Volume 59, Issue 9, 01 November 1973

Photoionization yields in N_{2} in the band series from 734 to 796 Å
View Description Hide DescriptionPhotoionization yields in the band series in N_{2} from 734 to 796 Å are computed using the narrow bandwidth (Δλ = 0.04 Å) photoabsorption cross sections of Carter and the relative photoionization cross sections of Berkowitz and Chupka (Δλ = 0.12 Å). The relative data are normalized to photoionization cross section data of Samson and Cairns. The results presented for the Ogawa‐Tanaka Rydberg series and Worley's third Rydberg series are in substantial agreement with the 0.2 Å bandwidth work of Cook and Ogawa although new data at higher principal quantum numbers (m = 7, 8, 9) are presented. Photoionization yields in the four Ogawa progressions are also reported. Even with less peak overlapping at higher resolution the underlying continuum appears to have an ionization yield less than unity. This result is in accord with findings in other simple diatomic molecules.

On the problem of the vibrational spectrum and structure of ice Ih: Lattice dynamical calculations
View Description Hide DescriptionIt is experimentally known that ice Ih is orientationally disordered. The vibrational spectrum has been previously interpreted by other authors in terms of a simplified point mass model. On the basis of this model long‐range forces, spectral activation by the disorder, fluctuating ordered polar domains, etc., were proposed. We present in this paper the results of a lattice dynamical treatment on a complete ordered model of ice Ih which includes the hydrogen atoms. A valence force field has been derived from optical and neutron spectra of H_{2}O and D_{2}O. The introduction of all the vibrational degrees of freedom and their possible interactions does affect the interpretation of the spectrum and the derived spectral conclusions. The interpretations of the spectral evidences on which the previous works were based are discussed.

Theoretical studies of the interaction of MgF_{2} with rare gas atoms
View Description Hide DescriptionNonempirical self‐consistent field wavefunctions have been used to obtain the dipole moment of MgF_{2} as a function of bond angle. These dipole moments have been used to determine the dipole‐induced‐dipole interaction between various rare gas atoms and MgF_{2} for several F–Mg–F bond angles. These calculations predict that the dipole‐induced‐dipole interaction between MgF_{2} and argon, krypton, or xenon is sufficient to distort MgF_{2} from a linear configuration. This suggests a plausible explanation for the difference between the geometry of MgF_{2} in the gas phase and in krypton matrices.

Absence of a host‐crystal deuterium effect on the phosphorescence lifetime of naphthalene
View Description Hide DescriptionPhosphorescence lifetimes have been measured for naphthalene and naphthalene‐d _{8} in benzene, benzene‐d _{6}, benzophenone, and benzophenone‐d _{10} host crystals at temperatures from 4 to 275°K. Within experimental error, there is no evidence for an intermolecular host‐crystal deuterium effect on the phosphorescence lifetime of naphthalene or naphthalene‐d _{8}. At the higher temperatures studied the naphthalene phosphorescence is weakened and the lifetime is shortened, yet there is no evidence for nonexponential decay or delayed fluorescence.

Kinetics and mechanism of the reaction of hydrogen and deuterium atoms with benzene and benzene‐d _{6}
View Description Hide DescriptionThe kinetics of the gas phase reactions of H (and D) atoms with benzene were investigated using fast flow techniques. Specific rate constants were obtained using two separate systems, one with ESR detection to monitor the decrease in atomic reactants and the other with mass spectrometry to follow the change in benzene concentration. The results from these two systems are in essential agreement with one another when discussed in the light of the proposed reaction mechanisms. The mass spectrometric studies lead to a recommended specific rate constant of (5.7 ± 1.0) × 10^{10} cm^{3} mole^{−1} · sec^{−1} at 300°K for the H+C_{6}H_{6}reaction. The activation energies for the D and H atom reactions with C_{6}H_{6} are equal, within experimental error, with the value of 2.70 ± 0.20 kcal/mole reported. For reasons discussed in this paper, it is concluded that this activation energy refers to the addition of the atomic reactant to the benzene ring. Since isotopic exchange reactions have been observed in these systems, the over‐all rate of the D+C_{6}H_{6}reaction obtained from the ESR studies is higher than the rate obtained mass spectrometrically for the H + C_{6}H_{6}reaction. Competitive experiments using C_{6}H_{6}/C_{6}D_{6} mixtures in reactions with H and D atoms revealed the absence of any primary kinetic isotope effect on reaction rates. Thus the rate determining step does not involve hydrogen (or deuterium) atom abstraction from the benzene ring. From the products observed mass spectrometrically, it is clear that the reaction of hydrogen atoms with benzene is an over‐all complex process and must include reactions leading to (a) isotopic exchange, (b) net addition to the benzene ring leading ultimately to cyclohexane formation, and (c) some cracking of the benzene ring with formation of C_{2}H_{6} and CH_{4} as well as probable other low‐molecular weight saturated molecules.

