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Volume 62, Issue 6, 15 March 1975

Nitrogen and proton hyperfine interactions in the triplet state of azanaphthalenes at zero field
View Description Hide DescriptionThe zero field optically detected ESR and ENDOR spectra of the triplet state of 1,8−diazanaphthalene are presented and completely interpreted in terms of a spin Hamiltonian which includes proton hyperfine interactions. The latter are shown to be of considerable importance at zero field even in systems containing quadrupolar nitrogen nuclei. The previously unassigned features in the zero field spectra of diazanaphthalenes are explained and some new assignments are proposed in quinoline.

Study of the structure of molecular complexes. X. Dipole moment surface for the lithium–fluoride–water complex
View Description Hide DescriptionThe dipole moment for 252 configurations of the Li−F−H_{2}O complex has been computed using Hartree−Fock wavefunctions. The computed values are fitted with an analytical expression. The results clearly indicate that the water dipole moment, having the expected form of point charge−induced dipole moment, acts only as a relatively small perturbance on the dipole moment of the LiF ion pair.

Paramagnetic hexafluoride anions of Group VI
View Description Hide DescriptionCertain isotropic ESR spectra observed in γ−irradiated SF_{6} and in γ−irradiated solid solutions of SeF_{6} and TeF_{6} in SF_{6} are attributed to the hexafluoride anions of the Group VI elements. Hyperfineinteraction measurements for the species 33SF6−, 77SeF6−, and 125TeF6−, observed in natural abundance, show that the central atom outer s orbital makes a very large contribution to the (totally symmetric) semioccupied orbital in these radicals. INDO MO calculations for SF_{6} ^{−} gratifyingly predict a half−filled orbital which has the representation A _{1g } in O _{ h } symmetry and which is primarily composed of S 3s and F 2p _{σ} atomic orbitals. An additional isotropic spectrum present in γ−irradiated 1% SeF_{6} in SF_{6} is believed to be that of SeF_{5} in which hyperfineinteraction with the unique (apical) F nucleus is not detectable.

Detailed echo‐shape fitting in NMR spin‐echo experiments
View Description Hide DescriptionIn NMR pulse experiments performed on liquids, the desired information has usually been obtained either from the echo maxima or from the Fourier transform of the free induction signal trailing a (1/2) π pulse or half of the last spin echo in a Carr−Purcell train. The present work explores the feasibility of extracting information directly from the echo shape by a fitting procedure. In principle, this technique can regain the selectivity and resolution lacking in the conventional high−power spin−echo methods. Possible applications to the studies of selective spin−spin relaxation, nuclear transfer processes, and molecular diffusion in multicomponent systems are discussed.

Dynamics of critical fluctuations of a macromolecular solution
View Description Hide DescriptionThe angular and the spectral distribution of scattered light intensity and the hydrodynamic shear viscosity from polystyrene (M n = 1.96×10^{5}, M w/M n < 1.02) in cyclohexane were measured at the critical solution concentration above the critical consolute temperature in the one phase region. In comparing the linewidth, correlation length, and shear viscosity data with the modified mode−mode coupling theory of Kawasaki, we note that the magnitude of a ’’scaled linewidth’’ Γ^{+} (≡6πη*_{ p }Γ/k _{ B } T K ^{3}) as a function of Kξ is a factor of 1.5−3 higher than the single universal curve of Kawasaki and Lo, where η*_{ p }, Γ, k _{ B }, T, K, and ξ are, respectively, the shear viscosity, the linewidth, the Boltzmann constant, the absolute temperature, the magnitude of the momentum transfer vector, and the correlation length. Since the theory describes only the critical part of the linewidth Γ^{ c }, we separate the decay rate due to critical fluctuations and the finite molecular size of the polymer. The resultant scaled linewidth Γ* (≡6πη*_{ p }Γ^{ c }/ k _{ B } T K ^{3}) as a function of Kξ can then be brought down to the universal curve. Our comparison between existing polymer data and theory represents a first attempt to take into account the finite molecular dimension of the system in decay rate of order parameter fluctuations. The data exhibit considerable scatter after the background correction. Consequently, there seems to be a need to consider more carefully the manner in which the backgrounds are subtracted before more crucial comparisons between experiments and theory can be made.

