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Volume 56, Issue 10, 15 May 1972

Molecular Rotational Zeeman Effect in Thioformaldehyde
View Description Hide DescriptionThe high‐field rotational Zeeman effect has been observed in thioformaldehyde. The magnetic susceptibilityanisotropies are and . The molecular g values with uniquely determined signs are , and . c is the out‐of‐plane axis and the a axis is the dipole axis. g_{aa} represents the largest molecular g value yet measured. Use of these five Zeeman parameters and the known structure gives the molecular quadrupole moments: ; the diagonal elements of the paramagnetic susceptibility tensor:; and the anisotropies in the second moments of the electronic charge distribution. By estimating the out‐of‐plane second moment of the electronic charge distribution as using free atom values, we have evaluated the remaining individual second moments of the electronic charge distribution to be and . The diagonal elements of the diamagnetic and total magnetic susceptibilitytensor also follow from the above estimation of and are , and , giving the bulk magnetic susceptibility as . These values are then compared to those of the oxygen analog, formaldehyde, and trends in this pair are compared to several other previously studied oxygen‐sulfur analogs.

Phase Transitions of the Classical Hard‐Ellipse System
View Description Hide DescriptionBy Monte Carlo calculations in the canonical ensemble, we have studied some properties of a two‐dimensional system of 170 long hard ellipses (whose axis ratio equals 6). This system can be considered as a two‐dimensional model for a nematic liquid crystal. We have shown that this system exhibits two first‐order phase transitions: a solid‐nematic type phase transition at high density and a disorientation phase transition at a density 1.5 times smaller. This result suggests that excluded volume effects might play an essential role in the disorientation phase transition of nematic liquid crystals.

INDO and MINDO/2 Crystal Orbital Study of Polyacetylene, Polyethylene, and Polyglycine
View Description Hide DescriptionApproximate valence electron self‐consistent field crystal orbital calculations using INDO and MINDO/2 parameters are described for polyacetylene, polyethylene, and polyglycine in a planar and α‐helical conformation. The electronic energy band structure and electronic charge distribution are discussed and compared with previous theoretical calculations and available experimental results.

Electrohydrodynamic Instabilities in Some Nematic Azoxy Compounds with Dielectric Anisotropies of Different Sign
View Description Hide DescriptionElectrohydrodynamic instabilities are observed in planar slabs of nematic azoxy compounds with values for between −0.2 and +0.2. Above a threshold voltage for negative Δε the well‐known cellular domain pattern is found. For positive Δε a reorientation only is observed in the nematic phase. However, for dc fields at the same voltage, cellular flow is present in the isotropic phase. Moreover, in this case domains can be introduced by a magnetic field. These different effects cannot be explained by considering stability criteria only. A discussion is given in which the orientating torques of the field on the nematic determine whether an instability leads to domains or not.

Magnetic Susceptibility of Tetraamminelithium(Zero) in the Range 1.5–194°K
View Description Hide DescriptionThe magnetic susceptibility of the compound tetraamminelithium (zero), Li(NH_{3})_{4}, has been measured by the Faraday method from 1.5 to 194°K. In the liquid the susceptibility is paramagnetic and shows a small positive temperature coefficient that can be attributed to variation of bandwidth with temperature. At the freezing point, 88.8°K, the susceptibility undergoes a 6% decrease, also attributable to a change in bandwidth. At 82.2°K, where there is a change from cubic to hexagonal structure, the susceptibility shows an abrupt 25% drop and Curie‐Weiss behavior down to about 15°K. Below 15°K, the susceptibility flattens out. Two models are presented to account for the observed behavior. In one, Li(NH_{3})_{4} is considered to be an antiferromagnetic metal with a Néel temperature of about 10°K; in the other, a nearly degenerate electron gas.Hysteresis at the 88.8°K and 82.2°K phase transitions has also been investigated. Fermi‐surface topologies for the cubic and hexagonal phases are discussed on the basis of the magnetic susceptibility measurements and existing x‐ray and optical data. The magnetic susceptibilities of pure lithium and pure ammonia have also been measured from 1.5 to 296°K. The lithiumsusceptibility is small, paramagnetic, and temperature independent both above and below the martensitic transformation. The ammonia susceptibility, which is negative, shows, in absolute value, a small decrease at the freezing point and a temperature‐dependent increase below 20°K.