Sequential adsorption of D_{2} and C_{2}H_{4} on single‐crystal planes of tungsten
View Description Hide DescriptionThe sequential adsorption of deuterium and ethylene has been studied on the (110), (100), (112), and (111) planes of tungsten at [inverted lazy s] 135°K using thermal desorptionmass spectroscopy.Adsorption of D_{2} followed by C_{2}H_{4} on both the (110) and (112) planes, respectively, leads to 0.24 and 0.37 monolayers of ethylene adsorbed with no displacement of deuterium for an ethylene exposure which would just be sufficient to saturate a bare surface. Since the resulting spectra are apparently superpositions of ethylene decomposition and deuterium desorption, it appears that ethylene and deuterium in part occupy separate sites. On both the (100) and (111) planes adsorption of ethylene occurs through displacement of 1.3 molecules of deuterium for each molecule of ethylene adsorbed. This displacement is more extensive on the (111) plane: θ _{C2H4 }=0.86 and θ _{D2 }=0.36 on the (111) plane vs θ_{C2H4 }=0.52 and θ_{D2 }=0.67 on the (100) plane. Displacement on the (100) plane occurs through adsorption of ethylene on sites separate from deuterium with the ethylene perturbing deuterium sufficiently to lead to desorption. Arguments are given for this interaction being relatively short range. On the (111) plane hydrogen displacement is a thermal process with both D_{2} displaced by C_{2}H_{4} and H_{2} by D_{2}. The D_{2} is able to displace an amount of H_{2} corresponding to all the β_{1} and β_{2} states and [inverted lazy s] 3/4 of the β_{3} state. The extent of this displacement indicates that there is extensive interchange between the β states on W(111). Previous data for the sequential adsorption of D_{2} and C_{2}H_{4} on polycrystallinetungsten were interpreted as a composite of contributions from individual planes with specifically the (100) plane contributing a high C_{2}H_{4}:D_{2} ratio and the (110) plane a low C_{2}H_{4}:D_{2} ratio. The single‐crystal results are shown to be in agreement with this. If we assume the polycrystalline surface was partially carbon contaminated, both the spectra and the coverages resulting from sequential adsorption of D_{2} and C_{2}H_{4} and the ethylene decomposition spectrum, can be reconstructed using a reasonable linear combination of the results from these four planes.

Rotational motion of molecules and neutron scattering
View Description Hide DescriptionThe differential neutron scattering cross section for scattering from a rigid rotating molecule in a general isotropic medium (condensed or gas state of matter) is presented. It is based on a model, which assumes the complete rotational motion to consist of a damped form of free rotations and of damped librations, respectively. The two phases of rotation are assumed to be coupled to microscopic density fluctuations in the medium in such a way that densities larger than the average allow only damped librations, whereas densities lower than the average allow only damped rotations. The cross section is derived with the aid of a step function formalism first used by Singwi and Sjölander. Further, use is made of Sears' earlier work on rotational scattering cross sections. The resulting cross section describes the molecular motions in a range of conditions from free rotations to undamped libration including all possible intermediate damped motions. The model differs from those created earlier insofar as the rotational diffusion is not necessarily described as a motion consisting of free rotations over smaller or larger angles interrupted by brief collisions. The collisions may in the present model be replaced by shorter or longer periods of libration. Numerical calculations of the Fourier transform,S _{1}(ω), of the first rotational relaxation function, F _{1}(t), is performed using explicit models for the librational and rotational relaxation functions and for such a choice of numerical constants, that the results should describe various hypothetical rotational motions of the methane molecule.

