Volume 55, Issue 5, 01 September 1971

Relative ^{14}C–^{13}C Kinetic Isotope Effects
View Description Hide DescriptionModel‐reaction calculations are used to show that relative ^{14}C–^{13}C kinetic isotope effects, defined as , should, within the framework of the presently accepted statistical‐thermodynamic theory of such effects in the harmonic approximation, generally be restricted to the range . Significant deviations from this range may occur when the individual ^{14}C and ^{13}C kinetic isotope effects are of unusually small magnitude and/or are associated with easily detectable temperature‐dependence anomalies. Reported cases of experimental values of r significantly outside the 1.8–2.0 range are examined with regard to the model‐reaction calculations. It is concluded that, if the reported effects in four of the five such cases are real, additional complications, not considered in the basic theory as usually applied, must be operative. The results of this study are in accord with, and qualify only slightly, a conclusion reached by Bigeleisen almost two decades ago.

Determination of Hyperfine Constants and Nuclear Shielding in Methyl Fluoride and Comparison with Other Molecules
View Description Hide DescriptionThe molecular‐beam electric resonancespectrum of methyl fluoride (CH_{3}F) was measured in several rotational states. From analysis of the spectra the hyperfine structure of the molecule was determined. The hyperfine constants are (kilohertz): for the spin—rotation interactions of the hydrogen nuclei, and for the spin—rotation at the fluorine. These results are combined with nuclear shielding data to calculate contributions to shielding and the electrostatic potential at the nucleus. Quantitative comparison is made with other molecules.

Monte Carlo Calculations on Polypeptide Chains. III. Multistate per Residue Hard Sphere Models for Randomly Coiling Polyglycine and Poly‐l‐alanine
View Description Hide DescriptionMonte Carlo studies of randomly coiling polyglycine and poly‐l‐alanine were carried out using the same hard‐sphere model for these polypeptides that was used previously in this laboratory in which the bond lengths and bond angles are held fixed, the peptidebond is fixed in the planar trans configuration, free internal rotation is assumed about the backbone N–C^{α} and C^{α}–C′ single bonds, and the individual atoms or groups of atoms interact pairwise by hard‐sphere potential functions. In these studies however, all the allowed conformational states per residue from the dipeptide maps taken in 10° increments in the rotational angles φ and ψ for rotation, respectively, about the backbone N–C^{α} and C^{α}–C′ single bonds are used whereas formerly only three states per residue had been used for poly‐l‐alanine and four states per residue for polyglycine. Non‐self‐intersecting chains of various chainlengths up to 180 amino acid residues were generated for both polyglycine and poly‐l‐alanine using the sample enrichment technique of Wall and Erpenbeck and then were used to calculate the average chain dimensions. Chains were also generated in which the hard‐sphere potential functions were omitted and from which the unperturbed average chain dimensions were calculated. As found previously for the four‐state per residue model of polyglycine and the three‐state per residue model of poly‐l‐alanine, the point by point attrition parameter λ_{ N } was found to be an increasing function of chainlength N over the entire range of N included in the calculations, and the data could be well fitted by the empirical equation , where λ_{∞} was 0.0500 for polyglycine and 0.0518 for poly‐l‐alanine. These values for λ_{∞} are the best estimates of the traditional attrition constants for these models. The mean square end‐to‐end distance and mean square radius of gyration for both non‐self‐intersecting and unperturbed chains were found to obey the equations and for large N. The parameters b and b′ were found to be very close to the exact theoretical value of 1.00 for unperturbed chains and to the value 1.20 for non‐self‐intersecting chains. As found in previous studies for the four‐state per residue model for polyglycine and the three‐state per residue model for poly‐l‐alanine, the ratio for the models used in this study passes through a maximum as a function of chainlength in the vicinity of chainlength 10–15 for both non‐self‐intersecting and unperturbed polyglycine and poly‐l‐alanine chains and then approaches, within the statistical reliability of the data, the exact theoretical value of 6 for the longest generated unperturbed chains and a value of about 6.4–6.6 for the longest generated non‐self‐intersecting chains. The results of calculations of the conformational entropy per residue are presented and the results of this study are briefly discussed in terms of Windwer's concepts of intrinsic excluded volume and excess excluded volume.

