Volume 61, Issue 6, 15 September 1974

Equilibrium OH^{−} + C_{2}H_{2} ⇄ C_{2}H^{−} + H_{2}O and the determination of
View Description Hide DescriptionThe kinetics of the proton transferreaction OH^{−} + C_{2}H_{2} ⇄ C_{2}H^{−} + H_{2}O have been investigated at 296°K with the flowing afterglow technique. The rate constants were determined to be k _{forward} = (2.2±0.4) × 10^{−9} cm^{3} molecule^{−1} sec^{−1} and k _{reverse} = (9.3±3.7) × 10^{−15} cm^{3} molecule^{−1} sec^{−1}. The ratio of rate constants,k_{f}/k_{r} = (2.4±1.0) × 10^{5}, was found to be in agreement with the equilibrium constant,K = (2.5±1.0) × 10^{5}, determined from equilibrium concentrations. The best estimate of the true value of K corresponds to a standard free energy change, ΔG°_{296}, of −7.3±0.2 kcal mole^{−1}. An estimate of the standard entropy change, ΔS°_{298}, of +3.6 cal deg^{−1} mole^{−1} leads to a standard enthalpy change, ΔH°_{298}, of −6.2±0.5 kcal mole^{−1} and a value for ΔH°_{ f,298} (C_{2}H^{−}) = 71.5±1.1 kcal mole^{−1}. O^{−} was observed to react rapidly with C_{2}H_{2}, k=(2.0±0.4) × 10^{−9} cm^{3} molecule^{−1} sec^{−1}, principally by associative detachment and proton transfer. The reaction of with C_{2}H_{2} was observed to be slow, k ≤ 1 × 10^{−12} cm^{2} molecule^{−1} sec^{−1}.

Interpretation of phenomenological rate constants in the Bodenstein approximation
View Description Hide DescriptionA new formula is derived for the phenomenological rate constants in terms of the rate constants of a more detailed reaction mechanism that involves intermediate chemical species. The formula is derived in the Bodenstein, or steady‐state, approximation and applies to the particular case of a purely first order system of chemical reactions. The new formula suggests a physical interpretation for the phenomenological rate constants. The phenomenological rate constantk_{ij} for the observed chemical reaction (for the reverse reaction,k_{ji} ) x_{i} ⇄x_{j} between chemical species x_{i} and x_{j} is seen to be the number of molecules of species x_{i} per unit time per unit concentration that are transformed into species x_{j} either in one reaction or in a sequence of two or more reactions in which the molecule is first transformed to one intermediate chemical species after another, finally being transformed into chemical species x_{j} . The new formula displays very explicitly the precise functional dependence of the phenomenological rate constants on the rate constants of the reaction mechanism. This particular dependence leads to a notion of the dependence and independence of phenomenological rate constants. It is shown that this dependence of phenomenological rate constants could be exploited in kinetics studies to infer the presence of intermediate chemical species present only in extremely small concentrations.

Improved modified wavenumber approximation applied to elastic collision
View Description Hide DescriptionA method to improve the usual modified wavenumber result is applied to an elastic collision problem. For an exponential repulsive potential, simple expressions for the phase shift are obtained. The partial cross sections obtained by this improved modified wavenumber approximation agree qualitatively with those of the exact numerical solutions. The total cross sections agree very well with the exact results.

Integral equation approach to collinear reactive scattering: A + BC → AB + C
View Description Hide DescriptionAn integral equation approach to collinear reactive scattering has been developed. The technique has been implemented on a computer for calculation of scattering matrices for the following reactions: H+H_{2}→H_{2}+H; D+H_{2}→HD+H; and F+H_{2}→HF+H. The results of these calculations are found to be in good agreement with those obtained by earlier workers. The attractive features of this method are discussed.

Fine structure of the metastable state of the helium molecule
View Description Hide DescriptionWe have measured the spin—spin, electronic fine structure of the metastable state of He_{2} by means of a molecular beam,magnetic resonance apparatus, with the flowing afterglow of a pulsed, helium discharge as the source. The zero field separations in the N=1 and N=3 rotational levels, probably in the ν=0 vibrational state, are (in MHz) N=1; J=0 ↔ J=1:2199.968 ± 0.01, J=1 ↔ J=2: 873.668 ± 0.0007; N=3: J=2 ↔ J=3: 1323.911±0.006, J=3↔J=4: 964.992±0.006, where the errors quoted are three standard deviations of the mean. From these measurements and from a separate determination of the level order, the interaction constants for these states are the following (in MHz): spin—spin: λ:−1098.773 ±0.005(N=1), −1096.803±0.004(N=3), spin‐rotation: γ: −2.421±0.003(N=1), −2.414±0.001(N=3), where the errors are 3σ.