On non‐RRKM unimolecular kinetics: Molecules in general, and CH_{3}NC in particular
View Description Hide DescriptionMonte Carlo rate constants for model CH_{3}NC isomerization, determined at 200, 100, and 70 kcal/mole, disagree with theoretical predictions. Also, three different approximate methods of generating initial conditions at 200 kcal lead to divergent results. The molecule does not appear to us to obey the random lifetime assumption of conventional unimolecular rate theory at any of these energies. A discussion is given of the systematics of this kind of effect, and comments are made on the relationship between our results and those obtained in the laboratory.

Naphthalene‐d _{8} phosphorescence in pressure‐perturbed media at 77 °K
View Description Hide DescriptionThe phosphorescence spectrum and triplet lifetime of naphthalene‐d _{8} have been measured as a function of pressure (1 atm‐35 kbar) at 77 °K in five matrices: poly(methylmethacrylate), EPA, perfluoromethylcyclohexane, pentane, and benzophenone. Compression of these matrices results in strong spectral broadening which is attributed to increased solvent inhomogeneity and enhanced coupling with the lattice. The pressure‐induced shift in the triplet energy is sensitive to the detailed interactions of host molecules with the solute molecule, and provides qualitative attitudes about the various types of interactions responsible for solvent perturbations of electronic processes.

Use of biorthogonal orbitals in calculation by perturbation of molecular interactions
View Description Hide DescriptionA Rayleigh‐Schrödinger type of perturbation expansion, using a partition of the Hamiltonian into non‐Hermitian parts, and biorthogonal orbitals, is developed to study excited molecular states. In particular an expansion of the molecular interactions is defined in which all intramolecular terms cancel exactly.

PMR spectra of the 4‐alkylnitrobenzenes
View Description Hide DescriptionEvidence of first‐order alkyl‐ring proton coupling is reported for the 4‐alkylnitrobenzenes. Typical coupling constants of 0.7 Hz and 0.3 Hz were found for α‐alkyl coupling with the ortho and meta ring protons, respectively, when the alkyl function was methyl, ethyl, and isopropyl. No β‐alkyl coupling with ring protons was observed for the ethyl, isopropyl, or t‐butyl groups, suggesting that the magnitude of the coupling constant is vanishingly small.

Measurement of the rate coefficient of the reactions H^{+} + 2H_{2} → H_{3} ^{+} + H_{2} and D^{+} + 2D_{2} → D_{3} ^{+} + D_{2} in a drift tube mass spectrometer
View Description Hide DescriptionThe rate coefficient of the reaction H^{+} + 2H_{2} → H_{3} ^{+} + H_{2} has been measured at a gas temperature of 300 °K and over a pressure range 0.25–0.50 torr. The transport properties and average energy of a given species of ion drifting in a gas in a uniform electric field are determined by E/N, where E is the electric field intensity and N is the gas number density.E/N is expressed in units of the townsend (Td), where 1 Td = 10^{−17} V · cm^{2}. Our measurements were made over a range 25–50 Td, where the lower value corresponds to an average energy for the reacting H^{+} ions which is very close to the thermal energy of the H_{2} molecules at 300 °K. No systematic variation of the rate coefficient was observed over the range of E/N which was covered. The measurements were made with a drift tube mass spectrometer and involved the detailed analysis of the arrival time spectra of the product ion. The rate coefficient was evaluated to be (3.05 ± 0.15) × 10^{−29} cm^{6}/sec. The same result was also obtained for the reaction D^{+} + 2D_{2} → D_{3} ^{+} + D_{2}.

