Volume 56, Issue 12, 15 June 1972

Span of a Polymer Chain
View Description Hide DescriptionThe x span of a polymer chain is defined as the difference between the largest x coordinate and the smallest x coordinate of any segments in the chain. The polymer chain is represented by a nearest‐neighbor lattice‐model random walk in which the mean square displacement of each component of a single step is . The distribution function of the x span of an N step random walk is obtained; and the following asymptotic formulas are obtained for its first and second moments, respectively, 2(2N/3π)^{1/2} and 4 ln2 N/3. The corresponding moments of the magnitude of the x component of the end‐to‐end distance are (2N/3π)^{1/2} and N/3. Excluded volume effects are not considered. It is noted that the problem of calculating the first moment of the x span is identical with the one‐dimensional case of the Dvoretzky‐Erdös problem, namely, the calculation of the average number of different lattice sites visited in an N‐step random walk on a d‐dimensional lattice.

Fine Structure, Dipole Moment, and Perturbation Analysis of CO
View Description Hide DescriptionTheedio‐frequency spectrum of the state of carbon monoxide from 5 to 1000 MHz has been measured in a molecular beam electric resonance spectrometer. Lambda doubling transitions in and several in have been measured to an accuracy of 1 kHz as a function of electric field. A simultaneous least squares fit to optical and radio‐frequency data on determines a set of fine structure constants which reproduce the optical and radio‐frequency measurements within their respective experimental errors. The vibrational dependence of the constants which determine the lambda doubling in the state is accounted for. of are perturbed by of , respectively. Analysis of the radio‐frequency lambda doublings and perturbed optical spectra determines two vibration‐independent matrix elements of the Hamiltonian off diagonal in electronic state which describe the interaction, and unitless. Extensive Stark effect measurements determine the dependence of the dipole moment of on v, J, and Ω. Analysis of the Stark effect data determines the transition moment between and , and the dipole moment of the state, .

Luminescence of the Tetrachloroferrate(III) Ion
View Description Hide DescriptionExcitation of a series of compounds containing the ion with ultraviolet or blue radiation at 85°K gave in each case a broad featureless luminescence band in the near infrared. Analysis of the decay curves obtained by using monochromatic excitation pulses and different observation wavelengths indicates that two emissive processes contribute to the emission. Excitation into a absorption band produces luminescence, whereas excitation into the low energy tail of the charge transfer absorption gives a second luminescence process, there being little or no tendency for the ion to cross from this luminescent state to the ^{4} T _{1}(G) although the latter is probably the lowest excited state. The ion under similar conditions gives a broad, near infrared luminescence band which also appears to consist of two transitions.

Examination of the Stochastic Process Underlying a Simple Isomerization Reaction
View Description Hide DescriptionA characterization of the concentration fluctuations in the isomerizationreaction is given based on the Liouville equation for the conditional probability. By separating the relaxation process into four qualitatively distinct time regimes, the approach in time to the birth and death equations of the usual stochastic theory can be followed. It is shown that these equations are approximately solved by a normal distribution which is generated by a modified Langevin‐type equation. In this time domain the stochastic process is stationary and Markov and as the fourth time domain is approached the process also becomes Gaussian as predicted by the fluctuating force theory of this reaction. Since the time scale in this last regime is the order of the time constant for the reaction, it is concluded that the fluctuating force theory is valid only near equilibrium.

Hydrodynamic Model Calculation of Momentum Correlation Functions at Long Times
View Description Hide DescriptionWe show that recent calculations, based on a hydrodynamic model, for the long‐time behavior of the linear and angular momentum autocorrelation functions for a molecular fluid contain internal inconsistencies which can lead to a physically unrealistic result. We remove these inconsistencies, and rederive the results of interest via an internally self‐consistent procedure. Finally, we show that these same long‐time results can be obtained by a more direct treatment of the linearized hydrodynamicequations.