Matrix Isolation Laser Raman Spectroscopy. I. Vibrational Raman Spectra and Depolarization Measurements for Matrix Isolated Group IVa Dihalides, MX_{2} and MXY (where M = Ge, Sn, Pb and X, Y = Cl, Br), in Solid Argon and Nitrogen
View Description Hide DescriptionThe vibrational Raman spectra together with polarization data are reported for most of the monomeric dihalides MX_{2} and mixed dihalides MXY of Group IVa (where M = Ge, Sn, or Pb and X, Y = Cl or Br) isolated in both argon and nitrogen matrices at 4.2°K. Laser induced resonance fluorescence effects which interfere with gas phase Raman studies are eliminated in Raman studies of matrix isolated dihalides. The isotope components of ν_{1} and ν_{3} are clearly resolved in the case of PbCl_{2} in argon and assigned to Pb^{35}Cl_{2}, Pb^{35}Cl^{37}Cl, and Pb^{37}Cl_{2}. Diffusion controlled warmup data are recorded for all species in the temperature range 4.2–40°K. All isolated monomers were found to diffuse rapidly at 30–35°K and only in the case of GeCl_{2} was a definite, stepwise polymerization process observed. The final spectrum obtained by warming GeCl_{2} showed the presence of a polymeric structure containing both terminal and bridging chlorine atoms. The matrix Raman results demonstrate that spectral sensitivities and resolution can be achieved which are comparable with the complimentary matrix infrared data and that matrix Raman polarizationmeasurements add a valuable new tool for matrix isolation studies.

Angular Time‐Correlation Functions from Spectra for Some Molecular Liquids
View Description Hide DescriptionDepolarized Rayleigh wing scattering data are reported for liquid chloroform, methyl iodide and methylene chloride. The calculation of orientation correlation functions from these results and from infrared vibration‐rotation bands is discussed. Fourier transforms of the infrared bands are corrected for shape changes due to variable refractive index,isotope splitting and hot bands. The resulting correlation functions are primarily a measure of orientational and collision‐induced changes in polarizability or dipole moment. It is argued that the collision‐induced contributions are important only at short times. The long‐time behavior of the correlation functions is then compared with several models for molecular reorientation in liquids, and it is concluded that the motion of these molecules is probably best characterized by models involving random walks in angular momentum space.

Proton Spin Echo NMR Spectra of 1,1‐Difluoro‐2,2‐dichloroethane: Subspectral Analysis
View Description Hide DescriptionFourier transformspin echoNMRspectra have been obtained for the protons in 1,1‐difluoro‐2,2‐dichloroethane as a function of rf pulse spacing. It is shown theoretically and experimentally that spin echospectra for this ABX_{2} spin system can be analyzed in terms of three distinct subspectra of the AB variety. Effects of transverse relaxation are considered. In principle cross relaxation invalidates subspectral analysis, but for the case of 1,1‐difluoro‐2,2‐dichloroethane such effects are shown to be small. The spin echospectra yielded a precise value for the proton proton coupling constant, and somewhat less precise values for the other spectral parameters. A few partially relaxed spectra were obtained by Fourier transformation of the free precession following individual spin echoes. The results of these experiments are in accord with previously developed theory, and show that derivation of selective relaxation rates from such spectra of coupled spin systems may be difficult in practice.

