Index of content:
Volume 72, Issue 6, 15 March 1980

Relativistic scattered wave calculations on UF_{6}
View Description Hide DescriptionSelf‐consistent Dirac–Slater multiple scattering calculations are presented for UF_{6}. These are the first such calculations to be reported, and the results are compared critically to other relativistic calculations. The results of all molecular orbital calculations are in good qualitative agreement, as measured by energy levels, population analyses, and spin–orbit splittings. The overall charge distribution is computed to be U^{+1.5}(F^{−0.25})_{6}. Polarization functions are found to be qualitatively unimportant. A detailed comparison is made to the relativistic Xα (RXα) method of Wood and Boring, which also uses multiple scatteringtheory, but incorporates relativistic effects in a more approximate fashion. For the most part, the RXα results are in excellent agreement with the present results. Some differences of possible significance are noted in the lower valence and core energies.

Effects of high pressure on molecular electronic spectra. II. Morse potential formulation
View Description Hide DescriptionThe effects of high pressure on electronic spectra are treated on the basis of a Morse potential by a method analogous to that used in deriving the well‐known Drickamer–Franck–Slichter model. Expressions are presented for evaluating configuration–coordinate parameters from spectroscopic data.

A simple model for examining mixing of pumped stationary states
View Description Hide DescriptionThe oxidation of cerous ion by bromate has been approximated by four irreversible bimolecular processes. When this mechanism is modeled numerically in a continuously stirred tank reactor (CSTR), wide ranges of conditions generate two different stationary states that are stable indefinitely for identical values of the pumping parameters. By simultaneous variation of the residence time and reactant input, it is possible to move from one to the other of these states without any discontinuity in stationary state composition. If equal volumes of the two states are mixed while pumping is continued, one or the other will become dominant. The value of the residence time generating states of equal ’’dynamic stability’’ is grossly different whether the mixing is performed instantaneously by removing a barrier between those states or gradually by increasing sizes of holes in that barrier. Because relative ’’dynamic stability’’ is extremely dependent upon path even for a process as a simple as ’’ mixing’’, it appears doubtful that useful state functions can be developed to predict the direction of evolution of open systems pumped far from equilibrium.

Generalized transition state theory calculations for the reactions D+H_{2} and H+D_{2} using an accurate potential energy surface: Explanation of the kinetic isotope effect
View Description Hide DescriptionRate constants are calculated for the reactions D+H_{2}→DH+H and H+D_{2}→HD+D and compared to measured values. An accurate potential energy surface, based on the a b i n i t i o calculations of Liu and Siegbahn, was used. Rates were calculated using both conventional transition state theory and canonical variational theory. In the former, the generalized transition state dividing surface is located at the saddle point; in the latter it is located to maximize the generalized free energy of activation. We show that, in the absence of tunneling corrections, locating the generalized‐transition‐state dividing surface variationally has an important quantitative effect on the predicted rate constants for these systems and that, when tunneling is included, most of the effect of using a better dividing surface can be included in conventional transition state theory for these systems by using a consistent transmission coefficient for quantal scattering by the vibrationally adiabatic potential energy curve. Tunnelingeffects are important for these reactions even for temperatures larger than 400 K. We show how to separate classical recrossing effects from quantal corrections on reaction‐coordinate motion in both the transmission coefficients and the kinetic isotope effects. Our most complete calculations are in excellent agreement with most of the measured rate constants and kinetic isotope effects.

An irreducible tensor method of deriving the long‐range anisotropic interactions between molecules of arbitrary symmetry
View Description Hide DescriptionThe long‐range, anisotropic interaction energy between two molecules of arbitrary symmetry is derived to second order in perturbation theory by using irreducible tensor methods. The resultant formulas can be used to express the interaction energy to any desired power of R, the separation of the two molecules. Group‐theoretical arguments are used to reduce the number of independent parameters in the theory and to determine which parameters are nonzero in particular molecular point groups. The theory is illustrated by being applied to the case of two linear molecules, and the interaction energy is given explicitly for linear molecules up to R ^{−5} for the electrostatic (first‐order) interactions and to R ^{−7} for the induction and dispersion (second‐order) interactions. Certain discrepancies in the published literature concerning the induction and dispersion interactions of two linear molecules are clarified.

Nonequilibrium decay effects in diffusion‐controlled processes
View Description Hide DescriptionIt is shown how to include decay or desorption at a boundary in systems with diffusive kinetics. A quantity, the mean equilibrium time, is defined and calculated for one‐dimensional diffusion. Both finite and infinite systems are considered.

