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Volume 70, Issue 7, 01 April 1979

Fluorescence spectra and kinetics of Cs_{2}
View Description Hide DescriptionThe fluorescence spectra of the A ^{1}Σ^{+} _{ u }–X ^{1}Σ^{+} _{ g } and a ^{3}π_{ u }–X ^{1}Σ^{+} _{ g } transitions in Cs_{2} have been measured as a function of temperature and Xe buffer gas density. The observed spectra were normalized to the Cs atomic emission. The Xe density dependence of the normalized fluorescence was used to determine an average formation rate constant for the A ^{1}Σ state of 4.2×10^{−30} cm^{6}/sec. Using a value of 10^{−29} cm^{6}/sec for the a ^{3}π formation rate constant, predissociation and quenching rate constants from the a ^{3}π to the x ^{3}Σ were determined to be 2.5×10^{9} sec^{−1} and 9.8×10^{−11} cm^{3}/sec. Also, the net collisional transfer rate constant from the A ^{1}Σ to a ^{3}π was 1.5×10^{−11} cm^{3}/sec. The fluorescence spectra were also used to predict the Cs atomic excited state fraction needed to produce an inversion on the A–X transition. The experimentally inferred value was 11% compared wit a theoretical prediction of 0.25%. This result, coupled with the large loss rates, indicate that Cs_{2} is not an attractive laser candidate on the A–X transition.

Atom−polyatomic collisions: The role of pair correlation functions
View Description Hide DescriptionFollowing a brief introduction to the relation between cross sections for atom−polyatomic collisions and the atom−pair correlation functions of the isolated polyatomic, we discuss properties of the correlation functions (such as sum rules and moments) relevant to experimental interpretation. Correlation functions are obtained analytically for polyatomics with harmonic vibrational motions, in their body−fixed reference frame. Rotational motions are then described within a short time expansion which provides a physical picture of rotational energy transfer for each vibrational transition. The obtained results are valid for multiquantum vibrational transitions. Gaussian rotational distributions are found for each vibrational transition, with parameters explicitly given by the theory. Relationships among collision times and rotational– vibrational periods, and the shapes of correlation functions vs. energy transfer are briefly discussed.

Transfer of electronic excitation in collisions of metastable argon atoms with nitrogen molecules
View Description Hide DescriptionMeasurements have been made of the product vibrational and rotational state distributions for the process Ar^{*}(^{3} P _{2,0})+N_{2}(X) →Ar(^{1} S _{0})+N_{2} ^{*}(C,^{3}Π_{ u }) by spectrometric observation of the C→Bfluorescence at the intersection of supersonic beams of the reactant species over the relative kinetic energy range 0.06–0.41 eV. The results are compared with the predictions of a ’’golden rule’’ model which gives the transition probabilities in the highly impulsive limit as the product of Franck–Condon and density of states factors. Below 0.17 eV, the model fits the experimentally determined v′=0/v′=1 population ratio reasonably well. At higher energies the experimental ratio rises, however, and reaches a maximum at 0.3 eV. A statistical population of rotational levels for v′=0 corresponding to rotational temperatures of 1300 °K and 1100 °K at 0.161 and 0.089 eV relative energy, respectively, is observed, while the ’’golden rule’’ predicts considerably higher rotational excitation in each case.

Classical model for electronic degrees of freedom in nonadiabatic collision processes: Pseudopotential analysis and calculations for F(^{2} P _{1/2})+H^{+},Xe→F(^{2} P _{3/2})+H^{+},Xe
View Description Hide DescriptionIt is shown how the classical version of a pseudopotential analysis can be used to obtain classical models for the electronic degrees of freedom in a molecular collision system. This allows one to construct a c o m p l e t e l y c l a s s i c a lmodel for electronically nonadiabatic collision processes, which has the virtue that electronic and heavy particle degrees of freedom are described dynamically consistently (i.e., by classical trajectories). Application of this approach to fine‐structure changing collisions of F by collision with H^{+} and Xe gives encouraging agreement with quantum mechanical coupled‐channel calculations, suggesting that this model may in general be of useful accuracy for describing electronically nonadiabatic processes.

An algorithm to solve open and closed‐shell and restricted MC–SCF equations
View Description Hide DescriptionAn algorithm, similar to the Jacobi matrix diagonalization procedure, is presented to obtain eigenvalues and eigenfunctions for the closed‐ and general open‐shell Hartree–Fock equations. A specific, restricted form of the MCSCF orbital equations, similar to the general open‐shell HF equations, is dealt with as well.

