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Volume 66, Issue 8, 15 April 1977

The determination of hydrogen coordinates in lanthanum nicotinate dihydrate crystals by Nd^{+3}‐proton double resonance
View Description Hide DescriptionThe EPR(electron paramagnetic resonance) and protonENDOR(electron nuclear double resonance) spectra of single crystals of lanthanum nicotinate dihydrate with Nd^{+3} dilutely substituted for La^{+3} have been obtained and described by appropriate spin Hamiltonian operators. The ENDOR signals of protons lying within 5 Å of the Nd^{+3} have been resolved and assigned to specific protons. The physical interpretation of the measured anisotropic rare earth ion–proton hyperfine interactions has been given. The spatial coordinates of the protons in the principal axis system of the electron Zeeman interaction matrix g_{ e } have been obtained with standard deviations ranging from 0.002 to 0.015 Å, with an average of 0.006 Å. The average standard deviation for the coordinates of the 4 H_{2}O protons nearest to the Nd^{+3} ion, three of which form hydrogen bonds with nicotinate nitrogen atoms, is 0.004 Å. The average standard deviation for their distances from the Nd^{+3} is 0.003 Å. It is clear that by means of suggested improvements of the reported techniques it should be possible to measure proton coordinates to 0.001 Å. The methods developed show promise for applications to problems concerning the structure of organic molecules, in particular organo–metallic complexes and large molecules of biological interest, such as proteins, to which paramagnetic ions may be attached.

On a multiple reflection time domain method in dielectric spectroscopy: Application to the study of some normal primary alcohols
View Description Hide DescriptionThe authors propose a time domain method of total reflected signals on a dielectric sample in a coaxial line. This method enables the determination of the complex constant of propagation of the medium to be studied and, consequently, its complex permittivity. Contrary to other similar methods employed up to now, this method needs neither iterative calculation nor nomograms. The validity of this multiple reflection approach is illustrated by the study of several primary alcohols. The values of the permittivities and relaxation frequencies thus acquired are in good agreement with those obtained elsewhere.

Laser excitation of rare gas metastables and the resulting fluorescence distribution
View Description Hide DescriptionLaser excitation spectra have been obtained from metastable states of the rare gas atoms, He, Ne, Ar, Kr, and Xe. The relative population of the atomic metastable states have been obtained several centimeters downstream from a dc discharge source. Dispersion of the laser‐induced fluorescence indicates that relaxation of the excited atomic levels is very extensive at the 1–10 torr pressures used.

A proton and deuteron spin–lattice relaxation study of the partially deuterated nematogens PAA and MBBA
View Description Hide DescriptionProton spin–lattice relaxation times (T _{1}) have been measured in methyl deuterated p a r a‐azoxyanisole (PAA‐d _{6}) and in ring deuterated p a r a‐azoxyanisole (PAA‐d _{8}) samples as functions of frequency and temperature. When compared with recent order fluctuation theory, the agreement between theory and experiment is not as satisfactory for the intermolecular contribution to the spin–lattice relaxation as for the intramolecular contribution. Deuteron spin–lattice relaxation times (T _{1Q }) have also been measured in a ring deuterated p‐methoxybenzylidene p‐n‐butylaniline (MBBA‐d _{8}) sample. The above order fluctuation theory fails to predict the observed temperature dependence and the observed frequency independence of T _{1Q } if the correlation time τ_{ c } for local motions is taken to be one‐third the dielectric relaxation time τ_{ D }. However, a fair agreement is obtained if one uses τ_{ c }= (1/100) τ_{ D }, a value consistent with Ref. 6.

On moment index displacement
View Description Hide DescriptionMoment index displacement can determine the amount of light scatter and zero point displacement in fluorescence time decay data. Two different types of light scatter are considered and shown to have significantly different effects on the analysis of the data. The amplitude correction factor determined by Eisenfeld and Mishelevich is experimentally verified.

Structure of phase boundaries
View Description Hide DescriptionThe boundary between plus and minus spin phases of the Ising model is studied for the bcc 〈110〉 boundary. The iterative calculation due to Weeks and Gilmer is interpreted as a modification of the Natural Iteration computation (with subsidiary conditions) for deriving a free energy minimum. A tetrahedron is used as the basic cluster in the cluster‐variation scheme for this problem. Two formulations are presented: one uses the scalar‐product formulation and the other the boundary sum method. Previous results of an order–disorder type phase transition within the boundary are confirmed. Results of calculations on the boundary excess free energy and the boundary profile are compared for the pair and the tetrahedron treatments.

