bluuebunny/crossref_metadata_2025 huggingface dataset:
Molecular Orbital Theory of Electric Polarizabilities and Magnetic Susceptibilities of Hydrocarbons
Authors: Amos Terry , Musher Jeremy
Published: February 2004

Hartree–Fock perturbation theory and the molecular orbital method are used to develop a consistent theory of the polarizabilities and susceptibilities of hydrocarbons. When each unperturbed MO is expanded in terms of a set of basis orbitals it is found that in the presence of an electric or magnetic field the corresponding perturbed orbitals have two parts, a molecular or “nonlocal” one and a “local” part which takes into account the effect of the field on the basis orbitals themselves. When certain integrals are neglected the polarizability and susceptibility can also be divided into local and nonlocal parts which is a result generally assumed without proof. For saturated hydrocarbons, the contribution due to the nonlocal terms in the polarizability is zero so that there are only local terms in the final expression, while for unsaturated molecules there are both local and nonlocal contributions. In the case of the magnetic susceptibility the molecular (nonlocal) parts of the paramagnetic term are important—and it is necessary they be treated accurately—because they cancel with terms from the diamagnetic part of the susceptibility and so give a final expression which is largely local in character.
Rare-Earth Infrared Lifetimes and Exciton Migration Rates in Trichloride Crystals
Authors: Gandrud W. B. , Moos H. W.
Published: February 2004

Lifetimes of trivalent rare-earth ion levels below 14 000 cm−1 have been measured in the LaCl3, GdCl3, and YCl3 hosts, using the infrared quantum counter and ir fluorescence techniques. Because of their low radiative and multiphonon relaxation rates, these levels are well suited to concentration-quenching studies. Temperature dependences provide evidence that the ion-pair decays of H63 and F33 in Pr3+ and I13/24 and I15/24 in Nd3+ occur resonantly (i.e., without phonon assistance) between excited Stark components. This enables the measured decay rates for these four levels to be used in estimating the rate for a single resonant transfer of all of the ion's energy to a neighboring ion. This latter process is the basic step of the excitation–migration process. From the lifetimes of a number of levels which are quenched by migration to “sinks,” an estimate of 4 × 105 is then obtained for the number of transfers that occur before a sink is reached. Levels quenched by migration to sinks are found to decay exponentially, with a lifetime which increases with increasing crystal purity.
Metal Complexes as Ligands. VI. Antiferromagnetic Interactions in Trinuclear Complexes Containing Similar and Dissimilar Metals
Authors: Gruber S. J. , Harris C. M. , Sinn E.
Published: February 2004

The magnetic properties of a series of discrete trinuclear transition-metal complexes derived from tetradentate Schiff bases have been investigated over the temperature range 80°–400°K. The complexes contain the groupings of metals CuMCu where M is Cu(II), Ni(II), Co(II), Fe(II), and Mn(II), and the three metal atoms are linked by oxygen bridges. For each grouping of metals, the observed magnetic moments are subnormal, and decrease markedly with decreasing temperatures. These magnetic properties are explained in terms of antiferromagnetic interactions between the central metal atom M and the adjacent copper (II) atoms. The magnetic moments calculated on the basis of this model of discrete antiferromagnetism are found to be in good agreement with the experimental results. Mutual interactions between the terminal copper atoms apparently exist to only a small degree or not at all.
Influence of the Host Lattice upon the EPR Coupling Parameters of Copper-8-hydroxyquinolinate
Authors: Rist G. , Ammeter J. , Günthard Hs. H.
Published: February 2004

Copper-8-hydroxyquinolinate was substituted into single crystals of phthalimide, phthalic acid, and 8-hydroxyquinoline in order to study matrix effects on the magnetic properties of the metal complex. The substitution yielded highly ordered solid solutions. The doped purely organic single-crystal matrices gave rise to well-resolved EPR spectra allowing complete resolution of 63Cu and 65Cu and of the nitrogen hfs structure. The g parameters and the copper and nitrogen hfs constants turned out to be sensitive to the surrounding host lattice. It is shown that the covalent bonding in d9 systems can be influenced by the matrix and that planar paramagnetic complexes act as probes to study the crystal field of a matrix at certain sites of a lattice. Evidence is given that the position of the g axes in the complex plane depends on the individual bonding conditions of a copper complex and is not a general property of all planar copper complexes with nearly orthorhombic symmetry.
Paramagnetic Resonance Spectra of O− Trapped in Alkali Iodide Crystals
Authors: Brailsford J. R. , Morton J. R. , Vannotti L. E.
Published: February 2004

The impurity ion O− has been introduced into alkali iodide crystals and detected at 4°K by EPR spectroscopy. A quantitative understanding of the g factor and 17O hyperfine interaction was obtained with the aid of equations derived in a recent analysis of the analogous S− impurity.
Photolysis of Methane at 1236-Å: Quantum Yield of Hydrogen Formation
Authors: Laufer A. H. , McNesby J. R.
Published: February 2004

Pure CH4 and CD4 have been separately but simultaneously photolyzed at 1236 Å by means of a split-cell technique in order to obtain accurate relative quantum yields for the various modes of production of H2 and D2. The split-cell technique has been used to obtain quantum yields by comparison with the CO2 actinometer. Molecular elimination yields for CD4 and CH4 (0.58) are found to be equal, while the H-atom yield greatly exceeds the D-atom yield. It is concluded from the results that a significant fraction of the atoms produced disappears by the association reaction M + H + CH3→CH4 + M. The effect of scavengers and inert gas also have been investigated. The total quantum yield for H and H2 formation is greater than unity and fragmentation of CH2 or CH3 formed in the primary process is suggested: CH3→H + CH2, CH2→H + CH. However, the lower limit for the quantum yield for D and D2 formation is 0.76 and indicates that fragmentation of CD2 or CD3 is less important than that of the corresponding protonated species.
Discontinuities in Some Thermodynamic Quantities at the Critical Point of an Analytical Fluid
Authors: Barieau Robert E.
Published: February 2004