Structural Relaxation and Ultrasonic Absorption in Aqueous Solutions of Alkali Halides
View Description Hide DescriptionThe ultrasonic absorption in aqueous solutions of a number of alkali halides has been measured in the frequency range 5–100 MHz. Lower as well as higher ultrasonic absorption than in pure water has been found depending on type and concentration of the ions present. A kinetic model of the structural relaxation processes in ionic solutions is presented with which the absolute values of the structural absorption as a function of ion concentration and temperature for different types of ions can be described quantitatively. The analysis of the ultrasonic absorption data of the alkali halide solutions with this model yields information concerning the kinetic properties as well as the number of solvent molecules at different distances from the ions. The relaxational parameters obtained are consistent with other experimental data of water and of the solutions.

Velocity of Ultrasound in Cesium‐Ammonia Solutions
View Description Hide DescriptionThe velocity of 10 MHz waves in solutions of cesium in liquid ammonia as a function of both temperature and metal concentration are presented. Comparison of these data with those previously reported for lithium‐, sodium‐, potassium‐, calcium‐, and barium‐ammonia solutions is made. An analysis of the concentration dependence of the sound velocity reveals a structural change in the solutions as the metal concentration is increased. No evidence for compound formation was detected.

Vibrational Relaxation of Laser‐Excited CO_{2}‐Polyatomic Mixtures
View Description Hide DescriptionLaser‐excited vibrational fluorescencemeasurements have given rates for vibrational energy transfer from the asymmetric stretch of CO_{2} to several polyatomic molecules. Rate constants for energy transfer to the nearly resonant CD stretching vibrations in the deuterated species CD_{4}, CD_{2}H_{2}, CD_{3}Cl, CD_{3}I, C_{2}D_{2}, CD_{2}CH_{2}, and C_{2}D_{4} are compared to the corresponding normal hydrogen isotopes, and to the alkanes C_{2}H_{6}, C_{3}H_{8}, C_{5}H_{12}, and C_{6}H_{14}. The deuterated molecules are between 2 and 90 times more effective than the hydrogen isotopes at vibrationally deactivating CO_{2}. Cross sections for energy transfer from CO_{2} to (CN)_{2}, HCN, CH_{3}CN, H_{2}Se, CS_{2}, and OCS are given, and rates for intermolecular and intramolecular energy transfer in several of the collision partners are deduced.

Complete Polarization Study of the Two‐Photon Absorption of Liquid 1‐Chloronaphthalene
View Description Hide DescriptionAn apparatus is described which permits the measurement of all three of the parameters governing the polarized two‐photon absorption of a fluid. The measurement is performed by using suitable combinations of linear and circular polarized photons. The apparatus permits an experimental check on the basic theory of two‐photon absorptions. We find that predictions based on second‐order p·A interactions are quantitatively obeyed. Knowledge of all three absorption parameters allows the use of exact symmetry rules to assign the symmetry of the excited state. In 1‐chloronaphthalene, we find that the region of greatest absorption (38 000–42 000 cm^{−1}) is governed by a nearly symmetric absorption tensor with nonzero trace, indicating a naphthalenelike transition of the molecule. In the weaker region (32 000–36 000 cm^{−1}) the tensor is assymetric with nonzero trace. This means that the weaker band cannot be due to any two‐photon allowed naphthalenelike transition. Structure is seen in the spectrum of the parameter indicating that it is probably the vibronically induced which is well known, lie close to this energy from one‐photon studies. We find that δ_{ F } and δ_{ H } are very similar throughout the spectrum, leaving open the possibility that in the theoretical expressions for the two‐photon absorption, the sum over states is dominated by a single most important virtual state.

Laser Excited Emission Spectroscopy of Azulene in the Gas Phase
View Description Hide DescriptionIn this paper we present the results of an experimental study of the radiative decay of the two lowest singlet states S _{1} and S _{2} of the azulene molecule in the gas phase excited by a Q switched ruby laser (14 400 cm^{−1}) and by its second harmonic (28 800 cm^{−1}). Spectroscopicinformation has been obtained concerning the energy resolved spectra of the and of the emission. The quantum yield data for the decay led to an estimate of the nonradiative decay time of S _{1}. The branching ratio between the and the emissions was utilized for the evaluation of the radiative decay time. The study of the consecutive two photon excitation leads to an estimate of the absorption cross section near the electronic origins of the two excited states. The decay characteristics of the lowest excited singlet state of the ``isolated'' azulene molecule confirm the theoretical prediction concerning nonradiative electronic relaxation in the statistical limit.

