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Volume 106, Issue 10, 08 March 1997

Densitymatrix–electronicoscillator representation of optical spectroscopy of semiconductor nanocrystals
View Description Hide DescriptionThe optical response of CdSesemiconductornanocrystals is investigated using the reduced singleelectron density matrix in real space, calculated by means of the timedependent Hartree–Fock technique. The spectroscopic signatures of exciton confinement are analyzed using the frequencydependent electronic coherence matrix (offdiagonal densitymatrix elements). The effects of Hartree and the Fock (exchange) type Coulomb interactions on the exciton binding energy are discussed. The latter result in almost dark excitons situated energetically below the main transition. Offdiagonal Coulomb matrix elements lead to larger exciton binding energies compared with previous calculations, and result in a better agreement of the size dependence of the lowest optical transition with experiment.

Time resolved four and sixwave mixing in liquids. II. Experiments
View Description Hide DescriptionFemtosecond four and sixwave mixing is employed to study intermolecular motion in liquids, using CS_{2} as a working example. Nonresonant fourwave mixing yields the total spectral response associated with the lowfrequency motions in the liquid. The results of optical Kerr effect and transient gratingscatteringexperiments can be modeled equally well by homogeneously and inhomogeneously broadened intermolecular vibrations. Femtosecond nonresonant sixwave mixing, where two independent propagation times can be varied, contains a temporally twodimensional contribution that provides information on the time scale(s) of these intermolecular dynamics. The sixwave mixing signal of CS_{2} shows distinctly different behavior along the two time variables. When the first propagation time is varied, both librational motion at short times and a picosecond diffusive tail are observed. Along the second propagation time, there is no sign of diffusive response and the signal is solely determined by the librational motions. Its shape depends on the first propagation time, when it is varied between 0 and 500 fs, but it is unaffected by further increase of that delay. This is a strong indication for a finite correlation time of the fluctuations in the intermolecular potentials. The interplay between the initial coherent motions and the diffusive behavior on longer time scales is far from clear. A widely used model in which these are treated as independent harmonic processes fails to describe the results.

New measurements of appearance potentials and optical absorption of Na_{2}F and Na_{3}O
View Description Hide DescriptionOxides and fluorides of sodium clusters were produced by reacting a beam of metal clusters with N_{2}O or SF_{6} in the region between nozzle and skimmer. The threshold for single photonionization was measured by using a pulsed, frequency doubled visible dye laser or a UVdye laser and detecting ions with a quadrupolemass spectrometer.Resonant twophoton ionization was employed to record optical spectra. Comparisons with previous measurements and theoretical predictions are discussed.

Exciton effects in the nonlinear optical susceptibilities of molecular crystals
View Description Hide DescriptionThe frequency dependence of quadratic and cubic susceptibilities given by the conventional expressions for molecular crystals is analyzed for resonances (poles) in the light of the dielectric theory of excitons.Exciton frequencies correspond to poles in the localfield tensors; in the nonlinear susceptibilities the poles in these tensors cancel out the poles that occur in the hyperpolarizability where the output and input frequencies coincide with molecular excitation frequencies, and replace them by poles at the exciton frequencies, including wavevector dependence and any Davydov splitting. In the cubic susceptibility, there are additional poles, through cascading, where the sum of any two input frequencies coincides with an exciton frequency.

Laser induced fluorescence spectra and carbonyl wagging potential energy functions for the S_{1}(n,π^{*}) excited states of tetrahydrofuran3one and tetrahydrothiophen3one: Correlation between inversion barrier and angle strain for cyclic ketones
View Description Hide DescriptionThe jetcooled fluorescence excitation spectra of the S_{1}(n,π^{*}) states of tetrahydrofuran3one, and tetrahydrothiophen3one, have been recorded and analyzed. The carbonyl inversion bands, which arise from doubleminimum potential energy functions in the excited states, were fit with functions of the form V=ax^{4}−bx^{2} or V=cx^{2}+d exp(−fx ^{2}). The furanone was found to have an inversion barrier in the S_{1}(n,π^{*}) state of 1152 cm^{−1} (13.8 kJ/mol) while the thiophenone has a barrier of 659 cm^{−1} (7.9 kJ/mol). The two molecules have their potential energy minima for the S_{1}(n,π^{*}) state at carbonyl wagging angles of 26° and 20°, respectively. The results here, together with previous data for several other cyclic ketones, demonstrate that the inversion barrier increases with the ring angle strain at the ketone carbon atom.

