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Volume 66, Issue 4, 15 February 1977

The hydrated proton H^{+}(H_{2}O)_{ n }. V. Observation of two diaquohydrogen ions, (D_{2}O⋅D⋅OD_{2})^{+}, in 5‐sulphosalicylic acid dideuterate. A neutron diffraction study
View Description Hide DescriptionThe crystal and molecular structure of 5‐sulphosalicylic acid dideuterate has been studied using three‐dimensional single crystalneutron diffraction data. The triclinic unit cell, space group P1̄, contains two formula units, with dimensions a=7.028(5), b=7.007(5), c=11.678(8) Å, α=71.49(4), β=94.07(2), and γ=109.35(2) °. A total of 2883 unique reflections were collected and full matrix least‐squares refinement on F _{0} ^{2} yielded an R=0.079. Two almost identical D_{5}O_{2} ^{+} cations were found, and both reside on centers of symmetry, suggesting that the cations are best formulated as (D_{2}O⋅D⋅OD_{2})^{+} species. The bridging deuterium atoms have their largest vibrational amplitudes a l o n g the O–O direction, which is indicative of a broad–flat anharmonic single‐minimum potential energy well. The slight deviations from this direction are correlated with the terminal oxygen atom vibrations. X‐ray versus neutron difference density maps show pronounced polarization of the C–H and O–D bonds.

Intermolecular potential surfaces from electron gas methods. II. Angle and distance dependence of the A′ and A ^{″} Ar–NO(X ^{2}Π) interactions
View Description Hide DescriptionAngle dependent intermolecular potential energy surfaces for the two states (^{2} A′ and ^{2} A ^{″}) that arise from the interaction of ground (X ^{2}Π) state NO with Ar are calculated using the electron gasmodel to obtain the short range interactions. The average and difference of the two interaction energies are fit to analytic forms convenient for use in scattering calculations and joined smoothly onto the long range van der Waals potential previously determined. The results, which appear to be of useful accuracy, and the applicability of the electron gasmodel to such open shell–closed shell interactions are discussed.

Monte Carlo study of a phase‐separating liquid mixture by umbrella sampling
View Description Hide DescriptionRecently developed nonphysical sampling methods—umbrella sampling—have been used to obtain the free energy and other properties of a binary liquid mixture exhibiting phase separation with an upper critical solution point. The system is a mixture of two identical Lennard‐Jones liquids in which the interactions between the components are characterized by a range parameter σ_{12} obeying the Lorentz rule, but an energy parameter ε_{12}= (1−α) (ε_{11}ε_{22})^{1/2} violating the Berthelot rule. The sampling methods enable one to cover wide ranges of temperature and composition with few Monte Carlo experiments, successfully sampling the metastable regions and obtaining the coexistence curve. The case α=0.25 is studied in detail, and compared with some theoretical predictions. An estimate is made of the minimum value of α required for phase separation at low pressures.

Computational tests of angular momentum decoupling approximations for pressure broadening cross sections
View Description Hide DescriptionThe utility of several approximate scattering methods for predicting collision induced spectral pressure broadening has been tested by comparison with accurate close coupling results. In particular, broadening of the pure rotational spectra of HD, HCl, CO, and HCN—all perturbed by low energy collisions with He atoms—has been computed using the effective potential formalism of Rabitz, the decoupled l‐dominant approximation of DePristo and Alexander, and the j _{ z }‐conserving coupled states method of McGuire and Kouri. For this last method, pressure broadening cross sections have been obtained with the new, correct expression recently derived by Goldflam and Kouri as well as with an earlier formalism based on an incorrect labeling of the scattering matrices. These methods were found to be generally disappointing for predicting pressure broadening w i t h t h e e x c e p t i o n o f t h e n e w, c o r r e c t l y f o r m u l a t e d j _{ z }‐c o n s e r v i n g c o u p l e d s t a t e s m e t h o d which was found to agree quantitatively (better than 5%) with close coupling values for all cases studied.

Photochemical kinetic equations in the absence of diffusion: An approximation for small conversion
View Description Hide DescriptionEquations are derived that describe the kinetics of a sample with slab geometry in which there is no diffusion of reactant or products. It is assumed that the photoproducts absorb radiation and that absorbing species not involved in the reaction are also present in the sample. The derivation is based on an approximation that greatly simplifies the kinetic equations. The approximation is valid only for short reaction times during which only a small amount of photoproducts are formed in the sample. Methods of employing the equations for the purpose of measuring quantum yield values are described.

