of other authors who, by using the strongly singular operators, found a positive sign for D.
Local Steric Hindrances and Conformations of Linear Polymer Molecules in Solutions. II. Generalization
Authors: Nagai Kazuo
Published: January 2005

A conformational partition function of a linear, stereoregular polymer molecule in solutions is constructed by taking into account the interactions among the rotations about consecutive skeletal bonds of any desired number. By using this partition function, two formally different but essentially equivalent expressions are derived for the mean-square end-to-end distance of the polymer molecule. Both bond lengths and bond angles are assumed to be variable. Freedoms in side chains are, though formally, taken into account. Short-range interactions between the polymer molecule and solvent molecules in which it is immersed, is considered implicitly. Long-range interactions such as the so-called excluded volume effect are neglected. All kinds of end effect are also neglected.
Local Steric Hindrances and Conformations of Linear Polymer Molecules in Solutions. III. Polyethylene
Authors: Nagai Kazuo , Ishikawa Toshihide
Published: January 2005

The mean-square end-to-end distance 〈R2〉 of linear, very long polyethylene molecules in solutions is calculated under the assumptions that (i) the internal rotational angle θ about skeletal bonds measured from the trans position may take only the three discrete values, θT, θG, and θG′ corresponding to the trans (T), gauche (G), and another gauche (G′) conformations, (ii) the G and G′ conformations are less stable than the T conformation by a statistical weight σ, (iii) the GG′ and G′G conformations for two consecutive bonds are inaccessible because of steric hindrances, and (iv) all interactions among the rotations about more than two consecutive skeletal bonds are negligible. Molecular averages such as the fraction of bonds being in the T conformation are also calculated. Typical numerical computations are carried out by setting the bond angle equal to the tetrahedral angle and θT=0 and θG=—θG′=120°. For equal values of σ, values of 〈R2〉/nb2 obtained are, as has been expected, remarkably larger than those calculated under the assumption of the independent rotation. Here n is the number of skeletal bonds and b is the bond length. Comparison at 140°C of theoretical values of d ln 〈R2〉/dT with the experimental value recently reported by Flory and his collaborators shows that the energy of the G and G′ conformations exceeds that of the T conformation by about 820 cal/mole if the entropy difference is assumed to be zero. The corresponding value of 〈R2〉/nb2 at 140°C is found to be about 8.0. Effects on 〈R2〉/nb2 of small changes in bond angle and θG, and of small fluctuations of θ about θT, θG, and θG′ are examined. Detailed discussions are given on validities of various assumptions made in defining the present physical model.
Sequential Substitution Reactions on B10H10−2 and B12H12−2
Authors: Hoffmann Roald , Lipscomb William N.
Published: January 2005

Predictions are made of the order of sequential electrophilic substitution on the B10H10−2 and B12H12−2 polyhedral ions. Simple LCAO—MO calculations are used and resonance and inductive effects are treated separately.
Molecular Rearrangement in the Mercury-Photosensitized Reaction of Butene-1
Authors: Cvetanović R. J. , Doyle L. C.
Published: January 2005

Mercury-photosensitized reaction of butene-1 has been studied at room temperature in the pressure range of 14 to 230 mm. Methyl cyclopropane is found to be formed by molecular rearrangement and its yield goes through a maximum at a pressure of about 65 mm. The dependence of the yield of this product on pressure is explained by postulating participation in the process of two excited states of equal lifetimes. These are, perhaps, the vibrationally excited triplets of butene-1 and of methyl cyclopropane, the latter being formed from the former by an internal 1,2- or approximately 1,4- migration of an H atom. Molecular rearrangement to butene-2 does not occur.
Ionization and Excitation Processes in Argon, Krypton, and the C2 Hydrocarbons Produced by Various Means
Authors: Melton Charles E.
Published: January 2005

Multiple ionization produced in argon and krypton by 3.5-keV electrons is reported. The ionization mechanism is tentatively proposed to be similar to that known for nuclear transitions, namely, a combination of electron shakeoff with primary ionization in one of the inner-orbital-electron shells (n=1 or 2) followed by Auger transitions.

