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Volume 43, Issue 9, 01 November 1965

Solution Dimerization of the Tetracyanoquinodimethane Ion Radical
View Description Hide DescriptionThe reversible dimerization of the anion radical of 7,7,8,8‐tetracyanoquinodimethane in aqueous solution has been studied spectroscopically. Analysis of the spectra yields an equilibrium constant for dimerization (2A^{−}⇆A_{2} ^{=}) at 25° of 2.5×10^{3} liter/mole and a heat of dimerization of −10.4 kcal/mole dimer.

Semiclassical Theory of Rotational Excitation of a Diatomic Molecule by an Atom
View Description Hide DescriptionThe problem of translation—rotation energy exchange is investigated for systems, like K–HBr, for which the energy exchange ΔE is a sizable fraction of the relative kinetic energy, the matrix elements of the potential of interaction are large, and the period of interaction is of the order of ℏ/ΔE. A representation of the wavefunction is chosen where the rotor functions are separately quantized along the moving interparticle axis. This choice implies a coupling scheme for the angular momenta, which is compared with two other schemes commonly used. The time‐independent Schrödinger equations for the three coupling schemes yield identical results for the transition probability if solved exactly, or in the first‐order Born approximation, but not if solved in the first‐order distorted wave approximation. Intermultiplet transitions are a non‐adiabatic effect and independent of the strength of the anisotropic part of potential in the (jμ) scheme, and hence their neglect leads to considerable simplication. The same results are shown to hold for the transition probability obtained from solutions of the time‐dependent Schrödinger equation obtained by using basis functions quantized along fixed or moving axes. The connection between the time‐dependent and time‐independent formulations is made with the choice of a suitable classical trajectory based on a WKB solution of translational motion. The quantum‐mechanical, time‐dependent differential equations for the coefficients in the (jμ) representation, obtained by the method of variation of constants with the time‐dependent potential derived from a classical trajectory, are solved numerically in the following article.

Semiclassical Calculation of Rotational Excitation
View Description Hide DescriptionIn the preceding article the Schrödinger equation and its solution are developed for the problem of translation—rotation energy exchange in a representation of rotor functions separately quantized along the moving interparticle axis. The quantum‐mechanical time‐dependent differential equations for the coefficients in this representation are obtained by the method of variation of constants with a time‐dependent potential calculated from a classical trajectory and a symmetrized, initial relative kinetic energy. These equations are solved numerically for a limited number of basis functions, with intermultiplet transitions neglected, for some atom—diatomic systems. The isotropic part of the potential is taken to be a Lennard‐Jones (12, 6) potential, with parameters appropriate for the cases K–HBr, Cs–HBr, and Li–HBr. For the present exploratory calculations the anisotropic part is assumed to be proportional to the inverse sixth power of the interparticle distance and to have P _{2} symmetry. Probabilities of inelastic collisions along given trajectories and total inelastic cross sections are calculated for the j=0→2, 2→4, 0→4, and 1→3 transitions. The total cross section for the 0→2 transition in the case representative of K–HBr is 5.74 Å^{2} for a reasonable estimate of the anisotropy of the assumed potential. A test calculation is made for the system He–H_{2} and agreement is found to 20% with Roberts' first‐order distorted wave calculation in which the translational motion is treated quantum mechanically. The effect of intermultiplet transitions is examined and it is estimated that their neglect may incur an error in the total cross section of about 50%.

Critical Opalescence of a Fluorocarbon—Hydrocarbon Binary Liquid Mixture: Normal Perfluoroheptane—Iso‐octane
View Description Hide DescriptionCritical opalescence of a binary liquid mixture, normal perfluoroheptane and iso‐octane has been investigated by light and small‐angle x‐ray scattering over a broad range of s/λ, where s=2 sin (θ/2), λ is the wavelength in the medium, and θ is the scattering angle. The scattering data show that the critical opalescence observed in this system is essentially the same as has been found in other binary liquid mixtures.

