Volume 57, Issue 12, 15 December 1972

Classical S‐Matrix for Vibrational Excitation of H_{2} by Collision with He in Three Dimensions
View Description Hide DescriptionComplex‐valued classical trajectories have been computed by direct numerical integration of the equations of motion for three‐dimensional collisions of He and H_{2}, and from such trajectories classical S‐matrix elements for transitions between specific rotational‐vibrational states of H_{2} have been constructed. At the collision energies employed (∼1–2 eV) all vibrationally inelastic transitions are classically forbidden, thus the need for analytically continued, complex‐valued trajectories. Comparison with the quantum mechanical calculations of Eastes and Secrest shows excellent agreement between the quantum and uniform semiclassical transition probabilities. Since, however, for three‐dimensional collision systems one is seldom concerned with individual S‐matrix elements, but rather sums over many of them, an important practical feature is developed which shows how one can combine the usual Monte Carlo classical treatment of some of the internal degrees of freedom with a semiclassical state‐by‐state description of others; i.e., one can ``quantize'' only those degrees of freedom that are highly quantumlike (e.g., vibration). This ``partial averaging'' approach also greatly simplifies the practical aspects of applying classical S‐matrix theory to systems with several internal degrees of freedom.

Magnetic Field Dependence of I_{2} B‐State Lifetimes
View Description Hide DescriptionA shortening of fluorescence lifetimes has been observed upon application of a magnetic field and is a function of the vibrational level of the upper electronic state and of magnetic field strengths. A suggested process is predissociation, due to mixing by the magnetic field of a repulsive state with the B state.

Structure of (KSO_{3})_{2}NO in X‐Irradiated Single Crystals of (KSO_{3})_{2}NOH
View Description Hide DescriptionThe nitrosyldisulfonate ion has been identified in x‐irradiated single crystals of potassium hydroxylaminedisulfonate. Principal values of the N^{14}hyperfine coupling constants are 27.5, 7.7, and 5.5 G. The principal g values are 2.0094, 2.0055, and 2.0026. Weak transitions due to hyperfine interactions with a proton from the host crystal are observed.

Microwave Dielectric Constant and Conductivity Measurements in the Phthalocyanines
View Description Hide DescriptionDielectric constant and loss measurements have been made on α, β, and X metal free and copper phthalocyanine at microwave frequencies. Measurements were carried out on pressed pellets of polycrystalline material. Dielectric constant data is analyzed in terms of a powderdielectric model. The relative dielectric conductivities of these phthalocyanines are examined along with similar measurements on various β transition metal phthalocyanines. Dielectric conductivities of these metal phthalocyanines appear to be consistent with dc conductivities reported in the literature.

Exact Solutions for Dynamics of Finite, Semi‐Infinite, and Infinite Chains with General Boundary and Initial Conditions
View Description Hide DescriptionThe exact analytic solutions in closed form for the dynamics of finite, semi‐infinite, and infinite linear chains of identical masses and ideal springs are presented. In addition to the harmonic interaction between nearest neighbors, each particle is harmonically bound to its equilibrium position and is subjected to frictional and other external time‐dependent forces. The motion of all the particles is expressed in terms of the given initial conditions and applied forces. In contrast with previous studies on the finite chains, very general (i.e., not necessarily ``periodic'') boundary conditions are used and the resulting solutions contain terms representing all the higher order multiple reflections from the two ends. The properties of the solutions are studied for all possible values of physical constants including the limiting values for uncoupled oscillators. By specializing some results of the present work, those of previous derivations on simpler systems by other authors are recovered. Some useful applications of the results are suggested.

Near Hartree‐Fock Calculations on the Ground State of the Water Molecule: Energies, Ionization Potentials, Geometry, Force Constants, and One‐Electron Properties
View Description Hide DescriptionNear Hartree‐Fock wavefunctions have been calculated for the ground state of the water molecule using both Slater and contracted Gaussian basis sets. Total energies of −76.063 hartree were obtained with a (5s4p1d/3s1p) Slater basis and a [6s5p2d/3s1p] contracted Gaussian basis derived from an (11s7p2d/5s1p) primitive set; these energies are estimated to be within 0.003±0.002 hartree of the Hartree‐Fock limit. The Hartree‐Fock wavefunctions account for ∼70% of the dissociation energy of water. The Hartree‐Fock vertical ionization potentials (in electron volts), 11.1(^{2} B _{1}), 13.3(^{2} A _{1}), and 17.6(^{2} B _{2}), are too low by 1–1.5 eV as expected. With the Gaussian basis set a potential surface was computed and the equilibrium geometry and harmonic force constants were calculated. The calculated bond length, 0.941 Å, and bond angle 106.6°, are in good agreement with the experimental values, 0.957 Å and 104.52°. In spite of the rather good agreement for the geometry, the force constants are in error by 15%–20%. This is attributed to an inadequancy of the Hartree‐Fock model. A number of one‐electron properties were also computed; they differ only slightly from those reported in earlier work and are in satisfactory agreement with experiment. Plots of the valence (canonical) molecular orbitals are given.