Flash photolysis‐resonance fluorescence kinetics study: Temperature dependence of the reactions OH + CO → CO_{2} + H and OH + CH_{4} → H_{2}O + CH_{3}
View Description Hide DescriptionTwo reactions involving the transient chemical species OH(ν″ = 0) and the reactants CO and CH_{4} have been investigated over a temperature range of nearly 140°C. Of particular importance were the measurements made below 300°C where data has heretofore been lacking. The rate constant expressions in Arrhenius form are k _{CO} = (2.15±0.19)×10^{−13} exp[−(160±80 cal mol^{−1})/R T] and k _{CH} _{4} = (2.36±0.21)×10^{−12} exp[−(3400±175 cal mol^{−1})/R T]. Units are cm^{3} mol^{−1} · sec^{−1}. Wide variations in the total pressure, H_{2}O concentration, initial OH concentration, and the nature of the diluent gas showed no indication of complex secondary reactions. The activation energies reported in this work for both processes, virtually zero for Reaction (1) and 3400 cal mol^{−1} for Reaction (2), are incompatible with those same quantities previously reported at elevated temperatures and indicate either nonlinear Arrhenius behavior for these OH reactions or possibly errors in experimental measurements.

Standardization of convention for zero field splitting parameters
View Description Hide DescriptionTransformation formulas have been derived for conversions between the various conventional systems for reporting zero field splitting data using the Hamiltonian . It is recommended that all future work be reported in the standard system corresponding to the range −1≤3E/D≤0.

Effects of ionizing radiation on tyrosine
View Description Hide DescriptionTwo oxidation products and one reduction product were identified in single crystals of tyrosine HCl irradiated at 4.2°K. Both oxidation products are associated with the loss of an electron from the phenol ring of tyrosine. The reduction product is the result of electron addition to the carboxyl group. The identification of these species followed from an analysis of proton hyperfine couplings measured by the ENDOR technique.

Relation between self‐diffusion coefficients and interdiffusion coefficients in methanol‐carbon tetrachloride and ethanol‐carbon tetrachloride systems
View Description Hide DescriptionDarken's binary diffusion equation was tested between interdiffusion coefficient and self‐diffusion coefficients for thermodynamically nonideal methanol‐carbon tetrachloride and ethanol‐carbon tetrachloride systems in which molecular association of the alcohols is known to occur. When the thermodynamic factor was calculated from equilibrium vapor pressures, Darken's equation did not hold for the two systems, but the thermodynamic factor approximately calculated from the mean degree of association of the alcohol better satisfied the equation for the systems within the low alcohol concentration range. Self‐diffusion coefficients of the respective components necessary for the present testing were measured for the methanol‐carbon tetrachloride system at 25°C. By assuming Darken's relation, mean degrees of association of the alcohols were reversely calculated for the high alcohol concentration range of the two systems.

Depolarized Rayleigh scattering in liquids. Molecular reorientation and orientation pair correlations in a nematic liquid crystal: MBBA
View Description Hide DescriptionThe spectrum and intensity of depolarized light scattered from binary solutions of the nematic MBBA and carbon tetrachloride have been measured. The results are interpreted in terms of pair correlations in the orientation of MBBA molecules. A systematic approach to the study of the orientational structure in nematic liquid crystals is proposed.