Theoretical studies of the valence electronic states and the ^{1}Π_{ u }←X ^{1}Σ^{+} _{ g } absorption spectrum of the F_{2} molecule
View Description Hide DescriptionThe twelve electronic states of F_{2} dissociating into ground state F(^{2} P) atoms have been investigated with a b i n i t i opolarizationconfiguration interactionwave functions. Using a [3s2p l d] contracted Gaussian basis, the theoretical spectroscopic constants (with experimental values in parenthesis) for the ^{1}Σ^{+} _{ g }ground state are: R _{ e }=1.427 Å (1.412 Å), D _{ e }=1.85 eV(1.66 eV), ω_{ e }=946 cm^{−1} (924 cm^{−1}), and ω_{ e } x _{ e }=−10.6 cm^{−1} (−22.2 cm^{−1}). The ^{3}Π_{ u } state is also found to be very weakly bound (R _{ e }=1.881 Å, D _{ e }=0.15 eV), while the remaining nine electronic states are strictly repulsive (aside from van der Waals minima). Molecular properties are reported for the ^{1}Σ^{+} _{ g } state and a detailed analysis of the ^{1}Π_{ u } ←^{1}Σ^{+} _{ g }absorption is carried out. The ^{3}Π_{ u } state appears to be the lower state in the 157 nm laser emission observed recently, which would correspond to the 2^{3}Π_{ g }→1^{3}Π_{ u } electronic transition.

Stochastic Liouville equation formalism for translational and rotational diffusiona)
View Description Hide DescriptionStochastic Liouville equations are used to study the relaxation behavior of position and orientation correlation functions of a fluid particle, if the second‐order velocity or angular‐velocity correlation is given. Two assumptions for reducing higher‐order (angular) velocity correlation functions to two‐point correlation functions are compared, the Gaussian assumption and ’’the assumption of vanishing higher‐order G‐cumulants.’’ In the case of translation both assumptions predict the same diffusion constant; only the latter one yields a Burnett coefficient that diverges in accordance with microscopic results. For rotational diffusion the second assumption is studied and compared with results obtained by Pomeau and Weber on the basis of the first assumption.

Criticality in exothermic chemical reactions: Upper and lower bounds of the Frank–Kamenetzki parameter
View Description Hide DescriptionA relatively simple method is employed to derive upper and lower bounds of the critical values of the Frank–Kamenetzki parameter, which represent a critical condition for the so‐called ’’thermal explosion’’. The resulting bounds are compared with the critical parameter values and their bounds which were derived by previous authors.

A classical analog for electronic degrees of freedom in nonadiabatic collision processes
View Description Hide DescriptionIt is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time‐dependent Schrödinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S‐matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S‐matrix theory) to the two‐state model problem shows that the approach provides a good description of the electronic dynamics.

Nickel tetracarbonyl, Ni(CO)_{4}. I. Molecular structure by gaseous electron diffraction. II. Refinement of quadratic force field
View Description Hide DescriptionThe molecular structure of gaseous nickel tetracarbonyl has been investigated by electron diffraction at room temperature. The analysis, based on an assumed T _{ d }molecular symmetry with corrections for the effects of vibrational motion, led to the following bond distances (r _{ g }) and amplitudes of vibration (l) with estimated uncertainties (2σ), all in angstroms: r (C=O) =1.141(2), r (Ni–C) =1.838(2), l (C=O) =0.039(2), l (Ni–C) =0.059(3), l (Ni⋅⋅⋅O) =0.061(3), l (C⋅⋅⋅C) =0.124(17), l (C⋅⋅⋅O) =0.176(11) and l (O⋅⋅⋅O) =0.244(34). The quadratic force field was refined using our structure and vibrational wave numbers from the literature in order to permit calculation of the distance corrections arising from vibrational averaging. The force constants are generally very similar to those from a previous spectroscopic study.