Quasistatistical Complexes in Chemical Reactions
View Description Hide DescriptionThe S matrix for inelastic and rearrangement collisions derived within Feshbach's theory of resonances can be written as the sum of S^{D} and S^{C} , where S^{D} refers to direct interaction processes, and S^{C} refers to complex (resonant) processes. For collision times short compared to characteristic times of internal motions of reactants, models of direct interactions, which assume S^{C} to be zero, have been developed. For collision times long compared to all characteristic times of internal motion, statistical models of complex formation, which assume S^{ D } to be zero, have been formulated. Although much experimental work can be classified with either of these extreme models, intermediate cases do occur. We examine a possible method for making quasistatistical (or partial statistical) approximations on S^{C} (for inelastic and reactive scattering), and indicate how well‐known statistical models can be modified with this method to describe quasistatistical behavior. The concept of doorway states provides another category of intermediate cases and is developed briefly. The classification of experimental results into the various categories (direct interaction, complete statistical complex, partial statistical complex, doorway states, and combinations of all of these) requires a number of different measurements. Possible deductions from the various experiments are discussed and examples of reactions for the different categories are cited.

Van der Waals Forces in Electrolytes
View Description Hide DescriptionThe continuum theory of van der Waals forces due to Lifshitz is extended to include the interaction between media which exhibit spatial as well as frequency dispersion. The case of electrolytes is considered in detail and the generalization of the theory to admit nonuniform equilibrium due to double layers is developed.

Intermolecular Potentials from Crossed Beam Differential Elastic Scattering Measurements. V. The Attractive Well of He_{2}
View Description Hide DescriptionThe van der Waals well of the helium pair potential has been studied by crossed molecular beamelasticscattering measurements. Low energy helium beams were produced by specially designed beamsources cooled with liquid hydrogen. Only five partial waves were found to contribute significantly to the differential cross section. A multiparameter potential function is used to construct the interatomic potential from experimental results. The potential parameters describing the location and depth of the attractive well are given by Å . The potential does not contain a bound state of zero angular momentum. Comparisons with other He_{2} potentials based on bulk properties and ab initio calculations are presented; the temperature dependence of the second virial coefficient is also discussed for the proposed potential.

Photoionization and Autoionization of H_{2}
View Description Hide DescriptionThe cross sections are calculated for direct photoionization and photoexcitedautoionization of H_{2} for light in the region 600–800 Å. Angular distributions of directly produced photoelectrons, lifetimes for vibrationally induced autoionization, some spectral assignments, and relative intensities of photoelectrons of various energies (from autoionizing states) are also given. The method by which the Rydberg and continuum state wavefunctions are derived is similar to the correlated pseudopotential method of Tully. The results indicate that correlation has only a small effect on the differential and total cross sections for photoionization. Agreement of theoretical and experimental lifetimes for autoionization is improved by the inclusion of correlation in the wavefunction. Critical tests of the calculations could be made by experimental study of the photoelectron spectra produced when H_{2} is excited to certain specific autoionizing states; for these states, the theory predicts anomalously efficient autoionization associated with transfer of two vibrational quanta into electronic excitation.

^{15}N Spin Lattice Relaxation in Liquid ^{15}NH_{3} and ^{15}ND_{3}
View Description Hide DescriptionThe spin‐lattice relaxation times (T _{1}) for ^{15}N in ^{15}NH_{3} and ^{14}ND_{3} have been determined and are presented and discussed. The magnitudes and temperature dependences of T _{1} for ^{15}NH_{3} and ^{15}ND_{3} indicate that spin‐rotational and intramolecular dipolar interactions together dominate the ^{15}N relaxation in ^{15}NH_{3}. Since , the dipolar term is small compared with the spin‐rotational term in ^{15}ND_{3} at room temperature. This allows one to separate the spin‐rotational and dipolar contributions in ^{15}NH_{3}. Values of τ_{ c }, τ_{sr}, and C _{N} are then derived from the experimental data for ^{15}NH_{3} and compared with values derived in other work.