On Singularities in Eigenfunctions
View Description Hide DescriptionThe relationship between some singularities of the eigenfunction and convergence of the Legendre expansion is studied for the ground state of the helium atom.

Vibrational States of the Hydrogen Molecular Ion
View Description Hide DescriptionThe energy levels of H_{2} ^{+} are computed for all vibrational quantum numbers and for rotational quantum numbers up to J=8. The accuracy of the energy of the uppermost levels is estimated to be better than 10^{−7}.

Microwave Absorption and Molecular Structure in Liquids. LXVI. The Dielectric Relaxation of the Water—Dioxane System and the Structure of Water
View Description Hide DescriptionThe dielectric constants and losses of a series of mixtures of water and dioxane (0.2–0.8 mole fraction) have been measured at wavelengths of 0.217, 1.223, 3.193, and 10.09 cm, and 575 m and temperatures of 1°,10°,25°,40°, and 55°C. The results show that the mixtures have two dielectric relaxation times in contrast to the single time found for water. The results are interpreted as indicating a very rapidly fluctuating structure for pure water in which the molecules are constantly forming, breaking, and reforming hydrogen bonds to their neighbors. At any given instant there are unbonded molecules, as well as singly, doubly, triply, and quadruply bonded molecules, and molecules in all intermediate stages of bonding. However, the fluctuations of structure are so rapid that, averaged over the extremely short time required for dielectric relaxation, the molecules and their immediate environments are approximately the same. In the water—dioxane mixtures, the dioxane molecules alter the environments of some of the water molecules and thereby introduce a second relaxation time.

Measurement by NMR of the Diffusion Rate of HF in Ice
View Description Hide DescriptionAn experiment is described by which the diffusion of fluorine in monocrystalline ice cylinders is followed quasicontinuously, using the protonmagnetic resonance spin—lattice relaxation timeT _{1} to measure the HF concentration along the sample. The diffusion coefficient D_{F} was evaluated for various temperatures between −30° and −4°C. The results show more scatter than the experimental error can account for. A least‐squares fit of our data yields D_{F} (−10°C)=0.8×10^{−6} cm^{2}/sec for the diffusivity and E=0.58 eV=13.4 kcal/mole for the activation energy, with root‐mean‐square deviations of 0.5×10^{−6} cm^{2}/sec and 0.08 eV, respectively. We find that the highest concentration of diffused HF which can be absorbed by monocrystalline ice is about 4×10^{−5} HF/H_{2}O. A possible explanation is offered for the large value and dispersion of the diffusivity.

Medium Effects in Nuclear Magnetic Resonance. IV. A Refined Theory for Nonpolar Gases
View Description Hide DescriptionFollowing the general theory for medium NMR shifts in gases as outlined in Part I of this series, two improvements are proposed. For the calculation of the van der Waals interaction a repulsive term has been added to the customary attractive term. Wherever intermolecular distances are required, a properly averaged distance between the site of the measured proton in the solute molecule and the center of the solvent molecule is used rather than the distance between the centers of the molecules. The implications of these corrections for nonpolar molecules are discussed, and new values for the bond parameters B are proposed.

Infrared‐Absorption Spectrum and Ferroelectric Behavior of Sodium Trihydroselenite
View Description Hide DescriptionThe infrared‐absorption spectra of sodium trihydroselenite have been investigated in both the ferroelectric as well as the nonferroelectric phases. The analysis of the data suggests that in the ferroelectric phase the units HSeO_{3} ^{−} and H_{2}SeO_{3} are distinct with hydrogen bonds connecting their oxygens. The transition to the nonferroelectric phase results in the two units becoming equivalent, each behaving like a pyramidal SeO_{3} ^{=} ion. This is explained in terms of the motion of the protons in a potential field which, in the ferroelectric phase, has an asymmetric double minimum. The transition to the nonferroelectric phase is accompanied by an even distribution of proton density along the bond length which, on the basis of our data, seems to be due to the potential field acquiring a single minimum.
Based on these results an attempt has been made to suggest a plausible switching mechanism in the ferroelectric phase and to correlate the spectral changes accompanying transition with the changes in the crystal structure.