Heat Capacity near the Consolute Point in Solid
View Description Hide DescriptionMeasurements are reported of the heat capacity at saturated vapor pressure (essentially C_{p} ) of the system near its solid‐solid consolute point (62°K, 65% Ar). In contrast to the behavior of the heat capacity at binary liquid consolute points, where there are striking anomalies, no large increase was observed for An abrupt increase of only about 13% occurred in the heat capacity near the transition. The possibility that the anomaly is suppressed by lattice strain effects is discussed.

Lifetimes of the A ^{2}π and B ^{2}Σ States of the CN Radical
View Description Hide DescriptionThe lifetimes of the and states of the CN radical have been measured from an analysis of the zero electric field limit linewidth of the level anticrossing spectrum. The measured value of was found to be in reasonable agreement with the most recent phase shift measurement. The value of was in serious disagreement with previous direct decay measurements on vibrational levels, but in essential agreement with previous microwave and intensity measurements on the perturbed v=10 level.

Effect of H_{2} Pressure on Pulsed H_{2}+F_{2} Laser. Experiment and Theory
View Description Hide DescriptionStimulated emission predictions and measurements for an H_{2}+F_{2} laser are compared for H_{2} pressures from threshold to stoichiometric, a range of several orders of magnitude. Slowly flowing, helium‐diluted, 50 torr mixtures are initiated photolytically. Two dilution ratios and two output couplers are considered, and good agreement is found for time‐to‐threshold and pulse duration vs H_{2} pressure. Spiking, relaxation oscillations, and possibly mode beating, features not modeled, are observable in some pulses; however, predicted intensity vs time generally agrees in pulse shape with laser output. Observed and predicted peak intensities nearly match for low H_{2} pressure, and the predicted increase of peak intensity with low H_{2} is followed fairly well. For H_{2} in the vicinity of one‐tenth stoichiometric, the peak intensity data show an abrupt leveling off, while the calculations predict a continuing increase. This disagreement most probably cannot be attributed to uncertainties in the kinetic model. All rate modifications considered have proven incapable of producing a change sufficiently large or abrupt to explain this feature of the data. Experimental results are presented supporting the notion that parasitic oscillations cause this change in laser output.

Bond Order in LCAO Molecular Orbital Theory
View Description Hide DescriptionOn the basis of LCAO theory, the following intrinsic definition of bond order is derived:where i and j index basis functions on different centers, p_{ij} is the corresponding charge‐and‐bond‐order matrix element, S_{ij} is the overlap integral, f_{ij} is a long range factor, and g_{ij} is an atomic hybridization and nonorthogonality factor. The term p_{ij}S_{ij} is the overlap population and the term p_{ij}f_{ij}g_{ij} is the associated net atomic population; the latter is defined by a reference homopolar bond constructed from normalized hybrids of compositions determined by the LCAO wavefunction. The bond order, B_{ij} , reduces in the appropriate special cases to the Coulson, Mulliken, and Wiberg bond orders. However, B_{ij} is not limited to these cases but is also valid for analysis of any LCAO wavefunction. It may also be combined with a Mulliken population analysis to resolve the total electron population into bonding terms and residual lone pair terms. Similarly, the valence electron population may be resolved into covalence, electrovalence, and free valence. Applications are given to HF, the Group I fluorides, and some organic molecules.

On the Energy Losses of Hot Atoms Colliding with Different Molecules
View Description Hide DescriptionExperimental α values for hot halogen atoms colliding with methyl halides disagree with the calculated values, assuming elastic collisions. This is attributed to the asymmetry of the target molecules which either render the interaction inelastic or are governed by a different scattering potential.

^{14}N NQR Spectroscopy of Some Amino Acids and Nucleic Bases via Double Resonance in the Laboratory Frame
View Description Hide DescriptionThe ^{14}N nuclear quadrupole resonance spectra and spin‐lattice relaxation times of the amino acids histidine, methionine, cystine, cysteine, and tyrosine as well as of the nucleic bases uracil, thymine, cytosine, and guanine have been determined by a ^{14}N‐proton double resonance technique in the laboratory frame. The experiments were performed on polycrystalline samples at 77°K or above this temperature. A theoretical estimate of the sensitivity of this method for a variety of experimental conditions is as well presented. It is shown that in contrast to usual double resonance techniques the method works even in the case of a short proton spin‐lattice relaxation time if only the nitrogen relaxation time is long.

Theory of Fluorescence Depolarization by Anisotropic Rotational Diffusion
View Description Hide DescriptionThe general expressions for the time‐dependent fluorescence depolarization caused by anisotropic rotation diffusion have been obtained. It is shown that after an instantaneous exciting light pulse, the parallel and perpendicular components of fluorescence can have a maximum of six exponential decays and the difference of these two components a maximum of five decays. The present results differ from those of previous studies and the differences are discussed.