The relative proportions of fragment ions produced in the C2 hydrocarbons by 3.5-keV electrons are also reported. These data bear a marked similarity to those obtained by the dissociative ionization of the C2 hydrocarbons with 75-eV electrons. However, ions produced by 3.5-keV electrons retain excitation energy longer as is shown by their respective rates of intramolecular decomposition (metastable transitions). Despite the longer retention of excitation energy, the reaction rate for 3.5-keV electron-induced ions in ion—molecule reactions is the same as that for 75-eV electron-induced ions. Reaction rates between neutral molecules and C2H4+ ions from different parent molecules appear to be independent of the parent, thus suggesting that the ions, initially probably different in configuration, all rearrange to the same configuration before reacting.

The fragment ion pattern produced in ethane by 50–75-eV electrons is strikingly similar to that produced by either 3.5-keV electrons or by 5-MeV α particles. In ethylene, likewise, the fragment ion patterns produced by 5-MeV α particles, β particles from Ni63, 3.5-keV electrons and 50–75-eV electrons are quite similar. This lends some support to the common practice of using 50–75-eV mass spectra to predict primary ion products in radiation chemistry.
Natural Expansions of Exact Wave Functions. I. Method
Authors: Davidson Ernest R.
Published: January 2005

A practical method is presented for finding the natural orbital expansion of a two-electron wave function involving r12. Also, a revised definition for the natural p state is presented which eliminates the difficulty that arises from degenerate occupation numbers.
d Orbitals in Compounds of Second-Row Elements. II. Comparison of H, C, F, and Cl as Ligands
Authors: Craig D. P. , Zauli C.
Published: January 2005

Calculations have been made to contrast the effects of H, C, F, and Cl as ligands on loosely bound d orbitals of second-row elements. Sets of one, two (at right angles), four (square), and six (octahedral) identical atoms are compared. The approximation is electrostatic, with the use of potentials derived from self-consistent field wave functions. The order of effectiveness is F>Cl>C≫H. The first three are more nearly equal in their perturbing power than expected from their electronegativities, and hydrogen is surprisingly ineffective.

The conclusions lend themselves to some generalization to the conditions of binding in second-row elements. These are discussed, and some examples given.
Hole Theory of Liquids and Dense Gases. I. Equation of State
Authors: Henderson Douglas
Published: January 2005

The hole theory of liquids is reconsidered in light of Eyring's more recent significant-structures theory. The free volume is assumed to be a linear function of the number of neighboring holes and the partition function is evaluated by means of the Bragg—Williams approximation. In contrast to previous hole theories, the cell dimensions are found to be virtually constant. The resulting equation of state is examined in detail and agreement with experimental data is good throughout both the liquid and dense gas regions.
Infrared Spectrum and Structure of Germyl Cyanide
Authors: Goldfarb Theodore D.
Published: January 2005

The infrared spectra of GeH3CN and GeD3CN have been investigated in the 260–4000-cm−1 region with prism and grating spectrophotometers. The expected C3v symmetry has been confirmed, and seven of the eight fundamental vibrational modes of each molecule have been assigned to observed bands of appropriate shape. The frequencies of the remaining skeletal bending fundamentals have been assumed to be one-half the frequency of their observed overtones. The rotational structures of two of the perpendicular bands of GeH3CN have been resolved and Coriolis coefficients have been determined. The spectrum in the region of the CN stretching fundamental indicates that the molecule is the normal cyanide. No evidence was obtained for the presence of the isocyanide. This observation is compared with those obtained for the alkyl germyl cyano and silyl cyano compounds which have been interpreted as equilibrium mixtures of the normal and the isocyanides.
Vibrational Relaxation in Carbon Dioxide. II
Authors: Witteman W. J.
Published: January 2005