Vibrational Relaxation Times of Oxygen and Oxygen Mixed with Several Light Gases
View Description Hide DescriptionVibrational relaxation times of τ of oxygen have been determined from sound absorptionmeasurements in the pressure range from 14 to 35 atm. Values of τ^{−1} were found to increase more rapidly with increasing pressure than the linear dependence expected if binary collisions alone were important. The effect of adding trace amounts of H_{2}, He_{3}, and He_{4} at a total pressure of 35 atm was also studied. Resulting relaxation times for and collisions were found to be in good agreement with earlier data at lower pressures. He_{3} was found to be 3.5 times more efficient than He_{4} in exciting vibration in O_{2}.

Theory of Reactive Scattering. II. Application of the τ Operator Formalism to a Linear Model for Three Body Rearrangements
View Description Hide DescriptionCoupled operator equations for the rearrangement channel operators τ_{αα} and τ_{βα} are employed in considering a simple collinear model for three body rearrangement collisions. The model is sufficiently general to permit dissociation of the bound atoms and in a certain limit the model becomes identical with that considered by Hulburt and Hirschfelder. We have been able to obtain analytical solutions for the coupled equations which may be used to calculate reactive and nonreactive scattering probabilities for both, when dissociation can occur and for the model of Hulburt and Hirschfelder. The numerical results for the Hulburt and Hirschfelder nondissociative model agree exactly with the results of Tang, Kleinman, and Karplus, and additional new numerical results are given for the more general model also. The present coupled equations may be generalized to three dimensional reactive collisions in a straightforward fashion.

^{93}Nb NMR Linewidths in Nonstoichiometric Lithium Niobate
View Description Hide DescriptionThe angle variation of the ^{93}NbNMRlinewidths is obtained for an off‐stoichiometry lithium niobate crystal. It is shown that the widths can be calculated on the basis of a model in which both the magnitude and direction of the electric field gradient are treated as random quantities. A second type of niobium, with a near zero quadrupole coupling constant, is shown to exist in off‐stoichiometric crystals. This amounts to roughly 6% of the total niobiums. This new resonance is undoubtedly associated with the mechanism of charge compensation and suggests that the excess niobium substitutes for lithium.

Solutions of Master Equations and Related Random Walks on Quenched Linear Chains
View Description Hide DescriptionFour separate but related contributions to the theory of quenched stochastic processes in one dimension are presented. First, Green's functions are derived for Laplace transformed master equations (here described in the language of, but not restricted to, hopping excitons) on finite chains with either periodic or free‐end boundary conditions, and with either a disruptive (substitutional impurity) or a nondisruptive quencher. We solve these problems in spectral form for short‐range quenching with arbitrary quencher location and quenching rate parameter Q _{o}. Second, the analogous random walk situations are treated. The solution of the generating function (finite‐difference analog of the Laplace transform) equation is identical to that of the Laplace‐transformed master equation with a disruptive quencher, but not with a nondisruptive quencher. Unlike the master equation case, slowly damped oscillations of the random walk chain excitation function can exist. Other differences also exist and are discussed; these occur at short times, with large concentration of quenchers, or in the presence of uniform decay processes like fluorescence. Third, the spectralsolutions of the master equations are applied to provide a closed analytical expression for the lowest moment of the chain excitation function on a particular chain in the presence of fluorescence, and to demonstrate the existence of an inflection point in the excitation function of an open chain excited and quenched at opposite ends. Fourth, we apply the coherent potential approximation to the master equation that describes a uniformly excited, randomly and nondisruptively quenched infinite chain. A closed analytic expression is obtained for the lowest moment of the excitation function in the absence of fluorescence, and is compared with previously obtained expressions for infinite chains with periodic nondisruptive quenchers or random disruptive quenchers. Finally, we discuss briefly the possibility of applying our results to the problem of metal‐ion quenching of the phosphorescence of polyriboadenylic acid.

