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Volume 92, Issue 8, 15 April 1990

Mie scattering from thin anisotropic spherical shells
View Description Hide DescriptionExact simple closed form solutions for the electromagneticscattering problem for a thin spherical shell composed of radially oriented optically anisotropicscattering elements have been obtained. The solution is valid for arbitrary shell size and index of refraction, but is limited to the case of small shell thickness compared to the shell radius. Connections with the Rayleigh–Debye approximation are clearly established and the polarizability of the shell is given in terms of the dielectric constants. It is found that the Rayleigh–Debye approximation correctly computes the effect of the anisotropy in this case. These results are useful in the interpretation of light scattering experiments from phospholipid vesicle dispersions.

Zeeman spectroscopy and deperturbation of the low‐lying states of NiH
View Description Hide DescriptionHigh resolution laser spectroscopy of the NiH molecule in a magnetic field has revealed strong homogeneous and heterogeneous perturbations among all of the low‐lying electronic states. Fully resolved Zeeman splitting patterns from transitions between NiH magnetic sublevels were recorded with the technique of Zeeman optical–optical double resonance (ZOODR) spectroscopy.U s i n g o n l y t h e z e r o‐f i e l d r o t a t i o n a l e n e r g y l e v e l s a s i n p u t t o a n e l e c t r o n i c s t r u c t u r e m o d e l, we have calculated Zeeman splittings (g values) for 19 rotational levels, and the predicted splittings are in very good agreement with observed Zeeman spectra. A group of 10 NiH molecular electronic states is seen to form a supermultiplet of levels originating from the Ni^{+} (3d ^{9})^{2} D atomic multiplet. We describe an effective Hamiltonian matrix that contains explicit terms coupling low‐lying states through spin–orbit, vibrational, and rotational interactions. Supermultiplet eigenvectors graphically illustrate the profound mixing hidden beneath the apparent regularity of term value plots for the low‐lying states of NiH. The success of the supermultiplet model for this simplest case (a single hole in a highly contracted 3d subshell), namely the successful prediction of strongly J dependent g values, makes us confident that this model will be applicable to other transition metal monohydrides.

The derivation of the rotational potential function from atom–atom potentials. IV. The symmetric tops NH_{3}D^{+} and NHD^{+} _{3} and the asymmetric top NH_{2}D^{+} _{2}
View Description Hide DescriptionA procedure is presented for computing the hindered rotational energy levels of symmetric and asymmetric tops in tetrahedral crystalline fields. By considering the equations used to derive the rotational potential function from atom–atom potentials, the change required in the potential function on going from spherical tops to symmetric and asymmetric tops has been determined. The rotational potential function of NH_{3}D^{+} and NHD^{+} _{3} in NH_{4}Cl, (NH_{4})_{2}SnCl_{6}, (NH_{4})_{2}SiF_{6}, and NH_{4}F have been derived from atom–atom potentials. The rotational potential functions of NH_{2}D^{+} _{2} in the first three compounds listed above have also been derived from atom–atom potentials. Only the J=4 term in the rotational potential functions has been found to be significantly different for symmetric and asymmetric tops than for spherical tops. The librational frequencies have been computed for the isotopic forms of the solids listed above. For some of solids that have been studied, tunneling frequencies have also been computed. For the symmetric tops NH_{3}D^{+} and NHD^{+} _{3}, there are two librational frequencies, one with A symmetry and the other with E symmetry. The difference in energies of these frequencies is due to the changes in both the kinetic energy term and potential energy term in the Hamiltonian on going from a spherical top to a symmetric top. The contributions of each of these terms to the splitting in the librational frequency has been determined for the compounds under study. The tunneling frequencies of CH_{3}D have been computed in phase II for both the methane molecules on the D _{2d } and O _{ h } sites. For the molecules on the D _{2d } sites, only the molecular field is considered. The potential function is due to the crystalline field for molecules on the O _{ h } sites. The computed tunneling frequencies of the molecules on both sites are in good agreement with the observed results of the INS of CH_{3}D in CH_{4}.

Hindered rotational energy levels of symmetric tops in trigonal crystalline fields
View Description Hide DescriptionThe energy levels for the hindered rotation of symmetric top molecules or ions in trigonal crystalline fields have been computed. The symmetry group of the Hamiltonian is C̄_{3v }×C _{3} , where C̄_{3v } is the trigonal group of rotations about the body‐fixed axes and C _{3} is the trigonal group of rotations about the space‐fixed axes. The tunneling frequencies of CH_{3}D on a Vulcan III powdered sample have been computed and compared to the observed results.