Anisotropy of Nuclear Spin‐Spin Coupling in Methyl Fluoride
View Description Hide DescriptionEquations for indirect nuclear spin coupling tensors are developed within the framework of Hartree‐Fock perturbation theory. Calculated values for CF, CH, HF, and HH spin‐spin coupling anisotropies (pseudodipolar couplings) in methyl fluoride are compared with the results suggested by recent experimental work. An estimate of the importance of including pseudodipolar coupling in the determination of molecular geometry by NMR in liquid crystals is made.

Raman Spectrum of Antimony Pentafluoride in the Gaseous Phase as a Function of Temperature. Evidence for a Trigonal Bipyramidal Shape for the Monomeric Species
View Description Hide DescriptionThe gas phase Raman spectrum of antimony pentafluoride as a function of temperature shows clearly the dissociation of a polymeric species. The infrared spectrum of the gas (under conditions where the Raman spectrum shows no evidence for the presence of monomer) is closely similar to that of the liquid. This spectrum is also similar to that found in previous matrix isolation studies when monomer was thought to be present. It is likely that the earlier assignment of a C _{4v } shape to monomeric antimony pentafluoride is erroneous.

Absolute Total Scattering Cross Sections of
View Description Hide DescriptionThe absolute total scattering cross section was measured to an accuracy of 1%–2% over the relative velocity range , corresponding to relative energies of 0.03–0.5 eV. The absolute cross section determines the radial scale of the interatomic potential, by reference to the average distance between target molecules. The present study is intended as an exemplary system investigation of inferences that can be drawn from more accurate absolute total cross sections, since currently it is believed that this class of total cross section is known to an absolute accuracy of 5%–10% [R. B. Bernstein and J. T. Muckerman, Advan. Chem. Phys. 12, 414 (1967)]. The primary finding is the value of the interatomic potential with an accuracy of about 5% over a span of the relatively large interatomic distances 6–8 Å. At 7 Å the potential is . In this region half of the error arises from the systematic error in the cross section and half from the ambiguity about the proper potential model to apply. The results should be useful for critically testing future model potential calculations and, in conjunction with differential scattering and other data, for giving a more exact and complete understanding of the potential. An apparatus was used that had been previously applied to molecule‐atom scattering, where angular resolution corrections were negligible and where absolute pressures were measured with a McLeod gauge modified to physically eliminate trap pumping error. A deconvolution procedure that took into account the effects of target motion upon the glory structure of the total cross section was applied to the data. An economical method for applying nonlinear least squares fitting of model interatomic potentials is described and is applied to the data.

Viscosity of the Binary Gaseous Mixtures and in the Temperature Range 25–700°C
View Description Hide DescriptionThe paper presents new relative measurements of the viscosity of the binary mixtures and , as well as repeated determinations of the viscosity of the pure gases. The experiments were performed using an oscillating‐disk viscometer; they were made at atmospheric pressure and in the nominal temperature range 25–700°C. The accuracy of the measurements is one of at 25°C, deteriorating to at 700°C. Tables of the thermal conductivity of the monatomic‐gas mixture are provided together with values for pure nitrogen. The binary diffusion coefficients for the mixtures have also been computed.

Effects of Deviations from the Bethe Model on LEED Intensities for an Exactly Soluble One‐Dimensional Model
View Description Hide DescriptionThe effects of deviations from elasticscattering from perfectly periodic potentials on LEED intensities is investigated for an exactly soluble one‐dimensional model. The model consists of a perfectly periodic semi‐infinite substrate with delta function scatterers and a selvage consisting of a finite number of arbitrarily spaced delta functions of arbitrary scattering strength. Inelastic processes are included by means of a complex potential. Calculations are performed for the perfect crystal, the crystal with surface scatterers of different strength than in the bulk, variable lattice spacing near the surface, both localized inelastic scattering at the lattice sites and bulk inelastic processes, and combinations of these conditions. The results, which include shifting of the center and decrease in intensity of the Bragg peaks, symmetric and asymmetric broadening of the peaks and peaks not associated with Bragg reflection from the bulk, are discussed in terms of the wavefield of the incident electron in the crystal.

