Volume 67, Issue 2, 15 July 1977
Index of content:

Ionization reactions of metal hexafluorides with alkali atoms and dimers
View Description Hide DescriptionIonizationreactions are observed in crossed beams, usually of thermal energy, of alkalis and MoF_{6}, WF_{6}, and UF_{6}. Previous studies have indicated large electron affinities for these hexafluorides, and this is confirmed here. Ionization at thermal energies proceeds with the alkali dimers A_{2} for the three hexafluorides, but with alkali atoms A only for UF_{6}. Several ionization paths are observed, allowing the deduction of molecular energies. A few experiments are done with eV‐range beams. Lower limits for the electron affinities are 4.5, 3.3, 4.9, 4.3, and 1.9 eV for MoF_{6}, MoF_{5}, WF_{6}, UF_{6}, and UF_{5}, respectively. Possible mechanisms are discussed.

Calculations of magnetic susceptibility of polyatomic molecules
View Description Hide DescriptionThe magnetic susceptibility of H_{2}O, NH_{3}, and CH_{4} molecules has been evaluated within the framework of coupled and uncoupled Hartree–Fock perturbation theories for the Fock–Dirac density matrix, employing several basis sets of gaugeless Gaussian functions. The results provided by the largest basis sets are in good agreement with experiment as well as with other a b i n i t i o calculations. Quantities necessary to assess the degree of gauge independence of the susceptibility and to evaluate this property for an arbitrary gauge origin are also reported. The reliability of the uncoupled approach suggested here is systematically analyzed by investigating the upper bounds to the error affecting the geometric approximation to the paramagnetic susceptibility. The results demonstrate the practicality of the simple and inexpensive uncoupled scheme with respect to the cumbersome coupled method.

Excess electrons in condensed media. A model for migration in dilute molecular solutions
View Description Hide DescriptionA theoretical framework is developed for analyzing the migration of excess electrons in one‐component molecular solids and liquids. The mean‐square distance traveled by an electron as a function of time 〈r ^{2}〉_{ t } is shown to depend both upon the diffusion of the solvent molecules and the rate of hopping and tunneling of the electron from one molecule to another. By introducing several physically motivated approximations, the quantities appearing in the final expression for 〈r ^{2}〉_{ t } are expressed in terms of solvent structure information (distribution function) and the electron–solvent interaction potential. Planned extensions of this initial work are also discussed.

Light scattering from orientational and density fluctuations in liquid 1,2,5‐thiadiazole
View Description Hide DescriptionThe orientational and density fluctuation spectra of liquid 1,2,5‐thiadiazole were determined by the light scattering technique. The viscosity and density of the pure liquid were also measured as a function of temperature. Results of concentration dependent studies of 1,2,5‐thiadiazole in an optically isotropic solvent having the same viscosity as the pure liquid show that the pair orientational correlation is very small. The experimentally determined reorientational relaxation times were found to be close to the prediction of the slip model for rotational diffusion. The sound velocity of the pure liquid was found to decrease linearly with increasing temperature. The sound dispersion was found negligible in the GHz frequency region.

A spectral analysis method of obtaining molecular spectra from classical trajectories
View Description Hide DescriptionVibrational classical trajectories of anharmonic molecules are used here to obtain the classical vibrational autocorrelation function and, via a Fourier transform, the power (or infrared) spectrum of the dynamical variables. In the vibrationally quasiperiodic regime the spectrum consists of sharp lines, for any given initial amplitude. The initial amplitudes are chosen semiclassically. The spectral lines are compared with quantum mechanical calculations for systems with two and three coordinates, with excellent agreement. The method is also useful for obtaining a classical spectrum in the ergodic regime; the spectral lines are then ’’broad’’ rather than narrow. The method can be used in the analysis of trajectories for unimolecular reactions, infrared multiphoton dissociations, and for obtaining molecular spectra from force fields. The spectralanalysis itself has implications for the theory of unimolecular reactions.