The derivation of the rotational potential function from atom–atom potentials. V. Hindered rotation of ammonia molecules in solid ammonia
View Description Hide DescriptionThe rotational potential functions of ND_{3} and NH_{3} are calculated from atom–atom potentials. The site symmetry of the ammonia molecules in solid ammonia is C_{3}. The hindered rotational energy levels of the molecules in ND_{3} and NH_{3} are computed by diagonalizing the Hamiltonian matrices. The librational frequencies and the activation energy of the ammonia molecules determined from the hindered rotational energy levels are compared to the observed results. The heat capacities of both NH_{3} and ND_{3} have been analyzed using the computed hindred rotational energy levels. The difference in the low temperature heat capacities of ND_{3} and NH_{3} is interpreted in terms of the hindered rotational energy levels of the molecules.

Theoretical line shapes for rotational spectra of HCl in Ar
View Description Hide DescriptionAn interaction potential for HCl–Ar recently derived from spectra of van der Waals complexes [J. M. Hutson, J. Chem. Phys. 8 9, 4550 (1988)] has been used to obtain converged close‐coupling scattering S matrices from which pressure broadening (linewidth, line shift, and line coupling) cross sections have been computed within the Fano–Ben‐Reuven formalism. Linewidths agree well with experimental data with the exception of the 0–1 line at low temperatures (an error of about 15% at 125 K). Line shifts, especially the largest, for the 0–1 line, are also in reasonable accord with experimental data. Line coupling is predicted to be quite small. The coupled‐states molecular scattering approximation is found to be accurate except at very low collision energies. The infinite‐order sudden approximations, on the other hand, is not reliable for this system. Inelastic scattering out of the spectroscopic levels accounts for only a fraction of the linewidth at thermal energies, especially in the lower rotational levels.

Selective spectroscopy of rigid and fluxional carbazole–argon clusters
View Description Hide DescriptionTwo size‐selective spectroscopic techniques were used to experimentally differentiate between nearly rigid (solid‐like) and highly fluxional (liquid‐like) carbazole⋅Ar_{ n } (n=4–6) clusters produced and cooled in supersonic molecular beams: (1) ionization potential selective resonant two‐photon ionization (IP selective R2PI) spectroscopy; and (2) spectral hole‐burning with R2PI detection. For each cluster size, separate and qualitatively very different electronic spectra were obtained by IP selective R2PI, depending on total ionization energy. At low ionization energies, broad bands of halfwidth ≊50 cm^{−1} (FWHM) were obtained, which are interpreted as due to fluxional clusters of high internal energy. When ionizing slightly above an abrupt step in the ionization efficiency curve, additional narrow (Δν≊5 cm^{−} ^{1}) features appear superimposed on the semicontinuous spectra; these are interpreted as due to (near) rigid clusters with low internal energy. The spectral hole‐burning experiments support this interpretation in that deep holes of ≊5 cm^{−} ^{1} width could be burned in the rigid cluster spectra, but no spectral holes could be observed in the broad bands. The latter fact is interpreted as due to spectraldiffusion of the fluxional subpopulation on a 10^{−} ^{8} s or faster time scale. These results are in good agreement with conclusions drawn from recent numerical simulations.

Electron paramagnetic resonance, electron nuclear double resonance, and electron spin echo envelope modulation of Fe(CN)^{3−} _{6} in a KCl lattice
View Description Hide DescriptionAn electron paramagnetic resonance(EPR),electron nuclear double resonance(ENDOR), and electron spin echo envelope modulation (ESEEM) study has been carried out on Fe(CN)^{3−} _{6} in a KCl lattice. The EPR spectrum showed the formation of a large number of centers, which correspond to different configurations of the charge compensating cation vacancies. The two major centers called center I _{ a } and I _{ b } have been well characterized. Both centers have orthorhombic symmetry and show a large ganisotropy. The principle g values are: g _{ x } =2.079, g _{ y } =3.054, and g _{ z } =0.400 for center I _{ a }; g _{ x } =2.007, g _{ y } =3.177, and g _{ z } =0.752 for center I _{ b }. The ligand field splitting and the orbital reduction factor k have been obtained through analyzing the spectra in terms of the generalized spin Hamiltonian. A number of unusual features observed in the EPR spectra have been found to be due to the high level of ganisotropy. The ENDOR and ESEEM measurements performed on center I _{ a } revealed nearly all the coupling tensors between the unpaired electron and the ^{1} ^{3}C and ^{1} ^{4}N nuclei. The principle values and tensor orientations were precisely determined by least‐squares fitting. The orientations of the coupling tensors give a detailed picture of the complex under the influence of the two cation vacancies. The coupling constants of ^{1} ^{3}C were found to be an order of magnitude larger than those of ^{1} ^{4}N. Level anticrossing was observed for the nuclear spin states of ^{1} ^{4}N.

