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Volume 69, Issue 6, 15 September 1978

Frequency‐dependent multipole polarizabilities. II. Application of a reduced Green’s function formulation of TDHF theory to the helium isoelectronic sequence
View Description Hide DescriptionA reduced Green’s function formulation of time‐dependent Hartree–Fock theory is developed using diagrammatic techniques. The resulting integral equations are transformed using a power moment approach. An asymptotic ansatz of the form exp{−[−2(ε_{ i } ∓ω)]^{1/2} r}am† polynomial is used to fit the radial functions φ^{±} _{ l }(r). From these functions, the frequency‐dependent dipole, quadrupole, and octapole polarizabilities of the helium isoelectronic sequence for Z=2–10 are calculated. Results are reported for the static case. It is found that the poles of the polarizabilities which correspond to TDHF excitation energies from the ground state can be accurately determined for highly excited states. These excitation energies are reported and are related to a Rydberg formula. The resulting quantum defects are also reported.

Analysis of aggregate optical spectra using moments. Application to the purple membrane of halobacterium halobium
View Description Hide DescriptionThe problem of extracting structural information from the optical spectra of aggregates of molecules interacting through their electronic transitions is studied. One serious difficulty common to all approaches to this problem is that of properly taking into account the effects of molecular vibrations. A series of exact relations derived previously which are correct with regard to molecular vibrations provide a number of independent, explicit connections between aggregate geometrical parameters and moments of experimental spectra. It is shown that, by applying these moment relations to the optical absorption and circular dichroismspectra of simple aggregates, a complete set of equations can be found, i.e., enough equations can be found to solve for all of the geometrical parameters which enter into the expressions for absorption and circular dichroismspectra. This procedure is applied in some detail to the purple membrane of H a l o b a c t e r i u m h a l o b i u m. The results are completely consistent with what is known about its structure.

The diffusion of an atom on a solid surface
View Description Hide DescriptionA microscopic model for the diffusional motion of an atom chemisorbed on a solid surface is presented. The atom located at a given site is described by a set of states which can be divided into two classes. One class is composed of states whose energy is located below the intersite barrier. A particle described by one of these states can go to a neighboring site only through tunneling. The second class of states have higher energy than the intersite barrier. They are delocalized and an atom occupying such a state can change its site with relative ease. The vibrational motion of the lattice can transfer energy to or take it from the particle and it can also change the intersite transfer probability. As a result the particle may undergo three types of processes: 1) change state but not site (vertical transitions); 2) change site and state (oblique transitions); or 3) change site but not energy (horizontal transitions). The theory derives a kinetic equation for the probability that at a given time the particle is located at a given site and has a specified energy. This is then used to compute the mean square displacement of the particle and its diffusion coefficient. All these quantitities are expresed in terms of rate coefficients for horizontal, oblique, and vertical transitions. Microscopic expressions are provided for these quantities as a function of the particle phonon coupling, intersite transfer probability, particle energies, and lattice properties. The temperature dependence of the rate coefficients is analyzed numerically. If tunneling is minimal and a change of site can occur only after the phonon transfer promotes the particle in a state located above the intersite barrier, an Arrhenius temperature dependence of the diffusion coefficient is observed. The form of the functional dependence of the pre‐exponential factor on temperature changes with anharmonicity, Einstein frequency, and phonon particle coupling. If the lattice is harmonic the activation energy is equal to the intersite barrier plus the energy of the distortion of the lattice upon chemisorption. If anharmonicity is important the activation energy is close or equal to the intersite barrier. If tunneling is important non‐Arrhenius temperature dependence may be observed.

Chemiluminescence and photoluminescence of CuF
View Description Hide DescriptionPhoton yields, chemiluminescence, and excitation spectra of gas phase reactions of atomic copper with F_{2}, NF_{3}, and SF_{6} have been obtained between 400 and 1000 nm. Distributions of excited state populations of the products of these reactions and vibrational constants of four previously unreported bands of CuF were measured. A pulsed tunable dye laser was used for excitation of CuF produced in chemical reactions or by thermal dissociation of CuF_{2}. Analysis of rotationally resolved excitation spectra gives a new value of B _{ o }=0.3692cm^{−1} for the B ^{1}Σ state of CuF. Radiative lifetimes of 7.3 μsec for the A state, 1.2 μsec for the B state, and 0.6 μsec for the C state have been measured through an exponential fit to decays of photoluminescence following laser pulses. Additionally a lifetime of 0.2 to 2 msec for the upper state of the red system has been estimated from relative intensity measurements of the four states observed in chemiluminescence.