For an analytical fluid it is shown that at the critical point the following discontinuities exist: CV(2 phasesn / VT = ρc) − CV ⧸ RZc = 3pal2paaa, d2p / dt2 − (∂2p / ∂t2)a = (Pat / 5paaa)[16pat − 10Paat + (3pat Paaaa) / Paaa], Tc[(d2G / dT2) − (∂2G / ∂T2)p](RZc)−1 = 15Pat / Paaa[Pat − 10paat + (3Pat Paaaa) / Paaa], where a = (ρ/ρc) − 1;p = (P / Pc) − 1;t = (T / Tc) − 1; G is the Gibbs free energy or chemical potential; CV is the heat capacity at constant volume; n is the total number of moles in the calorimeter; VT is the total inside volume of the calorimeter; ρc, Pc, Tc are the critical molal density, critical pressure, and critical temperature, respectively; Zc = Pc / ρcRTc; and p with subscripts indicates partial derivatives of p evaluated at the critical point.
Gas-Phase Photolysis and Radiolysis of Cyclopropane
Authors: Scala A. A. , Ausloos P.
Published: February 2004

The gas-phase photolysis of c-C3H6–O2, c-C3H6–NO, and c-C3H6–H2S mixtures has been investigated at 1470 Å (8.4 eV), 1236 Å (10 eV), and at 1048–67 Å (11.6–11.8 eV), that is, at photon energies below and above the ionization energy of cyclopropane (I.E. = 10.06 eV). Examination of the products formed in the gas-phase experiments at 1470 and 1236 Å as well as of those formed in a few solid-phase photolysis experiments indicate that the major primary act of the neutral excited cyclopropane molecule can be written as follows: c-C3H6 + hv→CH2CH2CH2*. The highly excited trimethylene decomposes by the following two processes; (a) CH2CH2CH2*→C2H4+CH2 and (b) CH2CH2CH2*. There is, however, also evidence for rearrangement CH2CH2CH2*→CH3CHCH2* which, at low densities, is always followed by fragmentation of CH3CHCH2*. The primary process c-C3H6 + hv→H2+C3H4 is of negligible importance, but detachment of H atoms before or after ring opening does occur, and increases in importance, at higher energies. At 1236 Å the quantum yield of excited cyclopropane molecules which decomposes is within experimental error equal to unity. In the photoionization region alkyl radicals such as C2H5 and CH3CH2CH2 which were entirely absent at the lower energies are formed. These alkyl radicals which are also formed in the radiolysis are ascribed to ion–molecule reactions involving C3H6+. Photoionization and radiolysis of c-C3H6–NO mixtures yielded evidence for the occurrence of the charge transfer processes: C3H6++NO [or (CH3)3N]→C3H6+NO+ [or (CH3)3N+] and (NO+)* + c-C3H6→C3H6+ + NO, where (NO+)* is a vibrationally excited NO+ ion. The C3H6+ ions involved in these events ultimately yield propylene as a neutral product.
Simplified Matrix Method for Statistical Mechanics of Linear Systems
Authors: Litan Adiel
Published: February 2004

A matrix method is useful for statistical-mechanical studies of linear systems of interacting units. For a large class of linear systems, the matrix method presented here leads to matrices whose orders are substantially lower than those obtained by the conventionally used matrix method and thus greatly facilitates mathematical operations. The applications of both the conventional and the simplified methods are illustrated for a DNA molecule; when the molecule has n nucleotide pairs the reduction in the order of the matrix is from 2n−1 to n. Next, for a more general type of systems, the order is shown to be reduced from 2n−1 to 4n–6. Finally, the general steps are outlined for applying the simplified method to any one-dimensional system of interacting units.
Experimental Investigations of Temperature and Host Effects on the Phosphorescent Triplet State in Mixed Organic Crystals
Authors: Harrigan Edward T. , Hirota Noboru
Published: February 2004

Detailed experimental studies on the temperature and host effects of phosphorescent guest molecules in mixed organic crystals are reported. Temperature-dependent triplet-state energy transfer from guest to host and guest to guest in the systems with small guest–host triplet-state energy separation was studied in a benzophenone host using phenanthrene-d10, naphthalene-d8, and 2-methylnaphthalene as guest. Rate constants and activation energies were estimated for this type of transfer. Detailed studies on the temperature dependence of the lifetimes of guest triplet states in various substituted benzene hosts were made. The possible causes of the temperature dependence of lifetimes in such systems are discussed in detail. Preliminary results of the host effect on the zero-field parameters and lifetime of naphthalene-d8 in some chloro-substituted benzene hosts are also reported.
New Expansion Procedure in Nonequilibrium Statistical Mechanics
Authors: Muriel A.
Published: February 2004

By modifying the projection technique of Zwanzig, an iterative solution for Pf, where P is any projection operator and f is the N-particle distribution function, is obtained as an expansion in the coupling parameter λ defined by the potential energy between two particles λV. The resulting expansion is valid for a system in a uniform external field of arbitrary strength and time dependence. Two examples are worked out to illustrate the utility of the expansion: (1) the short-time evolution of a density discontinuity; and (2) the one-dimensional gravitational gas.
Formation of Positive and Negative Ions on Rhenium, Oxygenated Tungsten, Hafnium, Lanthanum Hexaboride, and Thoriated Tungsten Surfaces
Authors: Persky Avigdor , Greene Edward F. , Kuppermann Aron
Published: February 2004