Resonance Raman spectra of t r a n s‐1,3,5‐hexatriene in solution: Evidence for solvent effects on excited‐state torsional motion
View Description Hide DescriptionResonance Raman spectra of t r a n s‐1,3,5‐hexatriene in cyclohexane, hexane, methanol, and perfluorohexane are compared with the corresponding vapor phase spectra. The absolute cross sections in cyclohexane indicate that the solvation induced electronic spectral breadth is partly homogeneous (amplitude level in the Raman process) and partly inhomogeneous. Overtones and combination bands involving torsional modes, particularly the central double bond torsion, are dramatically reduced in intensity upon solvation, the reduction being greatest in solvents that generate the largest red shift of the absorption. Quantitative modeling of the cyclohexane data shows that these intensity changes can be attributed only in part to the preferential damping of low‐frequency overtones induced by the increase in electronic homogeneous linewidth upon solvation. The remaining intensity reduction may arise either from a stiffer excited‐state potential surface for double bond twisting in solution or from coordinate‐dependent dephasing in the upper electronic state. Additionally, time‐dependent wave packet propagation techniques are employed to estimate the barrier to double bond twisting in the excited state from the experimental ratio of four‐quantum to two‐quantum Raman overtone intensities.

Triplet electron paramagnetic resonance detection of porphyrinoids in fluid liquid crystals at elevated temperatures
View Description Hide DescriptionThe photoexcited triplet state of two porphyrinoids, H_{2}TTP and a Cd complex of Texaphyrin (Cd‐TxP), oriented in liquid crystals were examined by time‐resolved electron paramagnetic resonance(EPR)spectroscopy as a function of temperature. The low probability of molecular tumbling in the liquid crystalline phase allows the detection of triplets by fast EPR, at temperatures (300 K) which are above the hosts’ melting points, and where the fluid properties of the matrices are maintained. Line shape and kinetic analyses of the triplet spectra provide data on spin relaxation rates, interchromophore interactions, and on the dynamic behavior of the liquid crystalline hosts, driven by the external magnetic field.

Pulsed‐nozzle Fourier‐transform microwave spectroscopy of laser‐vaporized metal oxides: Rotational spectra and electric dipole moments of YO, LaO, ZrO, and HfO
View Description Hide DescriptionThe rotational spectra of YO, LaO, ZrO, and HfO have been measured using a Fourier‐transform microwave spectrometer in combination with a laser‐ablation source. Here, a Q‐switched Nd:YAG laser (532 nm) was used to vaporize the metal oxides from a target source rod located in the throat of a pulsed‐molecular‐beam valve. A description of the instrument is given. The electric dipole moments of the four species have been measured and compared to a b i n i t i o results, where available. The experimental values are μ_{YO} =4.524(7), μ_{LaO} =3.207(11), μ_{ZrO} =2.551(11), and μ_{HfO} =3.431(5) D. Of special note are the extremely large nuclear quadrupole coupling constants, eQq, determined for the ^{1} ^{7} ^{7}HfO and ^{1} ^{7} ^{9}HfO isotopic species, with values of −5952.649(35) MHz and −6726.981(39) MHz, respectively. This is the first determination of nuclear quadrupole coupling constants for a molecule containing the Hf atom.

