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Volume 104, Issue 6, 08 February 1996

Line shape analysis of Doppler broadened frequency‐modulated line spectra
View Description Hide DescriptionWe present a method for recovering Doppler broadened absorptionline shapes from frequency modulated (FM) line spectra. The method of analysis is calibrated and demonstrated with thermalized CN radicals produced by photodissociation of cyanogen (NCCN), probed on the A–X system near 800 nm with a frequency modulated Ti: sapphire ring laser. Nonthermal, Doppler broadened lines from translationally nascent photofragments can also be recovered by direct transformations of experimental FM line profiles acquired with a time resolution exceeding 100 ns. The superior signal‐to‐noise afforded by FMspectroscopy, relative to other direct absorption methods, should encourage the application of transient FMspectroscopy to problems in photoinitiated reaction dynamics.

Geometry changes in molecular photoionization: The NH^{+} _{3} (X̃ ^{2} A _{2} ^{″})←NH_{3} (X ^{1} A _{1}) transition
View Description Hide DescriptionSingle‐photon threshold photoionization has been used to explore the ionizationdynamics of the NH^{+} _{3} (X̃ ^{2} A _{2} ^{″})←NH_{3} (X ^{1} A _{1}) transition which involves a pyramidal‐to‐planar geometry change. Rotationally resolved threshold photoelectron spectra are presented for four vibrational levels of the X̃ ^{2} A _{2} ^{″} cation state of NH^{+} _{3} corresponding to excitation of even and odd quanta of the inversion mode, ν^{+} _{2}. The rotational state distributions exhibit strong symmetry effects imposed by the nuclear spin statistics and vibronic parity of the neutral and cation out‐of‐plane bend levels. The observed rotational structure is consistent with dominant ΔK=0 transitions and parity assignments for specific transitions show that both l=even and l=odd photoelectron final states are excited. These observations indicate that the photoelectron experiences a non‐planar (pyramidal) cation potential. These results are discussed in light of previous rotationally resolved measurements on NH_{3} using multiphoton ionization and other systems which undergo bend excitation following ionization.

Electronic transition moment and rotational transition probabilities in CH. I. A ^{2}Δ–X ^{2}Π system
View Description Hide DescriptionVibrational band transition probabilities of the A–X electronic system of CH, v′=0, 1, and 2, have been measured in a low pressure flame using laser‐induced fluorescence. These results improve earlier experiments that were complicated by energy transfer contributions, and expand measurements to very weak off‐diagonal bands such as 0,2 and 1,3. The electronic transition moment derived from the vibrational branching ratio measurements differs slightly from ab initio calculations. Hönl–London factors using a mixed coupling scheme have been tested by experiment. Finally, a combination of these results with previously measured radiative lifetimes yields absolute absorption and emission coefficients for this system. A comparison between computed radiative lifetimes and collision‐free experimental lifetimes suggests a predissociation rate in v′=0, N′≳17 of ∼1.5×10^{5} s^{−1}.

An evaluation of existing potential energy surfaces for CO_{2}–Ar: Pressure broadening and high‐resolution spectroscopy of van der Waals complexes
View Description Hide DescriptionNine different potential energy surfaces for CO_{2}–Ar taken from the literature are tested for their ability to reproduce the spectra of the Ar–CO_{2} van der Waals complex and the pressure broadening of CO_{2} infrared lines by Ar. None of the potentials give a satisfactory account of all the experimental results. All the potentials are found to give significant discrepancies with at least some of the spectroscopicproperties of the van der Waals complex. Coupled‐states (CS) and infinite‐order sudden (IOS) calculations of the pressure broadening cross sections are compared for a few of the potential energy surfaces. The IOS approximation is found to be seriously inaccurate for some potential surfaces, especially for high‐j lines, so that CS calculations are essential when comparing with experimental line‐shape data. CS calculations of line‐broadening cross sections are therefore carried out on all nine different potential energy surfaces. For the pressure broadening coefficients, there are substantial uncertainties in the experimental results. Nevertheless, the only potential to give a satisfactory account of the pressure broadening is the electron gas potential of Preston and Pack, which is the least satisfactory of all for the spectra of the complex. It is concluded that a new potential that reconciles the different data sets is needed.