Yields are reported for the formation of positive and negative ions from molecular beams striking various surfaces. Negative ions are formed from beams of several halogen compounds and tetracynoethylene on Re, Hf, thoriated W, and LaB6 with efficiencies ranging up to a maximum of 2.6 × 10−2 for KCl on thoriated W (activated). This filament may be useful in detectors for some molecular-beam studies. The efficiencies for the formation of positive ions from K and potassium halides are generally in agreement with the Saha–Langmuir model. They are near unity on oxygenated W, Re, and thoriated W (deactivated by heating to deplete the thorium) but much lower (2.5–6.6×10−3) on thoriated tungsten (activated).
Interionic Vibrational Spectra of Electrolytes in Nonaqueous Solvents
Authors: French M. J. , Wood J. L.
Published: February 2004

Far-infrared spectroscopy is shown to provide a powerful new method for studying ion aggregates in solution. The interionic vibration frequency of Na+BPh4− is at 175 cm−1 in pyridine, 1,4-dioxane, piperidine, and tetrahydrofuran, indicating that bare, rather than solvated ions, produce the absorption. The isotope shift of the 198-cm−1 band in NH4+BPh4− to 183 cm−1 in ND4+BPh4− also fits a bare-ion model. The Li+BPh4− salt gives a band at 410 cm−1 in THF, which is probably due to a Li+ THF vibration, while the K+BPh4− band at 133 cm−1 arises from interionic vibration. The Na+, NH4+, ND4+, and K+ salt stretching force constants, based on a bare ion-pair model, are nearly identical, 3.85 ± 0.11 × 104 dyn cm−1. These force constants differ markedly from those predicted from the Pettit and Bruckenstein ion-pair potential used to interpret conductivity data of strong electrolyte solutions. Present observations indicate that the dominating terms in the ion-pair potential are −(e2 / R)+(B / Rn), where n≫7 (Pettit and Bruckenstein), and may approach 30 for a pair of polyatomic ions. The dependence of the band intensities on solvent, concentration, and the nature of the cation appear to be primarily due to variations in the proportion of absorbing systems, rather than in the intrinsic absorption coefficient, and support the assignment of the bands to ion pairs, rather than higher aggregates. Intensity measurements in a mixed benzene–pyridine solvent demonstrate the phenomenon of preferential solvation by pyridine.
Correlation Energy in Atomic Systems. V. Degeneracy Effects for the Second-Row Atoms
Authors: Veillard A. , Clementi E.
Published: February 2004

The degeneracy effects in the isoelectronic series of the second-row atoms are analyzed. New values are estimated for the correlation energies. The correlation energy diagram exhibits a remarkable similarity with the corresponding one for first-row atoms and ions. We have added a new table of data which summarizes the results for the first- and second-row correlation energies. These data make use of previously unpublished computations on the relativistic effects.
Spectra of Optically Pumped SrF2:Sm2+ and SrCl2:Sm2+
Authors: Huang J. W. , Moos H. W.
Published: February 2004

Strong absorption bands from the D05(4f6) state were found near 4750, 3170, 2850, and 2470 Å of optically pumped SrF2:Sm2+ crystals and near 4750, 3280, 2740, and 2470 Å of pumped SrCl2:Sm2+ crystals. The decay times of these bands agree with the fluorescence lifetimes of the D05(4f6) metastable state in the corresponding crystals at various temperatures. These bands were shown to be transitions from D05(4f6) to higher quintet states of the 4f55d configuration. The ground- and excited-state absorption spectra of both crystals show a correlation both between themselves and with the free-ion spectra.
Calculation of the Madelung Energy of Ionic Thiourea Complexes
Authors: Boeyens J. C. A. , Gafner G.
Published: February 2004

The Madelung interactions between the ions and dipoles in a typical complex of thiourea with an ionic salt have been calculated by numerical methods. The calculations show that the cohesion in the complexes is almost exclusively due to electrostatic interactions and that complexing only occurs, for energetic reasons, with ionic salts which have lattice energies of less than ∼160 kcal/mole.
Electron-Diffraction Study of Ammonia and Deuteroammonia
Authors: Kuchitsu Kozo , Guillory J. P. , Bartell L. S.
Published: February 2004

The gas-phase structures of NH3 and ND3 molecules were determined by the sector-microphotometer method of electron diffraction. The following internuclear distances rg and mean amplitudes le with estimated standard errors were obtained: For NH3, rg(N − H) = 1.0302 ± 0.002 Å, rg(H − H) = 1.662 ± 0.010 Å, le(N − H) = 0.0731 ± 0.002 Å, le(H − H) = 0.125 ± 0.006 Å, and for ND3, rg(N − D) = 1.0266 ± 0.003 Å, rg(D − D) = 1.654 ± 0.008 Å, le(N − D) = 0.0611 ± 0.002 Å, le(D − D) = 0.101 ± 0.006 Å, with the parameter κ representing bond-stretching anharmonicity fixed at 1.0 × 10−5 and 0.5 × 10−5 Å3 for N–H and N–D, respectively. Effects of anharmonicity and isotope differences in the structural parameters analogous to those in CH4 and CD4 were observed. The rα0 and re bond distances calculated from the above rg distances are found to be consistent with the corresponding rz and re distances derived from the spectroscopic rotational constants of Benedict and Plyler. The isotope effects reported by Bell and by Halevi for the dipole moment and polarizability of ammonia are discussed briefly in the light of the present results.
Transient Solvated Electron, Hydroxyl, and Hydroperoxy Radicals in Pulse-Irradiated Crystalline Ice
Authors: Taub Irwin A. , Eiben K.
Published: February 2004