Photodissociation spectroscopy of
View Description Hide DescriptionWe report on studies of the structure and dissociation of CaCH_{4} ^{+} and its isotopomer CaCD_{4} ^{+}, using photodissociation spectroscopy. Molecular absorption bands are observed to the red of the Ca^{+} (4p ^{2} P←4s ^{2} S) resonance transition. The photodissociation action spectrum shows evidence for spin–orbit doubling and complex rovibrational structure. No reactive quenching product is observed. The transition is assigned as ^{2} E←^{2}A _{1} in C_{3v} geometry. The spin–orbit constant in the upper state is found to be A ^{so}=111±4 cm^{−1}. The action spectrum shows a strong progression in the Ca^{+}–CH_{4} (CD_{4}) intermolecular stretch in the ^{2} E state with a fundamental stretch frequency of ω _{s} ^{ ′ } =270±16(244±4) cm^{−1}. Weaker intermolecular bending vibration is also apparent, with a fundamental bending frequency of ω _{b} ^{ ′ } =112±16(92±14) cm^{−1} for Ca^{+}–CH_{4}(CD_{4}). The resonances show evidence for predissociation broadening. These results differ markedly from our previous results on the analogous MgCH_{4} ^{+} system.

The direction of electric dipole moment of ICl A ^{3}Π_{1} state through the analysis of the Stark modulation spectroscopy
View Description Hide DescriptionRecently, two works were reported that the permanent electric dipole moment of the ICl A state has the same direction as that of the X state, through the analysis of electric and magnetic pendular spectra and through the direct analysis of the hyperfine structures under the Stark effect, respectively. We determined clearly and sensitively the direction of the dipole moment in the A (v=27) state of I^{35}Cl, through the line shapeanalysis of the Stark modulation spectra (SMS). While the result was the same as those of previous two works, the analysis of the line shape of the SMS was so useful to determine the relative direction of the dipole moment of the upper electronic state to that in the lower state, whichever of the firstorder or the secondorder Stark effect the state may show.

Superradiance of polaritons: Crossover from twodimensional to threedimensional crystals
View Description Hide DescriptionIn spite of the relative simplicity of the structure of Frenkel excitons in molecular crystals some questions concerning the theory of polaritons in such crystals remain controversial—especially those concerning the crossover from the twodimensional to the threedimensional case. In the present work a detailed microscopic study of Frenkel excitonpolaritons in crystal slabs of arbitrary thickness is performed for the states with the tangential wave vector k _{∥}=0. Starting from the microscopic quantum theory we have obtained two basic equations. One of them relates the complex energy of a polaritonE to the quantity q, which in the limiting case of bulk crystal comes to the normal component of the wave vector. When the number N of the monolayers in the pile is large, N≫1, this equation is reduced to the dispersionequation of the macroscopic electrodynamics which uses the dielectric function ε(ω). The other equation of our microscopic theory has the meaning of Ewald’s extinction rule and for N≫1 is reduced to Maxwell’s boundary conditions. Using the equations obtained we found the complete set of polariton terms for the arbitrary N from N=1 to N→∞. We have traced the rise and evolution of two branches of polariton terms with increasing N. Special attention was paid to the study of polariton superradiance—enormous radiative damping or very short corresponding lifetimes for some states. At small N≪λ/a, with λ being the light wavelength and a the lattice constant, the superradiantlinewidth is proportional to N(λ/a)^{2}Γ^{(0)} , where Γ^{(0)} is the molecular radiative width. After further increasing the thickness this linewidth is monotonously decreased to zero. We also show that for the macroscopic slabs the radiative broadening may be obtained as a result of taking into account multiple reflections of the polariton from the surfaces of the crystal. Illustrative calculations were performed using parameters of the anthracene crystal.