Determination of a Three Parameter Pair Potential from Second Virial Coefficients: Ar, Kr, and Xe
View Description Hide DescriptionTo prepare second virial coefficient data for use in determining the Ar, Kr, and Xe pair potentials, random errors in B(T) data are initially eliminated by least square fitting to a polynomial in T ^{−1}. After choosing an analytical form for the potential, optimum values for the potential parameters are obtained using a modified version of the method of selected points. This procedure permits rapid testing of three parameter model potentials without having extensive tables of reduced second virial coefficients. A piecewise potential (RMMV for rigid, Morse, Mie, and van der Waals) was selected and extensively compared with existing theoretical and experimental determinations of the pair potential for Ar, Kr, and Xe. The RMMV potential was found to be satisfactory, not only in the well region, but also in the short and long range limits.

Singlet‐Triplet Splitting in Diffusing Radical Pairs and the Magnitude of Chemically Induced Electron Spin Polarization
View Description Hide DescriptionA previous theory of anomalous electron spin resonance spectra of free radicals in solution attributes the electron spin polarizations to the combined effects of singlet‐triplet mixing by magnetic interactions in a diffusing radical pair and singlet‐triplet splitting by the exchange interaction when, and if, the diffusing radicals reencounter each other. This theory is studied in more detail by considering the exchange interaction at all times during the diffusive trajectory of the radical pair, in contrast to the original treatment of approximating it as a rectangular pulse which is nonzero only briefly during the second encounter of the radicals. Time dependent perturbation theory is used to calculate the radical pair wavefunction and the corresponding electron spin polarization to first order in the exchange interaction. The polarization is averaged over all possible diffusion paths of the radicals by averaging the exchange interaction over the distribution of radical pair separations obtained by solution of the diffusion equation with appropriate boundary conditions. These boundary conditions take into account the facts that polarization begins when the radicals separate to a point where the magnetic and exchange interactions are roughly equal, and that the developing polarization is destroyed by spin exchange if the radicals subsequently come too close together. The calculated polarizations are of the right order of magnitude to account for the experimental results, and the dependence of the polarization on the magnetic interactions and the diffusion parameters is essentially the same as predicted by the earlier simpler theory.

On the Reaction: An Endoergic Stripping Process
View Description Hide DescriptionWe have determined the product velocity vector distributions for the endoergic (ΔE _{0}°=2.23 eV) atom abstraction reaction at a number of values of the initial relative energy. Deuterium atom abstraction occurs at higher energies by a spectator stripping process. An energy threshold for the zero angle reactive scattering process is observed when the energy of the projectile relative to the abstracted atom is equal to the endoergicity of the reaction. The results show that the spectator stripping process is not to be uniquely associated with exoergic reactions or those which proceed along monotonically decreasing potential energy surfaces.

Self‐Diffusion in Liquid Water to −31°C
View Description Hide DescriptionThe self‐diffusion coefficient of water is reported to −31°C, where the activation energy reaches 11 kcal/mole compared with 4.5 kcal/mole at 25°C. The similarity of the temperature dependence of the fraction of broken hydrogen bonds, as inferred from Raman and infrared data, and the diffusion coefficient over the entire liquid range forms the basis of empirical support of the dominant role of hydrogen bonding in the fundamental diffusion mechanism.

Strengths and Collision Broadened Widths in the Second Overtone Band of Hydrogen Fluoride
View Description Hide DescriptionIndividual line strengths and self‐broadened half‐widths have been measured in the second overtone band of hydrogen fluoride. The electric dipole matrix element for the band has been determined from the measured strengths. Its value is:The m dependence of the measured half‐widths agree with the Anderson theory of collision broadening if off resonant collisions are taken into account.

Further Considerations on the Theory of Intermolecular Obstruction in Rubber Elasticity
View Description Hide DescriptionAn earlier theory which took into account intermolecular obstruction in rubber is reconsidered. On the basis of a revised procedure for counting configurations of polymer chains, a new equation of state is obtained relating stress to strain in uniaxial extension. The new relationship has the same from as a function of the strain but differs in its dependence on f, the fraction of the rubber volume occupied by the polymer chains. When applied to experiments, it leads to higher values of f. In addition, results presented previously only for uniaxial extension are generalized for arbitrary strains.

Formation of HeH^{+} from Low‐Energy Collisions of Metastable Helium and Molecular Hydrogen
View Description Hide DescriptionA merging‐beams technique has been used to study HeH^{+} formation resulting from the interaction of a composite beam of He(2^{1} S) and He (2^{3} S) with a beam of H_{2}. The experiments were conducted over a range of interaction energy W from 0.05 to 10 eV. It was learned that the dominant process for producing HeH^{+} is the rearrangement ionizationreaction, where He* represents the metastable helium. The experiment consisted of measuring the lab‐energy distributions of HeH^{+}. Relative and absolute cross sections were obtained from these distributions. The distributions indicate that, in the center‐of‐mass system, most of the HeH^{+} is scattered in the direction of the incident He*. The energies associated with the HeH^{+} at the peaks of these distributions are very close to those expected for spectator stripping. Conservation of energy for the reaction can only be achieved by assuming that the electron carries away a substantial portion of the available energy. It is shown that the two‐step model (where † indicates ground‐state or vibrationally excited satisfactorily explains the measured lab‐energy distributions near W=0.05 eV but does not agree completely with the results for .