Volume 58, Issue 11, 01 June 1973

Pulse radiolysis studies. XXI. Optical absorption spectrum of the solvated electron in ethers and in binary solutions of these ethers
View Description Hide DescriptionThe optical absorptionspectrum of the solvated electron has been determined by pulse radiolysis in the pure liquid ethers: tetrahydrofuran, methyltetrahydrofuran, diethyl ether, dimethoxyethane, diglyme, triglyme, and tetraglyme. The absorption maxima are at 4720, 4650, 4350, 4880, 5220, 5440, and 5580 cm^{−1}, respectively. The half‐widths of the bands have also been measured. The oscillator strength, determined for the first four ethers is approximately unity. The absorption bands have been determined in binary solutions with ethylenediamine and for tetrahydrofuran‐water over the entire concentration range. Calculations using a recent form of a cavity‐continuum model have been compared with the experimental results. The model shows agreement with the experimental values for the transition energy for an effective cavity radius of about 4 Å and a coordination number of 6 or 8. Kinetics for the attachment of solvated electrons to pyrene and for the reaction of the solvated electron with the solvent counterion have been investigated in several ethers and absolute rate constants determined.

Absolute total cross sections for Li‐molecule scattering
View Description Hide DescriptionAbsolute total scattering cross sections were measured for ^{7}Li scattered by D_{2}, N_{2}, CO, CO_{2}, CH_{4}, and SF_{6} over a range of Li beam velocities of corresponding to a range of relative kinetic energies of 0.04–0.33 eV for Li–D_{2} to 0.02–0.79 eV for Li–SF_{6}. In the observed cross sections random experimental errors were less than 1.5% and systematic errors were between −0.3% and +1.4%. Two spherically symmetric potentials, the Lennard‐Jones (12,6) and the Buckingham‐Corner were fit to deconvoluted and statistically smoothed data using a non‐linear least squares fitting routine. For each Li‐molecule system a satisfactory fit could be obtained with standard deviations of approximately 1%–2%. The best fit potentials gave accurate values for the average long range attractive part of the potentials over the range of limiting impact parameters. Evidence from high resolution differential cross section experiments is introduced that indicates that there should be relatively little damping of the glory features of the total scattering cross sections for the Li‐molecule systems studied here, and hence the ability of spherical potentials to reproduce the data is not surprising.

Molecular dynamics studies of the properties of small clusters of argon atoms
View Description Hide DescriptionMolecular dynamics calculations have been performed on clusters of 15, 30, 45, 60, 80, and 100 argon atoms at temperatures of up to 75°K. Values of the independent‐cluster thermodynamic functions are presented and compared with those obtained from the microcrystal model. This comparison indicates good agreement for values of the Gibbs free energy of formation. The transition from solidlike to fluidlike diffusion in the cluster occurs gradually; no semblance of a phase transition is noted. The radial variation of density in the clusters have maxima and minima reminiscent of those in the radial distribution function for bulk liquids. The temperature dependence of that function indicates that clusters expand quite rapidly as the temperature is increased. The radial distribution of potential energy indicates that there is no region inside the clusters where the environment resembles that in the bulk phases; the properties of the clusters are dominated by the ``surface region'' in which nearly all the atoms exist.

Dielectric properties of polyelectrolytes. IV. Calculation of dielectric dispersion by a stochastic model
View Description Hide DescriptionThe theory of the dielectric dispersion of a rodlike polyelectrolyte derived by Oosawa on the basis of thermal fluctuation of the counterion concentration is rewritten by a discrete charged site model and stochastic behavior of the counterions. The values of dielectric increment, conductivity increment and relaxation time are derived as functions of the charge density, number of sites, length of the polyion and transition rates of counterions between two adjacent sites. The expressions are given for two cases; the number of bound ions to a single site is 0 or 1, and in the other case the number is not limited, the latter case containing Oosawa's result. The effect of counterion‐counterion interaction on each Fourier mode of the fluctuation is evaluated in some cases. It is large for the fluctuation of longer wavelength, which broadens the dispersion pattern.