The vibrational energy rate of approach to thermal equilibrium of suddenly heated CO2 gas has been studied by using a shock tube and the integrated schlieren method for density measurements. The experimental results agree fairly well with the predicted direct excitation of bending mode and indirect excitation of valence mode in the temperature range 440°—816°K. The measured relaxation times for the direct excitation process range from 3.75 μsec at 440°K to 0.64 μsec at 816°K. The effects of impurities through leakage in the tube can be considered negligible. The average temperatures of the measured bending energies are slightly higher than the corresponding temperatures of the valence energies, which indicates that the time constant of the indirect excitation process is at least one order of magnitude smaller.
Nuclear Transverse Relaxation in Electron-Transfer Reactions
Authors: Johnson Charles S.
Published: January 2005

The problem of proton magnetic resonance linewidths for molecules that are taking part in one electron transfer reactions is re-examined, and it is concluded that the ``weak-pulse'' limit (aHτp≪1) is more generally applicable than the ``strong-pulse'' limit (aHτp≫1) that was discussed by McConnell and Berger. Density matrix equations are set up using the formalism of Alexander in order to calculate line shapes from the hyperfine splitting constants and the lifetimes of the diamagnetic and paramagnetic species; and it is shown that when more than one absorption line are observed, under certain conditions, the bimolecular rate constant for electron transfer may be determined without a knowledge of the concentration of unpaired electrons. These equations are applied to the electron transfer reaction between NNN′N′-tetramethyl-p-phenylene diamine and its monocation radical in acetonitrile, and we find that the rate constant for electron transfer is (2.0±1.0)×108 liter mole−1 sec−1.
Calculation of Heats of Vaporization and Fusion of Nonionic Liquids from the Rigid-Sphere Equation of State
Authors: Yosim S. J. , Owens B. B.
Published: January 2005

The heats of vaporization of the rare gases, diatomic, and polyatomic molecules were calculated from the isothermal reversible work required to compress a fluid of rigid spheres from the volume it occupies at a pressure of one atmosphere to the volume of the corresponding liquid. Similarly the heats of fusion of the rare gases were calculated from the additional work necessary to compress the rigid-sphere fluid from the volume of the liquid to that of the solid. Agreement between the calculated and observed values was, with few exceptions, very good.
Ionic Interactions in Aqueous Solution: A Raman Spectral Study
Authors: Vollmar P. M.
Published: January 2005

The vibrational and the electronic spectra of the nitrate ion change with concentration in aqueous solutions of metallic nitrates M (NO3)n, and the changes vary with the cation Mn+ present in the solution. The position, size, shape, and polarization of the ν1 Raman band of the nitrate ion and the position of the nearultraviolet absorption band of that ion have been measured as functions of concentration in solutions of the nitrates of Li, Na, K, NH4, Mg, Ca, Zn, and Al. Three correlations emerge from these data. (1) The changes in the peak frequency and in the half-width of the Raman band are inversely related, and both appear to depend on the degree of hydration of the cation. (2) The changes in the specific intensity of the Raman band are paralleled by shifts in the ultraviolet absorption band and are resonance Raman effects. (3) In solutions of ammonium nitrate the spectral changes are very small, apparently because of the similarity between the ammonium ion and the water molecule.
Molecular Rotation in the Solid State. Theory of Rotation of Trapped Molecules in Rare-Gas Lattices
Authors: Flygare W. H.
Published: January 2005

A theory is presented to explain the rotational perturbations experienced by a molecule trapped substitutionally in a rare-gas lattice at low temperatures (4°—20°K). The nonbonded repulsive interaction due to the Pauli exclusion principle between the molecule and the host lattice has been ignored in preference to the multipole charge interaction. In the case of an octahedral substitutional trapping site the dominant interacting term is the rotation of a permanent molecular hexadecapolar charge distribution interacting with the fourth gradient of the electric potential at the molecular center of mass due to all of the lattice charges. A general method of computing the fourth gradient of the potential due to the rotational independent induced-dipole—induced-dipole effect is given in the Appendix in terms of the molecular and atomic polarizabilities and ionization constants. Matrix elements are given for linear, spherical-top, symmetric-top, and asymmetric-top molecules.