Stress–strain behavior in polymer networks containing nonlocalized junctions
View Description Hide DescriptionTwo models of entanglement interaction in polymer networks are examined. One is based on Edwards’ principle of topological classification, the other on interstrand links which are free to slip along the strand contours. Relationships between stress and strain in simple elongation are developed for networks which contain such elements as well as permanent crosslinks. In each case departures from neo‐Hookean behavior are found. The apparent modulus decreases with strain in uniaxial tension and remains approximately constant in uniaxial compression as observed in real networks. If the network is expanded, such as would occur through addition of a swelling solvent, the departures from neo‐Hookean behavior become smaller, again as observed experimentally. It thus appears that chain entanglements, portrayed here by two different nonlocalized junction models, may account for many of the differences in behavior between real networks and predictions of the phantom network theories.

Ion–molecule reactions in SiH_{4}–D_{2} mixtures
View Description Hide DescriptionThe ion–molecule reactions characteristic of SiH_{4}–D_{2} mixtures have been elucidated and the reaction cross sections measured as a function of relative kinetic energy. D_{2} ^{+} reacts with SiH_{4} to yield SiH_{3} ^{+}, SiH_{2} ^{+}, SiH^{+}, and Si^{+} by exothermic processes that proceed with a total cross section near the Langevin orbiting value. D_{3} ^{+} reacts with SiH_{4} to form only SiH_{3} ^{+} with a cross section also near the Langevin value. The absence of SiH_{2}D^{+} suggests direct H^{−} transfer from SiH_{4} rather than the intermediate formation of SiH_{4}D^{+}. All reactions of Si‐containing ions in their ground states with D_{2} are endothermic. Energy thresholds for the deuterium atom pickup reactions of Si^{+} and SiH_{2} ^{+} yield thermochemical results in satisfactory agreement with values obtained by other methods. SiH_{3} ^{+} reacts with D_{2} to form SiH_{2}D^{+} solely, a result indicating that only HD is eliminated from an SiH_{3}D_{2} ^{+} intermediate and showing the nonequivalence of D and H in the silanium ion.

Dynamical charge transfer through hydrogen bonds: Hartree–Fock calculations of vibrational properties of formic acid monomer and cyclic dimer
View Description Hide DescriptionIn order to explain the observed changes in the vibrational spectra of formic acid from monomeric to cyclic dimeric form the SCF Hartree–Fock method has been applied to calculate minimum energy geometries, quadratic force constants, and net atomic charges. The set of a b i n i t i o quadratic force constants turns out to be acceptable and accounts for the observed vibrational changes. The a b i n i t i o interaction force constant between carbonyl stretching motions for the dimer accounts for what is considered to be an unusually large observed splitting of the C=O stretching frequencies in carboxylic acid dimers. Calculations suggest that such a large splitting originates from a dynamical charge transfer through the hydrogen bond. The possible existence of this phenomenon should in general be considered when dealing with the vibrational properties of hydrogen bonded systems.

Resonance Raman spectra of metalloporphyrins. Effects of Jahn–Teller instability and nuclear distortion on excitation profiles of Stokes fundamentals
View Description Hide DescriptionExcitation profiles of depolarized modes (b _{lg }, b _{2g }) in Ni etioporphyrin I exhibit marked 0–0 resonance Raman intensity upon Q‐band excitation. By contrast, inversely polarized Raman scattering (a _{2g }) is stronger with 0–1 excitation. Within the crude Born–Oppenheimer approximation, a theoretical model is presented which explains the 0–0 enhancements of depolarized modes as arising from interference of intermanifold (Q –B) and intramanifold (Q –Q) vibronic coupling. Comparison of computed and observed excitation profiles shows that a weak Jahn–Teller distortion is present in the Q state. The vibronic model predicts behavior of Raman intensity in the B (Soret) electronic state. Evidence of increased vibronic coupling of both 400 and 1365 cm^{−1} polarized vibrations (a _{1g }) is found in chromium tetraphenylporphyrin with the appearance of a supernumerary peak at 1400 cm^{−1} in the excitation profile of the 400 cm^{−1} vibration. Excitation profiles of a _{2g } modes in the chromium complex exhibit an apparent decrease in excited state vibrational frequencies due to increased coupling. Estimates of vibronic coupling strengths for the Q state are given for the nickel and chromiumporphyrins.