Vibronic interactions, resonance Raman spectra and bond strengths for the radical anion salts of tetracyanoethylene
View Description Hide DescriptionRaman spectra for the intensely colored salts of the tetracyanoethylene radical anion with sodium and potassium cations confirm previous assertions that the infrared salt spectra are completely dominated by vibronic interaction effects. As expected, strong Raman scattering has been observed at frequencies coincident with the intense infrared bands which have been assigned to totally symmetric modes activated by an ``electron‐vibration'' moment. The scattering intensities of the symmetric stretching modes (ν_{1}, ν_{2}, and ν_{3}) reveal a complex dependence on excitation frequency which is qualitatively consistent with the observed vibronic structure of the electronic absorption band. By confirming the assignment of several of the radical anion internal modes, the Raman data have also permitted the evaluation of reliable stretching constants for comparison with the neutral molecule force constants and quantum chemical predictions of bond order changes. New data and a subsequent force constant analysis have required the reassignment of

Magnetic properties of the configuration in low symmetry crystal fields
View Description Hide DescriptionThe actions of low symmetry crystalline electric fields and the spin‐orbit coupling in the electronic configuration have been considered for the interpretation of magnetic data (susceptibility. Mössbauer effect, etc.). The results of numerical calculations of the various spin Hamiltonian parameters (D.E.ḡ.Ā.efg) are tabulated and the applicable perturbation theory expressions have been worked out.

Three‐step photoselection and the assignment of the electronic states of the benzyl radical
View Description Hide DescriptionA contradiction between assignments of the first excited state of the benzyl radical, originally made by three‐step photoselection in rigid solutions, and later by gas‐phase rotational analysis, has been resolved. The photochemically produced radical in a rigid solution can be subject to rotational diffusion over the time duration of the experiment. This weakens (or even confuses) the crucial correlation with reference axes of the parent molecule necessary for achieving absolute assignments. By increasing the viscosity of the medium, such randomization can be considerably reduced and photoselection polarization ratios greater than 3/1 (a characteristic of three‐step photoselection) are obtained for p‐methylbenzyl. The photoselection data for the p‐methylbenzyl radical indicate that the first three observed excited states can be assigned ^{2} A _{2}, ^{2} A _{2}, ^{2} B _{2}, respectively. If the ^{2} A _{2} assignment for the lowest excited state of p‐methylbenzyl in a rigid solvent can be applied to the benzyl radical itself, then agreement is achieved with the gas‐phase rotational analysis.

Anharmonic force field of the metaborate ion in alkali halides
View Description Hide DescriptionThe anharmonic force field of metaborate isolated in KCl and KBr lattices has been calculated using the simplified quartic force field introduced by Smith and Overend. These force fields have been used to calculate approximate force fields of metaborate in other alkali halide lattices.

Effective charge tensors of atoms in a molecule and electric dipole shielding of nuclei
View Description Hide DescriptionExact formulas are derived for the electric shielding tensors of nuclei in a molecule bathed in a static, uniform, electric field. It is shown that the derived relations hold also in the coupled Hartree‐Fock approximation. The resulting equations should provide useful checks on the accuracy of the first‐order induced electron density, a quantity required for the calculation of the electric dipole polarizabilitytensor. A tensor quantity, which is a function of the electric dipole moment and its derivatives with respect to the internal coordinates, is proposed as an effective charge of an atom in a molecule.

Vibrational relaxation in CO_{2}/O_{2} mixtures
View Description Hide DescriptionThe acoustic absorption in mixtures of CO_{2} and O_{2} has been measured for 90%, 80%, and 70% concentrations of O_{2} at 300 °K. The absorption has been analyzed to extract the rate of energy transfer between the vibration of the bending mode of CO_{2} and the O_{2} vibration and the rate at which O_{2} de‐excites the bending mode of CO_{2} in a v‐t process. The rate constants for the v‐t de‐excitation of the bending mode of CO_{2} by O_{2} was found to be about the same as de‐excitation by CO_{2}. The v‐v exchange between CO_{2} and O_{2} increases only slightly from at 300 °K to at 600°K.

^{19}F nuclear magnetic resonance in CdF_{2}–ErF_{3}
View Description Hide DescriptionThe ^{19}F NMR of a single crystal of ErF_{3} has been investigated at 8 and 16 MHz. Weak NMR lines were observed whose shifts relative to the main CdF_{2} peak were found to be field dependent. These shifts showed axial symmetry about the [111] crystallographic directions with and . The small NMR lines are attributed to those lattice fluorides which have one nearest neighbor Er^{3+} occupying a normal Cd^{2+} site. The anisotropic portion of the shift is shown to be due to the dipolar contribution of spin on the erbium ion with no unpaired spin in the fluorine p orbitals. Analysis of intensity ratios supports a random distribution of Er^{3+} among Cd^{2+} sites with no preferential formation of clusters.

