Volume 59, Issue 10, 15 November 1973

Dissociative excitation of N_{2} by electron impact: Translational spectroscopy of long‐lived high‐Rydberg fragment atoms
View Description Hide DescriptionNitrogen atoms in long‐lived high‐Rydberg states have been produced in the dissociative excitation of N_{2} by electron impact. Four principal features were found in the time‐of‐flight distributions of the dissociation fragments and in the corresponding translational (kinetic) energy distributions. Appearance potentials and excitation functions were measured for high‐Rydberg atoms with known and well‐defined translational energies; for the slowest high‐Rydberg fragments the excitation function exhibits sharp, resonancelike structure near threshold. The core‐ion model of high‐Rydberg dissociation, which treats the Rydberg electron essentially as a spectator in the dissociation process, is described and used to interpret the data. Observed dissociation limits are assigned as one fragment being an N^{+}(^{3} P) core surrounded by a high‐Rydberg electron and the other fragment being a nitrogen atom or ion. In addition, the high‐Rydberg translational energy distributions are in reasonable qualitative agreement with kinetic energy distributions of N^{+} measured by dissociativeionization experiments. These observations provide substantial support for the core‐ion model. The available data on the dissociative core‐ion states of N_{2} ^{+} are discussed extensively. However, no unique assignments can be made for the molecular high‐Rydberg states which participate in the dissociation processes.

Phase‐space theory of electron detachment in slow atomic collisions
View Description Hide DescriptionA classical phase‐space theory for the excitation of electrons in slow atomic collisions is presented. An equation which governs the energy transfer between the electron and the heavy particles is derived for slow collisions (adiabatic approximation). This equation is analogous to the first law of thermodynamics for an open system. The theory contains only one adjustable parameter and gives excellent correlation for existing experimental measurements of detachment rate coefficients of F^{−} + (Ar, N_{2}, CO) and Br^{−} + Ar. Possible modifications to the present theory are summarized. It is anticipated that the theory should be applicable to other electronic rate processes such as ionization and charge transfer.

EPR studies of radiation damage in metal acetates: The hydrated lead (II) salt
View Description Hide DescriptionAn EPR study of x‐irradiated lead acetate trihydrate at 77 °K has strengthened the identification of two recently reported species, Pb^{1+} and PbH^{2+}. The first of these results from radiation‐induced electron trapping by coordinated Pb^{2+} ions, and the second center consists of a hydrogen atom that is weakly associated with a plumbous ion in the crystal lattice. The radical was also observed. A detailed study of the Pb^{1+} center reveals that the diagonal components of the ^{207}Pb hyperfine coupling tensor are very large and anisotropic, and that the characteristic gtensor is almost isotropic. These data are interpreted in terms of a bonding scheme that locates the unpaired electron in a hybridized molecular orbital that possesses 6s, 6p, and possibly some 5d, character. A comparison of our data for Pb^{1+} with published data for Pb^{3+} reveals striking differences.

Raman study of Fermi resonance, hydrogen bonding, and molecular reorientation in liquid ammonia
View Description Hide DescriptionThe Fermi resonance between the ν_{1} and 2ν_{4} bands in the polarized Raman spectrum of liquid ammonia was studied as a function of temperature. The resonance interaction was quantitatively analyzed at all temperatures through utilization of the coupled damped oscillator model. The results of this analysis furnish convincing evidence for reversal of the assignment of these bands from that most commonly assumed in the past. An analysis of the temperature dependence of the parameters obtained from the coupled oscillator model (linewidths, uncoupled peak frequencies, and the resonance interaction constant) showed all the results to be self‐consistent and in agreement with the behavior which has been found in other strongly hydrogen‐bonded systems. The polarized and depolarized linewidths of other bands in the spectrum were examined, and they, too, were found to be consistent, given the strong hydrogen bonding in liquid ammonia.

Measurements of relaxation cross sections for NH_{3} and OCS with a molecular beam maser spectrometer
View Description Hide DescriptionScattering cross sections for beams of NH_{3} and OCS are measured using a molecular beammaser spectrometer. The scattering gases used are NH_{3}, OCS, CF_{3}H, CH_{3}F, N_{2}, and He. In order to determine elastic and inelastic contributions to relaxation cross sections, measurements are made for (I) scattering of pure inversion or rotational state molecules, (II) scattering of molecules in a coherent superposition state, and (III) scattering of the whole beam in a distribution of rotational states. For dipolar scattering gases the cross sections for superposition states (σ_{II}) are significantly smaller than cross sections for pure states (σ_{I}). A theory of the scattering is presented in terms of phenomenological Redfield parameters and the S matrix. The theoretical description of scattering is used to separate elastic and inelastic contributions to the measured cross sections.