Zero field magnetic resonance of photoexcited triplet state species in naphthalene crystals and proton hyperfine structure
View Description Hide DescriptionWe have investigated the microwavemagnetic resonanceabsorption spectra produced at zero external magnetic field and ∼1.7°K by Hg–Xe arc irradiation of host naphthalene‐d _{8} crystals with and without added guest naphthalene‐h _{8} and also by irradiation of host naphthalene‐h _{8} crystals with and without guest naphthalene‐d _{8}. We have measured the values of the zero field energy splittings of the three components of the lowest energy triplet states for the naphthalene‐h _{8} guest molecule in naphthalene‐d _{8} host, for naphthalene‐h _{8} X‐traps in naphthalene‐h _{8} host crystals with and without added naphthalene‐d _{8} guest, and for naphthalene‐d _{8} X‐traps in naphthalene‐d _{8} host crystals with and without added naphthaplene‐h _{8} guest. We have determined the zero field line shapes and protonhyperfine structures for these various triplet species and find them to be in excellent quantitative agreement with our exact calculations for these systems. We have given a detailed discussion of our identification of the various triplet state species reported here.

Calculation of electric field gradients, electric fields, diamagnetic shieldings, dipole moment, second moment, and diamagnetic susceptibility of BH_{3}NH_{3}
View Description Hide DescriptionThe electric field gradient tensors at each of the four distinct nuclei of BH_{3}NH_{3} have been calculated from ab initio LCAO MO SCF wavefunctions constructed from a minimal basis set of STOs. In total 22 geometries have been examined of which 11 were eclipsed and 11 were staggered. From the equilibrium geometry the B–N bond length was expanded by 0.1 and 0.2 bohr, the B–H and N–H bond lengths were expanded and contracted by 0.1 bohr, and the ∠BNH and ∠HBN bond angles were increased and decreased by 5°. The values of 0.249 a.u. at H _{B}, 0.387 a.u. at H _{N}, 0.194 a.u. at B, and −0.765 a.u. at N have been calculated for the largest component of the electric field gradient tensor in the principal axis representation. The electric field, the diamagnetic shielding, the dipole moment, second moment tensor, and the diamagnetic susceptibility have been calculated as well.

Depolarized Rayleigh scattering and ^{13}C NMR studies of anisotropic molecular reorientation of aromatic compounds in solution
View Description Hide DescriptionMeasurements of reorientational relaxation times of simple aromatic compounds have been made by both depolarized Rayleigh light scattering and ^{13}C NMR spin‐lattice relaxation. Combination of the reorientation times determined by these techniques makes it possible to extract the reorientation times about the different molecular axes. The viscosity dependence of reorientation times about the individual molecular axes has been measured for benzene, mesitylene, toluene, and nitrobenzene. The viscosity dependence, which is highly anisotropic, is discussed in terms of a ``slip'' model of reorientational motion.

Off‐diagonal contribution to the hyperfine anisotropy of vanadyl and chromyl complexes
View Description Hide DescriptionThe off‐diagonal contribution involving the central ion and ligand orbitals to the hyperfine anisotropy for vanadyl and chromyl complexes is calculated. The calculations indicate that this contribution is approximately 10% of the diagonal contribution.

Analysis of the transient EPR signals in the photoexcited triplet state. Application to porphyrin molecules
View Description Hide DescriptionAnomalous EPR line intensities observed in the photoexcited triplet state of porphyrins at 100°K are discussed. A kinetic model consisting of the singlet ground state and the first excited triplet state is developed. The EPR signal intensities are expressed in terms of the kinetic rate constants and are given as linear combinations of two exponents. With these expressions the transient effects on the line intensities can be explained. Experimental results for two porphyrin molecules H_{2}TPP (tetraphenyl porphyrin free base) and H_{2}(PF)TPP (pentafluorotetraphenyl porphyrin free base) are presented and compared with the theory. From the analysis we evaluated the spin lattice relaxation rate W, the depopulation rate constants k_{p} and the ratio between the population rate constants A_{p} : For H_{2}TPP, k_{x} =(6±2)×10^{2} sec^{−1}, k_{y} =(3±1)×10^{2} sec^{−1}, k_{z} =(1.5±0.5)×10^{2} sec^{−1}, A_{x} :A_{y} :A_{z} ≃1:0.6:0.2, and W =3.3×10^{3} sec^{−1}. For H_{2}(PF)TPP, k_{x} =(5±2)×10^{2} sec^{−1}, k_{y} =(1.4±0.4)×10^{2} sec^{−1}, k_{z} =(1.0±0.3)×10^{2} sec^{−1}, A_{x} :A_{y} :A_{z} ≃1:0.2:0.3, and W =1.7×10^{4} sec^{−1}.