Near infrared reflectance spectra and analysis of H_{2}S frost as a function of temperature
View Description Hide DescriptionThe reflection spectra of H_{2}S frost in the near infrared region (1.6–4 μm), as a function of temperature to 62 °K, were measured. Analyses of these spectra were made, and assignments for the most intense combinations attempted. Dramatic changes in spectra are observed from 62–143 °K, connected with a phase transition between a tetragonal, low‐temperature phase and a cubic, high‐temperature phase, occurring at 125±5 °K. The data present evidence for only two phases being involved for H_{2}S frost.

Determination of diffusion coefficients by submicron droplet evaporation
View Description Hide DescriptionLennard‐Jones potential function constants, diffusion coefficients, and vapor pressures for relatively nonvolatile organics in gaseous media have been determined by measuring the evaporation rates of submicron droplets suspended in an electric field in a laser beam. A light‐scattering method was used to obtain the droplet size as a function of time for diffusion‐controlled evaporation.

Isostructural phase transitions due to core collapse. III. A model for solid mixtures
View Description Hide DescriptionOur earlier development of a statistical mechanical theory of isostructural phase transitions due to core collapse [J. Chem. Phys. 65, 2161, 2172 (1976)] is extended to the treatment of solid mixtures exhibiting isostructural transitions. Since mixtures in which two solid phases coexist are typically in states of mechanical but not material equilibrium, we consider the theory for states of mechanical equilibrium only, as well as the theory for coexisting phases in true stable thermodynamic equilibrium. Using an extremely simple Hamiltonian model we find good qualitative agreement between the results of a first‐order perturbation theory and the recent experimental results for Ce_{1−x }Th_{ x } mixtures. In particular, the theory accounts for the experimentally observed decrease in critical temperature with increasing x and for the dependence of the observed resistivity–temperature isobars upon x.

Chemi‐ionization in collisions of metastable argon with sodium
View Description Hide DescriptionAbsolute and relative cross sections were obtained for the Penning‐ionization (PI) reaction Ar*+Na→Ar+Na^{+}+e and the associative‐ionization (AI) reaction Ar*+Na→ArNa^{+}+e. The studies were made by a merging‐beams technique for a relative kinetic energy W of the reactants from nominally 0.01 to 10 eV for PI and 0.01 to 0.4 eV for AI. The Ar* represents a composite of Ar(4s ^{3} P _{2}) and Ar(4s ^{3} P _{0}). The PI is directed and occurs predominantly when the difference between the relative kinetic energy of the heavy products and the reactants is approximately 0.1 eV. Cross sections for AI are roughly proportional to W ^{−1}. Cross sections for total ionization (AI plus PI) vary as W ^{−1/3} for the lower W.

Self‐avoiding walks subject to boundary constraints
View Description Hide DescriptionA statistical study is carried out for self‐avoiding walks on infintely long square lattice strips, two and three lines wide. The two‐layer problem is solved completely and the three‐layer problem asymptotically. In each instance, the mean square end‐to‐end separation of a walk is found, as expected, to be asymptotically proportional to the square of the number of steps for long walks; in other words, 〈x ^{2}〉=a n ^{2}, where 〈x ^{2}〉 is the mean square x component of net distance traversed and n is the number of steps (assumed to be large). For the two‐layer problem, a=0.5236, and for the three‐layer problem, a=0.3899.

Thermodynamics of the MSA for simple fluids
View Description Hide DescriptionAn analytic study is made of the thermodynamic properties of the mean spherical approximation for a simple fluid and simple fluid mixtures. It immediately suggests several improved approximations.

Optical nonlinearities of conjugated molecules. Stilbene derivatives and highly polar aromatic compounds
View Description Hide DescriptionWe have investigated the influence of donor and acceptor substituents on the second and third order hyperpolarizabilities β and γ of large conjugated molecules such as stilbene and styrene derivatives. This was performed by two independent measurements of β and γ using the techniques of dc electric‐field induced second‐harmonic generation and tunable four‐wave mixing in liquids and solutions. For t r a n s−stilbene derivatives, β and γ are typically 10 times larger than for the corresponding benzene compounds, and are strongly correlated with the mesomeric effect of the substituents. A series of disubstituted molecules with strong donor–acceptor intramolecular charge transfer exhibit very large β, and it is shown that this enhancement can be predicted from the basic properties of the first electronic excited state.