The theory for a trapped linear molecule is applied to the vibration—rotation data of HCl trapped in an Ar lattice yielding a value of the single molecular hexadecapole moment in HCl of 3.9×10−42 esu cm4. Other effects discussed are: (1) higher-order terms in the potential expansion, (2) isotopic substitution in the molecule, and (3) the rotation of HCl in the other rare-gas lattices.
Space Charge in Growing Oxide Films. III. Multispecies Diffusion
Authors: Fromhold A. T.
Published: January 2005

Space-charge computations based on the steady-state macroscopic diffusion equation for a single species (previously published in this journal) are extended to several species diffusing simultaneously (e.g., vacancies and holes). The nature of the distribution of each diffusing species as a function of space-charge magnitude, film thickness, and external electric field is markedly different from the case of a single species because of the coupling between the species through the field. Qualitative differences are observed between the ion—electron system and the vacancy—hole system. Power series in position normalized to film thickness provide a formal solution to the coupled equations.
Electronic Spectral Shifts of Some Aromatic Compounds in Nonpolar Solvents
Authors: Stokes Suzanne
Published: January 2005

The near-ultraviolet absorption spectra of some substituted benzenes have been measured in n-pentane solution and in the vapor state. The shifts in frequency due to the n-pentane solvent are discussed in terms of the dispersion theory for electronic spectral shifts for weak transitions. Spectral shifts of the intense, high-energy transitions in benzene and in some hexasubstituted benzenes are considered briefly.
Solvent Effects and a Test of the Theory of Hypochromism
Authors: Vala Martin T. , Rice Stuart A.
Published: January 2005

The hypochromism of the 2600-Å absorption band of isotactic polystyrene (relative to atactic polystyrene) has been examined. It is shown that there are important solvent effects which modify the magnitude of the hypochromism. The theory of Tinoco and Rhodes does not include explicit solvent interactions and cannot account for all our experiments. For the case of chloroform as solvent, the theory is in (fortuitous) agreement with experiment if calculations are performed carefully and convergence is established (±10 rings for 2% residual). If the influence of the solvent may be neglected in this case, it may be concluded that the results obtained are consistent with the retention of local structure when isotactic polystyrene passes from the crystalline phase into solution.
Lower Bounds for Eigenvalues
Authors: Wilson E. Bright
Published: January 2005

Various methods for the calculation of lower bounds for eigenvalues are examined, including those of Weinstein, Temple, Bazley and Fox, Gay, and Miller. It is shown how all of these can be derived in a unified manner by the projection technique. The alternate forms obtained for the Gay formula show how a considerably improved method can be readily obtained. Applied to the ground state of the helium atom with a simple screened hydrogenic trial function, this new method gives a lower bound closer to the true energy than the best upper bound obtained with this form of trial function. Possible routes to further improved methods are suggested.
Lower Bounds for the Energy Levels of Anharmonic Oscillators
Authors: Reid Charles E.
Published: January 2005

The lower-bounds method presented by Löwdin in the preceding paper has been applied to oscillators perturbed by third- and fourth-power terms in the potential-energy expression. For favorable cases agreement between upper and lower bounds is easily carried to many more figures than are likely to be physically significant. In many cases the lower bounds agreed more closely to the true eigenvalue than did the corresponding upper bounds. For a given basis set, this method gives closer bounds than that of Bazley and Fox, except for energy levels too high to be satisfactorily treated in the given basis. The only disadvantage found was that for close bounds double precision proved necessary, indicating more than ordinary loss of computational accuracy.
Reduction of Group Representations
Authors: Gabriel J. R.
Published: January 2005

A new method for reduction of group representations is discussed heuristically and an example done.
Correlation Effect in the Time-Dependent Concentration Fluctuations of the Isobutyric Acid—Water System near its Critical Mixing Point
Authors: Chu B.
Published: January 2005

Measurements by the laser homodyne ``self-beating'' technique were made of the quasielastic Rayleigh linewidth in a critical binary liquid mixture, isobutyric acid—water (Tc=26.12°C), at temperature distances 0.071°, 0.196°, 0.36°, 0.73°, and 1.16°C above the critical solution temperature over a range of scattering angles. Deviations from the Landau—Placzek theory on the K2(K=ks, k=2π/λ, s=2 sinΘ/2) dependence of the half-width of the central (Rayleigh) component (T) have been observed. Experimental data are in good agreement with Fixman's modification which takes into account the effect of long-range correlations in binary liquid mixtures and has the form T=aK2(1+K2/κ2) with κ corresponding to the inverse correlation length of Ornstein and Zernike.
Molecular Beam Measurement of the Hyperfine Structure of 133Cs19F
Authors: English Thomas C. , Zorn Jens C.
Published: January 2005