The friction constant in a concentrated polymer–solvent system by Rayleigh scattering: Polystyrene in n‐butyl acetate
View Description Hide DescriptionUsing an optical heterodyne technique (homodyne, in the definition used by the Malvern group), the intensity of the light scattered by concentration fluctuations and their correlation time were measured for a series of solutions of polystyrene in n‐butyl acetate in the mass concentration range 0.18 to 0.57, between 0 and 70 °C. The elasticity deduced for the polymer matrix is found to be temperature independent, in contrast with polystyrene:cyclohexane and in conflict both with the Flory–Huggins theory and with recent scaling theories. This result is attributed to steric hindrances in the rotation of the solvent molecules. As in the case of polystyrene:cyclohexane, the diffusion constant D passes through a maximum as a function of concentration at a given temperature, indicating that the viscosity entering into the definition of D is a local viscosity and not that of the bulk solvent. On the assumption that the time constant T _{ r }, which is central to de Gennes’ theory of the macroscopic viscosity, is proportional to the local viscosity, the dependence of T _{ r } upon the coherence length ξ can be deduced without introducing explicitly the concentration dependence of these quantities. It is found that T _{ r }∝1/ξ^{3.35±0.18}, as compared with de Gennes’ theory, which predicts T _{ r }∝1/ξ^{2} in the semidilute regime.

On the transport properties of the van der Waals fluid. III. Explicit calculation of the shear viscosity
View Description Hide DescriptionWe present numerical data for the effect of the attractive forces on the shear viscosity, as they come out of the van der Waals theory developed by Résibois, Pomeau, and Piasecki.

Low frequency Raman modes in solid amorphous polystyrene and polymethyl methacrylate
View Description Hide DescriptionMeasurements of the low frequency Raman spectra of solidamorphous polystyrene and polymethyl methacrylate, below about 100 cm^{−1}, are reported, showing two previously unresolved broad bands in each case. For polystyrene the mode frequencies at room temperature are about 60 and 10 cm^{−1}; for polymethyl methacrylate about 60 and 20 cm^{−1}. The spectra of strained samples, showing no changes in these low frequency modes, and of crystalline isotactic polystyrene are also reported. The temperature dependence of the mode intensities in polystyrene is found not to deviate significantly from a first‐order variation in the temperature range from 125 to 250 °K and there is no evidence of frequency shifts in this range, within the accuracy of the determination of peak frequencies (±7 cm^{−1}). However, frequency shifts are found in both bands with variation in molecular weight. The frequency shift for the 10 cm^{−1} band between samples with molecular weights of 10^{5} and 340 is 8 cm^{−1}, both measurements being at 100 °K. For the 60 cm^{−1} band the corresponding shift is 11 cm^{−1}. Possible causes for these shifts are discussed, including changes in the density of states functions for skeletal normal modes, derived from a simple chain model. This model is, however, found to be inadequate in describing both the low frequency Raman spectrum and the anomalous values of low temperature specific heat of polystyrene.

Molecular beam photodissociation of TlI: Bond energy and state symmetry
View Description Hide DescriptionA beam of TlI is dissociated with a laser at 299.0 nm. The time of flight of the iodine atoms leads to a bonddissociation energy of 62.1±0.9 kcal/mol. Fragment angular distribution measurements made with a high pressure lamp show that both the 302.5 and the 380 nm bonds of TlI are transitions of mixed parallel and perpendicular symmetries.

A high pressure test of the theory of energy transfer by sensitized luminescence
View Description Hide DescriptionMeasurements have been made of sensitized luminescence in the phospor KCl:Ag:Tl in the fcc phase to 18 kbar. The studies include both lifetimes and relative emission intensities of the two dopants. Both the lifetimes and relative intensities gave quantitative agreement with theory over the pressure range. The calculated efficiencies ranged from ∼0.08 to ∼0.28. Measurements from 100 to 300 °K at 8 and 18 bar also agreed with theory. Some more limited measurements on KCl:Ag:Pb in the same pressure range also exhibited satisfactory correspondence to the theory.