Infrared chemiluminescence investigation of the reactions of methyl radicals with oxygen and fluorine
View Description Hide DescriptionThe technique of arrested relaxation infrared chemiluminescence has been used to study two methyl radical reactions. The reaction of methyl radicals with fluorine produces methyl fluoride with a statistical distribution of vibrational energy. In this reaction approximately half the energy available to the methyl fluoride product goes into vibration. The reaction of methyl radicals with oxygen atoms produces formaldehyde with so much vibrational energy that we can only put a lower limit of 30 kcal/mole on its vibrational energy.

Studies of shear waves and translation–rotation coupling of liquid nitrobenzene in neat liquid and in carbon tetrachloride solution by depolarized Rayleigh scattering
View Description Hide DescriptionHigh resolution depolarized Rayleigh spectra of nitrobenzene in CCl_{4} have been measured at several concentrations and temperatures. All spectra display a shear wave dip at the zero frequency. They are found to fit well to the form of a two‐variable theory in the low frequency regions studied. The various parameters such as the collective molecular reorientation rate Γ, the shear wave relaxation rate q ^{2}ν_{ s }, and the dynamic coupling coefficient R are obtained as a function of temperature and concentration. While the R value is found to be independent of temperature, it changes significantly with the nitrobenzene concentration. Moreover, the R value for pure nitrobenzene is found to be greater than 0.5, higher than any reported previously for a low viscosity liquid. The τ_{Ray} values are found to follow the classical Stokes–Einstein relation, with zero intercept. The pair orientational correlation affects the Rayleigh relaxation time.

Segregation of co‐adsorbed species: Hydrogen and carbon monoxide on the (111) surface of rhodium
View Description Hide DescriptionThe co‐adsorption of CO and H_{2} on Rh(lll) at low temperature (∼100 K) has been studied using thermal desorptionmass spectrometry (TDS) and low energy electron diffraction(LEED). The probability of adsorption of CO on rhodium pretreated with hydrogen has been found to vary nonlinearly with the amount of hydrogen on the surface. In addition, the effect to surface hydrogen on the CO LEEDpatterns indicates near complete segregation of hydrogen and CO. These results can be explained qualitatively in terms of a strong repulsive CO–hydrogen interaction and a mobile precursor model of CO adsorption.

The structure of ionic clusters: Thermodynamic functions, energy surfaces, and SIMS
View Description Hide DescriptionThe Helmholz free energy of several stable NaCl clusters was calculated. It is shown that the relative stability of clusters of the same size can change with temperature. For (NaCl)_{4}, the cubic configuration is preferred below 500 K, the eight‐ring configuration above. The energy surface was examined in order to determine the energy barrier separating stable configurations and thereby the time needed to establish thermodynamic equilibrium. In one case, (CaF_{2})_{5}, the barrier is so low as to permit tunneling from one configuration to the other. The relative stability of clusters having the composition Na_{ n }Cl^{+} _{ n‐1} was calculated and the results are compared with a recent SIMS investigation. Na_{5}Cl_{4} ^{+} is found to be a particularly stable charged cluster.

Ultrasonic absorption in aqueous binary mixtures. II. p‐Dioxan–water at 11° and 25 °C
View Description Hide DescriptionUltrasonic absorption has been measured in the p‐dioxane/water system at 25° and 11 °C at nine concentrations over the frequency range 0.3–630 MHz.It is shown that the frequency dependence can be fitted quantitatively by the ’’fluctuation’’ theory of Romanov and Solovev if NMR determined diffusion data are available. The experimentally determined amplitude of absorption agrees very well with that calculated using experimental thermodynamic data and the R–S theory. The ultrasonic relaxation times show the same concentration dependence as the high frequency dielectric relaxationmeasured by Garg and Smyth. The discussion considers the ultrasonic fluctuations as a dynamic analog of the clathrate hydrate forming proclivities of such solutes.