Alignment of the E,F ^{1}Σ^{+} _{ g }, v ^{’} _{ E }=1 state of H_{2} by two‐photon excitation
View Description Hide DescriptionThe alignment of the E,F ^{1}Σ^{+} _{ g }, v _{ E }=1 state of H_{2} produced by two‐photon excitation from the X ^{1}Σ^{+} _{ g }, v‘=0 ground state was investigated using two different techniques. First, in a single‐color experiment, photoelectron angular distributions were measured for the two‐photon resonant, three‐photon ionization of H_{2} via the Q(0) and Q(1) transitions to the E,F ^{1}Σ^{+} _{ g }, v ^{’} _{ E }=1 state. The photoelectron angular distributions are consistent with an unaligned E,F ^{1}Σ^{+} _{ g }, v _{ E }=1, J’=1 state. Second, in a two‐color experiment, the photoionization spectra of several vibrationally autoionizing (X ^{2}Σ^{+} _{ g })n p, v=1 Rydberg states excited from the v ^{’} _{ E }=1, J’=1 level of the E,F ^{1}Σ^{+} _{ g } state were measured as a function of the relative polarizations of the pump and probe beams. The polarization dependence of the relative intensities of the P(1) and Q(1) transitions was used to determine the alignment of the E,F ^{1}Σ^{+} _{ g }, v _{ E }=1, J’=1 state produced by the pump laser. Consistent with the angular distributionmeasurements, the polarization results indicate that the populations in the M’=0 and M’=±1 levels of the E,F ^{1}Σ^{+} _{ g }, v ^{’} _{ E }=1, J’=1 state are equal, within the experimental uncertainty of 15%.

Frequency‐domain observation of the ultrafast inertial response of the optical Kerr effect in CS_{2}
View Description Hide DescriptionTime‐domain experiments using femtosecond pulses have recently revealed the inertial aspect of the nuclear‐orientation component of the optical Kerr effect in carbon disulfide. We present frequency‐domain measurements, performed with the tunable‐laser‐induced grating technique, which also demonstrate the need to incorporate inertial behavior in models of the nuclear‐orientation contribution to this ultrafast response. No previously suggested model, however, yields a fit to our data that passes standard goodness‐of‐fit tests at an acceptable level.

Internal rotation of the methyl group in the radical cation of dimethyl ether
View Description Hide DescriptionThe radical cation of dimethyl ether has been studied by ESR in the temperature region of 6–140 K focusing on the internal rotation of the methyl groups. The methyl groups rotate almost freely at above ∼70 K to give a septet ESR spectrum. At temperatures below 40 K there emerge extra lines due to the tunneling rotation of the methyl groups. From the analysis of the line shape, the interaction potential for the rotation of the two methyl groups, if any, should be approximated as proportional to cos 3θ_{1} cos 3θ_{2}, where θ_{1} and θ_{2} denote the rotational angles of the methyl groups measured from the potential minima of the internal rotation of the methyl groups. The activation energy for the thermally induced internal rotation is determined to be ∼100 cal/mol at temperatures above 25 K, whereas at lower temperatures the apparent activation energy drops sharply, which is consistent with the quantum tunneling of the methyl protons. The small activation energy of 100 cal/mol for the radical cation is compatible with the result of a b i n i t i o MO calculation for the potential barrier.

Optical and near‐infrared spectroscopy of neutral indium phosphide clusters
View Description Hide DescriptionSpectra are obtained for a wide distribution of sizes and stoichiometries of indium phosphide clusters using photodissociation techniques. These spectra are presented at two different cluster temperatures throughout the spectral range of 0.65 eV (1900 nm) to 2.0 eV (640 nm) for indium phosphide clusters containing from 5 to 14 atoms. Though the spectral behaviors of the clusters are found to be qualitatively similar, significant quantitative differences exist. A Rice–Ramsberger–Kassel–Marcus (RRKM) dissociation model employing significant fitting constraints is found to accurately describe the observed dissociation behaviors at both temperatures. Dissociation energies ranging from 2.0 to 2.4 eV are determined for the In_{5}P_{ y }–In_{9}P_{ y } clusters using the RRKM model. Experimental evidence suggests that the dissociation process involves loss of a small phosphorus containing moiety such as P_{1–2} or InP_{1–2}. Results of the RRKM fitting process also clearly indicate that most of these In_{ x }P_{ y } clusters have nearly uniform absorption cross sections from 0.65 to 2.0 eV. This range extends well below the band gap of bulk InP. This is the first clear evidence of the presence of electronic states in closed shell semiconductor clusters at energies well below the band gap of the bulk material. Select clusters show significant deviations from pure RRKM behavior. Their behavior is consistent with the presence of spectral structure in their absorption cross sections in the energy range of 0.65–2.0 eV.