Infrared intensities: A model for the quantitative prediction of the vibrational strengths of SF_{6} and UF_{6}
View Description Hide DescriptionUsing an atomic polar tensor for the F atom obtained from an analysis of the experimental infrared intensities of CH_{3}F and normal coordinate analyses of SF_{6} and UF_{6}, the infrared spectra of SF_{6} and of UF_{6} have been predicted and compared with experiment. The absolute infrared intensities predicted for the infrared‐active fundamental vibrations of SF_{6} agree quite well with experimental values; for UF_{6}, the experimental values are less well‐determined, but the agreement also appears to be satisfactory. The intensities of the binary combination bands have also been calculated, using anharmonic force constants introduced by the use of curvilinear coordinates supplemented by terms in the valence‐bond stretching coordinates estimated from an assumed Morse potential, and using the calculated intensities for the fundamentals neglecting electrical anharmonicities. These predictions also appear to be in semiquantitative agreement with the experimental data.

A classical mechanical study of the effects of vibration in inelastic He–H_{2} scattering
View Description Hide DescriptionThe classical trajectory study method has been used to investigate the effects of H_{2} vibration on inelastic scattering in the system He+H_{2}. Specifically, earlier calculations which included H_{2} vibration have been repeated using the rigid rotor approximation. In addition, new calculations, both with and without H_{2} vibration, have been performed at total collision energies of 5 and 10 eV. It is found that H_{2} vibration exerts a noticeable effect at energies above 5 eV; however, even at 10 eV, the rigid rotor approximation works well for the most important transitions.

Nonsteady hydrodynamics of biopolymer motions
View Description Hide DescriptionMany biopolymers undergo conformational fluctuations in which large subunits move relative to each other under the influence of significant mechanical restoring forces. It is shown that nonsteady hydrodynamic effects may be important in the solvent response to such macromolecular motions. This result is in marked contrast to the familiar case of conformational fluctuations of random coil polymers, which move under the influence of weak entropic forces. The nonsteady solvent response is shown to affect the details of the biopolymer motion and to produce special qualitative features in the Raman light scatteringspectrum of such macromolecules.

The influence of molecular rotation on vibration–translation energy transfer
View Description Hide DescriptionThe role of molecular rotations in the exchange of vibrational and translational energy is investigated for collisions between anharmonic diatomic molecules and structureless atoms. A three‐dimensional, semiclassical, impact parameter description is applied with emphasis directed towards the influence of rotational coupling on the net rate of vibrational energy transfer summed over all final rotational states. These results are then related to the predictions of an equivalent collinear collision model, and their comparison allows an evaluation of the collinear approximation. The mechanisms of vibrational energy transfer including rotational transitions are shown to be separable into three classes, with the molecules belonging to each class identified first and foremost by their ratio of fundamental vibrational and rotational frequencies, ω_{ e }/B _{ e }, and second by the proximity of their initial state to a near‐resonant vibration–rotation transition with a small change in angular momentum. While the dynamics of molecules with ω_{ e }/B _{ e } ratios that are comparable to the range of angular momentumtransitions having strong coupling are found to require a complete three‐dimensional description, the rates of vibrational energy transfer in molecules with large ω_{ e }/B _{ e } ratios appear to be well approximated by a collinear collision model.

An atom–dipole interaction model study of the molecular second hyperpolarizability of selected haloalkanes
View Description Hide DescriptionThe group dipole interaction model of the molecular second hyperpolarizability is specialized to describe a molecule composed of interacting isotropic atoms. The model is applied to a set of selected haloalkanes, and using established values for the atom polarizabilities, the atom second hyperpolarizabilities for carbon, hydrogen, fluorine, chlorine, bromine, and iodine are evaluated. The experimental and theoretical molecular second hyperpolarizabilities agree to within an average of 15%.

Theoretical transition dipole moments and lifetimes for the A ^{1}Σ^{+} _{ u }→X Σ^{+} _{ g } system of Na_{2}
View Description Hide DescriptionMulticonfiguration self‐consistent field (MCSCF) calculations have been carried out on the X ^{1}Σ^{+} _{ g }, A ^{1}Σ^{+} _{ u }, and B ^{1}Π_{ u } states of Na_{2}. The calculated potential energy curves are in good agreement with the experimental X and A RKR curves of Hessel and Kusch. Both the A→X and B→Xtransition moments have been calculated as a function of nuclear separation using MCSCF wavefunctions. These calculations are in excellent agreement with the recent experimental determinations of the B→Xtransition moment. A values and lifetimes of several A‐state vibrational and rotational levels for the A→Xtransition have been calculated using the theoretical transition moment and the experimental potential curves of Hessel and Kusch. These again are in excellent agreement with the recently measured lifetimes.