Intermolecular potential of anisotropic systems: LiF–Ar and LiF–Kr
View Description Hide DescriptionHigh resolution differential cross sections for LiF scattering from Ar and Kr were measured in the thermal velocity range with varying LiF rotational temperature. An extremely narrow velocity distribution in the LiF beam, which reduced the equivalent temperature of the experiment to typically below 1 K, made it possible to resolve the high frequency oscillations of the differential cross section. Rainbow oscillations were identified and measured.Effects of experimental convolution were discussed and treated. Average potential well depths and radii were determined. It was inferred from the breadth of the primary rainbows that the potential well is not pathological in possessing extremely deep or shallow depths (ε) for certain orientations: standard deviation of ε is about 50%. The persistency of the high frequency oscillations with angle is evidence of a quite spherical locus of r _{ m }, although the locus is not necessarily concentric with the center of mass. The high frequency oscillations and in part the rainbow oscillations are damped by rotational transitions. The differential cross section is largely independent of the rotational state distribution. Calculations using an optical model for the scattering and assumed angular dependent potentials permitted a quantitative test of a theoretical long range potential model and also permitted a fit of an empirical angular dependent model at the radius of the onset of these transitions. The quantitative test indicated that neglected repulsive terms are important in the theory. The fitted empirical model was consistent with the measureddispersion in ε. The radius at which rotational transitions become significant has been determined and lies outside r _{ m }, approximately at the rainbow radius, but inside the radius probed by total scattering cross section measurements. The potential well parameter r _{ m }=3.8 Å, ε=4.1×10^{−14} erg and r _{ m }=3.7 Å, ε=5.3×10^{−14} erg were obtained for LiF–Ar and LiF–Kr, respectively.

Volumetric pretransition in cholesterics
View Description Hide DescriptionVolumetric studies of the phase transitions in the following cholesterol derivatives are reported: cholesteryl chloride, C. laurate, C. myristate, C. nonanoate, and C. oleate. Pretransition volumetric behavior in the smectic, cholesteric, and isotropic phases is interpreted in terms of a ’’critical’’ exponent. In the isotropic phase the data are consistent with the de Gennes–Landau theory. The transformation from the cholesteric focal conic texture to the ’’blue phase’’ has a transition enthalpy and volume of approximately 5% of the transition to the isotropic phase.

Effects of long range interactions on the conformational statistics of short polypeptide chains generated by a Monte Carlo method
View Description Hide DescriptionDistributions of end‐to‐end distances and characteristic ratios are calculated for short poly‐l‐ala and poly‐gly chains generated by a Monte Carlo method based on the procedure elaborated by Metropolis e t a l. Interactions between all the atoms of the chain are taken into account for the conformational energy calculations. The characteristic ratios obtained with the complete set of interaction terms are much smaller than those calculated according to the method of Flory. This collapse of the chain is interpreted as due to a bad solvent. Results in agreement with Flory’s are obtained by modifying the potential functions to simulate the behavior of the chain in a ϑ or even a good solvent. In this case an excluded volume effect appears for poly‐gly chains, whereas poly‐l‐ala chains are too stiff to present this effect with less than 16 residues.

Alkali halide surfaces: Measurements and modeling of adsorbate motions and reactions at surface defects
View Description Hide DescriptionResults are presented for a mass spectrometric study of reactions between alkali halide molecular beams and vaporizing single crystals of different alkali halides. Shuttering the beam yields a temperature dependent decay of reaction products from their steady state surface fluxes. We determined Arrhenius pre‐exponentials and activation energies from the decay rates of unreacted beam diatomic (monomer), dimer products, and beam–crystal ion exchange products (monomers). The kinetic curves were primarily composed of a slow decay with a smaller amount of a faster decay. The pre‐exponentials and activation energies exhibit a close correlation (lnAαE _{ a }) for energies ranging from 2–57 kcal/mole. This compensation effect has allowed our direct measurement of several processes in a narrow range of first order decay constants (0.02–4.0 sec^{−1}). Analysis of the decay curves and extensive modeling of the crystal surface defects identify the measured activation barriers with specific surface processes. We have assigned dimer product and unreacted beammonomeractivation energies to barriers against motion from ledge to surface desorption sites. Beam–crystal ion exchange reactions occur at kink defects and the rate determining step for monomer product formation is the dissociation of a dimer intermediate at the kink. Some decay measurements showed evidence for bulk diffusion of diatomic and atomic species.