Quenching of N(^{2} D) by O(^{3} P)
View Description Hide DescriptionA definitive measurement of the rate coefficient for the quenching of N(^{2} D) by O(^{3} P) is reported. The O(^{3} P) atoms were generated by titrating NO directly into the active nitrogen flow. Analysis of the results required that the rate coefficient for the reaction N(^{2} D)+NO→N_{2}+O be known accurately, and this was also determined. A finite mixing time correction is also necessary. The best estimate of the rate coefficient from this work is (6.9+0.7, −1.1)×10^{−13} cm^{3} s^{−1} at T=298 K, considerably smaller than a previous measurement [J. Phys. Chem. 9 2, 5977 (1988)] and in much better accord with values required by atmospheric models.

Characteristic modes of oscillatory chemical reactions
View Description Hide DescriptionWe show how eigenvectors of the Jacobi matrix J and its transpose J^{ T } at a supercritical Hopf bifurcation can be used for quantitative characterization and analysis of models of oscillatory chemical reactions.Eigenvectors of J determine the oscillations and the principal transients and can be expressed in terms of concentrations or reaction currents. Important reactions of a system can be easily identified this way. A pair of complex conjugate eigenvectors of J^{ T } associated with the bifurcation determines all independent quenchings of the oscillations. It can be used for quantitative comparison with experiment and in systematic search for better models. We combine the two sets of eigenvectors in a quantitative analysis of the effect of using a phase space of reduced dimension as an approximation to the full phase space. The analysis is illustrated by an explicit reduction of a five‐dimensional Oregonator based model of the Belousov–Zhabotinskii reaction to a four‐dimensional phase space involving a ‘‘quasi‐species.’’ The reduced phase space is tangent to a slow manifold at the bifurcating stationary point. Reconstruction of amplitudes and phases of the oscillations from incomplete quenching data is explained in terms of the reduced phase space.

Stochastic dynamics of the chlorite–iodide reaction
View Description Hide DescriptionA recently proposed theoretical framework appropriate to the study of the stochastic behavior of several chemical systems is used to analyze the irreproducibility of the observed reaction times in the chlorite–iodide clockreaction. Noise terms are incorporated through the kinetic constants and their intensity is further correlated with the inverse of the stirring rate. Analytical and simulation results are obtained for the first moments of the reaction time distribution. These results are compared with recent experimental data obtained by Nagypál and Epstein.

Time dependent thermal lensing measurements of V–T energy transfer from highly excited NO_{2}
View Description Hide DescriptionThe time dependent thermal lensing technique has been used to measure the vibrational relaxation of NO_{2} (initially excited at 21 631 cm^{−} ^{1}) by Ar, Kr, and Xe. The energy transferanalysis was carried out in terms of 〈〈ΔE〉〉, the bulk average energy transferred per collision. This quantity was found to have a very strong dependence on vibrational energy, with a marked increase at energies greater than about 10 000 cm^{−} ^{1}, where several electronic excited states (^{2} B _{2}, ^{2} B _{1}, and ^{2} A _{2}) mix with the ground state (^{2} A _{1}). This effect may be due to large amplitude vibrational motions associated with the coupled electronic states. Even at low energies, deactivation is faster than in other triatomic systems, probably because NO_{2} is an open shell molecule and electronic curve crossings provide efficient pathways for vibrational deactivation. The V–T rate constant for deactivation of NO_{2}(010) by argon is estimated to be (5.1±1.0)×10^{−} ^{1} ^{4} cm^{3} s^{−} ^{1}. Results obtained for NO^{*} _{2}–NO_{2} collisions gave 〈〈ΔE〉〉 values in good agreement with literature results from fluorescence quenching experiments, indicating that V–T may be more important than V–Venergy transfer in the quenching process.

Photoisomerization of diphenylbutadiene in low‐viscosity nonpolar solvents: Experimental manifestations of multidimensional Kramers behavior and cluster effects
View Description Hide DescriptionThe photoisomerization of diphenylbutadiene was studied by picosecond absorption spectroscopy over wide pressure and temperature ranges in liquid and supercritical alkanes, CO_{2}, SF_{6}, and He. The reaction shows typical features of a thermal unimolecular reaction on the S _{1}potential energy surface. The rate can be expressed by a combination of standard unimolecular rate theory and Kramers–Smoluchowski theory. However, multidimensional behavior manifests itself in the transition to the gas phase low pressure range as well as to the high density Kramers–Smoluchowski range: in the former case, the low pressure limit of a unimolecular reaction of the polyatomic molecule is approached; in the latter case, the effective imaginary barrier frequency shows a marked apparent temperature dependence. The experiments also suggest contributions of reactant–solvent cluster interactions, which modify the barrier height even in nonpolar solvents.