Electron propagator calculations of the photoelectron spectrum for open shell molecules with applications to the oxygen molecule
View Description Hide DescriptionAn approximate self−energy for the electron propagator is derived using the Grand Canonical averaging procedure for open shell molecules. The connection between the overlap amplitudes and the photoionization cross section is discussed. A direct pole and residue search is employed to solve the Dyson equation with a second order self−energy for the oxygen molecule, yielding a theoretical photoelectron spectrum in good agreement with experimental x−ray induced spectra.

Lifetime‐separated spectroscopy: Observation and rotational analysis of the BaO A′ ^{1}Π state
View Description Hide DescriptionThe BaO A′ ^{1}Π−X ^{1}Σ^{+} band system has been investigated using laser−induced fluorescence. The BaO is formed in the gas−phase reaction Ba + CO_{2} under single−collision conditions, and the A′ ^{1}Π and A ^{1}Σ^{+} states are simultaneously excited by a pulsed tunable dye laser with a 0.2 Å bandwidth. The weak, long−lifetime A′−Xfluorescence is separated from the strong, short−lifetime A−Xfluorescence by delaying the observation of the A′−X emission until the A−X emission dies away. The lifetime of the BaO A′ ^{1}Π state is found to be 9±1 μsec, more than an order of magnitude longer than that of the the BaO A ^{1}Σ^{+} state. We have observed the (v′,0) band progression for 9 ? v′ ⩽ 18 as well as the (10,1) and (13,1) bands of the A′−X system, and they are found to be represented by the A′ state vibrational constants ν_{00} = 17 573±10 cm^{−1}, ω_{0} = 442.38±1.1 cm^{−1} and ω_{0} x _{0} = 1.693±0.025 cm^{−1}. The (12,0), (17,0), and (18,0) bands have been rotationally analyzed, yielding the rotational constants B _{12} = 0.20849±0.00022 cm^{−1}, B _{17} = 0.20290±0.00012 cm^{−1}, and B _{18} = 0.20109±0.00014 cm^{−1}. These results confirm that the shapes of the potential curves for the A′ ^{1}Π and a ^{3}Π states of BaO are remarkably similar for low vibrational levels. We also conclude that the A′ ^{1}Π state is not the emitter responsible for the many−line emission spectrum seen in the Ba + N_{2}O and Ba + O_{3}reactions at low pressures, nor is it the ’’dark’’ precursor responsible for the high photon yields observed in these chemiluminescent reactions at high pressures.

Production efficiencies of electronically excited states of barium monohalides
View Description Hide DescriptionDiatomic barium monohalides (BaX) have been produced in the gas−phase reaction of Ba, entrained in a flowing inert carrier gas, with F_{2}, SF_{6}, Cl_{2}, Br_{2}, and I_{2}. Bright green chemiluminescent flames were observed at pressures from 0.1−10 torr. Emission spectra were obtained from 300−1200 nm. Near infrared emission from BaBr and BaI has been ascribed to transitions to the ground state from previously unobserved electronic states analogous to A and B states in BaF and BaCl. In BaBr, electronic state energies for B ^{2}Σ^{+}, A ^{2}Π_{3/2}, and A ^{2}Π_{1/2} have been found to be 11 325, 10 604, and 9980 cm^{−1}, respectively; in BaI, corresponding values are 10 417, 9921, and 9268 cm^{−1}. BaX molecules are produced with moderate efficiency into lower lying electronic states (80%−98% in A and B) with an absolute efficiency of approximately 1 photon for each 100 reacted barium atoms. There is a small dependence on pressure with maximum yields occuring near 4 torr. Spectra of C ^{2}Π−X ^{2}Σ^{+} transitions show Boltzmann distributions in both vibration and rotation corresponding to population temperatures of approximately 3000 K for BaF and 2000 K for BaBr, BaCl, and BaI. Electronic population temperatures show trends similar to those observed in vibration and rotation.