Molecular orbital investigation of chemisorption. I. Hydrogen on tungsten (100) surface
View Description Hide DescriptionThe relative bonding energies of hydrogen chemisorbed at three symmetric sites on a W(100) surface were obtained by means of the extended Hückel molecular orbital theory (EHMO). The preferred site for hydrogen chemisorption was found to be the single coordination number (1 CN) site or the site above a surfacetungsten atom. The W(100) surface was represented by finite arrays of tungsten atoms which were shown to be adequate for obtaining semiquantitative results. The basis set for the calculations contained the valence orbitals of tungsten and, initially, the 5p orbitals which were nonbonding but provided the necessary repulsion at small internuclear separation. The repulsive energy provided by these orbitals was replaced by an analytical exponential repulsive energy term. This allowed the 5p orbitals to be omitted from the basis set to simplify computation. Functionally, the energy change for the reaction W _{n} + H → W _{n} H was calculated for various assumed configurations of the W _{n} H ``molecule.'' The bonding between tungsten atoms was found to be changed as a result of W _{n} H formation, and the change varied with hydrogen position. Energy barriers to surfacediffusion were also calculated and found to agree reasonably with experimental values.

Theoretical study of spectroscopic properties. II. The 2p π_{u} electronic state
View Description Hide DescriptionVibration‐rotation eigenenergies are computed for the (2pπ_{u} ) ^{2}Π _{u} state of . Spectroscopic constants Y_{ij} are found from Dunham power series expansions of the vibrational potential and also from the eigenenergies. The Y_{ij} are much smaller in magnitude than ground state values because of the 2p π_{u} broadened potential and larger equilibrium separation r_{e} . The eigenenergies are used to determine B _{ν}, D _{ν}, and H _{ν} for all bound vibrational states, i.e., for 0 ≤ ν ≤ 11. Both the ΔG and B _{ν} curves have negative curvature at all ν. The D _{ν} and H _{ν} curves are similar in shape to the respective curves for the ground state. The D _{ν}'s decrease slowly at low ν but increase rapidly near dissociation. The H _{ν} curve has a small negative initial slope; the H _{ν}'s decrease very rapidly, becoming negative, at high ν. Origin wavelengths are listed for a few 2p π_{u} −1sσ _{g} bands predicted to be intense on the basis of the classical Franck‐Condon principle; these lie in the Lyman α region.

Theoretical study of spectroscopic properties. III. The 3d σ_{g} electronic state
View Description Hide DescriptionNumerical integration of the Schrödinger equation is used to determine vibration‐rotation eigenvalues for the state of up to ν = 58. Dunham power series expansions are used to determine the equilibrium separation r_{e} , potential coefficients a_{n} , and spectroscopic constants Y_{ij} . The eigenvalues are used to determine ΔG, B _{ν} D _{ν}, and H _{ν}. The ΔG and B _{ν} curves have positive curvatures at low and high ν and negative curvatures at intermediate ν; points of inflection for both curves are at very nearly the same values of ν. The D _{ν} curve is qualitatively similar to those for 1s σ_{g} and 2p π_{u} up to ν = 25; above ν = 30 the 3d σ_{g} D _{ν}'s reach a maximum and then apparently tend to zero as ν → ∞. As ν approaches 25, H _{ν} values appear to be heading negative; with further increase in ν the H _{ν}'s rise sharply and then appear to go to 0 as ν→∞.

Accurate dissociation energies from rotational predissociation and long‐range forces: B ^{1}Π LiH
View Description Hide DescriptionA new approach for determination of accurate dissociation energies from experimental predissociation data and the calculated long‐range potential is described. In this case long‐range predissociation in the rotational manifold of only a single vibrational level is required to yield a precise dissociation limit. The case of B ^{1}Π LiH is considered in detail and a dissociation limit of 34 492.5 ± 0.5 cm^{−1} is obtained, 2.5 cm^{−1} lower and 4 times more precise than the best previous result. Also presented is a reasonably good representation of the potential energy curve for the B ^{1}Π LiH molecule, constructed by an isotopically combined Rydberg‐Klein‐Rees method based on the concept of mass‐reduced quantum numbers: and ξ≡J(J + 1)/μ.