The microwave spectrum of the CD_{2} radical
View Description Hide DescriptionThe pure rotational spectrum of the CD_{2} radical in the X̃ ^{3} B _{1} ground state was observed in the frequency region of 257 GHz–526 GHz by using a frequency modulated submillimeter‐wave spectrometer. The CD_{2} radical was generated by the dc glow discharge of deuterated ketene, CD_{2}CO. Twenty one fine and hyperfine component lines of four rotational transitions were measured and were analyzed by a least‐square method. Rotational and fine‐structure constants were revised in higher accuracy than those of the previous laser magnetic resonance (LMR) study. The hyperfine coupling constants for the deuterium nuclei have been determined for the first time.

The generalized hyperfine sublevel coherence transfer experiment in one and two dimensions
View Description Hide DescriptionThe generalized hyperfine sublevel coherence transfer pulsed ESR experiment is described that consists of a nuclear coherencegenerator, a first evolution period, a nonselective microwave π pulse, a second evolution period, and a nuclear coherencedetector. Several incrementation schemes to perform one‐dimensional experiments are discussed, namely, a four‐pulse electron spin echo envelope modulation scheme for measuring combination frequencies, two types of nuclear coherence transfer echo experiments (DEFENCE) to record dead time free electron spin echo envelope modulation spectra of disordered systems, and a new hyperfine spectroscopy experiment for the direct measurement of hyperfine frequencies. The one‐dimensional experiments can be combined to four two‐dimensional schemes. In addition to hyperfine sublevel correlation spectroscopy (HYSCORE) where two nuclear frequency dimensions are correlated, three new two‐dimensional experiments are introduced that correlate the hyperfine with the nuclear frequency, the combination frequency with the nuclear frequency, and the combination frequency with the hyperfine frequency. With a properly selected two‐dimensional incrementation scheme the digital resolution and signal‐to‐noise ratio of the spectra can be improved and artifacts can be suppressed. The predicted features of the one‐ and two‐dimensional experiments are verified experimentally for both ordered and disordered systems using echo and coherent Raman beat detection.

Simple modeling of line‐mixing effects in IR bands. II. Nonlinear molecules applications to O_{3} and CHClF_{2}
View Description Hide DescriptionA simple semiempirical approach is developed in order to model the shape of infrared absorption bands. It is based on use of the strong collision model and of a classical representation of rotational levels. The absorption coefficient then has a simple analytical expression whose wavenumber and pressure dependencies are computed by using eleven parameters which depend on the considered vibrational transition, the temperature, and the nature of the perturber only. These quantities, which are band‐averaged values of the detailed spectroscopic and collisional parameters of the molecular system, can be deduced from direct fits of measured spectra. The model thus requires no previous knowledge of the characteristics of the molecules and is thus applicable to complex systems; in particular it seems a promising approach for very dense molecular spectra for which only absorption cross sections are now available. Tests are presented in the case of O_{3} and CHClF_{2} bands perturbed by N_{2} at room temperature for which new measurements have been made. They demonstrate the accuracy of our semiempirical approach in predicting the spectral shape in a wide range of density provided that effective parameters are used.