Numerical analysis of Solomon echo amplitudes in static solids
View Description Hide DescriptionFor the first time a numerical procedure for computing the Solomon echo amplitudes of halfinteger quadrupole spins (I=3/2, 5/2, 7/2, and 9/2) has been derived from a detailed analysis of the evolution of the spin system using the density operator formalism. As the firstorder quadrupole interaction is taken into account throughout the experiment, consisting in exciting the spin system with two pulses either in phase or in quadrature phase and separated by a delay τ_{2}, the results are valid for any ratio of the quadrupole coupling, ω _{Q} , to the amplitude of the pulses, ω_{rf}. These results are applicable to light nuclei at high magnetic field, for which the secondorder quadrupole interaction and the chemical shiftanisotropy are negligible. We predict (4I^{2}−1)(2I−1)/16 echoes and their positions in the detection period τ_{4}, (I−1/2)^{2} of which are allowed echoes, the others being forbidden echoes. All of these echoes are satellitetransition signals, which are superimposed on the free induction decay (FID) of the central transition following the second pulse. This means that τ_{2} must be short when compared to the duration of the centraltransition FID. In other words, during τ_{2} the magnetic dipole interactions have no time to affect the evolution of the spin system. The behavior of the τ_{4}=τ_{2} echoes versus the secondpulse flip angle ω_{rf} t _{3} is analyzed: in the hardpulse excitation condition (ω _{Q} /ω_{rf}≪1), the (±1/2↔±3/2) echoes generated by two pulses in quadrature phase are twice as large as those generated by two inphase pulses; the echoes of the other transitions have comparable amplitudes. The echo amplitudes in the softpulse excitation condition (ω _{Q} /ω_{rf}=1) are also presented.

Spectroscopy of ionic alkali rare gas excimers in matrices
View Description Hide DescriptionUsing a clean preparation technique of doping alkali atoms in argon matrices, VUV emissions of the chargetransfer states of the ionic xenon–alkali excimers (XeA)^{+} have been measured. With synchrotron radiation as an excitation source, the ionic species were generated in the matrix and energy and timeresolved spectroscopy has been performed with synchrotron radiation as an excitation source. The emissions of the chargetransfer reaction: (Xe^{+}A)→(XeA^{+})+hν have been observed for all ionic (XeA)^{+} excimers with energies in the VUV range between 6.05 and 7.4 eV. The excitation spectra revealed a primary formation process through direct ionization of the xenon; however, neutral xenon resonance states are also contributing. As obtained from lifetime measurements, the bands are assigned to the 0 _{I} ^{−} →0^{+} transition of the finestructure components which account for the long decay time. An increase of the xenon concentration favors the formation of ionic trimers (Xe_{2}A)^{+} whose emissions have also been identified.

Ab initio direct dynamics study of OH+HCl→Cl+H_{2}O
View Description Hide DescriptionWe report the firstprinciples computation of rate constants for atmospheric reactions, by combining variational transition state theory (VTST) and highlevel electronic structuretheory. Extending the direct dynamics approach, the rate constants for OH+HCl were computed, directly, using ab initioelectronic structuretheory at the secondorder manybody perturbationtheory [MBPT(2)] and coupledcluster singlesanddoubles with a perturbative triples correction [CCSD(T)] levels and variational transition state theory including tunneling. The computed roomtemperature rate constant, 7.03×10^{−13} cm^{3} molecule^{−1} s^{−1}, is in good agreement with experiment (8.0×10^{−13}). The rate constant was computed over the temperature range 138–1055 K. The methods developed in this work are quite general, and can be applied to obtain rate constants for many reactions of interest in atmospheric and combustion chemistry, in the absence of experiment.

Fourier transform infrared emission study of the mechanism and dynamics of HOI formed in the reaction of alkyl iodides with O(^{3} P)
View Description Hide DescriptionVibrationally excited hypoiodous acid (HOI) is observed as a product in the reaction of alkyl iodides with O(^{3} P). Fourier transform infrared emission techniques are used to detect the excited ν_{1}, OH, stretch of the HOI product, to determine the mechanism of HOI production, and to measure the vibrational product state distributions. The HOI product is formed by O atom reaction with twocarbon and larger straight or branched chain alkyl iodides and cyclic alkyl iodides, e.g., C_{2}H_{5}I, nC_{3}H_{7}I, iC_{3}H_{7}I, (CH_{3})_{3}CI, nC_{6}H_{13}I, and cC_{6}H_{11}I, but not with CH_{3}I. Experiments with selectively deuterated ethyl iodides provide direct evidence that HOI is formed in a betaelimination mechanism involving a fivemembered ring transition state. The O atom attacks the iodine and then abstracts a hydrogen from the beta carbon during the lifetime of the complex. Timeresolved experiments allow the extraction of nascent vibrational state distributions for the ν_{1} stretch of HOI (v=1:v=2:v=3) using different alkyl iodides and assuming the radiative rates are given by A_{ν→ν−1}=vA_{1→0} : C_{2}H_{5}I, 0.53(4):0.39(3):0.08(3); nC_{3}H_{7}I, 0.61(6):0.34(5):0.05(2); and iC_{3}H_{7}I, 0.54(6):0.38(4):0.08(3). These distributions are nonstatistical with the v=2 states having only slightly less population than those with v=1. For product molecules with up to three quanta of ν_{1} excitation, more than 50% of the reaction exothermicity is deposited into the OH stretch.