Infrared laser enhanced reactions: Temperature resolution of the chemical dynamics of the O_{3} ^{†} + NO reaction systen
View Description Hide DescriptionThe rate constant for the decay of vibrationally excited ozone, O_{3} ^{†}, in the O_{3} ^{†} + NO reaction system has been measured from 153 to 373 K. Vibrationally excited O_{3} was produced in the asymmetric stretch normal mode by absorption of square wave modulated emission from a CO_{2} laser tuned to the P (30) 9.6 μm transition. Under appropriate experimental conditions, a rapid V→V coupling process involving all three normal modes of O_{3} is believed to set up a Boltzmann population distribution among them. Reaction or relaxation of O_{3} ^{+} out of this subset of normal modes is observed to proceed through a weighted average of rate constants. From the effects of temperature and buffer gas pressures an assessment can be made as to the predominant loss mechanism for the various modes. While there are three separate convolution schemes which appear to fit our data, we are persuaded to emphasize one whereby all three modes contribute via a reaction channel described by k _{ D } = (2.0×10^{−11}) exp(−1525/T) cm^{3} molecule^{−1}⋅sec^{−1} while ν_{2} alone is active in a V→T relaxation process given by k _{ A } = (1.0×10^{−13}) exp(−39.2/T cm^{3} molecule^{−1}⋅sec^{−1}. A comparison of the Arrhenius parameters for the reaction channels of O_{3} ^{†} with parameters for the corresponding processes involving thermal O_{3} yields specific information about the effect of vibrational energy on the reaction dynamics.

A time‐dependent variation–perturbation method for the calculation of transition properties and its relation to the random phase approximation
View Description Hide DescriptionA time−dependent variation−perturbation (VP) formulation is presented for the simultaneous calculation of the ground statecorrelation function and the excited statewave function of an atomic or molecular system. The wave functions are chosen for the optimal calculation of transition properties with a relatively small number of molecular integrals. The VP equations so obtained for a singlet system are identical with the equations in the random phase approximation (RPA). On the other hand, if the ground state is a singlet and the excited state a triplet, the VP and RPA equations are different. The latter assumes a ground statecorrelation function with an open shell component, which is a poor approximation for a closed shell ground state. The orthonormalization condition in the VP scheme is different from that in the RPA. The consequence of this difference is discussed. It is also pointed out that the RPA excitation energy actually contains part of the ground state correlation energy; hence the RPA excitation energy is always lower than the corresponding values in the Tamm−Dancoff approximation and the self−consistent RPA. A variational formulation of the time−dependent problem gives a set of equations which resembles the higher RPA equations.

Phase equilibrium isotope effects in molecular solids and liquids. Vapor pressures of the isotopic carbon dioxide molecules
View Description Hide DescriptionThe vapor pressures of samples of enriched in and have been compared with normal over the temperature range 154−217°K. Over the entire temperature range the order of the vapor pressures is The results are explained by the small shift in the internal vibrations, which dominate the carbonisotope effect, and hindered rotation in the solid and liquid. While the isotope effect on melting is small for carbon substitution, it is found to be large for oxygen substitution. Hindered rotation is the major contribution to the oxygen isotope effect in the solid, while the hindered translation is the most important contribution to the oxygen isotope effect in the liquid. Model calculations of the logarithm of the reduced partition function ratios of the solid and liquid, are made in an anharmonic version of the Stern−Van Hook−Wolfsberg cell model. These calculations give good agreement with the experimentally determined values for the solid, liquid−vaporisotope fractionation measurements of Grootes, Mook, and Vogel, and lattice dynamic calculations.

Calculation of the lattice modes of the isotopic CO_{2} molecules and their reduced partition function ratios
View Description Hide DescriptionThe lattice dynamics of a unit cell with four CO_{2} molecules have been calculated from the Raman, infrared, and inelastic neutron scatteringspectra. The vibrational frequencies of the isotopic ^{12}C^{16}O_{2}, ^{13}C^{16}O_{2}, ^{12}C^{18}O_{2}, and ^{12}C^{16}O^{18}O are calculated in a pseudoharmonic oscillator approximation. From these vibrational frequencies and the gas phase frequencies, the reduced partition ratios of the various isotopic CO_{2} molecules are calculated in good agreement with experiment. The lattice dynamics calculation are also compared with calculation from a simple cell model. It is shown that the simple cell model is an excellent approximation for the calculation of the reduced partition function ratios as a consequence of the large separation between the eigenvalues of the internal and external modes, the magnitude of the external eigenvalues relative to k T, and the symmetries of the lattice and the molecule.