Alkali halide surfaces: Adsorbate binding energies and structures at surface defects
View Description Hide DescriptionWe describe an electrostatic method of calculating equilibrium configurations of alkali halide diatomic molecules (monomers) and tetratomic dimers adsorbed on rigid alkali halide crystal surfaces. Results are presented for adsorbate binding energies and geometries on the smooth surface, at single‐step ledge defects, and at kink (corner) defects. The results are consistent with our recent experimental measurements and we explore several features of the adsorbate–substrate interaction. Cyclic dimers are more weakly bonded than monomers on the smooth surface, but binding strengths for both are nearly equivalent at ledges. Linear dimers are stabilized at the defectbinding sites. For all species, the kink position is the strongest adsorption site. Adsorbate structures at the different sites are dependent on the relative magnitudes of adsorbate–adsorbate and adsorbate–substrate interactions.

Alkali halide surfaces: Potential energy surfaces for diffusion and dimer dissociations
View Description Hide DescriptionWe report results from electrostatic calculations of activation barriers for surface motions of alkali halides adsorbed on alkali halide (100) crystal faces. The results include energy surfaces for adsorbatediffusion along single‐step ledges and dimer motions at idealized kink defects. Activation barriers for diffusion and desorption along the crystal surface and ledges are nearly equal, which implies that the pre‐exponential factors for both rates are significant in determining diffusion distances for adsorbates. Dimer motions at kink defects either interconvert several possible stable isomers or lead to diatomic dissociation products. The kink’s role in such movements is to distort the different dimer configurations and to strongly bond one diatomic pair during dissociation. There is a direct relationship between the structure of the adsorbed dimer and the diatomic products formed from specific dimer motions.

Calculation of Raman scattering parameters for methane and halomethanes from an atom dipole interaction model
View Description Hide DescriptionDerivatives of molecular polarizabilitytensors with respect to vibrational normal coordinates are calculated using an atom dipole interaction model for CH_{4}, CD_{4}, CF_{4}, CCl_{4}, CHF_{3}, CH_{3}Cl, CHCl_{3}, CF_{3}Cl, CFCl_{3}, CH_{3}Br, CF_{3}Br, and CH_{2}Cl_{2}. Isotropic atom polarizabilities obtained from previous studies of molecular polarizability are used. Derivatives of atom polarizabilities with respect to bond lengths are adjusted to give a best fit to the mean polarizability derivative ?′ for 29 totally symmetric modes as found from published gas phase Raman scattering intensities and depolarization ratios. A satisfactory fit to ?′ is obtained, but the calculated anisotropies γ′ correlate only roughly with the experimental values. The signs of the calculated ?′ values are consistent with the view that the mean molecular polarizability increases with increasing bond length for all normal modes in which bond stretching motions predominate.

A b i n i t i o calculations of oscillator and rotatory strengths in the random‐phase approximation: Twisted mono‐olefins
View Description Hide DescriptionA b i n i t i o (STO‐nG) computations of ordinary and rotatory intensities of low‐lying electronic transitions are presented for twisted ethylene and twisted t r a n s‐2‐butene in the random‐phase approximation (RPA). The intensities are computed in both dipole length and dipole velocity forms, as well as the mixed form for the oscillator strength, and the convergence of these formally equivalent results is examined in the RPA and several other methods for constructing the electronic excitation: the virtual orbital, or single‐transition, approximation (STA), the monoexcited configuration‐interaction, or Tamm–Dancoff, approximation (TDA), and one version of the higher RPA (HRPA). We show that the RPA has consistent advantages over the TDA for calculation of CD as well as ordinary intensities. Our computations confirm that a localized, ethylenic chromophore is indeed adequate to account for the low‐lying CD spectrum in mono‐olefins. Further, even with minimal valence‐shell basis sets, our RPA rotatory strengths agree essentially completely in both sign and magnitude with the experimental results of Mason and Schnepp on t r a n s‐cyclooctene.