Universal binary theory of photochemical charge separation and distribution
View Description Hide DescriptionUsing integral formalism we developed the encounter theory of reversible photoionization followed by charge recombination. This is a problem that can not be approached with conventional (differential) formalism, unless ionization is highly exothermic and thus irreversible. In this limit, the integral theory supplemented by the recipe for calculating the ion distribution may be successfully reduced to the differential theory used in our previous work. However, there is no alternative to integral theory when ionization is quasiresonant and the back electron transfer to the excited state should be accounted for. Using the contact approximation we calculated the freeenergy dependence of the SternVolmer constant of reversible photoionization accompanied by charge recombination.

A comparison of two methods for direct tunneling dynamics: Hydrogen exchange in the glycolate anion as a test case
View Description Hide DescriptionTwo methods for studying tunnelingdynamics are compared, namely the instanton model and the approach of Truhlar and coworkers, which are based on the direct output of electronic structure calculations and thus are parameter free. They are employed to evaluate the zerolevel tunneling splitting due to intramolecular hydrogen exchange in the glycolate anion. The first method was developed in a series of recent studies and presents a combination of the instanton theory with quantumchemically computed potentials and force fields. For the compound at hand, which has 21 internal degrees of freedom, a complete potentialenergysurface is generated in terms of the normal modes of the transitionstate configuration. It is made up of the potentialenergy curve along the tunneling coordinate and harmonic force fields at the stationary points. The level of theory used is HF/6–31++G^{*} ^{*}. All modes that are displaced between the equilibrium configuration and the transition state are linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings affect the instanton trajectory profoundly and, depending on the symmetry of the skeletal modes, can enhance or suppress the tunneling. In the glycolate anion all modes have such displacements and thus are included in the calculation. Based on the similarity with malonaldehyde, it is argued that tunneling prevails in the studied process, and the zerolevel tunneling splitting is predicted. The latter is found within the computational scheme developed earlier, which avoids explicit evaluation of the instanton path and thus greatly simplifies the tunnelingdynamics. These results are tested by the method of largecurvature tunneling of Truhlar and coworkers implemented in a duallevel scheme. The potential energy surface needed for the dynamics calculations is generated at the semiempirical PM3 level of theory and then corrected by interpolation with highlevel HF/6–31++G^{*} ^{*} results for the stationary points. The code corresponding to this approximation is in the package MORATE 6.5. The tunneling splittings found by the two approaches are in quantitative agreement. We have found that the computational scheme based on the instanton model is much less time consuming both in the static and dynamics part. This computational efficiency, also demonstrated in a number of earlier studies, merits future application of the method to fairly large systems of practical interest, such as clusters and organic compounds with excitedstate proton transfer.

Effect of chemical reaction on diffusion of diluted gas: Simulations by means of two Monte Carlo methods
View Description Hide DescriptionTwo Monte Carlo methods are used to simulate a dynamics of molecules of a foreign gas , highly diluted in a carrier gas . Diffusion in the presence of bimolecular reaction products is studied. Nonequilibrium corrections to the reaction rate constant and diffusion coefficient are calculated for a wide range of molecular mass ratio and activation energies of the reaction. Some differences between simulation results of the two methods are observed. The deviation of the velocity distribution from the Maxwellian form is quantified by means of the fourth order cumulants. The nonequilibrium effects are most significant in the Lorentz range, that is for The simulation results prove that the theoretical predictions based on a perturbative solution of the Boltzmann equation are valid for not too small values of but are not correct in the Lorentz range.