The Ursell‐function structure of the memory function
View Description Hide DescriptionThe integrodifferential equation which defines a memory function f (t) in terms of the time−correlation function g (t) generates ordered Ursell functions having the cluster property. Thus f (t) has an expansion f ^{(2)} (t) + f ^{(3)} (t) + ... in which f ^{(n)} (t) is an n−1 fold time integral whose integrand vanishes when the interval between any two successive times is much greater than a certain correlation time of the system. An interaction representation is used in deriving these results and it is found that f ^{(n)} (t) depends, in a certain sense, upon the nth power of the interaction term H _{1} of the Hamiltonian. The integrand of f ^{(n)} (t) is closely related to the ’’cumulant averaged’’ Liouville operators introduced by Kubo and Tomita and developed further by Kubo, Freed, and van Kampen. Thus, in the Markoffian limit f ^{(2)} (t) is simply related to the Redfield relaxation matrix. However, the peculiar time−ordering problems of the cumulant expansion theory do not appear here. Except in very simple cases, all of these results depend upon identifying g (t) as a correlation matrix (Kubo) and the f (t) is the corresponding memory matrix. As a first application the memory function for the EPRrelaxation of aqueous Ni^{++} is calculated in terms of the spin parameters. It is assumed that fluctuating zero−field splitting causes the relaxation, but it is not assumed that the EPRrelaxation obeys Bloch’s equations.

Molecular polarizability and vibrational Raman tensor elements of the H^{+} _{2} molecule
View Description Hide DescriptionMolecular polarizability and Raman matrix elements for the bound vibrational states of H^{+} _{2} are calculated. The increase in the magnitude of these matrix elements with vibrational quantum number and the ’’structure’’ of the contributions from the intermediate vibronic continuum functions are explored.

Phase transition in metal hexammine complexes. II. The EPR spectra of Ni(NO_{3})_{2}6NH_{3} and Ni^{++} doped Zn(NO_{3})_{2}6NH_{3} and Cd(NO_{3})_{2}6NH_{3}
View Description Hide DescriptionThe cooperative effect of the ammonias in X(NO_{3})_{2}6NH_{3} (X = Ni,Zn,Cd) was investigated by EPR. In Ni(NO_{3})_{2}6NH_{3}, the linewidth of the single EPR absorption line undergoes a sudden broadening at T _{ c } = 243 K. This effect is probably a result of a cooperative freezing of the degrees of freedom of rotation of the ammonias, giving the appearance of a crystal field on the Ni^{++} ions. The crystal field does not split the single line, probably because strong exchange effects assemble the lines. The crystal field parameter D = 0.425 cm^{−1} was evaluated by applying the Anderson and Weiss theory for the exchange narrowing of the linewidth. Small quantities of the Ni^{++} ions in Zn and Cd salts do not exhibit strong exchange effects. So the single EPR absorption line above T _{ c } goes to a split line below T _{ c }. For Ni: Zn(NO_{3})_{2}6NH_{3}, T _{ c } = 231 K and D = 0.606 cm^{−1}. For Ni: Cd(NO_{3})_{2}6NH_{3}, T _{ c } = 198 K and D ? 0.3 cm^{−1}. Hysteresis in T _{ c } was also observed for all salts.

Semiclassical calculation of bound states in a multidimensional system. Use of Poincaré’s surface of section
View Description Hide DescriptionA method utilizing integration along invariant curves on Poincaré’s surfaces of section is described for semiclassical calculation of eigenvalues. The systems treated are dynamically nonseparable and are quasiperiodic. Use is also made of procedures developed in the previous paper of this series. The calculated eigenvalues for an anharmonically coupled pair of oscillators agree well with the exact quantum values. They also agree with the previous semiclassical calculations in this laboratory, which instead used integrations along the caustics. The present paper increases the number of systems capable of being treated. Using numerical counter examples for nondegenerate systems, it is also shown that an alternative view in the literature, which assumes that periodic trajectories alone suffice, leads to wrong results for the individual eigenvalues.

