Index of content:
Volume 64, Issue 12, 15 June 1976

Temperature and pressure dependence of the NMR transition frequencies of ^{27}Al in LiAl(SiO_{3})_{2}, spodumene
View Description Hide DescriptionEquations have been developed, correct to second order in the normal‐mode amplitudes for lattice vibration, which describe the constant‐volume temperature dependence of the NMR transition frequencies for a spin 5/2 nucleus located at a site of arbitrary asymmetry parameter. These equations indicate that an analysis of the temperature dependence of the transition frequencies will not yield rigorously the temperature dependence of the quadrupole coupling constant or asymmetry parameter unless all the transition frequencies are measured. The temperature and pressure dependences of two of the NMR transition frequencies of ^{27}Al in LiAl(SiO_{3})_{2} have been measured over a temperature range of 4.2–300 K at atmospheric pressure, and a pressure range of 0–7 kbar at 195, 273, and 298 K. From these measurements, as well as from measurements of the volume expansion coefficient and the compressibility, the temperature dependence of the transition frequencies at constant volume was calculated. An analysis of these results indicates that, with the assumption of three vibrational modes of characteristic temperatures of approximately 150, 675, and 2600 K, there is reasonable agreement between experiment and a simplified form of the theory.

Effective Hamiltonian methods for the semiclassical treatment of molecular collisions
View Description Hide DescriptionEffective Hamiltonian theory has previously been applied in a quantum mechanical framework, where the computational savings resulted from the reduced number of coupled equations. The present paper shows how effective Hamiltonian theory can be combined with classical S‐matrix theory. In this case the computational difficulty is reduced by lowering the number of degrees of freedom that must be semiclassically ’’quantized’’ via root‐searching techniques. It is shown, for example, that a full classical S‐matrix calculation for collisions of two rigid diatoms would require root searches in a four‐dimensional space while an effective potential calculation would need only two‐dimensional root searches. This can represent a substantial decrease in computational effort. A modified effective potential and the centrifugal decoupling method are formulated for application to classical S‐matrix theory. Also included is a description of the rotational coordinates and momenta needed for the semiclassical treatment of an arbitrary, nonreactive bimolecular collision.

Microwave spectrum, structure, and dipole moment of 3,3‐difluorocyclopropene
View Description Hide DescriptionThe microwave spectra of four isotopic species of 3,3‐difluorocyclopropene have been investigated in the region from 18–40 GHz. Structural parameters obtained are r (C_{1}C_{2}) =1.321±0.001, r (C_{1}C_{3}) =1.438±0.007, r (CH) =1.075±0.001 , r (CF) =1.365±0.005 Å, &FCF=105.5±0.5°, &C_{1}C_{3}C_{2}=54.6±0.4°, &HC_{1}C_{2}=148.4±0.1°. From the Stark effect the dipole moment has been determined to be 2.98±0.02 D.

Proton modulation of the electron spin echo envelope in a Nd^{3+}:aquo glass
View Description Hide DescriptionThe electron spin echo envelope has been measured at 4.2 °K for a frozen solution of NdCl_{3} in water and alcohol. Measurements were made at a frequency of 9.134 GHz and at Zeeman field settings of 2400, 3200, and 4000 G. At all these field settings the electron spin echo envelope showed a deep modulation associated with frequencies in the vicinity of ω_{ I } and 2ω_{ I }, where ω_{ I } is the free proton precession frequency. The components at ?ω_{ I } were clearly visible in the early portion of the envelopes, but components ? 2ω_{ I } tended to predominate towards the end. These results have been interpreted by means of a model in which it is assumed that the protons lie on one or more concentric spheres about the Nd^{3+} ion. In the simplest form of calculation based on this model the proton distribution was taken to be uniform over each of the spherical shells, and the envelope modulation function was calculated by summing contributions weighted according to the area of elements on the surface and the number of protons in the shell. In an alternative approach, the coordinating protons were assumed to be added in a random and uncorrelated manner on the surface of the sphere (or spheres) and a product formula was used to derive the result. Although the main qualitative features of the modulation envelope could be explained in this way, neither form of calculation was sufficiently exact to interpret the data to within the limits of experimental accuracy. The approximation on which the linear sum calculation is based breaks down in the magnetic field regime concerned here. The product calculation is on the other hand inherently inaccurate because of the assumption regarding the random placement of successive protons. We obtain a best value r _{1}= 3.0 ±0.1 Å for the radius of the first proton shell in the Nd:aquo complex. A more accurate value could probably be obtained by working with a higher microwave frequency and higher values of H _{0}. The significance of these results in relation to the design of electron spin echoexperiments in organic and biological materials is discussed.