Magnetothermodynamics of gadolinium gallium garnet. I. Heat capacity, entropy, magnetic moment from 0.5 to 4.2 °K, with fields to 90 kG along the [100] axis
View Description Hide DescriptionThe magnetic moment of a 2.44 cm diam spherical single crystal of gadoliniumgalliumgarnet has been measured with stabilized fields of 500, 1000, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G along the [100] axis, over the range 0.35 to 4.2 °K. The heat capacity was measured over similar ranges, except that 500 G was omitted and zero field included. The magnetic moment reached saturation at 0.35 °K and 90 000 G. The electronic and nuclear spin components of the heat capacity at 90 000 G could be separated from each other near 1 °K, thus locating a zero of entropy for the electronic system. By means of 34 adiabatics, corrected to isentropes, which crossed most of the isoerstedic heat capacity series, the entropies as a function of field and temperature were evaluated in terms of the zero reference. The sample has (0.4 ± 0.1) mole% excess entropy over the maximum R ln 8 for Gd^{3+} ion. Thus the sample must have contained 0.4 mole% excess Gd over the stoichiometric amount for Gd_{3}Ga_{5}O_{12}. Using the correction factor 0.9960, the saturation value for Gd_{3}Ga_{5}O_{12} is found to be 39 095 G · cm^{3}/mole Gd^{3+}. This corresponds to a g = 2.000 ± 0.002. Smoothed correlated values of the heat capacity,entropy, enthalpy, internal energy, magnetic moment, and its differential isoerstedic temperature coefficient, differential isothermal magnetic susceptibility, and the isothermal work of magnetization have been tabulated over the ranges 0–90 kG and 0.5–4.2 °K.

Characterization of inverted populations in chemical lasers by temperaturelike distributions: Gain characteristics in the F + H_{2} → HF + H system
View Description Hide DescriptionWith the aid of the temperature parameters characterizing product state distributions in a number of chemical reactions, frequently used concepts in chemical laser studies can be expressed in a compact form. The assumption of a rotational‐translational microcanonical equilibrium in the product atom‐diatom system leads to simple expressions for population inversions and gain factors. (However, the equilibrium assumption is not necessary; the expressions will retain their simple form also when the vib‐rotational distributions are more specific.) The main advantage is that of using only one or two parameters instead of different vibrational and rotational temperatures for every transition. Two special situations are considered in detail: (a) a nonrelaxed initial product population and (b) a vibrationally nonrelaxed but rotationally thermal population. As a specific example, the HF laser with F + H_{2} → HF + H as the pumpingreaction is studied. Rate equations governing the emission of different laser transitions are solved. In the solution, cascading and pumping effects are considered but not rotational or vibrational relaxation. The detailed rate constants of HF formation in different vib‐rotational levels used in the calculation are those which lead to equipartition (microcanonical equilibrium) of rotational and translational energies. Comparison with experimental results indicates that the model calculations are in agreement with some chemical laser and trajectory studies which show initial population peaked at some high rotational states. The chemiluminescence measurements for low reagents energies show relatively lower peaks.

Ring‐puckering vibration of μ‐aminodiborane
View Description Hide DescriptionThe ring‐puckering vibrations of μ‐aminodiborane and ND_{2}–B_{2}H_{5}, NH_{2}–B_{2}D_{5}, and ND_{2}–B_{2}D_{5} have been investigated. The 0 → 1 transitions are assigned to the Q branches at the frequencies 337.6, 333.6, 244.6, and 243 cm^{−1}, respectively. The potential function for this vibration is V(Z) = 8.695 × 10^{5} Z ^{4} + 6.859 × 10^{4} Z ^{2} (cm^{−1}), where Z is the displacement coordinate in angstroms. Inclusion of terms in the kinetic energy to account for the dependence of the reduced mass on coordinate suggests that the vibration involves equal bending about the diagonals in the ring‐hydrogen analogs and bending about the B‐B diagonal in ring‐deuterium molecules. The concept of torsional‐strain energy in ring molecules is introduced.