Molecular structure of the linear C_{3}H radical: Microwave spectrum of the ^{13}C substituted species
View Description Hide DescriptionThe rotational spectra of three ^{13}C isotopic species of the linear C_{3}H radical in the ^{2}Π_{ r } ground vibronic state and the ^{2}Σ^{μ} vibronic state of the ν_{4} (HCC bending) vibrational mode were observed by using a source‐modulated spectrometer. The radical was produced in a free‐space cell by a glow discharge in a mixture of C_{2}H_{2}, He, and ^{13}CO. The rotational, spin‐rotation interaction, Λ‐type doubling, and hyperfineinteraction constants were determined from the analysis of the observed spectra, where vibronic interaction between the ^{2}Π_{ r } and ^{2}Σ^{μ} states was taken into account. The r _{ s } structure of C_{3}H, denoted by C_{α}C_{β}C_{γ}H, was derived from the rotational constants for the normal, deuterated, and three ^{13}C species: r _{ s }(C_{α}–C_{β})=1.3263(1) Å, r _{ s }(C_{β}–C_{γ})=1.2539(2) Å, and r _{ s }(C_{γ}–H)=1.0171(1) Å. The short C–H distance is interpreted in terms of a large amplitude motion of the ν_{4} mode, whose vibrational energy is very low due to the Renner–Teller effect. An ab initio molecular orbital calculation was carried out, and the structure in which the HCC angle is bent was found to be slightly more stable than the linear structure. The spin densities of three carbon atoms are derived from the hyperfineinteraction constants, and they are discussed in connection to the quasilinear nature of the molecule.

Infrared spectroscopy of Ar_{2}CO_{2} trimer: Vibrationally averaged structures, solvent shifts, and three‐body effects
View Description Hide DescriptionAr_{2}CO_{2} is studied using direct absorptioninfrared spectroscopy. The van der Waals molecules are formed when a mixture of CO_{2} and Ar gases is expanded in a supersonic slit jet. To probe the clusters, the ν_{3} asymmetric stretch of the CO_{2}monomer is then monitored in absorption. Sixty‐one trimer transitions are assigned and fit to a Watson asymmetric top Hamiltonian. Rotational constants for the upper and lower vibrational states permit determination of vibrationally averaged molecular structures, which indicate that the Ar atoms lie in the plane that bisects CO_{2} and is perpendicular to the CO_{2} intramolecular axis. These geometries are consistent with an equivalent ‘‘T‐shaped’’ ArCO_{2} geometry for each Ar atom. Vibrational origins for the ν_{3} CO_{2} asymmetric stretch frequency in Ar_{ n }CO_{2} are found to shift approximately linearly for zero, one, and two Ar atoms. Calculations using pair potentials are used to extrapolate these red shifts out to the bulk phase and to compare the results to experimental matrix data. Finally, the slight nonlinearity in the red shift between ArCO_{2} dimer and Ar_{2}CO_{2} trimers is interpreted in the context of three‐body forces.

Evolution of ion internal energy during collisional excitation in the Paul ion trap: A stochastic approach
View Description Hide DescriptionA first‐order model is developed for collisional activation as effected via resonance excitation and helium buffer gas in the Paul ion trap. For an ion population at steady‐state under specified experimental conditions, the kinetic theory of ion transport in gases is first used to calculate an effective temperature shown to be identical to the internal temperature for molecular ions in an atomic gas. The evolution of the ion internal energy is then followed by a random walk simulation designed to be representative of the actual collisional energy transfer process, except ion losses due to dissociation and reactive processes during collisional activation are excluded. During the simulation, inelastic ion‐neutral collisions increase the average ion internal energy via small energy changes (both positive and negative) until a steady‐state condition is reached in which excitation and deexcitation processes are balanced. Histogramming the simulated data reveals a Boltzmann‐type internal energy distribution whose average internal energy is the same as that calculated for a true Boltzmann distribution at the same internal temperature.

Avoided resonance overlapping beyond the energy independent formalism. II. Electronic predissociation
View Description Hide DescriptionThe transition between the diabatic and the adiabatic zero order representation when the electronic potential coupling increases, is studied in the partitioning method (PM) and in the complex coordinate method (CCM) implemented in a discrete variable representation (DVR). The model is a C^{+} type predissociation in a diatomic system with a crossing between a Morse potential energy curve and an exponentially repulsive curve. In the weak coupling regime (isolated diabatic metastable states), both methods confirm the linear variation of the resonance widths with the strength of the electronic interaction, as expected in a perturbative treatment. When the coupling is large in the diabatic representation (strong overlap regime), the formation of narrow resonances supported by the upper adiabatic potential can be related, in PM, to the process of avoided resonance overlapping among interfering states. The complete change of representation can be described in the initial diabatic basis set in PM. However, the full energy dependence of the discrete‐continuous matrix elements must then be taken into account. The deformation and the final splitting of a diffuse spectral line with increasing coupling is re‐examined in terms of these energy dependent eigenvalues of the effective Hamiltonian. The use of the appropriate representation, either diabatic or adiabatic, according to the strength of the electronic coupling, has been found decisive in CCM so as to observe the correct migration of the resonance positions towards the zero order adiabatic states, and the decrease of their widths. No relevant results have been obtained for the intermediate strength of the coupling in CCM. Analytical expressions for the derivative coupling matrix elements (∂/∂R) in the fixed node DVR (corresponding to the particle‐in‐a‐box wave functions) have been established.