The magnitudes and signs of the hyperfine interaction constants for 133Cs19F in the J = 1, v = 0, 1, 2 states have been measured with a molecular beam electric resonance spectrometer. The results for v = 0 are: eQ1q1 = 1.2370(13) MHz, c1 = 0.70(7)kHz, c2 = 15.1(6)kHz, c3 = 0.92(12)kHz, c4 = 0.61(10)kHz. The numbers in parentheses are uncertainties in units of the last digit given. eQ1q1 is the quadrupole coupling constant for the cesium nucleus, c1 and c2 are the spin-rotation coupling constants for the cesium and fluorine nuclei, respectively, and c3 and c4 are the coupling constants for the tensor and scalar parts of the nuclear spin—spin interaction. These constants are obtained from the radio-frequency spectrum of CsF taken under veryweak-field conditions (Edc = 1.5 V/cm; H<0.05 Oe); some previously ignored contributions of the fluorine spin—rotation interaction and the spin—spin interaction are clearly evident. The observed variation in eQ1q1 with vibrational state shows only qualitative agreement with theory. An appendix gives compact expressions for the very-weak-field hfs energy levels of a 1Σ molecule in which only one nucleus has a quadrupole moment.
Neutron-Scattering Study of Hindered Rotations in Methylbenzenes
Authors: Rush J. J.
Published: January 2005

The low-frequency modes of a number of methylbenzenes in their solid and liquid phases have been investigated by the energy-gain scattering of cold neutrons. The compounds studied include benzene, o-xylene (1, 2), hemimellitene (1, 2, 3), mesitylene (1, 3, 5), durene (1, 2, 4, 5), prehnitene (1, 2, 3, 4), and hexamethylbenzene. The neutron spectra for molecules with adjacent methyl groups (e.g., o-xylene) exhibit bands peaked near 170 cm−1, which are assigned primarily to the 1→0 transitions of the torsional oscillations of the methyl groups. The hemimellitene and prehnitene spectra appear to show a second broad maximum in the region of 100 cm−1, which is attributed to torsional or hindered rotational modes due to methyl groups centered between two adjacent groups. Previous results on hexamethylbenzene show torsional bands peaked at 120 and 137 cm−1, respectively, above and below the λ transition near 115°K. The mesitylene spectra indicate a very low barrier to rotation of the methyl groups in this compound, with hindered-rotational levels below 100 cm−1. In addition, the results for all the compounds in their solid phases show broad bands below 90 cm−1, which are assigned to whole-molecule librations and translations. If simple threefold cosine potentials are assumed, an ``average'' barrier to rotation of about 2 kcal/mole is calculated from the average of the observed torsional peaks (170 cm−1) for methyl groups with one adjacent group. The lower-energy bands for the ``centered'' methyl groups suggest greater rotational freedom for these groups. A comparison of these results indicates that methyl groups surrounded by two adjacent groups on the benzene ring experience a considerably different potential (and possibly a significantly lower barrier) than that experienced by methyl groups with one neighboring group. The neutron results are compared in detail with NMR and thermodynamic data.
Ring-Puckering Motion of 2,5-Dihydrofuran
Authors: Ueda T. , Shimanouchi T.
Published: January 2005

The far infrared absorption spectrum of 2,5-dihydrofuran was measured in the 500–50-cm−1 region. A successive series in the spectrum was observed. The analysis of the series leads to the following ring-puckering potential as a function of the ring-puckering coordinate Z: V(Z)=1.557×104Z2+1.152×106Z4 (V in cm−1, Z in angstroms). No potential hump is found in this molecule. The origin of the potential and the treatment of higher-order terms in the kinetic energy are discussed.
New Absorption Spectra of Atomic and Molecular Oxygen in the Vacuum Ultraviolet. II. Rydberg Series from O I(1D2) and O I(1S) Metastable States
Authors: Huffman R. E. , Larrabee J. C. , Tanaka Y.
Published: January 2005