Absolute Rate Constants for the Reaction of Atomic Oxygen with Ethylene over the Temperature Range 232–500°K
View Description Hide DescriptionRate constants for the reaction of atomic oxygen with ethylene were measured over a temperature range of 232–500°K using the flash photolysis‐resonance fluorescence technique. The rate constant at room temperature was also determined using a flash photolysis‐kinetic absorption spectroscopy system and a discharge‐flow system coupled to a mass spectrometer. Within the experimental errors of the three techniques, good agreement was found for the rate constant at 298°K. The bimolecular rate constant was also found invariant to changes in both total pressure and reactant concentration. Over the temperature range of the experiments, the rate data could be fitted by a simple Arrhenius expression of the form,

Experimental Determination of the Repulsive Potentials between K^{+} Ions and Rare‐Gas Atoms
View Description Hide DescriptionIntegral elasticscattering cross sections have been measured by the attenuation method for potassium ions with an energy selected in the range of 500–4000 eV scattered by room‐temperature He, Ne, Ar, and Kr atoms through effective laboratory angles greater than 5×10^{−3} rad. The repulsive potentials have been derived from the measured values of the cross sections with allowance for the density distribution across the beam in the collision chamber. The potentials are well represented by the following expressions: and where V(r) is in electron volts and r in angstroms.

On Singlet‐Triplet Transitions Induced by Exchange with Paramagnetic Molecules and the Intermolecular Coupling of Spin Angular Momenta
View Description Hide DescriptionThe theoretical basis of the singlet‐triplet transition mechanism by exchange coupling with neighboring paramagnetic molecules is examined. Attention is drawn to the two implicit assumptions of this exchange coupling model: (1) the validity of ``perfect'' permutational exchange of electrons between the neighboring molecules, and (2) the validity of the conservation of total spin angular momentum of the two neighboring molecules. With respect to the first assumption, it is found that the finiteness (vs perfection) of exchange overlap has not been sufficiently allowed for in the conventional (electrostatic) exchange mixing of allowed singlet and charge‐transfer states and in the conventional transitionsonly among the composite states of the same total spin angular momentum (e.g., ). It is derived that there exists a direct transition moment (between the two molecules) weighted by overlap integrals, which may not be much smaller than the allowed transition moment weighted by (the indirect) exchange mixing coefficients, and which may exhibit interference effect with the latter. It is pointed out that if exchange energy is finite and spin interactions are sizable, transitions to other states of different spin multiplicities (e.g., and ), which are not split sufficiently far apart, may contribute to intensity through spin interactions. With respect to the second assumption, it is shown that the small but finite spin interactions, especially interelectronic spin interactions, which do not commute with the assertedly conserved total angular momentumS ^{2}, have not been accounted for. A comprehensive formalism is developed to treat simultaneously exchange interaction along with spin interactions and to provide for various ranges of their relative magnitudes. These spin interactions are also shown to exhibit interference effects with the exchange interaction in the total intensity expression. All transitions, including and ,, are considered. Matrix elements of the direct transition, of the exchange mixing of allowed singlet and charge‐transfer states, and of the spin‐orbit, spin‐other‐orbit, and spin‐spin interactions are computed for general molecular orbitals and for the case of three and four electrons. The commutation and noncommutation of spin operators with S ^{2} are traced to permutation symmetry and are treated by isomorphism to C _{3v } (for three electrons) and T_{d} (for four electrons) point groups. Irreducible representations of the linear as well as quadratic forms of spin and orbital operators and their interactiontensors are derived. Their relationship to spin eigenfunctions of given permutational symmetries is discussed.