Generalized hydrodynamics and the depolarized Rayleigh doublet in anisaldehyde
View Description Hide DescriptionHigh resolution depolarized Rayleigh light scatteringspectra of anisaldehyde (4‐methoxybenzaldehyde) at several temperatures are presented. The depolarized q dependent doublet is well resolved at temperatures > 20 °C and disappears as temperature is lowered. Over the temperature range studied (6–79 °C) the value of q ^{2}η/ρΓ_{22} varies from 0.04 to 1.5. All spectra are found to fit well the form predicted by a ``two‐variable'' theory in the low frequency regions studied. It is furthermore concluded on the basis of physical intuition and our previous work on solutions that the spatial Fourier transforms of the transverse velocity density and the second rank orientation tensor density are the appropriate variables.

Depolarized Rayleigh scattering and orientational relaxation of molecules in solution. II Chloroform and nitrobenzene
View Description Hide DescriptionMeasurements of orientational relaxation times of chloroform and nitrobenzene in a variety of solvents have been made by depolarized light scattering. At constant concentration a plot of reorientational relaxation time of nitrobenzene versus solution viscosity was found to fit a straight line with nonzero intercept. The reorientational relaxation time of both solutes increased with increasing solute concentration (at constant viscosity). For nitrobenzene and chloroform, plots of the reorientational relaxation time versus solute concentration were linear. This concentration dependence is attributed predominantly to pair correlations. The ``static'' correlation parameter f and the ``dynamic'' correlation parameter g are determined for both chloroform and nitrobenzene. The carbon‐13 spin‐lattice relaxation time (T _{1}) for both solutes in solution has also been determined. The reorientational relaxation time of chloroform determined by NMR agrees well with the reorientational relaxation time determined by depolarized light scattering extrapolated to zero solute concentration.

Depolarized Rayleigh scattering and orientational relaxation of molecules in solution. III Carboxylic acids
View Description Hide DescriptionDepolarized Rayleigh linewidths have been measured for several carboxylic acids dissolved in carbon tetrachloride and water. The correlation times derived from the spectra are determined mainly by over‐all molecular reorientation and are relatively insensitive to molecular internal rotations and changes in chemical state. The dependence of the reorientational correlation times on intermolecular interactions such as hydrogen bonding and chemical effects such as dimerization is studied. It has also been found that the polarized and depolarized Rayleigh spectra are insensitive to the rate of the reaction CF_{3}COOH⇄CF_{3}COO^{−} + H^{+} in aqueous solutions of CF_{3}COOH.

Scattering of fast potassium ions by small molecules
View Description Hide DescriptionMeasurements have been made of the effective total cross sections for the scattering of potassium ions with energies between 100 and 2350 eV by room temperature O_{2}, N_{2}, CO, NO, CO_{2}, and N_{2}O. The repulsive interaction potentials were deduced from the energy dependence of the cross sections using both the inverse power and exponential representations of the potential function. The results appear to be self‐consistent, indicating no measurable difference between the potentials for K^{+} interacting with O_{2}, N_{2}, NO, or CO, or between the potentials for K^{+} interacting with CO_{2} or N_{2}O. Where it is possible to compare with other work, significant differences are found, as happened previously in reports of potentials of K^{+} interacting with several rare gas atoms. The potentials were compared to those determined in this laboratory by scattering argon beams with the same molecules and the potentials for the two isoelectronic systems were found, in all cases studied, to be essentially identical and actually cross in the energy range studied.

Experimental interaction dipoles for the rare gases
View Description Hide DescriptionInteraction dipoles for He–Ar, He–Kr, He–Xe, Ne–Ar, Ne–Kr, Ne–Xe, Ar–Kr, and Ar–Xe were determined by adjusting the parameters of flexible dipole moment functions to reproduce the experimental collision‐induced translational spectra. The present limitations of this approach to interaction dipoles — which to date is the only experimental one available — are discussed.

Computer study of the collective modes of a one dimensional disordered chain
View Description Hide DescriptionIt is found, on the basis of molecular dynamics experiments, that the density fluctuation of wavenumber k, in a one dimensional disordered chain of Lennard‐Jones rods, decays like a damped cosine with frequency ω_{ k } and lifetime τ_{ k } such that the dispersion relation ω = ω_{ k } is very similar to that of an harmonic chain and that τ_{ k } goes as k ^{−1/3} at small k. This latter observation is shown to be consistent with the conjecture that the single particle velocity autocorrelation function behaves asymptotically as t ^{−3}. It is concluded that the Lennard‐Jones chain does not display a hydrodynamic decay.