We have extended our previous work [J. Chem. Phys. 46, 2213 (1967)] on absorption series from the O I 3P2,1,0 ground state by measuring and classifying eight series having metastable O I 1D2 or 1S0 as the lower state. For O I 1D2 as the lower state, series have been classified with the following upper states: (2D0)ns′:1D20, and 3D20,(2D0)nd′:1F30, 1D20, and 1P10,(2P0)ns′′:1P10,(2P0)nd′′:1D20.The one series with O I 1S0 as the lower state has the upper state (2P0)nd″ 1P01. The classifications are tentative in some cases. The spectra were observed primarily in absorption through a microwave dischage of a dilute O2 mixture with helium in a flow system using the Hopfield helium continuum (600–1000 Å) as background. New atomic energy levels for a number of O I singlet terms are given. The metastable 1D2 and 1S0 atoms disappear rapidly in the downstream region, and it is suggested that they react to form the metastable O2 molecules (a 1Δg and/or b 1Σg+) known to be present in the discharge products.
Theoretical Analysis of the Electronic Structure and Molecular Properties of the Alkali Halides. I. Lithium Chloride
Authors: Matcha Robert L.
Published: January 2005

Results of a theoretical investigation of the electronic structure of LiCl within the SCF—LCAO—MO framework are discussed, giving special emphasis to the evaluation of various molecular properties. Computed values (followed by experimental values in parentheses) for the total energy E, equilibrium separation Re, spectroscopic constants ωe, ωexe, and Be, and the dipole moment μ, are E=−467.05466 a.u., Re=3.825 a.u. (3.819 a.u.), ωe=671.5 cm−1 (641 cm−1), ωexe=4.67 cm−1 (4.2 cm−1), Be=0.704 cm−1 (0.706 cm−1), μv=7.2182+0.0753 (v+12)+0.0002 (v+12)2, and μv(exptl)=7.0853+0.0864 (v+12)+0.0006 (v+12)2. Computed dissociation energies, coupled with relativistic and correlation energy contributions estimated from atomic data, result in a value for De of 0.174 a.u. as compared with the experimental value of 0.178 a.u. Computed values for the field gradients at the nuclei have been combined with experimental values of the quadrupole coupling constants to yield, for the nuclear quadrupole moments of lithium and chlorine, QLi=−0.050×10−24cm2, Q37Cl=−0.084×10−24cm2, Q35Cl=−0.106×10−24cm2.
S Limit in Helium. Movement of a System on an Energy Surface in Parameter Space
Authors: Handler George S. , Joy Hubert W.
Published: January 2005

As part of a variational examination of angular correlation in electronic systems, a careful examination of the movement of a system on an energy surface in parameter space has been made. The results indicate that the surface is highly convoluted, and that minimization techniques must take explicit account of this. An eight-term result close to the S limit in helium is given.
Far-Infrared Spectrum of HCl Dimers
Authors: Katz B. , Ron A. , Schnepp O.
Published: January 2005

HCl absorptions have been observed in the wavelength region 150–250 cm−1 in solid rare-gas solutions. From the dependence of the absorption intensity on sample preparations it is concluded that these spectra are due to polymers formed on condensation. In solid xenon, the isotopic pattern of the spectrum requires the assignment to cyclic dimer molecules of HCl. In the other solid solutions additional bands appear in this region, which have not been definitely assigned. The hydrogen-bond stretching force constant has been calculated from the measurements.
Triplet States of Naphthalene Derivatives. I. 1,4-Dibromonaphthalene
Authors: Castro George , Hochstrasser Robin M.
Published: January 2005