Measurements of vibrationally excited molecules by Raman scattering. I The yield of vibrationally excited nitrogen in the reaction
View Description Hide DescriptionThe reaction of nitrogen atoms with nitric oxide leads to vibrationally excited nitrogen. In the presence of molecular nitrogen, V‐V exchange processes rapidly establish a modified distribution for which a measurement of N _{2}(ν=1) is adequate to determine the total vibrational energy yield of the reaction. The measurements of N _{2} (ν=1) have been made by Raman spectroscopy using the intensity of the Q branch of the anti‐Stokes line at 4382 Å (using 4880 Å Ar^{+} laser radiation). The system sensitivity is determined using heated nitrogen. The measurements have established that of the available energy (3.27 eV) appears as vibrational energy and that the vibrationally excited nitrogen is an initial product and does not result from collisions of translationally hot oxygen atoms with nitrogen.

Zeeman effect of nuclear quadrupole resonance in 1‐chloro‐2,4‐dinitrobenzene
View Description Hide DescriptionThe Zeeman effect of NQR was studied in 1‐chloro‐2,4‐dinitrobenzene. A low value of the asymmetry parameter (0.10) was obtained. Four physically inequivalent field gradients were located and their orientations in the crystallographic abc system were determined using symmetry considerations. From these data the orientations of the molecules in the unit cell were determined. The results agree well with the two‐dimensional x‐ray structural data. The bond characters of the bond were calculated, and the values compare well with those generally obtained for bonds in chlorine derivatives of benzene.

Cross sections for production of the Fourth Positive band system and O(^{3} S) by photodissociation of CO_{2}
View Description Hide DescriptionExcitation cross sections were measured for producing by photodissociation of CO_{2} from threshold to 635 Å· Above 685 Å the cross section is of the order and exhibits considerable structure while below 685 Å the cross section rapidly drops to a nearly constant value of . The structure below 790 Å correlates with predissociation from known Rydberg states of CO_{2} demonstrating the competition between preionization and predissociation. An upper limit of 6% of the cross section was inferred for producing O(^{3} S). Although not directly observed, evidence was obtained that the production of is accompanied by production of O(^{1} D) and O(^{1} S) at incident photon wavelengths less than 800 and 700 Å, respectively. The vibrational intensity distribution was obtained with 7 Å resolution for 16.69 eV photon impact and is similar to a 20 eV electron impact produced distribution.

Infrared circular dichroism and linear dichroism of liquid crystals
View Description Hide DescriptionIn order to test the validity of our recently reported theory of optical activity near absorption bands of cholesteric liquid crystals, we have measured the infrared linear dichroism (LD) of the nematic liquid crystalp‐methoxy‐p′‐n‐butylaxoxybenzene and the circular dichroism (CD) of the cholesteric phase of this liquid crystal obtained by doping with 0.75 mole‐% cholesteryl‐2‐(2‐ethoxyethoxy)ethyl carbonate. Using the measured LD data to define the optical properties of the individual layers of the cholesteric structure, we calculate the CD of the cholesteric material by means of our macroscopic theory. The calculated signs, amplitudes, positions, and shapes of the CD bands agree closely with observation. This demonstrates that the CD is quantitatively explained by introducing frequency‐dependent complex terms into the spiralling dielectric tensor of the Oseen‐de Vries model for cholesteric liquid crystals.

Recombination rate measurements in nitrogen
View Description Hide DescriptionA method of generating an atmospheric pressure high‐electron‐density plasma with arbitrary electron temperature is described and applied to measurement of electron ion recombination rates in N_{2}. The recombination rate for N_{2} is shown to be independent of pressure in the region investigated and is given as function of E/N and electron temperature.

Spectroscopic investigation of van der Waals molecules. I. The infrared and visible spectra of (O_{2})_{2}
View Description Hide DescriptionThe infrared and visible spectra of gaseous oxygen have been examined at temperatures around 90°K using a long path absorption cell. At all temperatures the infrared and visible spectra show a broad band which can be assigned as collision‐induced absorption. However, at low temperatures small but discrete features appear with integrated intensities dependent on the square of the gas density. These features are assigned to bound state van der Waals molecules of the type (O_{2})_{2}. The visible absorption of (O_{2})_{2} studied corresponds to the simultaneous transition. The part of the spectrum attributed to bound dimers shows a progression of eight fine structure bands superimposed on the broad simultaneous transition absorption. The fine structure has been assigned to combinations of electronic and vibrational transitions involving the stretching mode of the van der Waals bond of (O_{2})_{2}. In the ground state each oxygen molecule is in the state, while in the excited state one oxygen molecule is in the state and the other is in the state. The spacings and convergence of the dimer vibrational levels provide a determination of the dissociation energy of the ground and excited dimer states, giving . The infrared spectrum of (O_{2})_{2} occurs near the infrared inactive fundamental vibration of O_{2} and shows three regions of discrete absorption superimposed on the broad collision‐induced band. The discrete absorption bands have been assigned to fundamental and combination bands of (O_{2})_{2}. The combination band features involve hindered rotor transitions associated with the internal rotations of the O_{2} molecules within the dimer. From an analysis of the infrared vibration‐rotation band contour of one of the dimer fundamentals, an average distance of 4.8 Å between the centers of mass of the two O_{2} molecules was determined for the (O_{2})_{2} van der Waals molecule. Applying the usual band analysis formulas to determine the geometry is an uncertain procedure since the data indicate that (O_{2})_{2} is weakly bonded and has a floppy structure. It was subsequently not possible to choose among possible linear or nonlinear dimer equilibrium configurations with the present experimental or theoreticalinformation. All the spectroscopic evidence obtained here is consistent with the description of the weak bonding in (O_{2})_{2} as due to van der Waals‐type interactions. There is no need to suggest a pairing of the electrons in oxygen into some sort of weak chemical bond that might stabilize (O_{2})_{2}.