Model for calculating spin‐orbit interactions with applications to photoelectron spectroscopy
View Description Hide DescriptionA semiempiricalmodel has been developed for estimating spin‐orbit interactions in molecular ion states derived by ionization of closed‐shell neutral molecule states. A perturbation approach is used with an effective spin‐orbit interaction operator H _{so} and approximate Mulliken‐Wolfsberg‐Helmholz molecular orbital (MO) wavefunctions. Effective spin‐orbit parameters ζ_{ v } were obtained by interpolation with respect to atomic charges derived from the MO calculations. The He I photoelectron spectra of the PX_{3}(X = Cl, Br, I) and PYX_{3}(X = Cl, Br; Y = O, S) series have been measured. Splittings observed in some of the ionization bands of this series have been successfully interpretated as spin‐orbit splittings using the newly developed model.

NMR in the quadrupole regime: Polycrystalline spectra
View Description Hide DescriptionNMR in the quadrupole regime for a spin I = 3/2 nucleus involves the transition between the two lowest levels of the nucleus in a strong electric field gradient and an applied magnetic field. The exact theory of the frequency of this transition in the presence of quadrupolar asymmetry and anisotropic chemical shift was presented in earlier papers, in conjunction with experimental results on single crystal samples. This paper studies application of this method to polycrystalline specimens. Perturbation expressions are used to derive the resonant intensity distribution (powder pattern), while histographic techniques are used in the presence of quadrupolar asymmetry (η ≠ 0). The powder pattern is widely distributed over frequency, exhibiting three distinct features (a singularity and two edges), each of which is shown to arise from crystallites whose field gradient tensors have specific orientations with respect to the applied field. Exact theory is easily applied to a study of the field dependence of the transition frequency of each feature. Only two of the aforementioned features were observed in our experiments on powdered paradibromobenzene. The precisely known pure quadrupole transition frequency for this substance was used to increase the precision of the determination of η and of σ_{ x } and σ_{ y }, two components of the chemical shift. For practical reasons related to the small magnitude of η in paradibromobenzene, the interpretation of the field dependences of the two observed features could not yield η, σ_{ x }, and σ_{ y } independently. The results of this experiment are consistent with earlier work on single crystal specimens, particularly with concurrent work in which η, σ_{ x }, σ_{ y }, and σ_{ z } were independently determined.

Three‐state computer calculation of chemi‐ionization in oxygen‐alkali collisions
View Description Hide DescriptionA model of three coupled states, based on the (pseudo) crossing of molecular potential curves, has been applied to the process of chemi‐ionization (ion‐pair formation) for oxygen atoms colliding with Na, K, Rb, or Cs. The semiclassical impact parameter method has been employed in the calculation of total and differential cross sections for oxygen kinetic energies of from 300 eV to 10 keV. It is shown that rotational coupling of the magnetic substates is of considerable importance.

Classical phase space description of rotationally inelastic scattering
View Description Hide DescriptionThis article is concerned with establishing a general formalism for rotationally inelastic scattering. The method for achieving this is within the scope of the Prigogine‐Résibois formalism, as recently applied by Miles and Dahler, and Eu. The starting point is the Liouville equation of motion for the two‐body system comprised of a linear rotor and a structureless particle. Many parallelisms with quantum scattering theory encountered by these authors, such as evolution operators for handling the time development of the system, the Lippmann‐Schwinger equation for governing the steady‐state distribution, and the optical theorem continue to appear also in this investigation. In addition, there arise here for consideration some new features, such as polarizations, and correlations in the orientation and angular momentum, which have their origins in the internal degrees of freedom of the rotor. Finally, a perturbation type of solution for the distribution function is set up, and expressions for transition probabilities and cross sections are obtained.

Rotationally inelastic molecular scattering. Computational tests of some simple solutions of the strong coupling problem
View Description Hide DescriptionPartial cross sections (opacity functions) for rotational transitions in atom‐diatom collisions are computed in the infinite‐order sudden (IOS) approximation and compared with accurate close‐coupling (CC) calculations. Agreement is good in the dominant coupling (small total angular momentumJ) region. Simple methods for calculating integral inelastic cross sections are discussed, and it is found that accurate cross sections can often be computed very simply, even when large numbers of channels are coupled together, by using IOS or first‐order sudden (FOS) approximations for small J and CC or exponential Born (EBDW) methods for large J.