A doublet structure is observed in the T1←S0, T2←S0, and S1←S0 spectra of single crystals of 1,4-dibromonaphthalene. The crystal structure is known to contain asymmetric units, and the spectral band doubling is attributed to the difference in dispersion interactions at the two sites. The observed asymmetric site splittings are 52 cm−1(T1), 103 cm−1(T2), and 85 cm−1(S1). Each of these values is in reasonable accord with expectations for certain diagonal Coulomb terms in the exciton matrix. The vibrational analyses of the T1, T2, and S1 states are presented. These states are located at 20 197 cm−1(T1), 29 783 cm−1(T2), and 30 357 cm−1(S1). The triplet spectra are briefly discussed with reference to the polarization of the vibronic bands.
Deactivation of O(1D)
Authors: Young Robert A. , Black Graham
Published: January 2005

Emission at 7618 Å from O2(b 1Σg+) produced in the energy-transfer reaction O(1D)+O2→O2(b 1Σg+)+O(3P),whose rate coefficient is greater than 10−11 cm3/sec, was measured as a function of [O2] and [He]. The O(1D) was produced by photolysis of O2 at 1470 Å. The decrease of O2(b 1Σg+) when N2, CO, CO2, NO, and N2O were added was measured. It was also found that O2 perturbs O2(b 1Σg+) during a collision and increases its rate of emission. The rate coefficients of these processes are reported.
Minimum Property in the Hulthén-Type Variational Methods
Authors: Ohmura Takashi
Published: January 2005

The nature of the extremum of the phase shift in the variation principles, which are all based on the Schrödinger differential equation directly, is investigated in detail. If the system has no bound state, the scattering length determined by the original Hulthén method (5, 29) is proved to have the minimum character. The minimum nature is maintained even for the system which has several bound states, if the trial function is taken to be orthogonal to the bound state wave functions. The Kohn method and the second Hulthén method (15) give neither an upper bound nor a lower bound for the phase shift in general. The sufficient condition is, however, obtained for each case, under which the stationary expression for the scattering length has the minimum character. The condition does not hold true for the electron-hydrogen atom scattering for the Kohn method and for the second Hulthén method. It is pointed out that a comparison of approximate values obtained by different methods using the same trial function does not afford any information about the ``proper source of errors'' of the results.
Formal Solution of Liouville's Equation
Authors: Von Roos Oldwig
Published: January 2005

A formal solution of Liouville's equation both for the classical and for the quantum mechanical case is presented. The derivation follows closely the approach employed by Feynman in his papers on the theory of positrons (Phys. Rev. 76, 749 (1949), ibid. 76, 769 (1949)). A scattering operator S is found which connects the distribution function at time t′ with the distribution function at any later time t. Each term of this scattering operator can be represented uniquely and conveniently by a diagram. The topological structure of these diagrams is the same in the classical as well as in the quantum mechanical case. Applications of the method will be given in a forthcoming paper.
Electrical Conduction in Deformed Isotropic Materials
Authors: Pipkin A. C. , Rivlin R. S.
Published: January 2005

The current density in a deformed conductor is assumed to be a function of the electric field and the deformation gradients. The form of the relationship is restricted by invariance under changes in orientation of the physical system. Material symmetries impose further restrictions. The resulting form for isotropic materials is given. Simplifications are obtained in the cases of small deformation and large homogeneous deformation. Generalizations and further applications are pointed out.
Description of the Extended Tube
Authors: Grossmann A.
Published: January 2005

Necessary and sufficient conditions are given for the belonging of an n tuple of complex four-vectors to the extended tube.
Pair Distribution Function of a Hard Sphere Bose System Calculated by the Pseudo-Potential Method
Authors: Garcia-Colin Leopoldo S.
Published: January 2005

The pair distribution function for a hard sphere Bose system has been calculated by using a method in which the hard sphere potential is replaced by the so-called pseudo-potential. The problem is carried through using the quasi-particle formalism of Bogoliubov. In this calculation one considers a system of bosons interacting via the pseudo-potential which can be regarded as a weak interaction when the system is very dilute. The Hamiltonian of the system is diagonalized by means of a canonical transformation which has the effect of separating the energy into two parts, one of which is the ground state energy and the other corresponds to an ideal Bose gas composed of ``elementary excitations'' or ``quasi-particles.'' This formalism is applied to the calculation of the pair distribution function. This quantity is calculated by averaging over a grand canonical ensemble constructed with the total number of elementary excitations. A result which is seen to be valid both for the condensed and gaseous phases of the system and also for any distance r between the particles is obtained.