A reinvestigation of the Raman spectrum of water
View Description Hide DescriptionThe Raman spectrum of liquid water has been reinvestigated using a technique which automatically records the depolarization ratio along with the polarized Raman spectrum. The exceptionally accurate depolarization ratios thus obtained, as well as the isotropic and the anisotropic spectra of water, indicate that the libration region extends to higher frequencies than previously thought and that a new polarized band originating from restricted translation occurs near 290 cm^{−1}. The translational spectrum is in good agreement with that calculated by Weres and Rice.

Three and four center elimination of HCl in the multiphoton dissociation of halogenated hydrocarbons
View Description Hide DescriptionThree and four center unimolecular elimination reactions of HCl have been investigated for CHF_{2}Cl, CHFCl_{2}, CH_{3}CCl_{3}, CH_{3}CF_{2}Cl, and CHClCF_{2} in a molecular beam experiment using infrared multiphoton absorption to energize the molecule. The translational energy distributions obtained in this work show that the average translational energy released to the fragments is around 8–12 kcal/mole, except for the three center elimination reaction from CHClCF_{2}, which gives a value of 1 kcal/mole. In four center eliminations, the translational energy released is less than 20% of the potential energy barrier of the back reaction. This is somewhat less than previous indications that approximately 30% of the potential energy barrier of the exit channel in four center reactions should be released into translation.

The glass transition of atomic glasses
View Description Hide DescriptionThe nature of the glass transition in liquids composed of monatomic species is discussed using a hard sphere model. Recent molecular dynamics calculations by Woodcock [J. Chem. Soc. Faraday II 72, 1667 (1976)] indicate that a hard sphere fluid undergoes a glass transition when it is compressed to a high enough density. This calculation provides one of several independent methods of estimating the packing fraction at the glass transition, η_{ g }, for hard spheres. The estimated value of η_{ g } for hard spheres, 0.533 ±0.014, is substantially lower than 0.637, the packing fraction of dense random packed hard spheres. The effective η_{ g } for a number of atomic glass forming liquids with continuous interatomic potentials also are estimated, and are found to lie in or near the range of estimated values of η_{ g } for hard spheres. The liquids considered are a Lennard‐Jones fluid for which the liquid–glass transition has been studied by a molecular dynamics calculation [A. Rahman, M. Mandell, and J. McTague, J. Chem. Phys. 64, 1564 (1976)], and several real glass forming metal–metalloid alloys. The similarity of η_{ g } for the hard sphere fluid, for the Lennard‐Jones fluid, and for metal alloys suggest that it is the short ranged repulsive forces acting between atoms which are responsible for the glass transition. These results also suggest that in general, η_{ g }=0.53±0.02 for atomic liquids. This provides a criterion for predicting the glass transition temperatures for materials which have not yet been observed in the glassy state.

Lattice model studies of the effect of chain flexibility on the nematic–isotropic transition. III. Completely flexible chain solutes in rigid rod solvents
View Description Hide DescriptionA steric, mean field, simple cubic lattice model using DiMarzio lattice statistics for mixtures of completely flexible chain solutes in rigid rod solvents is presented. The chain solutes depress the nematic–isotropic transition temperature of the pure solvent. The slopes of the two‐phase coexistence curves in the reduced temperature/mole fraction plane, solute and solvent order parameters, and solute activity coefficients for mixtures of rods and chains of various lengths are discussed and compared with relevant experimental data. The results indicate that although completly flexible chains in this model are too flexible compared with n‐alkane solutes, the chain flexibility of the solute is important in determining the ability of the solute to disrupt the nematic order of the solvent.

Electronic to vibrational energy transfer from I(5 ^{2} P _{1/2}). II. H_{2}O, HDO, and D_{2}O
View Description Hide DescriptionTime‐resolved infrared fluorescence from I* (*=^{2} P _{1/2}) and vibrationally excited water has been observed following pulsed laserdissociation of I_{2} at 500 nm. The time dependence of the fluorescence signals has been used to determine the rates for the total quenching of I* by H_{2}O, HDO, and D_{2}O as well as for the vibrational self‐relaxation of two modes of H_{2}O and D_{2}O. H_{2}O and HDO are roughly 50 times more efficient in quenching I* than D_{2}O. Analysis of relative fluorescence amplitudes shows that the quenching of I* by H_{2}O and HDO is due entirely to an electronic‐to‐vibrational mechanism which produces two quanta of stretching vibration in the water molecule. The E→V mechanism is also likely to be the dominant mechanism for quenching of I* by D_{2}O.

