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Volume 63, Issue 4, 15 August 1975

Combinatorial and topological methods in nonlinear chemical kinetics
View Description Hide DescriptionCombinatorial and topological techniques are developed to classify nonlinear chemical reaction networks in terms of their qualitative dynamics. A class of N coupled equations, based on a hypothesis concerning biological control by Monod and Jacob is derived. Transitions between volumes in concentration space for these equations are represented as directed edges on N cubes (hypercubes in N dimensions). A classification of the resulting state transition diagrams for N=2,3 is given. A version of a topological theorem by Poincaré and Hopf is derived which is appropriate for application to chemical systems. This theorem is used to predict the existence of critical points in continuous nonlinear equations with oscillation and bistability on the basis of their state transition diagrams. A large number of nonlinear kinetic equations proposed in previous studies by other authors are classified in terms of their state transition diagrams.

Deuteron quadrupole coupling constants in CD_{3}F and 1,3,5‐C_{6}D_{3}F_{3}
View Description Hide DescriptionThe deuteron quadrupole coupling constants in the deuterated methyl fluoride and 1,3,5‐trifluorobenzene molecules have been determined from nematic phase studies using a pulsed FT NMR spectrometer. The values obtained in the molecular symmetry axis system are as follows: χ_{ z z } = −47.8±1.5 kHz (in CD_{3}F) and χ_{ z z } = −94.4±0.7 kHz (in 1,3,5‐C_{6}D_{3}F_{3}). If the field gradient tensor is assumed to be diagonal in the C–D bond axis system, the values of the coupling constants referred to the C–D bond are given by χ_{CD} = 133±7 kHz (in CD_{3}F, η = 0.03±0.03) and χ_{CD} = 180±3 kHz (in 1,3,5‐C_{6}D_{3}F_{3}, η = 0.05±0.01).

Energy partitioning and assignment of excited states in the ultraviolet photolysis of HI and DI
View Description Hide DescriptionPhotofragment spectroscopy has been applied to the photolysis of hydrogen iodide and deuterium iodide at 37 550 cm^{−1} (266.2 nm). The extent of excited I(^{2} P _{1/2}) atom production and the symmetry of the excited molecular states leading to dissociation are derived by measuring the translational energy and angular distributions of the recoiling H and D atoms. It is found that for HI, 36%±5% of the I atoms are formed in their excited state, while for DI the fraction is 26%±3%. In both cases, the transition leading to excited atoms is parallel, agreeing with Mulliken’s spectral interpretation. These results, together with measurements reported by others at different wavelengths, are used to analyze the first absorption continuum of HI and DI. This continuum is found to be consistent with overlapping transitions to ^{3}Π_{1}, ^{3}Π_{0} _{ + }, and ^{1}Π excited states, as predicted by Mulliken. A nonlinear curve fitting technique is applied to the available data to separate each state’s contribution to the total continuum absorption and to provide estimates of the shape of each excited state potential energy curve.

Two‐photon circular dichroism
View Description Hide DescriptionOptically active molecules will show differential absorption, as between opposite handedness of the radiation, for two‐photon absorption. A theoretical estimate is made of the expected ratio of the differential rate to the total rate and an order of magnitude of this ratio for a simple helical model is found.

Theoretical studies in photoelectron spectroscopy: Use of angular distribution data to deduce molecular orobital parameters. IV. Calculation of angular distributions for ejection of low‐energy photoelectrons from molecules having 1sσ^{2} _{ g }, 2pσ^{2} _{ g }, or 2pσ^{2} _{ u } configurations
View Description Hide DescriptionAngular distributions are calculated for the ejection of photoelectrons in the energy range of less than 1 eV to above 50 eV from molecules having 1sσ^{2} _{ g }, 2pσ^{2} _{ g }, or 2pσ^{2} _{ u } configurations. The continuum wavefunction for the photoelectron is calculated in the ’’static‐exchange’’ approximation of electron–molecular ion scatteringtheory by numerical integration of the one‐electron integrodifferential equations appropriate for this approximation, accounting accurately for screening and exchange effects in the photoelectron–molecular ionic system. These equations are coupled in the radial partial waves relative to the center of mass of the nuclei, and they are solved both for the case of complete uncoupling and for the cases of coupled s and d waves, for ejection from a 2pσ_{ u } molecular orbital, and of coupled p and f waves, for ejection from a 1sσ_{ g } or 2pσ_{ g } molecular orbital. Formulas are presented for the asymmetry parameter β for each of these cases. Provided enough data are available it may be possible to use these formulas to interpret experimental results in the absence of calculations. We study partial wave coupling in the photoelectron–molecular ionic motion. It is found that a molecular ionic core in the 1sσ_{ g } state provides a field in which the coupling between partial waves is weak, even at fairly large internuclear distances. A core in the 2pσ_{ g } state provides a field in which the coupling is weak to moderate, and a core in the 2pσ_{ u } state provides a field in which the coupling is moderate to strong as a function of energy and internuclear distance. The possibility of the interpretation of the over‐all qualitative features of angular distributions for many‐electron molecules in terms of a paradigm of results for photoionization of a molecule with a filled n lσ_{ i } shell is discussed with reference to experimental results for N_{2}, and it is proposed that the effective charge parameter of the molecular orbitals belonging to the neutral and ionic systems and the bare nuclear charge could be treated as adjustable parameters to provide a crude but qualitatively correct description of the screening in the many‐electron molecule.