Vibration—Rotation Energy Transfer
View Description Hide DescriptionA simple two‐parameter model for vibration→rotation energy transfer fits the vibrational relaxation data for 25 different molecules with small moments of inertia. Thirty‐five data are fit within a factor of 3. The model is limited to molecules in which the rotational velocities of the atoms are greater than the translational velocity of the molecule and in which the rotational level spacings are small compared to kT. The successful correlation of nearly all of the data available on these molecules leads to the conclusion that vibration→rotation energy transfer is a real and important effect. The theory provides an explanation of vibrational relaxation in a number of mixtures.

Absorption Spectrum of Na and K in Rare‐Gas Matrices
View Description Hide DescriptionThe absorptionspectrum of Na and K in Ar, Kr, and Xe matrices in the region from 2000 to 8000 Å has been studied as a function of temperature and, at 4°K, as a function of concentration. Observations on some spectra of Na in Ne are also included. The first member of the principal series, , can be observed in all matrices. Higher members are weak and can, in most matrices, not be assigned. At alkali concentrations≥0.5%, strong additional absorptions are observed which seem to be due to alkali—alkali interaction.
Most transitions appear blue shifted and have triplet structure. The spectra are sharp in xenon but become increasingly diffuse in lighter rare‐gas hosts. The line shape indicates fine structure in most absorption features. During the warm‐up, the ^{2} P←^{2} Sabsorption broadens and shifts to the red. For a given ratio of observation temperature to melting point of host lattice, atomic absorption of the alkali metals seems to have the same linewidth in all of the observed matrices.

Intrinsic and Lattice‐Induced Distortion of the Tetrachlorocuprate Ion
View Description Hide DescriptionIn an effort to determine how much of the distortion of the tetrahedral complex, CuCl_{4} ^{2−}, may be ascribed to the Jahn—Teller effect, we have studied the changes in the optical and EPR spectra which occur when this ion is embedded in several different lattices. Although the corresponding lattice constants of the isostructural crystals Cs_{2}CuCl_{4} and Cs_{2}ZnCl_{4} differ by only about 3%, gross differences exist between the gtensors of CuCl_{4} ^{2−} suspended in these lattices. These findings are corroborated by a comparison of the optical spectra of the two complexes. The effects are discussed in terms of an LCAO—MO analysis of the primarily 3d(Cu)wavefunctions of the complex, and it is shown that the changes in ionic properties are connected principally with a change in the amount of ligand character in the e, primarily 3d orbitals. The analysis points towards the conclusion that the low symmetry (point group C_{s} ) of the ion is an intrinsic property and that the dominant mechanism of the tetragonal component of the distortion of the ionic symmetry from T_{d} is the Jahn—Teller effect.

Molecular Rydberg Transitions in Rare‐Gas Matrices—Evidence for Interaction Between Impurity States and Crystal States
View Description Hide DescriptionAs a first step in characterizing molecular Rydberg states in the solid state, the absorption spectra arising from acetylene and benzene impurity states in solid krypton and argon in the far‐ultraviolet region have been obtained. The first member of the acetylene Rydberg series, which appears at 8.155 eV in the gas phase, is observed to be shifted to 8.67 eV in a krypton matrix and to 9.01 eV in an argon matrix. These large energy shifts are discussed, particularly with reference to the optical spectra of rare‐gas solids and rare‐gas alloys, where similar large blue shifts are observed. The far‐ultraviolet spectra of benzene trapped in krypton and argon matrices show a qualitatively different phenomenon. The Rydberg states of benzene are observed to interact with conduction‐band continuum states to exhibit anomalous Fano‐type line shapes. The Rydberg states repulse the neighboring continuum states to produce sharp decreases in the continuum absorption intensity. These results are discussed in connection with other systems which show Fano‐type line shapes.