Rate constants for the reaction of OH radicals with CH_{2}=CHF, CH_{2}=CHCl, and CH_{2}=CHBr over the temperature range 299–426 °K
View Description Hide DescriptionAbsolute rate constants for the reaction of OH radicals with vinyl fluoride, vinyl chloride, and vinyl bromide have been determined over the temperature range 299–426 °K using a flash photolysis–resonance fluorescence technique. The Arrhenius expressions obtained were k (CH_{2}=CHF) = 1.48×10^{−12} e ^{(775±300)/R T } cm^{3} molecule^{−1} sec^{−1}, k (CH_{2}=CHCl) = 1.14×10^{−12} e ^{(1045±300)/R T } cm^{3} molecule^{−1} sec^{−1}, and k (CH_{2}=CHBr) = 1.79×10^{−12} e ^{(805±300)/R T } cm^{3} molecule^{−1} sec^{−1}, with rate constants at room temperature of (5.56±0.56) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}, (6.60±0.66) ×10^{−12} cm^{3} molecule^{−1} sec^{−1}, and (6.81±0.69) ×10^{−12} cm^{3} molecule^{−1} sec^{−1} for CH_{2}=CHF, CH_{2}=CHCl, and CH_{2}=CHBr, respectively.

Interference effects in rotational state distributions: Propensity and inverse propensity
View Description Hide DescriptionSemiclassical scattering theory has been used to investigate interference effects in rotational state distributions for inelastic atom–diatom collisions. The Δj=even selection rule for homonuclear molecules is seen semiclassically to be an interference effect, and when this symmetry is weakly broken—i.e., an ’’almost homonuclear’’ molecule, one for which the odd anisotropy is much smaller than the even anisotropy—the interference persists in the form of a propensity rule, σ (odd Δj) ≪σ (even Δj). If the odd anisotropy is sufficiently large, however, one can see an inversion of the normal propensity, i.e., it can happen that σ (odd Δj) ≳σ (even Δj). It is suggested that rotationally state‐selected experiments which resolve this interference structure would be an extremely sensitive measure of the anisotropy in the interaction potential.

Entanglement probabilities for a harmonically bound macromolecule
View Description Hide DescriptionWe discuss a general scheme to derive various statistical properties of a macromolecule whose repeating units interact with a straight line and which is entangled with that line. In the case of harmonic forces an exact expression is found for the probability that a ring shaped macromolecule is n‐times entangled with the line. For more general interactions, the low and high temperature limits of the entanglement probabilities are discussed briefly.

Study of Ni(II) coordination in aqueous solution by EXAFS analysis
View Description Hide DescriptionExtended x‐ray absorption fine structure (EXAFS)spectroscopy has been applied to the study of water coordination of the Ni(II) ion in aqueous solution. High resolution x‐ray spectra were measured for Ni(NO_{3}) ⋅6H_{2}O salt and its 0.1M aqueous solution using a synchrotron radiationsource.Analysis of the spectra by Fourier transform reveals first sphere coordination in agreement with x‐ray diffraction results. In addition, a second coordination sphere is detected and a tentative distance from the Ni(II) ion to the second sphere water molecules of 3.2±0.1 Å is measured.