Neutral, crystalline ice samples were pulse irradiated in order to study phase and temperature effects on the properties of transient intermediates produced in radiolyzed water. These studies demonstrate that optical absorption bands with peaks near 670, at 280 ± 5, and at 230 ± 8 nm are detectable. The transient visible absorption is attributed to a solvated electron es−. Its spectrum, though unaffected by phase change, is influenced by temperature, dEmax / dT being −1.2 × 10−3 eV/deg. Ges− also depends on temperature, decreasing markedly from −5° to −40°C, but only slowly thereafter. The decay of es−, which is second order at −14°C (k = 1.5 × 1011 M−1·sec−1) and partly first order from −40° to −100°C [k(−60°C) = 1.1 × 104sec−1; ΔEact = 9 ± 2 kcal/mole], becomes slower with decreasing temperature. Over-all spectral, yield and kinetic considerations indicate that es− is structurally similar to eaq−, forms via pre-existing traps, and though immobile as a unit, decays both by reaction with H3O+ and by means of an equilibrial, mobile partner em−. These findings are viewed in terms of the polaron theory and other models for the solvated electron. The transient 280-nm absorption is assigned to a hydrogen-bonded hydroxyl radical OHt·. ESR data showing chemical and kinetic characteristics similar to the optical results confirm this assignment. Its molar extinction coefficient at −196°C is estimated as ε280 = 560 ± 50 M−1·cm−1 [using GOHt· (stable) = 0.8]. The over-all OHt· decay is complex. After prolonged irradiation, pseudo-first-order kinetics representing reaction with H2 and/or H2O2 is primarily observed. For low doses and at temperatures below −100°C, separate fast and slow decaying portions can be distinguished, the former attributable to H· reacting with OHt·, the latter to reaction involving only OHt·. Based on an empirical 32-order kinetic treatment [k(−59°C) ≤ 1 × 104 M−1 / 2·sec−1], ΔEact for the slow decay is determined to be 5.7 ± 0.7 kcal/mole. Qualitatively, this decay and the reaction with products are reconcilable with a mechanism involving OHt· in equilibrium with a mobile species OHm·. Second-order kinetic behavior observed at −14°C (k appears to be ∼108 M−1·sec−1) may also be consistent with this scheme. The full transient yield at −131°C is estimated to be 1.2. These findings imply that OH· is structurally different in both phases, but chemically similar. The relatively stable absorption at 230 nm is ascribed to HO2·. Spectral, chemical, and possibly, ESR evidence support this identification. Its yield is low, and it decays only very slowly at −14°C.
Electron–Ion and Ion–Ion Dissociative Recombination of Oxygen. I. Electron–Ion Recombination
Authors: Chan F. T.
Published: February 2004

The rate coefficient for electron–molecular-oxygen-ion recombination is calculated quantum mechanically. The quantum treatment due to Warke is presented in detail. A simple one-electron model is used. The positive molecular ion is approximated by a rotating dumbbell consisting of O(3P) and O+(4S), and the electron–atomic oxygen interaction is treated as the perturbation for the recombination process. In the one-electron approximation, only six final continuum states are possible. By assuming that one of them, the repulsive Σg+1 of O + O, crosses at the ground vibrational state of O2+, the overlap integrals are then carried out. The calculated rate coefficient, α = (2.8 ± 0.2) × 10−7cm3 / sec at T = 300°K, is close to the experimental results αexptl = (2.2 ± 0.4) × 10−7cm3 / sec.
Electron–Ion and Ion–Ion Dissociative Recombination of Oxygen. II. Ion–Ion Recombination
Authors: Chan F. T.
Published: February 2004

The rate coefficient and the thermal cross section for the oxygen ion–ion dissociative recombination are calculated using the semiclassical formalism. The motion of the heavy particles (positive and negative ions) in their mutual Coulomb field is treated classically. At certain ranges of the ion–ion separation (determined from energy conservation), the electron tunnels from the negative ion to the positive ion. Using the experimental data on the electron binding energy of O2−, this tunneling effect is calculated in the WKB approximation. It is found that the linewidth of the levels due to the dissociative effect is important for the electron tunneling and the molecular dissociation. The rate coefficients and the thermal cross sections have been calculated between 200° and 500°K, and have the orders of magnitude 10−8 − 10−7 cm3/sec and 10−12 cm2, respectively. We find that they both decrease as the temperature increases, and have the following approximate relations: α∝T−1/2, σ(th) ∝T−1. No direct laboratory data is available, but the theoretical results are in agreement with indirect observations from the ionosphere.
Dielectric Relaxation, Far-Infrared Absorption, and Intermolecular Forces in Nonpolar Liquids
Authors: Garg S. K. , Bertie J. E. , Kilp H. , Smyth C. P.
Published: February 2004