Degenerate Excited State in the Structure of B_{2}O_{3}
View Description Hide DescriptionA degenerate excited state is essential to the description of structural rearrangements which account for the relaxational heat capacity,thermal expansion, and compressibility of vitreous B_{2}O_{3}. These relaxational responses cannot be simultaneously described by a two‐state model, or by any model involving a single ordering parameter, as shown by the magnitude of the Prigogine—Defay ratio . The apparent two‐state behavior of the temperature derivatives, Δα and Δc_{p} , and failure of a two‐state model to predict a sufficiently large compressibility (pressure derivative), suggest an analysis of structural rearrangements in vitreous B_{2}O_{3} in terms of a single ground state and a twofold degenerate excited state which is characterized by different volumes.

Optical Spectra of Vanadium Ions in Yttrium Aluminum Garnet
View Description Hide DescriptionOptical absorption and emission spectra of vanadium impurities in Y_{3}Al_{5}O_{12} crystals are reported. Crystals doped with vanadium only and with vanadium counterdoped with charge‐compensating calcium and silicon ions were studied. Possible valence states for vanadium include V^{2+}, V^{3+}, V^{4+}; possible substitutional sites in the garnet lattice include octahedral Al^{3+}, tetrahedral Al^{3+}, and dodecahedral Y^{3+}. The observed spectra are interpreted as arising from octahedrally coordinated V^{3+} and V^{4+} and tetrahedrally coordinated V^{3+} and V^{4+}. No spectral evidence of V^{2+} or of vanadium in dodecahedral sites was found. Vanadium‐to‐neodymium energy transfer was also investigated and is discussed.

Theory of the Coupling of Electronic and Vibrational Excitations in Molecular Crystals and Helical Polymers
View Description Hide DescriptionThe effect of the internal vibrations of monomers (or molecules) on the electronic absorption spectra of aggregates with either helical or three dimensional translational symmetry is considered using molecular excitontheory. In this treatment the single‐particle excitations (vibronic excitons) are coupled to all those two‐particle manifolds in which vibronic and ground vibrational excitons occupy different lattice sites. This allows for collective coupling among single‐particle levels overlapped by two‐particle continua. The main approximations invoked are (a) the crude Born—Oppenheimer approximation to factorize the wavefunctions of isolated monomers, (b) neglect of electron exchange between monomerwavefunctions (tight binding), and (c) the neglect of any mixing of different electronic states by intermonomer forces. Wave sums of exciton resonance interactions are eliminated in favor of a density of sums function. To test the range of coupling strengths for which the theory is valid calculations are performed for a one‐dimensional polymer model with only nearest‐neighbor interactions and a three‐dimensional crystal model with a simple density function. For intermediate coupling the influence of three‐ and higher‐particle states becomes important and these states are included in the energy calculations by an extended fraction type of technique. Other calculations explore the effect of (a) a change in the vibrational frequency of the monomer after electronic excitation, (b) changes in the energy of the optical levels with direction of the exciting radiation, and (c) changes in the transition intensity of the isolated monomer.

Far‐Ultraviolet Spectra of Fluoroethylenes
View Description Hide DescriptionThe vacuum ultraviolet spectra of the complete series of fluoroethylenes were measured from 2000 to 1150 Å under moderate resolution. The transitions are easily identified in all the spectra. In most cases their maxima are only slightly displaced from their position in ethylene, but a very large hypsochromic shift is found in going from the tri‐ to the tetrasubstituted derivative. Three Rydberg series are observed in all the spectra, converging to the ionization potential. They all exhibit vibrational fine structure dominated by stretching and twisting vibrations. In the highly fluorine substituted ethylenes the first Rydberg band is well separated from the band (at about 1900 Å) as in the highly alkyl substituted derivatives. There is no evidence for transitions of σ electrons in this part of the spectrum except perhaps at the high frequency end of the range (1200 Å).

Hyperfine Interaction, Chemical Bonding, and Isotope Effect in ZnH, CdH, and HgH Molecules
View Description Hide DescriptionESRspectra of ZnH, CdH, HgH, and HgD molecules in their ground states were measured while trapped in solid argon matrices at 4°K. gtensors and hyperfine structure (hfs) constants for interaction with H, D, ^{111,113}Cd, and ^{199,201}Hg nuclei were observed. Coefficients of approximate LCAO wavefunctions are derived from these magnetic parameters and correlated with chemical bonding trends in the series and with the limiting united‐atom model. Replacing H by D in HgH causes an increase of spin density on Hg and a decrease in g∇. This is shown to be largely due to the small decrease in interatomic distance and is discussed relative to other spectroscopic observations.

Interaction Second Virial Coefficients in Binary Systems
View Description Hide DescriptionInteraction second virial coefficients of some binary gas mixtures are higher than either of the pure component values within certain temperature ranges. For other systems and temperature ranges the interaction second virial coefficient is lower than the pure component values. Conditions under which these situations may occur are investigated in terms of the intermolecular potentials and force constants, and examples from literature experimental data are given.