Precision neutron diffraction structure determination of protein and nucleic acid components. XVII. Molecular and crystal structure of the amino acid glycine hydrochloride
View Description Hide DescriptionThe amino acid salt glycine hydrochloride, H_{3}N^{+}⋅CH_{2}⋅COOH⋅Cl^{−}, crystallizes in the space group P2_{1}/c, a=7.117(2) Å, b=5.234(2) Å, c=13.745(3) Å, β=97.25(1) °. The crystal structure has been refined from three‐dimensional neutron diffraction data to a final R value based on F ^{2} of 0.058. Estimated standard deviations in bond distances and angles are approximately 0.002 Å and 0.2°, respectively. There is a network of hydrogen bonds with the chloride ions linking three neighboring glycines to form layers parallel to the a b plane. One ammonium group hydrogen is involved in two weak electrostaticinteractions; these interactions join the single layers to form parallel double layers but are probably too weak to be termed hydrogen bonds.

Short range electrostatic interactions in dielectric media
View Description Hide DescriptionThe electrostatic theory for a dielectric sphere with arbitrary charge distribution within it is presented. The sphere is located in a dielectric medium which either contains another similar sphere or is separated from another dielectric medium by a planar interface. It is shown that the case of two dielectric spheres is simply related to that of a sphere near a planar interface. The cases of a point charge or a point dipole at the center of the sphere are analyzed in detail. For the point charge case, the numerical results for both the electrostatic potential energy and forces for a wide range of values of the ratio of dielectric constant of sphere to that of medium are given. In addition, approximate analytical expressions are given and constrasted with the exact numerical results. The asymptotic expression occasionally used is shown to provide a good approximation for equal and oppositely charged cavities embedded in a medium of very high dielectric constant. An analytical expression, similar in structure to the exact one for metallic spheres, is derived and shown to provide an excellent approximation over the whole range of dielectric constants and arbitrary charge combinations. Approximate expressions using Padé approximants and simple variational approaches are also given. For the point dipole case, extensive numerical results are presented. It is shown that, for the case of a dielectric cavity, embedded in a medium of high dielectric constant and in contact with another similar cavity with the dipoles oriented along the lines of centers, the potential energy can be expressed in terms of tabulated analytical functions. This also applies for a dielectric cavity in contact with a planar dielectric interface with dipoles oriented perpendicular to the interface.

Electric field gradients in CuBr_{2}
View Description Hide DescriptionThe electric field gradients at both the Br^{−} site and the Cu^{2+} site in a single crystal of CuBr_{2} have been calculated using a point charge model and taking the effect of chemical bondings into consideration. Comparison with experimental data in NQR has been made and the value 〈r ^{−3}〉_{3d } of the electrons of Cu^{2+}, as well as the shielding effect of the inner electron core are discussed. The ionicity is also deduced.

Low frequency depolarized light scattering in the VH geometry from quinoline
View Description Hide DescriptionLow frequency depolarized light scatteringspectra in the VH geometry are measured in liquid and supercooled quinoline from 37 to −35 °C and compared with the theory of Gershon and Oppenheim. The spectra are separated into contributions of different modes which can be dissipative and/or vibrating according to Gershon and Oppenheim’s results, and it is shown that a central dip does not necessarily mean dissipative modes, e.g., at 2 °C. Shear viscosities deduced from the spectra are close to values measured macroscopically. Orientational relaxation times obtained are exponential vs 1/T over the temperature range measured, and the coupling parameter between the orientational and the linear momentum densities is about proportional to the viscosity width.

The scattering of noble gas atoms (He, Ne, Ar) from (100) copper. (Space and velocity distribution)
View Description Hide DescriptionThe scattering of He, Ne, and Ar from (100) copper has been studied experimentally. Both space and velocity distributions were measured. Special attention was paid to the cleanliness of the surface and to the effect of possible surface contamination. The influence of the beam incidence, the crystal azimuth, and the temperature are discussed. The behavior of the reflection lobe is in agreement with the phenomenological description of Merrill. The velocity distribution suggests that there is always superposition of elastic and inelastic scattering. Many‐phonon processes predominate in the scattering of Ne and Ar, while the helium case may be described by an elastic, single‐phonon process. A comparison of these experimental data with existing theoretical calculations (many‐phonon by G. Armand, single‐phonon by F. O. Goodman) is given.