On the two state model for electrons in nonpolar liquid hydrocarbons
View Description Hide DescriptionAssuming that electrons are partially free and partially trapped in nonpolar liquid hydrocarbons, we have treated theoretically the scavenging and neutralization processes in these systems. The square root law in scavenging at low cencentrations and the t ^{−1/2} law in the decay of the survival probability at long times which are experimentally observed and theoretically derived for the one state model, can also be derived for the two state model in these respective limits. However, the Laplace transform relation between the probability of scavenging and that of survival against neutralization, which obtains for the one state model, is no longer strictly valid in the two state model.

Molecular theory of dielectric relaxation
View Description Hide DescriptionA new formal relation is obtained for the frequency−dependent dielectric constant of a polar material in terms of a dipole ’’memory function,’’ i.e., a modified correlation function with projected propagator. In contrast to conventional expressions for the dielectric constant in terms of dipole−dipole correlation functions, the memory function expression does not depend on sample shape. The memory function may thus be calculated either by considering the total dipole moment of a molecular sample in vacuum or the dipole moment of a smaller region embedded in the sample. It is shown that this formalism agrees with usual expressions for the dielectric constant and particular relations between the dielectric constant and dipole correlation functions of embedded regions.

Photovoltaic effects of metal–chlorophyll‐a–metal sandwich cells
View Description Hide DescriptionThe microcrystalline chlorophyll−a film prepared by the method of electrodeposition is shown to have strong photovoltaic effects. The photovoltaic cell (M_{1}‖Chl‖M_{2}) has lamellar arrangement with the Chl−a film sandwiched between two metal electrodes. With dissimilar electrodes of different work functions, φ_{M}, the cell usually exhibits a dark rectification behavior. A large forward bias current is seen when the metal with a lower φ_{M} is the negative electrode. The rectification is small when the same metal is used as both electrodes. A blocking contact or Schottky barrier is evidently present at the Chl−a‖metal junction particularly fo the metal having a low φ_{M}. A p−type semiconduction in Chl−a is implicated. In the photovoltaic mode, cells such as (Al‖Chl‖Hg) and (Al‖Chl‖Au) have an open circuit voltage ranging from 200−500 mV. The power conversion efficiency for these cells is on the order of 10^{−3}% which is among the highest in photovoltaic cells using organic materials. The direction of the photovoltaic current and the shape of its action spectrum are strongly dependent on the electrode materials. The blocking contact at the Chl−a‖metal junction is primarily responsible for the photovoltaic activity of the cell. When this blocking contact is established at the directly illuminated electrode the action spectrum closely matches the absorptionspectrum of the Chl−a film. An inverse type response is found when the blocking contact is at the indirectly illuminated electrode with the Chl−a layer essentially acting as an inner filter. The photocurrent is shown to increase when the cell is reverse biased. A minimum quantum yield for charge generation of about 0.03 is found in (Al‖Chl‖Hg) and (Al‖Chl‖Au) cells.

Resonance vibrational energy transfer in liquids in the repulsive potential region
View Description Hide DescriptionIt was found that the resonancevibrational energy transfer caused by the short−range repulsive part of the intermolecular (perturbing) potential may play an important role as mechanism to produce broadening of vibrational band contours of molecules in the liquid state. The value of the full bandwidth at the half peak height (Δν_{1/2}) for the ν_{4} (C−H deformation) fundamental of neat chloroform (8.2 cm^{−1}) was reduced to 6.2 cm^{−1} at infinite dilution with deuterochloroform. This difference in Δν_{1/2} can be reproduced by either the above repulsive mechanism or by resonanceenergy transfer caused by the long−range transition dipole−transition dipole interactions. Physical aspects of these mechanisms are discussed and compared with those of NMR relaxation. The significance of the repulsive resonance transfer process with respect to transition state theory is indicated.