Thermal Electron Attachment to Nitrous Oxide
View Description Hide DescriptionThermal electron attachment to nitrous oxide was investigated in the range −66 to 215°C. The attachment was found to be dissociative in nature with an activation energy of . The activation energy is thought to arise from electron attachment to molecules thermally excited primarily in the bending mode. In an attempt to explain the activation energy a simple Morse function was employed. Potential energy as a function of internuclear distance for both N_{2}O and N_{2}O^{−} was generated at different N_{2}O bond angles. In this manner a three‐dimensional surface for the reaction, was obtained. The potential surface has a minimum at a bond angle . The electron affinity of N_{2}O is estimated at from the calculated N_{2}O^{−} potential‐energy surface. This is in general agreement with other reported values.

Helix to Random Coil Transition in n‐Stranded Molecules with Excluded Volume Effect
View Description Hide DescriptionThe Lifson—Zimms' theory for helix to random coil transition has been extended to n‐stranded polynucleotides. Formulas are derived which relate the stacking free energy and ring closure index to the maximum slope of the helix to coil transition in matching and dAT:dAT polynucleotides. The effect of inter‐ and intrastrand excluded volumes on transition point and on the stacking free energy in double stranded molecules has been examined. Both excluded volume effects have been expressed by a single parameter γ, which appears in the relation between the mean square end‐to‐end distance and the number of units in a given polymer. It is concluded that the interstrand excluded volume effect shifts the transition point, descreases the τ value, and increases the ε value for double‐stranded molecules.

Energy Transfer Reactions of . IV. Measurement of the Radiative Lifetime and Study of the Interaction with Olefins and Other Molecules
View Description Hide DescriptionThe rate constants and products from the interaction of the first triplet state of nitrogen, , with C_{2}H_{4} and cis‐C_{4}H_{8} have been measured in a discharge flow apparatus. The reactions are fast with rate constants near 10^{14} cc mole^{−1}·sec^{−1} and give products which are typical of other triplet—triplet donor reactions with olefins. The product yields were used to measure the concentration of molecules. This concentration was combined with the absolute emission intensity from the transition to estimate the radiative lifetime of . The data support the recently published low lifetime value reported by Shemansky and Carleton. Rate constants were measured for quenching of by acetylene, cyanogen, propene, benzene, 1,4‐butadiene, cyclopropane, oxygen, sulfur dioxide, carbon monoxide, nitrous oxide, and ammonia. The first‐order removal of by the quartz surface also was characterized.

PVT Behavior of Water at Negative Pressures
View Description Hide DescriptionMeasurements have been made of the extension of a column of liquid water in a centrifugal field. Schlieren photographs of the meniscus position were made at rotational speeds up to 18 000 rpm at temperatures from 5 to 35°C. The data were analyzed using a form of the Tait equation. All of the data were able to be represented well within experimental error, . The constants in the equation, found by regression of these negative pressure data, are very nearly those which describe the positive pressure region.

Theory of Light Scattering from Fluctuations of Membranes and Monolayers
View Description Hide DescriptionGeneral linear viscoelastic response relations are used to obtain the long‐wavelength fluctuations of a thin membrane separating two viscous fluids. The intensity and spectrum of coherent light scattered inelastically from thermal fluctuations are calculated. It is found that the intensity is large enough to allow measurements on black membranes. Our theory includes clean surfaces, interfaces, and insoluble monolayers as special cases.

Microwave Spectrum of Iodostannane, SnH_{3}I
View Description Hide DescriptionThe pure rotational spectra of seven isotopic species of the chemically unstable symmetric top molecule iodostannane, SnH_{3}I, have been measured in the region 28.3–31.6 GHz, using a microwave spectrometer. Each transition exhibited a complex K structure due to quadrupole coupling and centrifugal distortion. A quadrupole coupling constant and centrifugal distortion constant were obtained from the analysis. Rotational spectra of vibrational excited states were observed for the most abundant isotopic species.

Ion—Molecule Reactions in an O_{2}+–H_{2}O System
View Description Hide DescriptionA sequence of reactions which occur in ionized O_{2}–H_{2}O mixtures has been studied with the following results: The measurements were made at 295°K in a flowing afterglow system, operated in both fixed and variable reaction length modes. The results indicate that .