Dissociation dynamics of quasibound levels in the state of H Characterization of the continuum
View Description Hide DescriptionDecay pathways and photofragment anisotropy parameters have been determined for a series of rovibrational levels of the state in molecular hydrogen using fastbeam photofragment spectroscopy. The =4) levels are found to be weakly predissociated by homogeneous interaction with the lower lying =2 state and by rotational coupling with the state. The observed photofragment anisotropy reveals fine and hyperfine structure depolarization. The decay of =5) levels is dominated by barrier tunneling. The anisotropy parameters identify the symmetry of the continuum to be of mixed and character, which implies that hydrogen molecules can tunnel through two different barriers. The determination of the kinetic energy and the anisotropy parameter of the photofragments have resulted in a number of spectral reassignments.

Gas phase reactions of some positive ions with atomic and molecular hydrogen at 300 K
View Description Hide DescriptionThe reactions of CO^{+}, CO_{2} ^{+}, SO_{2} ^{+}, NO_{2} ^{+}, CS_{2} ^{+}, CN^{+}, C_{2}N_{2} ^{+}, and C_{2}H_{3} ^{+} with H atoms and H_{2} molecules have been studied in a selected ion flow tube operated at (300±5) K. The H atom reactions proceed variously by the processes of atom exchange and charge transfer (when allowed), none proceed at the Langevin rate, and the rates of several of them appear to be influenced by the spin states of the product species. Most of the H_{2}reactions proceed by H atom abstraction and at a large fraction of the Langevin rate.

Photoinduced chargetransfer dissociation in van der Waals complexes. V. Na⋯XCH_{3} (X=F, Cl, and Br)
View Description Hide Descriptionvan der Waals complexes Na⋯XCH_{3} (X=F, Cl, and Br) have been generated by crossing a beam of sodium with the expansion region of a supersonic jet of the appropriate halide, seeded with a rare gas. The identity of these complexes was determined by photoionizationtimeofflight mass spectrometry. The primary route for photodepletion of these complexes is thought to be the excitation of the Na chromophore followed by a chargetransfer dissociation: Na⋯XCH_{3}+hν→[Na^{*}⋯XCH_{3}]^{‡}→[Na^{+}⋯XCH_{3} ^{−}]^{‡}→NaX+CH_{3}. Measurement of the photodepletion cross section as a function of the excitation wavelength provided an approach to the study of these harpooning reactions starting in selected transition states. The action spectra for the three complexes consisted of up to four broad peaks. An assignment, made by ab initio calculations, was based on the electronically excited states of Na^{*} perturbed by the halide molecule in the complex. Peaks, ranging from the red (∼700 nm) to the blue (∼400 nm), were assigned to a superposition of Na^{*} states 3 ^{2} P_{x,y} , and to successively higher excited states 3 ^{2} P_{z} , 4 ^{2} S, and 3 ^{2} D. The transition probabilities computed for the various Na⋯XCH_{3}→[Na^{*}⋯XCH_{3}]^{‡} transitions were generally in qualitative accord with experiment. Vibrational progressions of the covalent excited states 3 ^{2} P_{x,y,z} were observed and analyzed.

Collisional reactions of Na with NO
View Description Hide DescriptionA collisional reaction of a sodium cluster ion, with a nitrous oxide molecule, O, was investigated by using a tandem massspectrometer equipped with four octopole ion guides. Two types of ions, and were produced by the reaction; and result from oxidation and direct collisional dissociation of the parent cluster ion, respectively. The absolute total cross section and partial cross sections for the (oxidation) and (direct dissociation) production were measured as a function of the collision energy of a given parent cluster ion, in the energy range up to 5 eV (centerofmass frame). The cross sections and their collisionenergy dependence show that the oxidation proceeds when electron harpooning from to NO occurs and otherwise the direct collisional dissociation proceeds.

Potential energy surfaces for the Ta^{+}+C_{2} reaction
View Description Hide DescriptionRelativistic completeactive space selfconsistent field and multireference configuration interaction computations including spin–orbit coupling are made on the TaC_{2} ^{+} cation, the most abundant of metalcarbides observed in direct laser vaporization and Knudsen effusion–mass spectrometric experiments. The suggested mechanism of TaC_{2} ^{+} formation via recombination reactions between Ta^{+} and C_{2} is consistent with the calculated potential energy curves for the lowlying electronic states. Two nearly degenerate unsymmetrical linear (Ta–C–C^{+}) and symmetrical C_{2v} (C–Ta–C^{+}) isomers suggest that the products can include a mixture of both isomers.