A discussion of the difference between these results and the ones obtained in a previous calculation and a comparison between both results and the experimental ones is also given.
On the Pair Distribution Function of a Hard Sphere Bose System
Authors: Garcia-Colin Leopoldo S. , Peretti Jean
Published: January 2005

The pair distribution function for a quantum Bose gas is expressed as a power series in terms of the fugacity, the coefficients of which are temperature dependent. For the hard sphere case, these coefficients have been evaluated to the first order in a/λ, (a being the scattering length and λ the thermal wavelength) by using torons with two fixed points, or alternatively U cluster functions. The result gives the first order correction to the ideal gas formula of London and Placzek introduced by the interactions between the particles.
Linearized Plasma Oscillations in Arbitrary Electron Velocity Distributions
Authors: Backus George
Published: January 2005

This paper is a mathematical examination of the linearized small disturbances in the steady distribution f0(q) of the velocities q of the electrons in an electrostatic, collisionless plasma with motionless protons. It is assumed that g0(u)=∫∫f0(u,v,w)dvdw has an integrable derivative with respect to u for all axis orientations. An existence and uniqueness theorem for the initial value problem is given, and it is shown that no disturbance can grow faster than expωpt, where ωp is the electron plasma frequency. Consequently, one can base a stability theory on Laplace transforms with respect to time, as Landau has done. The limits of validity of Landau's stability criterion are explored: that g0(u) is stable if there are no wave numbers k for which L(s)=k2ωp−2−∫−∞∞g0′(u)(u−s)−1du has zeros in the upper complex s half-plane. To ensure instability, the zeros must have positive imaginary parts or a multiplicity of 2 or greater. To insure stability, the initial disturbance must be not only integrable, but square integrable with respect to u. The Maxwell distribution is unstable to certain integrable disturbances. All isotropic, three-dimensional distributions f0(q) = h(q2) for which x¼h(x) is absolutely continuous and square integrable, and h(x)+2xh′(x) is bounded, are stable to integrable, square integrable disturbances. This explains Van Kampen's ability to solve the initial value problem by superposing normal modes (solutions with complex, exponential time dependence) with real frequencies; he implicitly introduced stability by considering only isotropic distributions f0(q). His method is extended to unstable f0 as a technique independent of Landau's for solving the initial value problem. If f0 is unstable, the normal modes are not complete, and a normal mode analysis can lead to erroneous positive conclusions about stability. Finally, the linear theory predicts that in stable plasmas the neglected term will grow linearly with time at a rate proportional to the initial disturbance amplitude, destroying the validity of the linear theory, and vitiating positive conclusions about stability based on it. In a thermonuclear plasma with T = 108 °K and N = 1015 electrons/cm3, a disturbance of wavelength 1 cm and initial amplitude 1 v can no longer be treated by the linear theory after 220 μsec.
Nodal Expansions. III. Exact Integral Equations for Particle Correlation Functions
Authors: Meeron Emmanuel
Published: January 2005

The density expansions of the pair distribution function and potential of average force are analyzed topologically in terms of cutting points and bifocal points. The analysis leads to conversion of the expansions into series with cluster integrals involving products of the total correlation functions, h(r) = g(r) − 1, at finite density, rather than the usual zero-density Ursell f-functions. An integral equation for the pair potential of average force and the pair distribution function is thus obtained. The equation is formally exact and closed in pair space, involving no triplet distributions such as occur in the treatments of Kirkwood and Yvon-Born-Green. Solution of the equation also yields directly the Ornstein-Zernike direct correlation function. Equations for the free energy in terms of the direct correlation function are presented, thus providing a unified and self-consistent treatment of all thermodynamic properties of a many-body system. The relation of the new equation to the Ornstein-Zernike theory of liquids and to phase transitions is discussed. The possibility of derivation for condensed phases is briefly noted. A simple approximation, involving only the convolutory terms in the cluster expansions of correlation functions, is proposed.