Measurements of dielectric constant and loss at 2.1-mm wavelength have been carried out upon benzene, cyclohexane, n-heptane, carbon disulfide, carbon tetrachloride, and tetrachloroethylene, and similar measurements at centimeter wavelengths have been carried out where needed. The infrared absorption spectra of the liquids were measured from 17–170 cm−1. The points for dielectric absorption fit on a smooth curve drawn through the infrared absorption points. Similar measurements have been made upon several binary mixtures of these liquids. Measurements upon liquids to which very small quantities of water have been added show that the effect of water can be corrected for or disregarded. Relaxation times calculated from the dielectric constant and loss measurements are close to 1 × 10−12 sec for all of the liquids, which is the magnitude of the time between the collisions of a molecule in the liquid with its neighbors. Apparent dipole moments calculated for the molecules from these measurements are close to 0.1 D and in satisfactory agreement with values of the dipole moments calculated as induced by the quadrupole or octopole moments of neighboring molecules.
Method for Calculation of the Conformation of Minimum Potential-Energy and Thermodynamic Functions of Molecules from Empirical Valence-Force Potentials—Application to the Cyclophanes
Authors: Boyd Richard H.
Published: February 2004

A method for determining the conformation of minimum potential energy of molecules from empirical valence-force potentials is presented. The energy is written in terms of valence coordinates, expanded through quadratic terms about an assumed geometry, and transformed to Cartesian coordinates. It differs from steepest-descent methods in that the linear equations resulting from differentiation to find the minimum are solved directly to find a set of displacements. These displacements are used to calculate a new geometry, and the process repeated. It is found to converge rapidly in practice. In addition, the final coefficient matrix of the linear equations is used to calculate the vibrational frequencies of the molecule, and, along with moments of inertia from the final geometry, the gas-phase thermodynamic functions are calculated. The method is illustrated by calculations of the structures, strain energies, and thermodynamic functions of four cyclophanes.
Bond-Function Analysis of Rotational Barriers: Ethane
Authors: Sovers O. J. , Kern C. W. , Pitzer R. M. , Karplus M.
Published: February 2004

The barrier potential to internal rotation in ethane is examined with bond-orbital wavefunctions. It is found that reasonable values of the barrier height are obtained over a wide range of bond polarities if the wavefunction is constrained to satisfy the Pauli exclusion principle. By contrast, for a Hartree product of local nonorthogonal bond orbitals, the barrier is very sensitive to bond polarity. On integration of the Hellmann–Feynman forces from the determinantal bond-orbital functions along a path that requires only force differences between staggered and eclipsed ethane, barrier values are calculated that closely parallel the corresponding total energy differences; use of an alternative path introduces a much larger error into the force calculation. The bond-function results are utilized to examine the question of error cancellation in barrier calculations and for a comparison with other studies of the ethane barrier. It is concluded that the dominant contribution to the barrier is the overlap (exclusion-principle) repulsion between closed-shell, localized C–H bond orbitals and that the direct electrostatic and dispersion force interaction between these orbitals is relatively unimportant.
Self-Consistent Approximations in Kinetic Theory
Authors: Green H. S. , Hoffman D. K.
Published: February 2004

A method is explained for obtaining generalizations of Boltzmann's equation which are consistent with the macroscopic conservation equations to any desired order in the density. The important feature of the method is the use of correlated stream velocity functions and temperatures, which can be derived from the statistical mechanics of equilibrium. Generalized conservation equations are obtained which serve as consistency conditions in the determination of the generalized velocity distribution functions. A self-consistent method of approximation to these functions is developed, and illustrated by the derivation of a form of Boltzmann's equation, correct to terms quadratic in the density, and valid even when bound states are possible.
Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates
Authors: Marcus R. A.
Published: February 2004

The coordinates of earlier papers of this series are extended from linear collisions to reactions in three dimensions. Termed “natural collision coordinates,” they have a unique property of passing smoothly from those suited to reactants to those suited to products. Potential applications to bimolecular reactions are described.
Analytical Mechanics of Chemical Reactions. IV. Classical Mechanics of Reactions in Two Dimensions
Authors: Marcus R. A.
Published: February 2004

The natural collision coordinates of Part III are used to treat the analytical mechanics of chemical reactions, AB + C→A + BC. Other than in Part II, the classical analytical mechanics of chemical reactions on a smooth potential surface have not been explored previously in the literature. A Hamilton–Jacobi formalism is used, apparently for the first time in calculating a reaction rate. The “vibrationally adiabatic” reaction serves as the zeroth-order approximation and nonadiabatic corrections are obtained. Theoretical expressions yield the rotational and vibrational energy distribution of reaction products, angular distribution, and reaction probability, as a function of impact parameter, initial translational velocity of relative motion, and initial rotational–vibrational state of reactants. The results are not intended to apply to reactions which show very large excursions from vibrational adiabaticity. In the zeroth approximation (vibrational adiabaticity), an adiabatic separation of variables is achieved. Here, the vibrational action is constant; however, the rotational–orbital action changes by a known increment from one constant value to another, on transition of that motion into a bending vibration. The resulting “adiabatic” correlation shows several interesting features. For reactions in which there are no large mass ratios, the state of vibration of AB, of rotation of AB, and of orbital motion of AB + C correlate with the state of vibration of BC, of rotation of BC, and of orbital motion of A + BC, respectively. For reactions with unusual mass ratios, such as H + Cl2→HCl + Cl, the correlation equations show instead the “adiabatic” transformation of Cl2 rotation into HCl + Cl orbital motion, thereby reflecting the expected result of angular momentum conservation. Had the rotational–orbital cross term in the kinetic energy been neglected, an incorrect correlation would have resulted in the latter case. Extension of the present work to three dimensions involves an added approximation, to be given in a subsequent paper. The expressions and method also permit comparison of one- and two-dimensional computer results on a more similar basis and, because of certain similarities in computer results for energy distributions in two and three dimensions, perhaps comparison with experimental results on energy distributions. In conjunction with the computer results information can be obtained on various approximations, such as near adiabaticity. The present theory can also be used to analyze and perhaps extend various statistical-type theories in the literature.
Evaluation of Molecular Quadrupole Moments from Broadening of Microwave Spectral Lines. II. Calculation of the Quadrupole Moments and Discussion
Authors: Berendts B. Th. , Dymanus A.
Published: February 2004