Contribution of relaxation and chemical shift results to the elucidation of the structure of the water‐DMSO liquid system
View Description Hide DescriptionProton spin‐lattice relaxation times (T _{1}) of water and dimethyl sulfoxide (DMSO) in H_{2}O–DMSO (I), H_{2}O–DMSO‐d _{6} (II), and D_{2}O–DMSO (IV) systems at 9.8, 18.7, 29.9, and 41.4°C exhibited minima near 0.65 mole fraction of water (X _{H2O}). The depth of the minimum, relative to T _{1} values at higher and lower X _{H2O}, increased as the temperature was lowered. The intramolecular contribution to the relaxation of DMSO protons was always greater than the intermolecular DMSO–DMSO contribution and the former showed a minimum at X _{D2O}≈0.6 as compared with the latter's minimum at X _{D2O}≈0.4–0.6. There is almost no contribution to water protonT _{1} from the interaction of water protons‐DMSO protons in the DMSO‐rich mixtures, while this contribution is rather significant in the DMSO‐poor mixtures. The protonchemical shifts of water with reference to DMSO protons (over a temperature range of −60−45°C) moves to higher fields with rising temperatures, and this temperature dependence is affected considerably by the changes in composition. All these experimental results suggest the presence of strong intermolecular interactions between water and DMSO molecules that contribute to the ``structuring'' of this binary mixture. The structure of this liquid system is very sensitive to composition and temperature.

Scattering of alkali halides by electrons. II. CsCl
View Description Hide DescriptionScattering of CsCl by 0.47–15.7 eV electrons has been measured using the molecular beam recoil technique. Center of mass differential cross section models are adjusted to the scattering after transformation to apparatus space. Absolute total cross sections, approximately equal to the first Born approximation point dipole prediction at 15.7 eV, fall to one‐fourth of the theory at 0.47 eV. Momentum transfer cross sections are dramatically smaller than the theory at low energies.

Scattering of alkali halides by electrons. III. KI
View Description Hide DescriptionScattering of KI by 0.81–15.7 eV electrons has been observed using the molecular beam recoil technique. Center of mass cross section models are adjusted to fit the apparatus space scattering pattern. Absolute total cross sections agree at high energies with the first Born approximation and are a factor of 4 smaller at the lowest energy. At low energies the momentum transfer cross sections are an order of magnitude below theory. The measured cross sections are nominally identical to those measured in CsCl.

Magnetic properties of verdazyl free radicals. VII. π‐Bridged verdazyl biradicals with triplet ground state
View Description Hide DescriptionMagnetic susceptibilities of two π‐bridged verdazyl biradical solids have been measured in the temperature range 1.8−300°K. Paramagnetic Curie constants of 1.0±0.1 and 0.90±0.05 K·emu/mol have been found in 1,4‐bis(1,5‐diphenyl‐3‐verdazyl)benzene (P‐verdazyl) and 1,3‐bis(1,5‐diphenyl‐3‐verdazyl)benzene (M‐verdazyl), respectively. Both Curie constants suggest the presence of the triplet ground state. The intramolecular positive exchange integrals, J/k, of these biradicals are much greater than 300°K. The susceptibility of P‐verdazyl exhibits a maximum at 19±1°K, which implies a negative exchange interaction between the triplets, its magnitude being estimated to be about 7°K.

Europium in the ultraphosphate lattice: Polarized spectra and structure of EuP_{5}O_{14}
View Description Hide DescriptionThe polarized emission and absorption spectra of single crystals of europium ultra(penta)phosphate, EuP_{5}O_{14}, were measured and interpreted. Most of the observed transitions were identified and the energy level structure of the ^{7} F multiplet defined. The over‐all site symmetry is found to be extremely low (C _{1}), but in the immediate vicinity of the Eu^{3+} ion the local symmetry appears to deviate little from C _{2v }. Crystal field calculations were performed for such symmetry and gave a respectable fit to the observed Stark splittings of the ^{7} F multiplet. A simple structuralmodel for the first coordination shell of the Eu^{3+} ion is proposed, consistent with the spectroscopic behavior and with the signs and relative magnitudes of the calculated crystal field parameters. Finally, the decay times of the ^{5} D _{0} and ^{5} D _{1} emitting states of the ion were calculated and found to be consistent with measurement.