Vibrational circular dichroism observed in crystalline α‐NiSO_{4} · 6H_{2}O and α‐ZnSeO_{4} · 6H_{2}O between 1900 and 5000 cm^{−1}
View Description Hide DescriptionAxial circular dichroism (CD) of crystalline α‐NiSO_{4} · 6H_{2}O and α‐ZnSeO_{4} · 6H_{2}O is measured between 1900 and 5000 cm^{−1} at room temperature. Three CD bands with rotational strengths of 7 × 10^{−44}, 3 × 10^{−44}, and 1 × 10^{−42} erg · cm^{3} per molecule of water are observed at 5000, 4050, and 2300 cm^{−1}, respectively, in α‐NiSO_{4} · 6H_{2}O. These CD bands are due to combination bands of H_{2}O vibrations in the crystals. Substitution of H_{2}O with D_{2}O on α‐NiSO_{4} · 6H_{2}O shifts the 5000 cm^{−1} band to a frequency lower by the expected factor of . The 5000 and 4050 cm^{−1} CD bands are also observed in α‐ZnSeO_{4} · 6H_{2}O with the same intensities as in α‐NiSO_{4} · 6H_{2}O. Their positions are, however, shifted by 50 cm^{−1} toward higher energy. Due to strong absorption, the CD of fundamental vibrational modes of H_{2}O in the crystals could not be measured. The CD is interpreted as a consequence of the linear k dependence of the effective charge of E mode optical phonons near k = 0.

Absorption of ultrasound in liquid NH_{3} and ND_{3}
View Description Hide DescriptionData on the absorption of ultrasound in liquid NH_{3} and ND_{3} as a function of frequency and temperature are presented. These data indicate that the absorption is both frequency and temperature independent for frequencies above 30 MHz at a value two times the classical value. There is a relaxation occurring at the lower frequencies indicated by an increase in the absorption coefficient as the frequency is lowered. This is interpreted to be a thermal relaxation and not a structural relaxation, which is what might be expected for an associated liquid such as NH_{3}.

Quantum mechanical first Born binary encounter theory of electron impact ionization. II Electron Compton scattering
View Description Hide DescriptionThe first Born binary encounter theory of electron Compton scattering is developed. The theory includes the relationship between the usual x‐ray Compton profile and its electron scattering counterpart including corrections for scattering from pairs of target electrons (a correction also necessary in the x‐ray case at small scattering angles) and for exchange and interference scattering. In addition correction terms are derived for the difference between the complete first Born treatment and the binary encounter model. The corrections in the angular range of 10°–60° at an incident electron energy of 25 keV are shown to be negligible. The target electron pair corrections at an incident electron energy of 25 keV are important only for small angle scattering for the lighter elements (< 7° for He) but may extend to larger angles for the heavier elements (< 30° for Ar). Exchange and interference between exchange and direct scattering become significant at the 1% accuracy level at a scattering angle of 4° at the same incident energy. Between 4° and 45° interference between the exchange and direct amplitude dominates the correction term which can amount to 25% of the direct scattering contribution at 35° although it largely vanishes at 45°. Beyond 45° the pure exchange terms rapidly dominate the scattering with increasing angle, and relativistic corrections become increasingly important. In this region the theory can break down and it is suggested that accurate experimental data could be helpful in arriving at a detailed description of the exchange process. A definition for an electron Compton profile including exchange and interference corrections from which the one‐electron target momentum density can be extracted is suggested. The theory is also compared with recent experimental work for the case of He, and predictions for the scattered electron intensity as a function of energy loss and scattering angle are made for He at an incident electron energy of 25 keV.

Theory of inelastic collision: Extension to multiple turning point problems of uniform WKB theory
View Description Hide DescriptionThe uniform WKB theory developed in the previous papers of this series is extended so as to deal with cases of multiple turning point problems. It is found that the results of the previous studies are in general usable piecewise with appropriate initial conditions and reference equations in each interval. Two‐ and three‐turning point problems occurring in two‐channel inelastic collision processes are specifically dealt with in this paper.

Cluster expansions for hydrogen‐bonded fluids. I. Molecular association in dilute gases
View Description Hide DescriptionThe cluster expansion method of Mayer is formulated in a way that is convenient for calculating the equilibrium pair correlation function of hydrogen‐bonded fluids. The topological properties of cluster diagrams for these fluids is investigated, and a cancellation theorem is presented which permits the neglect of certain types of diagrams in these cluster expansions. A method is presented for renormalizing the hydrogen bond in such expansions, and a technique for summing the graphs which define the renormalized hydrogen bond is discussed. The present paper deals only with low density gases, and future work will extend the results to dense liquids.