Molecular quadrupole moments of OCS, CHF3, N2O, NO, H2, HD, D2, N2, and CO2 have been obtained from the fit of the calculated line-broadening constants Λaa for self-broadening and Λab for foreign-gas broadening to the experimental results reported in a previous paper. The theoretical line-broadening constants were calculated using Anderson's theory on pressure broadening in the modification of Tsao and Curnutte. The interaction mechanisms taken into account were: dipole–dipole, dipole–quadrupole, quadrupole–dipole, quadrupole–quadrupole, and London dispersion. The results for quadrupole moments in 10−26 esu are summarized in the table below in which the rows are numbered by the absorbing molecule and the columns by the colliding (perturbing) molecule. The general conclusion is that Anderson's theory with the commonly used matching condition at low values of the impact parameter does not allow a reliable determination of molecular quadrupole moments, most probably because of overestimation of the dipole–dipole contribution. The theory fails completely for CHF3 broadening and is very sensitive to experimental errors in the case of OCS, and the influence of bmin is rather questionable in the case of N2O.
Soft-Sphere Model for Closed-Shell Atoms and Ions
Authors: Gilbert T. L.
Published: February 2004

Using recent spectroscopic data for the alkali halide monomers, it is shown that approximate additivity rules of the form Rij = Ri + Rj and ρij = ρi + ρj hold for the radii and hardness parameters in the Born–Mayer repulsive potential, Uij(R) = fρijexp[(Rij − R) / ρij].
Ion–Molecule Reactions in a 50-MHz Discharge
Authors: Studniarz Stanley A. , Franklin J. L.
Published: February 2004

Extensive investigations of the dependence of the relative ionic composition of a high-frequency plasma on the discharge conditions (particularly the pressure) and of the relative ionic composition of the plasma as a function of the translational energy of the ions issuing from the orifice of the sampling probe at constant pressure were made by the use of a quadrupole mass spectrometer employing a retarding-potential grid system. The results indicate that the ions collected and observed are formed in a narrow region in the plasma (approximately 1 mm in depth) in front of the probe orifice and that these ions gain most of their energy from the electric field of the sheath in a distance that is much less than a reaction mean-free path (∼0.01 mm). The average time available for reaction (reaction time) was a few tenths of a microsecond and independent of the vessel geometry and dimensions. The reaction time was relatively insensitive to changes in pressure and was reasonably constant for ions in several different gases. An explanation is given in terms of a distrubance to the electric fields of the plasma in the vicinity of the probe aperture.
Photoionization of 1,3-Butadiene, 1,2-Butadiene, Allene, and Propyne
Authors: Parr Albert C. , Elder Fred A.
Published: February 2004

Using a photoionization mass spectrometer, the ionization potentials of the parent molecules and the appearance potentials of the fragment ions, observed below 13 eV, have been determined for 1,3-butadiene, 1,2-butadine, allene, and propyne. The ionization potentials of 1,3-butadiene are 9.07 ± 0.02 eV, 9.80 ± 0.04 eV, and 11.7 ± 0.04 eV. The adiabatic ionization potential of 1,2-butadiene is 9.23 ± 0.02 eV. The adiabatic ionization potential of allene is 9.62 ± 0.04 eV. The ionization potentials of propyne are 10.38 ± 0.02 eV and 11.30 ± 0.02 eV. The heat of formation of C3H3+ and C4H5+ is calculated to be 11.18 ± 0.04 eV and 10.45 ± 0.04 eV, respectively. Derived bond energies for the ionic states are given. The data are shown to be consistent with rearrangement of 1,3-butadiene via hydrogen migration in the excited molecular ion. At threshold for fragmentation, the C4H5+ and C3H3+ ions from 1,3-butadiene and 1,2-butadiene are identical.
Molecular Beam Kinetics: Transition between Rebound and Stripping Mechanisms in Reactions of Alkali Atoms with Polyhalide Molecules
Authors: Wilson K. R. , Herschbach D. R.
Published: February 2004

Angular distribution measurements have been made for reactive and elastic scattering of K, Rb, or Cs atoms from two series of polyhalide molecules (listed in order of decreasing reaction yield): PBr3>PCl3≫ BBr3; and CBr4>̃SnCl4>CCl4>CHCl3>SiCl4. For PBr3, PCl3, CBr4, and SnCl4 the reaction cross sections are very large (>̃150 Å2) and stripping behavior is predominant: most of the alkali halide recoils into the forward hemisphere with respect to the incident alkali-atom beam. For CCl4 the laboratory alkali halide distributions are bimodal, corresponding in the center-of-mass system to conical, sideways-peaked distributions of the recoil velocity vectors. The half-angle of the cone is roughly 50° for Cs, 70° for Rb, and 90° for K. For CHCl3 the alkali halide distribution favors the backward hemisphere. The angular distribution of alkali atoms scattered without reaction likewise shows a strong correlation with the reaction yield. As compared with the much less reactive reference systems BBr3 and SiCl4, the elastic scattering at wide angles falls off more and more rapidly as the reaction yield increases; beyond 90° the elastic intensity for SnCl4 is only >̃2% of that for SiCl4. Regardless of the size of the reaction cross section, however, the total scattering (alkali atoms plus alkali halide) is very similar in both magnitude and angular distribution to that for the reference molecules. The variations in reactivity agree well with the early Polanyi flame results and are also qualitatively correlated with the electron-capture coefficients of the reactant molecules.
Energy Migration in Organic Liquids at High Temperatures
Authors: Levin E. , Furst M. , Kallmann H.
Published: February 2004