Theory of photogeneration and fluorescence quenching
View Description Hide DescriptionWe give the exact solution of the geminate recombination probability of a pair of oppositely charged particles, corresponding to the boundary condition of a partly absorbing sphere of finite radius at the origin. In the limit of an infinite recombination velocity (κ→∞) and a vanishing radius (a→0) we recover the well‐known result of Onsager. We use the solution in the formulation of a model of photogeneration and fluorescence quenching in organic solids, with thermalization lengths which are comparable to the lattice spacing. As an illustration we analyzefluorescence quenching and quantum efficiency data for x‐metal‐free phthalocyanine, assuming the extreme case of complete internal conversion and no thermalization length. We discuss the form of the slope‐to‐intercept ratio for small applied fields determined from the solution for the generalized escape probability.

Photodissociation and photodetachment of Cl_{2} ^{−},ClO^{−}, Cl_{3} ^{−} and BrCl_{2} ^{−}
View Description Hide DescriptionAbsolute cross sections for the photodestruction of Cl_{2} ^{−}, ClO^{−}, Cl_{3} ^{−}, and BrCl_{2} ^{−} were measured over the wavelength range of 3500–7600 Å using a drift tube mass spectrometer–laser apparatus. The photodissociation cross section for Cl_{2} ^{−} has two bands, as has been observed for the isoelectronic Ar_{2} ^{+} ion. The wavelength dependence of these bands is used to adjust the calculated potential curves of the ion in the Franck–Condon region. The photodestruction cross section for ClO^{−} has a narrow band peaked at 4300 Å with a width of 400 Å, superimposed on a continuum that slowly increases with photon energy. The narrow band is attributed to photodissociation and the continuum to photodetachment. Cl_{3} ^{−} and BrCl_{2} ^{−} have no significiant photodestruction cross sections for wavelengths longer than 4700 Å. At shorter wavelengths, the cross sections increase with increasing photon energy. The photodestruction of these ions is attributed to photodissociation. The present gas phase measurements are compared with optical spectra for the ions obtained in different environments.

A Mössbauer study of xenon compounds
View Description Hide DescriptionA large number of xenon compounds have been synthesized and studied by nuclear gamma resonance of the 39.6 keV transition in ^{129}Xe. The quadrupole interaction strengths (Q.S.) of all divalent xenon compounds with linear F–Xe–F groups lie close together, but a small increase of the Q.S. with the acceptor strength of adduct groups is observed. For compounds with F–Xe–O– and –O–Xe–O– groups a reduction of the Q.S. of up to 10% is found. The tetravalent compounds exhibit a Q.S. with absolute magnitude very close to that of the divalent compounds, consistent with a square planar configuration and nearly equal contributions to the Q. S. for each Xe–F bond. Hexavalent xenon in XeF_{6} also exhibits an appreciable Q.S., indicative of distortion of the octahedral fluorine configuration around the xenon atom in the polymeric solid. An increase of the Q.S. relative to XeF_{6} is observed in the adducts and in hexavalent compounds with mixed oxygen/fluorine bonding. This is interpreted as due to increased distortion around the central xenon atom.

Ionization potentials and electron affinites for a spacially nondegenerate doublet state in a second‐order electron propagator approach
View Description Hide DescriptionThe identification of poles in approximate electron propagator calculations on open shell systems has been analyzed. The electron propagator consistent through second order in electronic repulsion has been derived for a ^{2}Σ reference state. Calculations are performed on Li, Na, and BeH and the accuracy of the result is comparable to the one obtained for closed shell systems.

Near resonance interactions associated with the temperature dependence of fluorescence self‐quenching of Sm^{3+} in POCl_{3}:SnCl_{4}
View Description Hide DescriptionElectronically excited Sm^{3+} ions in POCl_{3}:SnCl_{4}(^{4} G _{5/2}) interact with adjacent Sm^{3+} ions in their ground state (^{6} H _{5/2}) leading to fluorescence self‐quenching (k _{Sm}3+), as well as with the solvent, POCl_{3}, leading to fluorescence quenching by the solvent (k _{solv}). The interactions leading to fluorescence self quenching are temperature dependent, associated with an activation energy barrier equal to 1.3 kcal/mole. This dependence is attributed, at least in part, to conditions of near resonance established between the interacting states at higher temperatures, brought about by populating their higher energy Stark components. Values of k _{Sm}3+, corrected for such near resonance conditions, exhibit very negligible temperature dependence. An average value of (2.8±0.2) ×10^{3} M^{−1} sec^{−1} is obtained for (k _{Sm}3+) corrected at temperatures ranging from −15 to 55°C. The quenching of the ^{4} G _{5/2} state of Sm^{3+} by POCl_{3} is temperature independent. The appropriate rate constant, k _{solv}, has a maximum value of 32 M^{−1} sec^{−1} which corresponds to about 320 sec^{−1}.