Ion—Molecule Reactions in NO^{+}–H_{2}O System
View Description Hide DescriptionThe following reaction sequence which occurs in ionized NO–H_{2}O or air—H_{2}O mixtures has been studied: The measurements were made at 295°K in a flowing afterglow system, and reactions were measured for M = He, Ar, and N_{2}.

Comparisons of Dispersion Force Bounding Methods with Applications to Anisotropic Interactions
View Description Hide DescriptionComparisons and applications are made of the various procedures which have been devised recently for obtaining bounds to dispersion force coefficients. Particular attention is given to the methods based on approximate Gaussian quadratures and on Padé approximants, both of which require oscillator‐strength sum rule values for their implementation. The equivalence of the bounds obtained from the two procedures, when identical input information is employed, is demonstrated to all orders, and the improvements that can result from the introduction of additional information, in the form of experimental transition frequencies and other sum rules, is investigated in the course of numerical applications. Comparisons with alternative bounding methods, such as those based on variational principles and related inner projection techniques, show that these procedures, which can also employ sum rule values for their implementation, are similar to the Gaussian quadrature and Padé methods and provide identical results if the same input information is employed. There also exists a second class of procedures which provides bounding inter‐relations directly among the dispersion force coefficients, without reference to sum rule values, thus forming a useful complement to the former procedures. Numerical applications to molecular hydrogen, nitrogen, and oxygen, and the inert gases and alkali atoms, using both theoretical and semiempiricalsum rule values, indicate that the bounding procedures can provide anisotropic dispersion force estimates of greater accuracy than those which can currently be extracted from rotational relaxation and related experiments. Comparison with more approximate methods for estimating the anisotropies in dispersion interactions, based on static polarizabilityanisotropies, serves to delineate the limits of accuracy of such approximations. The polarizabilityanisotropy approximation is found to provide overestimates in every case.

Ion Cyclotron Resonance Power Absorption: Collision Frequencies for CO_{2} ^{+}, N_{2} ^{+}, and H_{3} ^{+} Ions in Their Parent Gases
View Description Hide DescriptionThe complete solution for the equation of motion of an ion in the ICR cell is shown to give results for the instantaneous power absorption in excellent agreement with experiment at all pressures. The instantaneous power absorption at resonance initially increases linearly with time, and at high pressures levels off to a constant value at saturation where the energy gained by ions from the rf electric field is equal to the energy dissipated in collisions. An expression is also derived for the average kinetic energy of an ion at saturation in the steady‐state limit. Pulsed ICR techniques are used to obtain the instantaneous power absorption curves for , and ions in their parent gases as a function of pressure, from which are calculated the momentum transfer rate constants k, and the dependence of the rate constants on ion kinetic energy. At 293°K, , and . For ions in N_{2} and ions in CO_{2}, the rate constants are both significantly greater than that predicted by polarizationtheory and both rate constants increase significantly with increasing ion kinetic energy. This behavior is most likely a consequence of long‐range resonant charge transfer outside the orbiting impact parameter.

Self‐Diffusion Coefficients and Rotational Correlation Times in Polar Liquids. II
View Description Hide DescriptionSelf‐diffusion coefficients and rotational correlation times have been measured in several polar liquids by pulsed nuclear magnetic resonance techniques. Self‐diffusion coefficients are reported for CH_{3}OH, CH_{3}NO_{2}, (CH_{3})_{2}CO, C_{6}H_{5}NO_{2}, and C_{6}H_{5}Cl; proton, deuterium, and chlorine‐35 relaxation times are given for these liquids. Deuteron quadrupolar coupling constants for the deuterated molecules were measured directly for the solids at low temperature. Methyl groups in CH_{3}OH, CH_{3}NO_{2}, and (CH_{3})_{2}CO have correlation times that are considerably shorter than the correlation time for the tumbling of the entire molecule. The Ivanov theory of large amplitude molecular jumps is generalized to the case of two kinds of jump about different axes and an explicit expression for the over‐all correlation time is given. The pre‐exponential factors of the methyl group correlation times appear to change drastically in CH_{3}OH and CH_{3}NO_{2} upon melting. Rotational correlation times for molecular tumbling are in good agreement with those calculated from quasilattice random flight model. In methanol there is evidence that rotation of the molecule about the OH bond direction occurs more rapidly than the over‐all tumbling of the molecule. Molecular rotation also appears to be anisotropic in nitrobenzene as evidenced by a factor of 2 difference between the nitrogen and deuteron rotational correlation times. The pressure dependence of the intramolecular relaxation rate in C_{6}H_{5}Cl reported by Bull and Jonas is also shown to be in reasonable agreement with the prediction of the quasilattice model.