Brillouin–Rayleigh scattering studies of polypropylene glycol. III
View Description Hide DescriptionA comprehensive Brillouin scattering experimental study of polypropylene glycol (PPG), average molecular weight of 1025, 2025, and 4000, has been carried out. The hypersonic velocity,attenuation coefficient, the modulus of elasticity, and the Landau–Placzek ratio have been obtained as a function of temperature for each polymer. The PPG 425 data reported earlier are also included for comparison. For all the quantities measured, only the Laudau–Placzek ratio (below ambient temperature) is molecular weight dependent; the hypersonic velocity,attenuation coefficient, and elastic modulus are found to be independent of molecular weight in the present 425–4000 weight range. The differences in the Landau–Placzek ratio between the different polymers are attributed to different degree of frozen‐in density fluctuations due to the difference in the medium’s viscosity; the mechanism of structural relaxation is not sufficient to explain the increase of the Landau–Placzek ratio of each polymer below ambient temperature. All polymers display the velocity dispersion and sound attenuation maximum. However, contrary to that observed in the ultrasonic frequency region, the maximum of the hypersonic attenuation coefficient appears to lie close to the beginning of the velocity dispersion curve and not its middle. The present results on the sound velocity and attenuation can be satisfactorily fit to a theory developed by Isakovich and Chaban, who have modeled the highly viscous liquid as a microinhomogeneous medium.

Infrared and Raman spectra of the M^{+}Cl_{3} ^{−} ion pairs and their chlorine–bromine counterparts isolated in argon matrices
View Description Hide DescriptionThe argon matrix reactions of alkali chloride salts with Cl_{2} have been investigated through infrared and Raman spectra. In each infrared experiment, an intense product band was observed between 327 and 375 cm^{−1} and assigned to the antisymmetric stretching vibration ν_{3} of the Cl_{3} ^{−} anion in the ion pair M^{+}Cl_{3} ^{−}. Raman spectra of these reaction mixtures yielded the same ν_{3} bands and, in addition, new signals between 253 and 276 cm^{−1} which are assigned to the symmetric stretching vibration ν_{1} of Cl_{3} ^{−} in the M^{+}Cl_{3} ^{−} species. The observation of two stretching modes in the Raman spectra indicates that the Cl_{3} ^{−} ions are asymmetric in these ion pairs. Bromine counterparts and the mixed chlorine–bromine anions were also formed, and used to verify that the anion in the M^{+}X_{3} ^{−} species contains three halogen atoms, with the metal ion beside the anion in an asymmetric ’’T’’ shaped structure.

Temperature dependent activation energy for electron transfer between biological molecules
View Description Hide DescriptionThis paper considers electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium. This theoretical approach is analogous to an extended quantum mechanical theory of outer sphere electron transfer processes, incorporating the effects of both low‐frequency medium phonon modes and the high‐frequency molecular modes. An explicit, compact and useful expression for the electron transfer probability is derived, which is valid throughout the entire temperature range, exhibiting a continuous transition from temperature independent tunneling between nuclear potential surfaces at low temperatures to an activated rate expression at high temperatures. This result drastically differs at low temperatures from the common, semiclassical, Gaussian approximation for the transition probability. The experimental data of De Vault and Chance [Biophys. J. 6, 825 (1966)] on the temperature dependence of the rate of electron transfer from cytochrome to the chlorophyll reaction center in the photosynthetic bacterium Chromatium are properly accounted for in terms of the present theory.

Variational localized‐site cluster expansions. I. General theory
View Description Hide DescriptionCluster expansions in terms of general sites (which may be spin orbitals, spin‐free orbitals, shells, component atoms in a molecule, etc.) are developed for electronic wavefunctions. Emphasis is placed upon the potential simplification of such expansions in the case that the sites are localized. Formulas for both diagonal and off‐diagonal matrix elements for such cluster expanded wavefunctions are given, and approximations to these general formulas are discussed.

Variational localized‐site cluster expansions. II. Trees and near trees
View Description Hide DescriptionCluster expanded wavefunctions involving localized‐site states and only pair excitations between nearest neighbor sites are considered. In the case that the bonds connecting these nearest neighbor sites form a tree graph (without rings), exact matrix element formulas are obtained in terms of the inverse of a modified type of topological matrix associated with this tree graph. The treatment of some near‐tree cases, without any touching rings, is also discussed.