Simulation of n‐butane using a skeletal alkane model
View Description Hide DescriptionA simulation of a fluid n‐butane system has been carried out using a straight‐chain skeletal model. The calculations reported here involve fluid densities from 288.80 to 721.99 kg/m^{3} at several distinct temperatures. In the course of this investigation the linear self‐diffusion constant, the rate of torsional g a u c h e/t r a n s relaxation and rotational tumbling of the fluid have been studied. This model shows a high degree of cooperativity between the molecular vibration and rotation, and the bulk fluid motion.

Rate constants for rotational excitation in NH_{3}–He collisions
View Description Hide DescriptionThe semiclassical method (classical translational motion and quantum mechanical rotational motion) is used to calculate cross sections and rate constants for (J?3, K) → (J?4, K) rotational excitations in NH_{3}–He collisions on Green’s uniform electron gas (Gordon–Kim) potential surface. The assumptions involved in the use of the rigid rotor approximation for the inversion motion are examined in some detail. Agreement between semiclassical and accurate close‐coupling cross sections is good, comparable to the agreement between the coupled‐states and the close‐coupling cross sections. A ’’semiclassical coupled‐states’’ approximation was found to give reliable cross sections except at low energies. Microwave double resonance ΔI/I values were calculated from the rate constants and compared with experiment. Good agreement was found for the Δk=3 transitions, but poor agreement for the Δk=0 transitions. Possible explanations for the discrepancies are discussed.

Negative ion properties of fluoranil, chloranil, and bromanil: Electron affinities
View Description Hide DescriptionBound and excited negative ion states of p‐fluoranil (FA), p‐chloranil (CA), and p‐bromanil (BA) are studied from experiments involving collisions of electrons, Na, K, and Cs beams with FA, CA, AND BA. Reaction thresholds for producing FA^{−}, CA^{−}, and BA^{−} are determined as a function of the temperature of the target molecules. The electron affinities corresponding to 0 °K were measured to be 2.92±0.2 eV for FA, 2.76±0.2 eV for CA, and 2.44±0.2 eV for BA. FA, CA, and BA attach ∼ 0 eV electrons and FA attaches 0.5 eV electrons to form metastable parent negative ions with lifetimes in the millisecond range. These lifetimes are a function of the electron energy. Dissociative and nondissociative resonances observed via electron attachment to p‐benzoquinone (PBQ) and the ’’anils’’ are correlated with the optically determined ^{2} B _{3g′}, ^{2} B _{1u,} and ^{2} A _{ u } states of PBQ^{−} and the anion radicals of several substituted quinones.

General method for calculating the escape probability in diffusion‐controlled reactions
View Description Hide DescriptionWe present a general method for calculating the escape probability in diffusion‐controlled reactions. This method is applied to several cases of practical interest, including the escape probability from a pair of reactive sinks.

Crossed molecular beam studies on the interaction potential for F(^{2} P)+Xe(^{1} S)
View Description Hide DescriptionFor the evaluation of the ground state XeF interaction potential, angular distributions of F atoms scattered off Xe were measured in crossed molecular beam experiments at collision energies of 2.11, 10.5, and 13.9 kcal/mole. F atoms, produced by thermal dissociation of F_{2} at 700 °C in a supersonic expansion using rare gas carriers, contain ∼78% F (^{2} P _{3/2}) ground state and ∼22% F (^{2} P _{1/2}) spin–orbit excited state. Consequently, three electronic states X1/2, I3/2 emerging from the ^{2} P _{3/2} +^{1} S _{0} asymptote, and II 1/2 from the ^{2} P _{1/2}+^{1} S _{0} asymptote are involved in the scattering. A simple elastic approximation, neglecting interstate coupling, is used for the calculation of differential scattering cross sections in the evaluation of interaction potentials. Experimental results are found corroborating the spectroscopically derived potential of Tellinghuisen e t a l. (ε=3.359 kcal/mole, r _{ m }=2.293Å) for V _{ X1/2}(r), and the conclusion that V _{ I3/2}(r) and V _{ I I1/2}(r) are in close resemblance to the ground state Ne+Xe interaction potential.