Eigenparameters for the 1sσ_{g} and 2pσ_{u} Orbitals of H_{2} ^{+}
View Description Hide DescriptionEigenparameters for the 1sσ_{g} and 2pσ_{u} electronic orbitals of the hydrogen molecule ion are investigated. The appropriate parameters are tabulated for the internuclear separations R=1.0(0.5)30.0 a _{0}, and more extensive tabulations, available elsewhere, are described.

Density Distribution of Polymer Segments in the Vicinity of an Adsorbing Interface
View Description Hide DescriptionAt a small distance from the interface corresponding to the effective thickness of the segments, the density drops suddenly by an amount that is the greater, the stiffer the chain. Beyond this distance the density is exponential in the distance from the interface for long chains and relatively weak adsorption.

Effect of Translational Energy on Ion—Molecule Reaction Rates. II
View Description Hide DescriptionA number of ion—molecule reactions have been studied by a method which allows considerable ion energy resolution in the region below 1 eV. The experiments show clearly that both the proton or hydrogen‐atom transfer reactions as well as the condensationreactions studied can readily be explained in terms of the slow‐ion theory of Gioumousis and Stevenson. Results for the three permanent dipole molecules studied, NH_{3}, H_{2}O, and HCl, indicate that the protonated molecular‐ion formation can be explained using the energy‐dependent cross section developed by Moran and Hamill. The application of this collision cross section expression leads to the conclusion that one collision in three produces the protonated parent for both NH_{3} and H_{2}O and one collision in five for HCl.

ESR Investigation of the Dynamical Behavior of Hydrogen Atoms in CaF_{2}
View Description Hide DescriptionThe techniques of ESR are employed to investigate the motion of H atoms in the lattice of CaF_{2}. It is found that the atoms are quite stable against motion at temperatures below 100°C but migrate readily through the lattice at temperatures >114°C. The character of the initial decrease in intensity of the spectrum seems to be ``bimolecular.'' Later stages are exponential, and are governed by an activation energy of 1.2 eV.

Microwave Spectrum and Barrier to Internal Rotation in Trifluoronitromethane
View Description Hide DescriptionThe microwave spectrum for CF_{3}NO_{2} has been observed for the J = 1→J = 2 through the J = 4→J = 5 transitions. Some 35 lines in these transitions are assigned, and the Stark effects for three of these were studied quantitatively and interpreted. A discrepancy in the Stark effect of a 4→5 transition can be accounted for by properly adjusting the sixfold barrier to internal rotation. The parameters used to obtain the best fit for the spectrum are the following: B + C = 4917.4±0.4 Mc/sec, B — C = 453.9±5 Mc/sec, A (NO_{2}) = 13205±150 Mc/sec, A (CF_{3}) = 5700 Mc/sec (assumed), V _{6} = 780 000 Mc/sec = 74.4±5 cal/mole. The dipole moment obtained from the Stark‐effect measurements is 1.44±0.03 D.

Temperature Dependence of Vibronic Transitions in Crystals and Spectroscopic Observation of a Phase Transition
View Description Hide DescriptionThe temperature dependence of vibronic absorption bands, corresponding to either one phonon absorbed or emitted simultaneously with an electronic transition in a crystal having an octahedral UCl_{6} ^{2−} complex was measured and found to agree with the theoretically expected results. A phase transition was observed by the weak appearance of the pure electronic transition above a transition temperature. The latter exhibits hysteresis favoring a first‐order transition. Selection rules and general symmetry arguments show that the distortion must be one of D _{2}, D _{3}, S _{4}, D _{2d } (special) about the uranium site. The particular arrangement of atoms enables a further reduction in the possible distortions to D _{2d } or D _{3}. From the relative intensity of pure electronic to vibronic transitions one can estimate the size of the distortion to be of the order of 2×10^{−3} times the lattice constant.