Optical potential for molecular rearrangement collisions: Computational study of collinear CH_{3}I+K→KI+CH_{3}
View Description Hide DescriptionThe imaginary part of the optical potentialU _{α} for molecular collisions involving rearrangements developed by Lin and Kouri is calculated for a collinear reaction K+ICH_{3}→KI+CH_{3}. The potential surface employed is that of Blais and Bunker as modified by Raff and Karplus. Calculations have been made for several total energies ranging from 0.1 up to 0.3 eV. The total absorption is related to (φ_{α} ^{+}[U _{α}−U _{α}]φ_{α} ^{+}), where φ_{α} ^{+} satisfies a Lippmann–Schwinger equation in which U _{α} acts as a potential. The present calculations approximate (U _{α}−U _{α}) φ_{α} ^{+} by a Born approximation so that we compute ImU _{α}χ, with χ representing the initial unperturbed state in channel α. Then ImU _{α}χ is a local quantity and we examine its spatial variation to gain a picture of the region where chemical reaction occurs. The result is a proposed mechanism for the reaction of K+ICH_{3} on the particular model surface used. The resulting picture is that (1) vibrationally excited ICH_{3} reacts more readily, (2) the reaction occurs most readily when the K–I distance is highly compressed and concommitantly energy disposal in the reaction favors vibrationally excited KI product molecules, and (3) the reaction cross section is an increasing function of the total energy of reactants over the energy range studied. An alternative method for analyzing the reaction is to examine complete (Born) matrix elements of ImU _{α}. It can be shown that this is a negative semidefinite matrix and we compute the eigenvalues and eigenvectors of this matrix at several total energies. We arrange the eigenvalues in increasing order and define them to be the ’’reactivity’’ of the corresponding eigenstates. Analysis of the associated eigenvectors shows that each is dominated by a single ICH_{3} vibrational state so that we gain information on the role of vibrational excitation of the reactants in the collision. It is found again that the v=0 vibrator state has the lowest reactivity, v=1 is next, and v=2 is highest. These conclusions are consistent with the results of earlier studies on this K+ICH_{3} surface using, e.g., classical trajectories. Because of the computational simplicity of the present approach, it is felt that the calculation of such optical potentials and their associated eigenvalues (reactivities) and eigenvectors can provide significant insight into reactive scattering relatively inexpensively. The present approach to reactive scattering also leads in a natural way to Franck–Condon type factors which govern the probability of reaction. These enter because the matrix elements of ImU _{α} are of the form 〈χ‖V _{β}δ (E‐K _{β}) V _{α}‖χ〉 and these can be expressed in terms of Franck–Condon factors.

Forced diffusion of molecules with internal rotation
View Description Hide DescriptionThe dipolar correlation function for a system of independently relaxing molecules containing rotatable groups is calculated by solving the forced diffusion equation. It is found that the correlation function has the same form as a previous result for spheroids. This result follows from the assumption that the equilibrium distribution function is constant, an assumption made to allow linearization of the diffusion equation. Procedures for relieving the assumption are outlined and applied to a hindered internal rotation case. The presence of a barrier to internal rotation makes the correlation function decay more slowly. The relation between the multimolecular correlation function and the complex dielectricpermittivity is investigated.

Fluctuations of polarization and magnetization in dielectric and magnetic media
View Description Hide DescriptionWe consider thermal fluctuations of polarization, magnetization, and the associated electromagnetic fields in dielectric magnetic media which are allowed to be anisotropic and spatially nonhomogeneous. The theory is purely macroscopic and is based on an application of the fluctuation–dissipation theorem. It is shown that the correlation functions can be elegantly expressed in terms of the Green functions for Maxwell’sequations.

Assignment of the triplet factor group states of benzene
View Description Hide DescriptionThe pure electronic ^{1} A _{ g }–^{3} B _{1u } transition of crystalline benzene has been measured by photoexcitation techniques. Polarization and Zeeman measurements on single crystals provide the following assignment of the factor group states (energies relative to the mean value): B _{3u }−7.8 cm^{−1}, A _{ u }−0.3 cm^{−1}, B _{1u }+2.6 cm^{−1}, B _{2u }+5.5 cm^{−1}. These results are in contradiction with the most recent calculations performed within the neutral exciton model. The relative intensity of the factor group states suggests that other crystal states do contribute to the transition.