The particle scattering factor of branched macromolecules: computer simulation
View Description Hide DescriptionTheoretical prediction of the particle scattering factor I (ϑ) is possible for a limited number of molecular shapes (random coils, spheres, cylinders), which can be described in terms of distances only. Given the importance of branched macromolecules, where angles also play a role, we have devised a computer procedure for calculating the particle scattering factor. Scattering was simulated for trees with alternate and with opposite branches, with straight branches and with broken branches, 2‐dimensional as well as 3‐dimensional, and also for systems consisting of two trees acting as a single scatterer. To elucidate various factors affecting I (ϑ), several parameters were varied, including angles between trunks and branches, angles between two linear fragments of a broken branch, and densities of linear fragments. Light scattering by generalized trees consisting of unconnected segments has been discussed. For normal trees representing real molecules, procedures enabling considerable savings in computing times have been devised.

Molecular theory of lipid membrane ordera)
View Description Hide DescriptionStarting from the inter‐ and intramolecular interactions of the hydrocarbon chains the orientational long‐range order in lipid membranes is calculated to study the ordered‐fluid phase transition. The positional order is described by the lateral packing density and treated as an external parameter, in addition to temperature. The results for the orientational order parameter, the phase transition temperature, and the latent heat are analyzed to distinguish between the effects of the different chain interactions, the van der Waals interaction, steric hindrance, and flexibility. The dependence of the results on chain length is compared with existing experimental data.

Infrared laser single photon absorption reaction chemistry in the solid state. I. The system SiH_{4}–UF_{6} a)
View Description Hide DescriptionThe reaction between SiH_{4} and UF_{6} under thermal gas phase and photon initiated conditions in cryogenic matrices has been investigated. The gas phase thermal reaction begins at 130–140° C producing HF, SiH_{3}F, and a soliduranium fluoride product. When the UF_{6} is matrix isolated within SiH_{4} at 12 K and exposed to low power infrared radiation of 25 mW cm^{−2} using laser emissions resonant with the ν_{3} band of UF_{6}, a reaction also occurs. This reaction produces SiH_{3}F, UF_{5}, and UF_{4} as products. The same reaction is also catalyzed using a broad band incoherent source with a photon flux density of 10 μW cm^{−2}. The activation energy for the photoreaction (1.8 kcal mol^{−1}) is considerably lower than the thermal activation barrier for the gas phase reaction. These experiments are part of the bases for uncovering a process of photochemistry of reactants in fixed relative configurations–single photon absorptionreaction chemistry in the solid state (SPARCSS). This process is a manifestation of a previously unrecognized, general matrix phenomenon in which spatial configurations dramatically affect potential energy surfaces for reaction.

NMR in rotating solids
View Description Hide DescriptionThe NMRfree induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second‐order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τ_{ c }≲1 sec).

Electrical conduction of hemoprotein in the solid phase: Anhydrous cytochrome c _{3} film
View Description Hide DescriptionCytochrome c _{3} can be reduced with molecular hydrogen under the action of hydrogenase [hydrogen: ferricytochrome c _{3} oxidoreductase, EC 1.12.2.1] even in the solid state. The electrical conductivity of a cytochrome c _{3} anhydrous film containing a trace amount of hydrogenase was measured at physiological temperatures as a function of temperature and hydrogen pressure. Ferricytochrome c _{3}(oxidized form) and ferrocytochrome c _{3} (reduced form) equilibrate at a given temperature and pressure by a catalytic action of hydrogenase. Under these conditions, the conductivity of cytochrome c _{3} showed an unusual temperature dependence: The activation energy was positive under higher hydrogen pressure, but was negative under lower pressure. These findings are interpreted as a thermal equilibration between the ferri‐ and ferro‐ forms using the Hill equation for the reduction ratio and applying the theory of semiconduction to the electrical conductivity. The theory predicted that the activation energy of conductivity would coincide with the free energy difference between ferri‐ and ferrocytochrome c _{3}, which is confirmed by measurement of the temperature dependence of the equilibrium constant. The temperature and hydrogen pressure dependences of the conductivity were reproduced well by the above theory.