Bounds to dispersion energy coefficients
View Description Hide DescriptionStarting from the second‐order perturbation energy expression and utilizing inner projection and operator inequalities techniques, easy to evaluate expressions for the bounds to dispersion energy coefficients are obtained in terms of ground statesum rule values of the separated atoms for two sets of basis functions. The resulting bounds are narrower than those obtained starting from the Casimir‐Polder integral formula and bounding each of the polarizabilities in that expression by using either the present technique and basis set or the [1,0] Padé approximants. The bounds obtained here from the larger basis set are of comparable quality to those reported using Gaussian quadrature or the [2,1] Padé approximants to bound the polarizabilities in the Casimir‐Polder formula. A derivation of the Kramer‐Herschbach combination rule from one of the bounds is also presented.

Quenching rate constants for
View Description Hide DescriptionThe quenching rate constants for with H_{2}, D_{2}, N_{2}, O_{2}, NO, CO, CO_{2}, COS, CS_{2}, SO_{2}, NH_{3}, C_{2}N_{2}, CH_{4}, C_{2}H_{2}, C_{2}H_{4}, C_{2}H_{6}, C_{2}F_{6}, and SF_{6} have been measured in a discharge‐flow apparatus. The sources of were the interaction of Ar(^{3} P _{0, 2}) or He(2^{3} S) atoms with carbon dioxide. The bimolecular‐quenching coefficients are , except for N_{2}, CO_{2}, C_{2}F_{6}, and SF_{6}, which range from 10^{−11} to 10^{−12} cm^{3} sec^{−1}. Only the rate constants for N_{2}, CO, and CS_{2} showed a dependence upon the vibrational excitation of CO(a). For these reagents, the mechanism for quenching is discussed; the reaction with N_{2}(X) yields significant amounts of N_{2}(A). The CO(a) + NO(X) reaction is of particular interest because the β‐ and γ‐band emission can be used to identify the NO(A and B) products and to provide a diagnostic test for the presence of . The reaction between and CO(X) is discussed in an appendix.

Intramolecular vibrational energy transfer: A study of representations
View Description Hide DescriptionIn this paper we report a study of possible representations for the description of intramolecular energy transfer. Our ultimate goal is the definition of a scheme suitable to the description of a molecule undergoing dissociation which is valid everywhere along the reaction path. For this reason we study three sets of basis functions for dynamical calculations of intramolecular vibrational energy transfer in one‐dimensional, bound or metastable, triatomic molecules having one harmonic and one Morse bond. The different sets result from different definitions of bond coordinates and different methods for separating the bond motions. For Basis Set 1, the two bond coordinates are internuclear distances between adjacent atoms and the interbond coupling is caused by kinetic energy cross‐terms. For Basis Sets 2 and 3 the coordinates are the distance between adjacent atoms in the harmonic bond and the distance between the dissociable atom and the remaining diatomic. The separation of coordinates for Basis Set 2 is analogous to the ``static'' resolution of bond motions in collision theory while the separation of coordinates for Basis Set 3 is an adiabatic separation. The nature and mechanism of bond coupling in the adiabatic approximation is analyzed in detail and dominant contributions are identified. We find that the relative merits of the basis functions depend strongly on the masses of the atoms and the harmonic frequencies of the bond. When the vibrational frequency of the harmonic bond exceeds the frequency for small oscillations of the Morse bond, Basis 3 is usually superior to both Bases 1 and 2. When the opposite condition holds and the mass of the central atom is (modestly) large relative to the masses of the other atoms, Basis 1 is usually superior. The conditions which favor the adiabatic separation are similar to those which favor the ``perturbed stationary states'' approximation in collision theory. The weak energy‐dependence of the basis sets is explained in terms of a strong dependence of the optimal bond coordinates upon the interatomic distances.