Measurements of longitudinal and transverse ultrasonic wave velocities in compressed solidified argon and their relationship to melting theory
View Description Hide DescriptionMeasurements of longitudinal and transverse ultrasonic wave velocities have been made on compressed, solidified argon for pressures up to 6 kbar (600 MPa) corresponding to melting temperatures in the range 123–206 K. Velocities in the solid phase were measured along isochores to within ∼10^{−3} K of the melting line. The Lindemann melting parameter, obtained from appropriate physical quantities at the melting line, was constant within the limits of error of the measurement (±2%).

Proton radiolysis of CHCl_{3} and CHBr_{3} at high dilution in argon during condensation at 15 °K. Infrared spectra of the CHX^{+} _{2}, CHX^{−} _{2}, and CHX^{−} _{3} molecular ions
View Description Hide DescriptionMatrix samples of chloroform and its deuterium and bromine analogs have been subjected to irradiation by a 2.0 keV protonbeam during deposition, and the products trapped in an argon matrix at 15 °K. Several infrared absorptions have been observed and assigned to a number of new molecular species. Extremely photosensitive bands observed at 652, 621, 593, and 570 cm^{−1} have been assigned to the CHCl^{−} _{3}, CHCl_{2}Br^{−}, CHClBr^{−} _{2}, and CHBr^{−} _{3} molecular anions, respectively. Absorptions at 998, 907, and 839 cm^{−1}, which were decreased by operating an exposed bulb filament, have been attributed to the isolated cations CHCl^{+} _{2}, CHClBr^{+}, and CHBr^{+} _{2}. Bands stable to the bulb filament at 1044, 988, and 898 cm^{−1} were assigned to the CHX^{+} _{2} (X^{−}) species and similar bands at 838, 795, and 735 cm^{−1} were assigned to the CHX_{2} ^{−} anions. In addition, bands attributable to the species CX_{3}, CX_{2}CX_{3} ^{+}(X^{−}), CHX_{2}, and HX^{−} _{2}, which have been identified previously, were observed here as well.

Benzene dimer: A polar molecule
View Description Hide DescriptionThe electric deflection of molecular beams of (C_{6}H_{6})_{2}, produced by adiabatic expansion, has been measured. The benzene dimer is observed to be a polar species. It is likely that the structure of this species is that of two perpendicular planes, as is observed for nearest neighbors in crystal and liquid benzene.

Kinetic processes determining the time dependence of vuv emission in He
View Description Hide DescriptionWe present an interpretation of the data by Bartell, Hurst, and Wagner (BHW) on the time resolved vuv emission from He excited by pulses of fast charged particles. Here we argue that the very large term, linear in pressure, observed in the decay rate of the He(2 ^{1} P) population represents He(2 ^{1} P) + He(1^{1} S) →He(2 ^{1} S) + He(1 ^{1} S) and that the dominant mechanism for this reaction is strong rotational coupling of the adiabatic states ^{1}Π_{ g }(1 ^{1} S+2 ^{1} P) and ^{1}Σ^{+} _{ g }(1 ^{1} S+2 ^{1} S) in the region of internuclear separation near the potential curve crossing at R?2.04 Å. The accurate prediction of the reaction rate, together with the fact that no other singlet states appear accessible at room temperature, leads to the conclusion that in nearly pure He most of the large He(2 ^{1} P) population is converted to He(2 ^{1} S) either by radiative transitions, the two‐body process described above, or by the related predissociation of B ^{1}Π_{ g }(1 ^{1} S+2 ^{1} P) when the molecule is formed in a high vibrational state. Thus, most of the continuum radiation comes from the A ^{1}Σ^{+} _{ u } and possibly the D ^{1}Σ^{+} _{ u } molecules, and the time dependence of radiation from the A ^{1}Σ^{+} _{ u } molecule is rate‐limited by decay of He(2 ^{1} S) by various collisional processes.

Calculated and experimental electronic structure of gaseous MnO_{3}F and MnO_{3}Cl
View Description Hide DescriptionThe gas phase electronic absorption spectra of MnO_{3}F and MnO_{3}Cl have been measured in the visible and near ultraviolet regions. Interpretation has been made by comparison with a molecular calculation for each molecule by the SCF–Xα–SW method in terms of C _{3v } symmetry. The calculated ground and excited states and observed electronic transitions correlate directly with those for the parent MnO^{−} _{4} cluster. The lowest excited state,^{1} E ^{ a }, which correlated with the first ^{1} T _{1} state of MnO^{−} _{4}, retains the characteristics of the parent state. The charge transfer originating from the halide atom is first observed in the ^{1} E ^{ c }excited state in each molecule correlating with the second lowest ^{1} T _{2} state in MnO^{−} _{4}.