Feshbach projection operator calculation of the potential energy surfaces and autoionization lifetimes for He(2 ^{3} S) –H and He(2 ^{3} S) –H_{2}
View Description Hide DescriptionA new technique has been developed for calculating potential energy surfaces and widths for autoionizing molecular systems. The method is based on the use of the Feshbach projection operators P and Q, which are defined within the space of configurations generated from a basis set of square‐integrable orbitals. Autoionizing states are then obtained by diagonalizing a particular subblock of the finite Hamiltonian constructed by the CI procedure. These states decay because they are only approximate eigenfunctions of the full finite Hamiltonian. Their lifetimes are evaluated using continuum functions which are expanded in the basis orbitals. Such an expansion is shown to be sufficiently accurate. The present technique is compared with the stabilization method and is found to illuminate certain features of that procedure. Potential surfacesV* and widths Γ have been calculated for the Penning ionization transitions He(2 ^{3} S)+H→He+H^{+}+e ^{−} and He(2 ^{3} S)+H_{2}→He+H_{2} ^{+}+e ^{−}.

Penning ionization of H_{2} by He(2 ^{3} S): Quantum mechanical scattering calculations within the rigid‐rotor approximation
View Description Hide DescriptionElastic, rotationally inelastic, and total ionization cross sections have been calculated quantum mechanically for the scattering of metastable He(2 ^{3} S) atoms by H_{2} in the energy range 0.010–0.500 eV. The potential surfaceV* and autoionization width Γ previously calculated by the authors were used. The scattering calculation was based on the Arthurs and Dalgarno formalism for the scattering of an atom by a rigid rotator. The coupled channel equations were solved numerically for the complex, angularly dependent potential V*−(i/2) Γ. The results show that the total ionization cross section σ_{ i } increases sharply with energy. Hence the ionization rate constant has a strong temperature dependence. The calculated rate constants are in good agreement with the experimental results of Lindinger e t a l.

A simple theoretical model for the van der Waals potential at intermediate distances. I. Spherically symmetric potentials
View Description Hide DescriptionA simple potential model is presented, which uses available a b i n i t i o calculated short range SCF Born–Mayer parameters and the perturbation theoretical dispersion terms for the long range potential. In the intermediate region two corrections are shown to be necessary to take account of the divergence of the dispersion expansion and the influence of electron overlap. These corrections can be predicted from the known asymptotic parameters and atomic properties. The resulting potential model, which contains only seven potential parameters, is shown to predict the van der Waals potential parameters R _{0}[V (R) =0], R _{ m } (well location), and ε (well depth) for six rare gas–rare gas atom combinations and six open shell–rare gas atom combinations. The predicted potential shape for Ar–Ar is in excellent agreement (≲3%) with the best experimental determination. The model is used to predict Born–Mayer parameters from measured values of R _{ m } and ε.

Microwave optical double resonance spectrum of NH_{2}. II. Collision‐induced transitions in ? ^{2} A _{1} and observations of a new vibronic state
View Description Hide DescriptionStrong microwave optical double resonance (MODR) signals have been observed for NH_{2} around 6.4 GHz and 15.7 GHz. These transitions occur between a previously unobserved rovibronic level and, respectively, the J=1/2 and J=3/2 spin–rotational levels of 1_{10}, ? ^{2} A _{1} π (0,10,0). This previously unknown level has been tentatively assigned as the 2_{20}, J=3/2, ? ^{2} B _{1} (0,12,0). The N and J assignments are certain, the K _{ a } is fairly certain, and the vibronic assignment is very tentative. In addition to MODR signals observed by direct laser excitation of the levels involved in the microwave transition, these microwave transitions are MODR active when a number of rotational levels of the ? ^{2} A _{1} (0,10,0) band are excited. These collision‐induced signals are interpreted qualitatively in terms of a simplified model. Observations of the collision‐induced transition (tentatively assigned as) 2_{20}, J=3/2←3_{22}, J=5/2, ? ^{2} B _{1} (0,12,0) are also reported.