Nuclear Spin Polarization During the Photolysis of Di‐t‐buytl Ketone
View Description Hide DescriptionDi‐t‐butyl ketone photolyzes in perfluoromethylcyclohexane to give pivalaldehyde, isobutylene, and 2‐methylpropane which exhibit enhanced absorption and emission proton magnetic resonances as a result of nuclear spinpolarization. Upon addition of CCl_{4} to the solution, the proton spin polarization in 2‐methyl‐propane disappears whereas the other products including a new product, t‐butyl chloride, still exhibit the effect. Piperylene also prevents proton spin polarization in 2‐methylpropane. These results are consistent with a model in which nuclear spinpolarization occurs in radical pairs formed via dissociated radicals and via excited states of the ketone. Analysis of the spectra is presented in detail. For this purpose, the quantum yields for reaction from the excited states were obtained from fluorescence quenching experiments and reaction quenching data in the literature.

Investigation of Certain Auxiliary Functions Occurring in the Study of Molecular Integrals
View Description Hide DescriptionThe auxiliary functions introduced by Barnett and Coulson in their approach to many‐center integrals are related to the auxiliary functions A_{n} (p), B_{m} (pt) occurring in evaluations of overlap integrals in elliptical coordinates. The explicit formulas for Z functions in terms of the auxiliary functions A_{n} and B_{m} are given. They may provide the simplest way yet for obtaining numerical values of Coulson‐Barnett Z functions. In the case of Z functions of small indices, the overlap integrals involving unconventional Slater‐type orbitals arise. Z functions may be defined as particular overlap integrals. An application of this analysis leads to several relationships between different overlap integrals. In particular, when it is shown that not all overlap integrals are linearly independent. Similarly Coulomb, hybrid, and penetration integrals can be expressed in terms of selected overlap integrals. This was previously shown by Harris for Coulomb integrals only.

Vibrational Energy Transfer and De‐excitation in the HF, DF, , and Systems
View Description Hide DescriptionThe laser excited fluorescence method has been employed to determine the key rate constants for energy transfer and deactivation processes in the HF, DF, , and chemical laser systems at a temperature of 350°K. The self‐deactivation rates for HF and molecules by ground state molecules were found to be and , respectively. The measured rates of transfer from and to the CO_{2}(00^{0}1) state were and . The respective deactivation rates of CO_{2}(00^{0}1) by ground state HF and DF were determined to be and . The large rates for these processes can be attributed to energy transfer to rotation under the influence of a sizable attractive (hydrogen bonded) intermolecular potential well and enhanced repulsion at close range.

Absorption Spectrum of Matrix‐Isolated Ca Atoms
View Description Hide DescriptionThe absorption spectra of Ca atoms isolated in Ar, Kr, and Xe matrices at 16–20°K were obtained from 3000 to 7000 Å. In Kr and Xe matrices an asymmetric triplet was observed which was assigned to the transition. In concentrated Kr: Ca samples new low‐energy peaks appear which are assigned to well‐defined metal aggregates, probably Ca_{2}. The results for Ar: Ca could not be correlated with the other matrices, and it is suggested that atomic isolation was not attained in this matrix.

Torsion‐Vibration‐Rotation Interactions in Methanol. II. Microwave Spectrum of CD_{3}OD
View Description Hide DescriptionThe microwave spectrum of CD_{3}OD has been investigated in the 8–40 GHz region. Lines of the transition have been measured up to the fourth excited torsional state and fitted to Kivelson's semiempirical formula. The moments and product of inertia have been obtained, and the barrier height V _{3} determined to be 362.8 cm^{−1}.