Rotational tunnelling in methylpyridines as studied by NMR relaxation and inelastic neutron scattering
View Description Hide DescriptionNuclear magnetic resonance(NMR) and inelastic neutron scattering (INS) techniques have been applied to study the phenomenon of methyl group tunnelling of various picolines and lutidines in the crystalline state over a wide range of temperatures. In most of these materials, two maxima—one is field independent—and two different apparent activation energies in the proton spin lattice relaxation rate have been observed. The NMR‐T_{1} results are discussed in terms of Haupt’s model, where nuclear relaxation occurs via successive coupling of the spins with the tunnelling CH_{3} rotator and the phonon system. The meaning of correlation times and associated activation energies, and the connection between classical and quantum mechanical theory are considered. By INS, the tunnel splittings and the energy differences between the lowest torsional states have directly been determined. For 3,5‐dimethylpyridine the tgemperature dependence of the tunnel splitting has been measured; there is agreement between this data and the NMR average tunnel frequency. Potential curves have been derived using tabulated eigenvalues. The INS results confirm Haup’s model.

A new red‐edge effect in aromatic molecules: Anomaly of apparent rotation revealed by fluorescence polarization
View Description Hide DescriptionMeasurements of stationary fluorescencepolarization at wavelengths of excitation that yield limiting polarizations close to 1/2 and 1/7, respectively, permit the characterization of the rates of in−plane and out‐of‐plane rotation in aromatic compounds. Propylene glycol solutions of 1‐ and 2‐naphthylamine, some of their derivatives, anthracene, and indole show the expected dependence of the rate of rotation upon limiting polarization, but all of them additionally display on excitation at the red edge of the absorption, a decrease in the rotational rate, which then approaches the rate observed for pure out‐of‐plane rotations. Differential phase measurements of the polarized components of the fluorescence of 1‐naphthylamine confirm this effect. After careful check of the effects of temperature and excitation wavelength upon the emission spectrum and the fluorescence lifetimes, it is concluded that the red‐edge rotational anomaly arises from the existence of out‐of‐plane transition moments in absorption and emission in this spectral region. The physical origin of the effects and their relation to other observed red‐edge phenomena are discussed.

Mobility of localized and quasifree excess electrons in liquid hydrocarbons
View Description Hide DescriptionThe dependences of excess electron mobility on temperature and conduction state energy in saturated liquid hydrocarbons are measured in order to evaluate the mobilities in the localized and in the quasifree state and the energies of the localized state. These quantities appeared earlier as adjustable parameters of a two‐state electron model. Localized electron mobility is described in terms of the motion of a microscopic bubble. The transport of the quasifree electrons is regarded as that of a plane wave scattered by density fluctuations of the liquid. This model, combined with the mobility equation of Cohen and Lekner, finds reasonable agreement with experimental values which vary between 34 and about 400 cm^{2} V^{−1} sec^{−1}.

Magnetization modes and evolution matrices for some simple spin systems in anisotropic media
View Description Hide DescriptionThe time evolution of complete sets of coupled magnetization mode variables for the A X _{2}, A X _{3}, and X _{3} spin one‐half systems are presented. The chosen modes prove to be the natural kinetic variables for free and partially constrained nuclear magnetic relaxation studies in both spacially isotropic and spacially anisotropic environments. The relationship between spacial anisotropy, the concomitant failure of time reversal symmetry, and the appearence of complex valued angular correlation time constants is also discussed. It is rationalized that the absence of time reversal symmetry necessitates the introduction of certain zero frequency phase coherence variables which linearly couple into the magnetization (population) mode variables. Thus, relaxation studies may indeed distinguishbetween degenerate irreducible multiplicities.

ESR study of radiation‐induced radicals in the sugar‐phosphate region of nucleotides. III. The alkoxy radical in deoxycytidine 5′‐phosphate
View Description Hide DescriptionThe unstable radical at 77 K in a gamma‐irradiated single crystal of deoxycytidine 5′‐phosphate was analyzed by ESR. A very anisotropicgtensor (g _{1}=1.9997, g _{2}=2.0095, and g _{3}=2.0773) and two approximately equal β‐proton couplings with isotropic values of 8.0 G were interpreted to represent a radical of the O–CH_{2}–R form. The radical is formed by the breakage of the phosphate–ester bond. The calculated spin densities on H _{(5′)} and H′_{(5′)} in the INDO MO approximation are in agreement with the observed couplings. The lack of any hydrogen bonding in the radical is believed to bring about much smaller β‐proton couplings from those previously observed and assigned to the same radical.

Dispersion forces between noble gas atoms
View Description Hide DescriptionThe coefficients of the R ^{−6}, R ^{−8}, and R ^{−10} terms in the series representation of the dispersion interaction between helium, neon, and argon at distance R are calculated using an elementary variation method.