Simulation of molecular spectra: A linear equation solving method
View Description Hide DescriptionThe difficulties in using diagonalizing algorithms in the calculation of molecular spectra are discussed. An alternative method is proposed in which the complex matrix equation is solved directly. The inherent inefficiency of this method is largely bypassed by first reducing the matrix into Hessenberg or triangular form by means of similarity transformations. This method is found to yield accurate line shapes even for matrices for which many diagonalizing algorithms fail.

MCSCF potential energy surface for photodissociation of formaldehyde
View Description Hide DescriptionThe ground statepotential energy surface for the dissociation of formaldehyde H_{2}CO→H_{2}+CO is calculated with the a b i n i t i o MCSCF method with an extended (4–31G) basis set. The location, barrier height, and force constants of the transition state are determined and the normal coordinate analysis is carried out. The calculated barrier height is 4.5 eV. Based on the calculated quantities, the detailed mechanism of the photochemicaldissociation is discussed.

Determination of the proton affinity from the kinetics of proton transfer reactions. VI. The relative proton affinities of N_{2}, Xe, and CO_{2}
View Description Hide DescriptionThe position of equilibrium was investigated with the flowing afterglow technique for the proton transferreactions N_{2}H^{+}+Xe?XeH^{+}+N_{2} at 297, 378, and 800°K, N_{2}H^{+}+CO_{2}?CO_{2}H^{+}+N_{2} at 700 and 798°K, and XeH^{+}+CO_{2}?CO_{2}H^{+}+Xe at 800°K. The equilibrium constantsmeasured at each temperature provided values for the proton affinity differences PA(Xe)−PA(N_{2}) =0.63±0.19 kcal mole^{−1} and PA(CO_{2})−PA(Xe) =9.7±1.5 kcal mole^{−1}. Rate constants were also determined for the three reactions proceeding under nonequilibrium conditions.

Absolute rate parameters for the reaction of atomic hydrogen with hydrazine
View Description Hide DescriptionAbsolute rate parameters for the reaction of atomic hydrogen with hydrazine H+N_{2}H_{4}→H_{2}+N_{2}H_{3} have been determined in a direct manner using flash photolysis of dilute mixtures of hydrazine in helium and time dependent observation of H via resonance fluorescence. By measuring the H‐atom decay under pseudo‐first‐order conditions, the bimolecular rate constantk _{1} was obtained over the temperature range 228–400°K. The data were fitted with good linearity to the Arrhenius expression k _{1}= (9.87±1.17) ×10^{−12} exp(−2380±100/R T) cm^{3} molecule^{−1}⋅sec^{−1}. The data were shown to be free of any contributions from secondary reactions involving H as a reactant or product. A comparison of the present results with those from previous studies employing discharge flow methods is presented.

Normal vibrational modes resulting from the lifting of degeneracies in anisotropic crystals: The internal optic modes of K_{2}SO_{4}
View Description Hide DescriptionThe vibrational normal coordinates of internal optic modes originating in molecular normal modes whose degeneracies have been lifted through site group effects are discussed. The normal mode frequencies are calculated in a molecular dipole formalism. The coupling between different Cartesian components of a phonon mode is described with particular attention to the symmetry based sufficiency condition for that coupling to occur.

The adsorption of neon on graphitized carbon in the submonolayer and multilayer region between 1.5 and 30°K
View Description Hide DescriptionHeat capacities and heats of adsorption (calorimetrically measured) together with equilibrium pressures are reported for coverages up to three monolayers. The data indicate that neon remains localized up to 30°K in the submonolayer region. Phase transitions of the adsorbed neon were observed in the temperature and coverage range of this investigation. The regions in which these transitions take place are shown in a coverage vs temperature plane. In region II of this plane, a phase transition takes place which results in excess heat capacities in the submonolayer region. In region III, a transition of a different nature takes place which resembles the ’’melting’’ process. The ’’two‐dimensional gaslike’’ phase could only appear at temperatures higher than those attained in this work. In region I, the adatoms behave as highly localized oscillators, and those at the high energy sites contribute a major portion to the heat capacity below 3°K. The residual entropy was calculated for the two submonolayer coverages and was found to be equal to zero within the experimental error. The Ne–solid interaction energy is 2990 J/mole at 24°K and 2770 J/mole at 29°K. The integral heat of adsorption at 0°K was calculated in the submonolayer and multilayer region, and the difference between the first and subsequent monolayers is found to be more than 700 J/mole. The integral adatom–adatom interaction energy of adsorbed neon in the submonolayer region at 24°K varies almost linearly with coverage and is approximately equal to 290 J/mole at the completion of the first monolayer. The monolayer capacity of the adsorbent for neon depends on temperature and the coefficient of the thermal expansion of the first monolayer in the x y plane is estimated to be about 0.002 deg^{−1} in the temperature range 24–29°K. For higher coverages a substantially higher coefficient is observed, and this is attributed to a phase change which takes place in the structure of the film. Finally, the degree of homogeneity of graphitized carbon, Spheron 6, i.e., the ratio of the high energy sites to the planar sites of graphitized carbon, is found to be approximately equal to 0.1.