Rotational energy effect upon the branching fraction for reactive decay of the CsF+K collision complex
View Description Hide DescriptionThe influence of the rotational energy of the CsF molecule upon its reactivity with K has been measured by the crossed molecular beam technique over a range of relative translational energy Ē_{tr} from 3–6 kcal mol^{−1}. The experiments involve the endoergic (1.8 kcal mol^{−1}) reaction CsF+K⇄[CsFK]→Cs+KF, for which the reactive branching fraction F _{ R } had been previously measured in this laboratory using velocity‐selected but otherwise ’’thermal’’ (Boltzmann)beams. In the present investigation, beams of low rotational states of CsF have been prepared by means of a quadrupole state selector focusing field placed beyond the usual slotted‐disk velocity selector. This arrangement provides so‐called ’’low‐J’’ beams of CsF, with known speed distributions, which are then crossed with a well‐characterized K beam. The measurements consist of angular distributions of reactive (i.e., Cs) and nonreactive (i.e., CsF) scattering for the ’’low‐J’’ beam compared to the ’’thermal’’ reactant beam at essentially the same Ē_{tr}. The reactive yield and thus the reactive branching fraction F _{R} is found to be significantly smaller for the ’’low‐J’’ beam relative to the ’’thermal’’ beam of CsF. An analysis of the state selection and focusing properties of the quadrupole lens sytem has been carried out which accounts satisfactorily for the observed velocity dependence of the CsF focused beam intensity. This analysis yields a calculated rotational state distribution P (J), from which the average rotational energy Ē_{rot} of the reactant CsF molecules is obtained at each of the Ē_{tr} values studied. Ē_{rot} ranges from 0.13 to 0.04 kcal mol^{−1} for Ē_{tr} in the range 3–6 kcal mol^{−1}, whereas Ē_{rot} for the ’’thermal’’ CsF beam is 2.52 kcal mol^{−1}. (Thus the effect of applying the rod voltage to the quadrupoles is to ’’switch off’’ some 2.4 kcal mol^{−1} of CsF rotational energy.) This analysis also predicts the observed enhancement of the total scattered signal due to the focusing, which implies that the cross section for complex formation is the same (within ≈±10%) for the low‐J and the thermal reagent molecules. By combining the data on the Ē_{tr}‐dependence of F _{R} for the rotationally cold CsF beams with the previous results for thermal beams it is possible to compare the relative importance of rotational versus translational energy at a given total energy. It is found that rotational energy of the CsF is significantly less effective than relative translational energy in promoting reactive decay of the complex. The theoretical implications of this result are discussed.

Spin diffusion effects in partially spin–lattice relaxed NMR spectra of solid block copolymers
View Description Hide DescriptionRoom‐temperature proton NMR measurements of 65 wt % poly(dimethylsiloxane) (DMS) and 35 wt % bisphenol‐A polycarbonate (BPAC) block copolymers with number average DMS block lengths ranging from 20 to 100 monomer units have shown effects which can be explained in terms of a gradient of net spin population along the DMS blocks during recovery from a nonselective 180° spin inverting pulse. This gradient occurs because the spin–lattice relaxation of the BPAC component is faster than that of the DMS component and spin diffusion takes place along the DMS blocks to the BPAC, causing spins at the centers of the DMS blocks to relax slower than those at the ends. High‐resolution solid NMR spectra were obtained with a multiple‐pulse technique, which permitted independent measurements of the DMS and BPAC relaxations. Unusual line shapes in partially relaxed broadline spectra were interpreted as being caused by enhanced motional narrowing of the protons at the centers of the DMS blocks in addition to the gradient of net spin population along the DMS blocks. The results of a spin diffusion model, which was developed to aid interpretation of the experimental results, were in quantiative agreement with the data. This model fits the data only if the diffusion process is limited by diffusion along the length of the DMS blocks and not by a single diffusion barrier between the DMS and BPAC blocks.