The energy-transfer process in organic liquids has been studied at temperatures from 20°–240°C. The results are consistent with the migration model, according to which electronic excitation energy undergoes a series of hops between neighboring solvent molecules, followed by a short-range jump to a solute molecule. The mean hopping time τh is related by theory to an experimentally determinable parameter α, which is directly related to the hopping frequency. Values of α, all on the order of 1012 sec−1, were found for a number of solutions. For a temperature increase of 200°C, α was generally found to decrease by about 50%, depending on the solvent utilized. Relationships between the temperature dependence of τh and that of mean intermolecular distance are discussed. Material diffusion in the energy-transfer processes is estimated to be quite small compared with hopping, at least for efficient solvents. Anomalies in the energy-transfer properties of anisole are noted.
Photodissociation of HN3 in the Vacuum-Ultraviolet Production and Reactivity of Electronically Excited NH
Authors: Okabe Hideo
Published: February 2004

Photodissociation processes of HN3 yielding electronically excited species have been studied in the vacuum ultraviolet. The fluorescence originating from these species has been investigated in the spectral region from 1700–6000 Å. The predominant excited species are NH c1Π, NH A3Πi, and probably N2 B 3Πg. The yield of the NH c1Π production is at most 2%. The (0, 0) band is most intense among the (0, 0), (1, 0), and (0, 1) bands of the NH c1Π–a1Δ system observed both at the Kr and Xe lines. The intensity of the (1, 0) band is 7% of that of the (0, 0) band. Rotational levels in the (0,0) band are populated up to K = 18. Direct formation of the NH A3Πi, a spin-forbidden process, appears to be minor. The pressure dependence of the ratio, NH A3Πi to NH c1Π, indicates that the NH A3Πi may be formed largely by the reaction of electronically excited N2, most probably N2B3Πg, with HN3. The absorption coefficient of HN3 has been measured in the vacuum-ultraviolet region in order to examine its correlation with dissociation processes. It was concluded that the NH c1Π may be formed from predissociation of electronically excited HN3 below 1450 Å, while above 1450 Å apparently from direct dissociation. The NH c1π is quenched almost in every collision with H2, CO, O2, and NO. It was found that the main quenching process by paramagnetic gases, O2 and NO, is the conversion of the c1Π to the A 3Πi. Other primary processes are discussed in conjunction with the present work.
Use of Pseudopotentials in Atomic-Structure Calculations
Authors: Weeks John D. , Rice Stuart A.
Published: February 2004

Taking the general point of view that the ideas of pseudopotential analysis can be usefully applied to the removal of orthogonality constraints in a wide class of problems, we describe a generalization of the method of pseudopotentials which is applicable to many-electron systems. The generalized pseudopotential derived herein reduces to the phillips–Kleinman pseudopotential under the one-electron Hartree–Fock approximation, and a study of its structure helps to clarify some of the properties of one-electron pseudopotentials. The generalized formalism is then applied to ions with one valence electron, such as Be+ and Mg+, where it suggests a simple model potential which gives a good description of the Rydberg spectra of these ions. The relationship of the pseudopotential to the model potential is discussed. The theory is then applied to atoms with two valence electrons, such as Be and Mg, and it is shown how the use of one-electron pseudopotentials or model potentials can simplify, for example, the “exact pair” equations describing the motion of the valence-electron pair in the Hartree–Fock sea and permit the removal of orthogonality constraints on the pair wavefunction. Good results are obtained in calculations of the valence-pair energy of Be and Mg. Further approximations are discussed which allow calculation of the valence-pair energy when the core orbitals are not known. The approximate methods are applied to Be, Mg, and Sr with good results.
Some Comments on a Formal Theory of Photochemical Dissociation Reactions
Authors: Rice Stuart A. , McLaughlin Ian , Jortner Joshua
Published: February 2004

In this paper we present a formal theory of photochemical fragmentation reactions for the case that intramolecular energy transfer is of importance. The zero-order spectrum of the molecule is assumed to consist of a discrete level in resonance with a dense set of levels belonging to another electric manifold, which in turn is in resonance with a translational continuum representing molecular fragmentation. The exact eigenstates of the system are computed formally and shown to be resonant scattering states. Explicit formulas are derived for the probability of the system being in a nonstationary state represented by a wave packet localized in the discrete state, or the dense set of states resonant with the discrete state. In the case that the resonant scattering state may be approximated by a quasistationary bound state, an explicit formula relating the rate of unimolecular photochemical decomposition to the coupling matrix elements and densities of eigenstates of the system is derived. The general relationship between translational motion and internal molecular motion is discussed, as are some aspects of the dissociative decay process, the nature of the excited states, and the possible role of interference phenomena involving coherently excited states.
Raman Spectra of BaClF, BaBrF, and SrClF
Authors: Scott James F.
Published: February 2004

The frequencies and symmetries of the even-parity lattice vibrations of BaClF, BaBrF, and SrClF are determined by means of polarized Raman scattering from oriented single crystals. The polarizations and frequencies of the vibrations are interpreted in terms of symmetry coordinates.
Transient Negative-Ion States in Alicyclic and Aromatic Fluorocarbon Molecules
Authors: Naff W. T. , Cooper C. D. , Compton R. N.
Published: February 2004