Photodestruction of ions containing sulfur dioxide
View Description Hide DescriptionPhotodestruction cross sections have been measured for six ions containing SO_{2} over the photon energy range 1.55–3.5 eV using a drift tube mass spectrometer and rare gas ion and dye lasers. The cross section for SO_{2} ^{−} increases smoothly with photon energy from (0.9 to 2.4) ×10^{−18} cm^{2}. The photodestruction spectra of SO_{2} (SO_{2})^{−} and O_{2} (SO_{2})^{+} consist of broad, structureless bands. These bands are attributed to direct dissociation through repulsive excited states. Cross section for O_{2} (SO_{2})^{−}, NO_{2} (SO_{2})^{−}, and NO_{3} (SO_{2})^{−} are measurably different from zero only at the upper end of the photon energy range.

Infrared laser multiple photon ionization
View Description Hide DescriptionThe production of ions as a result of the interaction of intense CO_{2}‐ laser pulses with a variety of organic molecules is reported. The laser frequency dependence of the ionization follows closely the linear infrared absorptionspectrum of the respective molecule. The extent of ionization depends very strongly on laser energy fluence. The ion‐production process is found to have a strongly collisional character. Various possible mechanisms of laser‐induced ionization are discussed, and evidence is presented favoring laser‐induced chemi‐ionization.

Diffusion modulated donor–acceptor energy transfer in a disordered system
View Description Hide DescriptionThis mainly theoretical paper treats, in a disordered system, the time‐dependence of irreversible donor–acceptor energy transfer in the limit of low acceptor concentrations. The transfer is modulated by diffusion of energetic donor molecules relative to acceptors. Though donor dynamics will be touched upon, the main emphasis of the paper is on the risetime dynamics of the concentration of energetic acceptors in the nanosecond and subnanosecond regimes following excitation of donors with a brief pulse of light. It has been found that the fastest acceptor risetimes occur in the limit of slowest donor diffusion. The reason for this apparent anomaly, which reverses intuition, is that diffusion aids attainment of a steady state, and the steady state donor distribution gives rise to slower acceptor risetimes than transient contributions. The result has been verified in some preliminary experiments where quasidonor diffusion, caused by donor–donor energy transfer, has been retarded by dilution with inert molecules. Faster risetimes also result from shortening the range of the donor–acceptor transfer interaction. A very striking effect on acceptor risetimes can come about from the presence of local order of donors surrounding an acceptor. Providing the peak of the donor radial distribution function is sufficiently close to the acceptor compared with a characteristic transfer distance, acceptor risetimes can be substantially speeded up. Because of the sensitivity of acceptor dynamics to local order and transfer behavior, the possibility is raised of using the acceptor as a ’’probe’’ for these effects in future picosecond and subpicosecond experiments.

QMSCC calculations on the thermal quenching of the uranate luminescence in uranium‐doped tungstates with perovskite structure
View Description Hide DescriptionQMSCC calculations have been performed on the thermal quenching of the uranate luminescence in perovskite‐type compounds with compositions A_{2}BW_{0.997}U_{0.003}O_{6}(A_{2}B=Ca_{2}Mg, Sr_{2}Mg, Ba_{2}Mg, Ba_{2}Ca, Ba_{2}Sr or Ba_{2}Ba). Using a three states SCC model the luminescence quenching could be described quantitatively. The model was checked for Ba_{2}MgWO_{6}–U by investigating the luminescence properties of Ba_{2}MgWO_{6}–Eu and Ba_{2}MgWO_{6}–Eu, U.

An efficient approach to CI: General matrix element formulas for spin‐coupled particle–hole excitations
View Description Hide DescriptionA new, efficient algorithm for the evaluation of the matrix elements of the CI Hamiltonian in the basis of spin‐coupled ν‐fold excitations (over orthonormal orbitals) is developed for even electron systems. For this purpose we construct an orthonormal, spin‐adapted CI basis in the framework of second quantization. As a prerequisite, spin and space parts of the fermion operators have to be separated; this makes it possible to introduce the representation theory of the permutation group. The ν‐fold excitation operators are Serber spin‐coupled products of particle–hole excitations. This construction is also designed for CI calculations from multireference (open‐shell) states. The 2N‐electron Hamiltonian is expanded in terms of spin‐coupled particle–hole operators which map any ν‐fold excitation on ν‐, and ν±1‐, and ν±2‐fold excitations. For the calculation of the CI matrix this leaves one with only the evaluation of overlap matrix elements between spin‐coupled excitations. This leads to a set of ten general matrix element formulas which contain Serber representation matrices of the permutation group S ^{ν}×S ^{ν} as parameters. Because of the Serber structure of the CI basis these group‐theoretical parameters are kept to a minimum such that they can be stored readily in the central memory of a computer for ν?4 and even for higher excitations. As the computational effort required to obtain the CI matrix elements from the general formulas is very small, the algorithm presented appears to constitute for even electron systems a promising alternative to existing CI methods for multiply excited configurations, e.g., the unitary group approach. Our method makes possible the adaptation of spatial symmetries and the selection of any subset of configurations. The algorithm has been implemented in a computer program and tested extensively for ν?4 and singlet ground and excited states.