Theoretical investigations on the light scattering of spheres. XVII. Angular and spectral location of intensity maxima and minima
View Description Hide DescriptionComprehensive data were collected on the angular location of the various types of maxima and minima of Mie scatterers within the m range 1.050–1.333. Detailed comparison with the extrema calculated for the simple Rayleigh–Gans–Debye case of (m−1) →0 led to a relatively simple correction equation which allows one to calculate with fairly good accuracy the angular location of Mie extrema quickly and easily and within a wide range of α and m values the limits of which are defined. Application of the results is discussed for fast particle size determinations in monodisperse systems of isotropic homogeneous spheres.

Graph theory and molecular orbitals. XV. The Hückel rule
View Description Hide DescriptionThe topological analysis of the Hückel (4m+2) rule is carried out and shows its dependence on the structural features of conjugated systems. The proof of the validity of the Hückel rule for a given molecule is also presented.

Chemistry of nuclear recoil ^{18}F atoms. VIII. Mechanisms and yields of caging reactions in liquid phase 1,1‐difluoroethane and 1,1,1‐trifluoroethane
View Description Hide DescriptionNew procedures are reported for the specification of caging yields in nuclear recoil chemistry experiments. All five hot ^{18}F substitution channels in CH_{3}CF_{3} and CH_{3}CHF_{2} exhibit caging at large density. The respective total caged yields at 195 °K are 4.0%±0.6% and 5.6%±0.6%, and the total yields of stabilized substitution products are 8.9%±0.4% and 8.6%±0.6%. The simplest plausible caging mechanism involves primary Franck–Rabinowitsch radical recombination of ^{18}F atoms with aliphatic radicals. Density‐variation results cannot be used for the qualitative detection of caging reactions unless excitation‐stabilization complications have been shown to be unimportant.

Electronic structure of the luminescent centers in rare earth oxysalts doped by bismuth
View Description Hide DescriptionA cluster model is assumed for the luminescent centers in Y_{2}O_{3}:Bi, BiOCl, and LnOCl:Bi (Ln=La,Y). A semiempirical self‐consistent charge and configuration molecular orbital theory has been used to determine valence MO energies and populations. Including spin orbit and configuration interactions, we compute the pattern of the excited levels. Changing the number and the nature of the ligands in the cluster, one can see the variation of the localized charge with respect to the constitution and symmetry of the several environments. Dependence of the electronic levels on distance indicates a large substitution effect comparing with presently available experimental data. The results confirm the presence of allowed electronic excited states with strong oscillator strength in the near uv range, and trap levels. One of the latter always is the lowest electronic level and thus suggests an interpretation of the luminescent processes similar to that proposed for the La_{2}O_{3}:Bi phosphor.

Electrical properties of KF‐doped hexagonal ice
View Description Hide DescriptionKF dopedicesingle crystals were grown between platinum electrodes from water of about 5 MΩ cm resistivity and their electrical ac conductance G _{ac} and capacitance Cmeasured over a temperature range of −10 to −90 °C and a frequency range of 50 to 20×10^{3} Hz using a Wayne–Kerr B 641 ac bridge. The activation energyE _{σ} for ac conduction was determined from the plot lnG vs 1000/T (concentration range of KF, 10^{−6} to 10^{−3} N). The dielectric relaxation time τ was obtained from the Debye dispersion relation and the activation energyE _{τ} of dielectric relaxation found from the plot lnτ vs 1000/T. For the same KF ice,E _{σ} was 5.9 kcal/mole and E _{τ} was 4.06 kcal/mole. In KF iceE _{σ} was always found to be greater than E _{τ}. Direct current conductivity G _{dc} obtained from plots of ε_{ m } ^{″}ω vs f ^{2} also showed a temperature dependence and hence an activation energyE _{σ} (determined from the plot lnσ_{dc} vs 1000/T) implying that it is unnecessary to invoke the mechanism of quantum mechanical tunneling for dc conduction. The static dielectric constant ε_{ s } for KF ice was found to decrease with decreasing temperature, the values ranging from 15 to 50×10^{2} for the temperature range −90 to −13 °C. The experiments indicate that the predominant mechanism for ac conduction is that of propagation of Bjerrum defects and that the dopant (F^{−} ions, KOH, or HF) is incorporated into the ice lattice substitutionally.