The formation of short-lived (lifetime ∼10−15 − 10− 13  sec) and long-lived (lifetime ∼10 − 6−10−3 sec) temporary negative-ion states in 12 cyclic fluorocarbon molecules is studied in the gas phase with monoenergetic electron beams. The long-lived molecular ions exhibit a systematic increase of autoionization lifetime from 7 μsec for C4F6− possessing 24 vibrational degrees of freedom to 800 μsec for C7F14− having 57 vibrational degrees of freedom. This 100-fold increase of lifetime with increasing number of degrees of freedom qualitatively conforms to the previous theoretical model describing nondissociative electron attachment in polyatomic molecules. All of the long-lived ions (C4F6−, C6F6−, C4F8−, C5F8−, C7F8−, C6F10−, and C6F12−) have a maximum attachment cross section at some energy less than 0.05 eV, and the widths of the attachment resonances observed in the beam experiments were instrumental with the exception of C7F14−, whose width at 12 maximum was approximately 0.2 eV. The SF6 scavenger technique is employed to detect short-lived transient negative-ion states in the fluorinated benzenes, and the peak of the resonances occurred at 1.35 eV for C6H5F, 0.6 eV for 1,3-C6H4F2, 0.3 eV for 1,3,5-C6H3F3, and at ∼0 eV for 1,2,3,4-C6H2F4 and C6HF5. The peak energies of the temporary negative-ion resonances show an approximately linear decrease as a function of the number of fluorines added to the ring, and evidence is given that addition of each fluorine to the benzene ring increases the electron affinity by ∼0.4 eV. The completely fluorinated benzene ring attaches thermal energy electrons into a negative-ion state which has a lifetime of 12 μsec.
Electronic Structures from X-Ray Spectra. II. Mostly ClO3 − and ClO4−
Authors: Best P. E.
Published: February 2004

New measurements of the chlorine Kα and Kβ x-ray emission spectra from ClO3 − and ClO4 − ions are reported. The Kα energy shifts give chlorine net 3s, 3p occupations of 5.5 and 4.9 in ClO3 − and ClO4 − respectively. Three lines are observed in the K spectrum of ClO3 −, two in the spectrum of ClO4 −. These emission features are interpreted as transitions from MO's and particular assignments are made. Chlorine 3p contributions to these orbitals are deduced and the ionization-potential differences are estimated. The widths of x-ray spectral features are considered. Evidence is presented which suggests that the argon compound isoelectronic with ClO4 − is unstable; that with ClO3 − is stable. A relationship between heats of formation and x-ray ionization thresholds is discussed.
Statistical-Mechanical Analysis of the Theory of Diffusion-Controlled Chemical Reactions. III
Authors: Paul R.
Published: February 2004

The theory of diffusion-controlled chemical reactions, as presented by Waite [T. R. Waite, Phys. Rev. 107, 463 (1957)] using phenomenological arguments, is analyzed from a statistical-mechanical standpoint, and the approximations needed to arrive at Waite's starting equation are examined.
Vibration-to-Vibration Energy Transfer in Gas Mixtures Containing Nitrous Oxide
Authors: Yardley James T.
Published: February 2004

Fluorescence from the asymmetric stretching vibration (Δυ3 = 1) of N2O is observed following excitation by a Q-switched N2O laser. The time dependence of the fluorescence is used to measure the rates of relaxation of N2O(00°1) at 25°C as the result of intermolecular collisions with N2O, He, Ne, Ar, Kr, H2, and D2. The rate of energy exchange between N2O(00°1) and N2(υ = 1) is also determined.
Temperature Dependence of the Magnetic Susceptibility of Water
Authors: Cini R. , Torrini M.
Published: February 2004

The results of an experimental investigation of the temperature coefficient of the magnetic susceptibility of water in the temperature range from 0°–80°C are reported. The experimental accuracy of the measurements exceeds 0.02%. The equation which best fits the experimental data is presented. The variation of magnetic susceptibility with temperature is correlated with the number of hydrogen bonds calculated from two statistical thermodynamic theories of liquid water. The excellent agreement with one of the two theories allows the quantitative change of diamagnetism to be obtained for water molecules having one and two hydrogen bonds.
Index of Refraction of Isopentane and Mesitylene as a Function of Pressure
Authors: Langer Dietrich W. , Montalvo Ramiro A.
Published: February 2004

The change of the refractive index of isopentane was determined by an interferometric method at room temperature between 1 and 10 kbar, and of mesitylene—between 1 and 3.4 kbar, which is roughly its freezing point at room temperature. The results are combined with P − V data of Bridgman and compared to an equation by Böttcher, rendering average molecular radii and polarizabilities for these two substances.
PVT Properties of Water. III. Virial Coefficients of D2O in the Range 150°–500°C
Authors: Kell G. S. , McLaurin G. E. , Whalley E.
Published: February 2004

The equation of state of D2O has been determined at 25° intervals from 150° to 500°C by the methods used previously for H2O in which no measurements of the vapor volume are required. The conditions reproduced those used for H2O, and the results were analyzed to give the differences in the second virial coefficient of D2O and H2O to maximum precision. The enthalpy and energy of dimerization is about 20 cal mole−1 lower for D2O than for H2O, and the entropy of dimerization is about 0.03 cal deg−1·mole−1 lower. These values agree qualitatively with other related evidence; a quantitative comparison is not possible at present because the large effects of the quantization of the intermolecular motions, particularly rotational and vibrational, are not known well enough.