Fluorescence of monochlorobenzene in the vapor phase
View Description Hide DescriptionThe vapor phase fluorescence of monochlorobenzene has been measured in the presence of ethane, propane, or n‐butane. The excitation wavelength effect on the fluorescence quantum yield indicates that there should be a fast nonradiative decay channel, an intermediate isomer, at around 240 nm. Pressure effect of a foreign gas on the fluorescence quantum yield is also studied and the nonradiative relaxation processes are discussed.

A Hartree–Fock interaction potential between a rigid asymmetric top and a spherical atom: (H_{2}CO,He)
View Description Hide DescriptionA basis set of better than ’’triple zeta plus polarization’’ quality is used to compute the interaction potential between a rigid H_{2}CO(^{1} A _{1}) and He(^{1} S). The highly anisotropic energy surface has a slight attraction arising from induction effects at intermolecular separations around 9 a.u. It is fitted to a spherical harmonic expansion to facilitate scattering applications.

The electronic structure of the vanadate and chromate ions as calculated by the MS Xα method
View Description Hide DescriptionUsing the MSXα method, calculations of the electronic structure of the tetrahedral VO^{3−} _{4} and CrO^{2−} _{4} complexes have been carried out. The choice of the MSXα parameters and their influence on the results is discussed. The calculations are done in such a way so as to allow a full comparison with the corresponding results obtained by Johnson for the MnO^{−} _{4} complex. The calculated electronic structures of the vanadate and the chromate ions are compared with the x‐ray emission spectra and a new assignment of the spectral bands is proposed. The transition state procedure is used to calculate both ionization energies and optical transition energies. The results agree well with the observed ESCA and optical spectra, the agreement being better than that previously obtained from a b i n i t i o and semiempirical calculations.

Direct vibrational excitation via charge exchange in symmetric ion–molecule collisions
View Description Hide DescriptionIntegral and differential cross sections for vibrational excitation in symmetric H^{+} _{2}(X ^{2}Σ^{+} _{ g }, v′_{0}) + H_{2}(X ^{1}Σ^{+} _{ g }, v ^{″} _{0}) collisions have been determined for incident kinetic energiesE (keV) in the range 0.01<E<2.0. A multistate impact parameter description of the collision was used. At low kinetic energies, the inclusion of a relatively small number of states in the wavefunction expansion of the system achieves converged cross sections while at high energies a large number of product states are needed. The inelastic channels in this symmetric system are strongly coupled to each other and to the energy resonant charge exchange channels. Differential cross sections for excitation of individual product channels have been computed as a function of scattering angle within the multistate impact parameter approach. Small angle scattering within several degrees is dominant with forward inelastic scattering becoming more pronounced as the ion kinetic energy is increased. Integral cross sections for individual channels and integral cross sections summed over all product channels are presented as a function of both ion kinetic energy and reactant internal energy.

Continuous emissions of argon and krypton in the near ultraviolet
View Description Hide DescriptionThe spectroscopic and kinetic study of argon and krypton luminescence is carried out using two complementary methods. Over the range of wavelengths from 200 to 800 nm, the optical spectrum of these gases, determined by means of a single photoelectron spectrophotometer, shows the presence of atomic lines and continuums. In the case of argon, between 400 and 500 nm, a weak continuum appears. This continuum had never been observed under similar experimental conditions. The decay of the luminosity is reconstituted by means of the time‐amplitude conversion method. The decrease of light of continuums is described by a difference of exponential terms. The variation of time constants with pressure allows the kinetic scheme which describes the mechanisms of the postluminescence to be deduced. The study of the continuums has confirmed the formation of diatomic molecules of rare gases as the result of triple collisions. The kinetic scheme is as follows: Al→^{ k } ^{ 1 } Al^{′}+hν_{1}, Al+2A→^{ k } ^{ 3 } A _{2}+A, and Al_{2}→^{ k′} _{1} Al_{2}+hν_{0} (continuum). The molecular states created have a very short lifetime (k′^{−1} _{1} ∼ 5 ns) compared with those of the lowest radiative states (3–5 μs). The rate constant k _{3} is very important (k _{3} ∼ 10^{−30} cm^{6}s^{−1}). The atomic states responsible for the creation of dimers certainly belong to the configurations 3p ^{5} 5p in argon and 4p ^{5} 6p in krypton.