Rayleigh–Bénard instability in reactive binary fluids
View Description Hide DescriptionWe study the hydrodynamic stability of reactive, binary fluids in the Bénard geometry, and the Boussinesq approximation, with both the Soret and Dufour effects included. The boundary conditions are rigid, perfectly conducting walls impermeable to mass flow, conditions which are experimentally approachable. For fast reactions, the reactive fluid is less stable against convection than the one‐component fluid with the same values of transport and thermodynamic coefficients, due in part to the presence of a ’’chemical boundary layer’’. A slow reaction stabilizes the fluid if the heat of reaction is large and the fluctuations in temperature and concentration relax on the same time scale (gases). When the separation of these two time scales is large (liquids), reaction is always destabilizing. The influence of the Soret and Dufour effects on stability is most pronounced for slow reactions. We provide some interpretations of the role of chemical reactions on hydrodynamic stability.

Rayleigh–Bénard instability in n‐component reactive fluids
View Description Hide DescriptionWe study the hydrodynamic stability of n‐component reactive fluids undergoing a single reversible reaction in the Bénard geometry and the Boussinesq approximation, and take the Soret, Dufour, and cross‐diffusion effects to be negligible. The boundaries are assumed to be rigid and perfectly conducting; the dependence of the critical Rayleigh number on the assumed boundary conditions for concentrations is discussed in the limit of fast reactions. In this limit we show that, if the boundaries are impermeable to mass flow (the easiest to achieve experimentally), the critical Rayleigh number, R _{∞} ^{cr}, is proportional to the one for nonreactive binary fluids. Apart from multiplicative factors, R _{∞} ^{cr} depends only on a single dimensionless parameter δ which vanishes when all the diffusion coefficients are equal. For δ≳0 (<−1) stationary convection may set in only if R _{∞} ^{cr}≳0(<0); for intermediate values of δ there exist both positive and negative solutions for R _{∞} ^{cr}.

Direct inversion method for obtaining anisotropic potentials from rotationally inelastic and elastic cross sections
View Description Hide DescriptionA method is given for the direct inversion of rotationally elastic and inelastic differential scattering cross sections, to yield the underlying intermolecular anisotropicpotential surface. The scheme presented applies to molecules of large rotational spacings, for which the inelastic transitions are relatively weak. Semiclassical considerations and the exponential distorted‐wave approximation are used in developing the method. Employed also is a peeling transform that, in effect, determines the interaction at each distance range from a different angular range of the data. The method is tested by application to simulated data, calculated for N_{ e }+D_{2} from a known potential at 0.07 eV collision energy. The inversion procedure recovered the anisotropic part of the interaction to within a few percent error.

Dynamics of cross relaxation in modulated systems: Application to nuclear magnetic double resonance of glassy polymers
View Description Hide DescriptionA statistical mechanical analysis, based on Mori’s generalized Langevin equation, is presented for the dynamics of cross relaxation in modulated systems. Relaxation rate constants are given by Onsager’s kinetic coefficients where the effects of lattice (heat bath) modulations are examined in terms of the spectral density of lattice motions as well as the transitions among the energy levels involved. Applications of the theory to nuclear magnetic double resonance relaxations of natural abundant ^{13}C in glassy polymers are discussed. For a moderate rf field of 30–40 G (32–43 kHz), it is found that whenever lattice motions have sufficient power at these frequencies, a torsional amplitude of a few degrees suffices to yield a rotating frame longitudinal spin relaxation timeT _{1ρ}(C) of the order of milliseconds. This is much shorter than the rigid lattice value of T _{1ρ}(C) which is equal to T _{12} (ADRF), the cross relaxation time under adiabatic demagnetization in rotating frame condition. The validity of the Markoffian approximation which leads to the usual time independent relaxation rate constant is examined. It seems that for proton deficient systems this approximation breaks down for the cross relaxation in matched spin–lock experiments. The origin of this breaking down is discussed and the interpretations of the cross relaxation T _{12}(S L) in spin–lock experiments are also given.