Reduced dimensionality calculations of quantum reactive scattering for the H+CH_{4}→H_{2}+CH_{3} reaction
View Description Hide DescriptionThe dynamics for the H+CH_{4}→H_{2}+CH_{3}reaction has been studied using reduced dimensionality quantum‐mechanical theory. The system is treated as a linear four‐atom chemical reaction, reducing the system to a three‐dimensional scattering problem. The vibrational modes of ν_{1} and ν_{4} of CH_{4}, the stretching vibration of H_{2}, and the umbrella ν_{2} mode of CH_{3} are taken into consideration in the reaction dynamics based on the vibrational analysis along the reaction path. The semiempiricalpotential energy surface which has recently been developed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)] is employed. Rotationally averaged cross sections and thermal rate constants are calculated using an energy‐shifting approximation in order to take into account the effect of all the degrees of freedom. It is shown that excitation of the ν_{1} mode of CH_{4} significantly enhances the reactivity, indicating that there is a strong coupling between the ν_{1} mode of CH_{4} and the reaction coordinate. The vibrational state distributions for the products H_{2} and CH_{3} have also been studied. In the energy range considered here, the population of vibrationally excited H_{2} is found to be very small, while the umbrella ν_{2} mode of CH_{3} is found to be excited.

State‐to‐state rate constants for the collisional interaction of Xe(7p), Xe(6p′), and Kr(5p′) atoms with He and Ar
View Description Hide DescriptionOne‐photon laser excitation of Xe(6s[3/2]_{2}) and Kr(5s[3/2]_{2}) atoms that were generated in a discharge‐flow reactor was used to study the collisional relaxation of the Kr(5p′[3/2]_{1}, [3/2]_{2}, and [1/2]_{1}), the Xe(7p[3/2]_{2}, [3/2]_{1}, [5/2]_{2}, and [5/2]_{3}), and the Xe(6p′[3/2]_{1}, [3/2]_{2}, and [1/2]_{1}) states in He and Ar. Both cw and pulsed laser excitation techniques were utilized to obtain the total deactivation rate constants and product formationrate constants at 300 K. Collisions with He mainly produce Xe* and Kr* product states with small energy defects, but the rate constants can be as large as 20×10^{−10} cm^{3} atom^{−1} s^{−1}, which correspond to thermally averaged cross sections of 150 Å^{2}. Because of the rapid collisional coupling of populations in nearly isoenergetic levels, multicomponent exponential decay of the initially produced state is frequently observed. The deactivation rate constants for Ar are smaller than for He, but the product distributions tend to be more diverse than for He, and arguments based only on energy defects are not necessarily a good guide to the favored product state(s) from Ar collisions. The magnitude of the quenching cross sections for Ar is consistent with the crossing of an entrance channel with several diabatic exit channel potentials. However, the superlarge quenching cross sections for Xe*–He to just one or two product levels require special considerations. The Kr(5p′) and Xe(6p′ and 7p) rate constants with He are discussed with respect to collisional effects upon the use of cw optical pumping to convert populations in the metastable Xe(6s[3/2]_{2}) and Kr(5s[3/2]_{2}) levels to the Xe(6s′[1/2]_{0}) and Kr([5s′[1/2]_{0}) levels.

State‐resolved, three‐dimensional product recoil velocity spectroscopy
View Description Hide DescriptionWe describe a conceptually and experimentally simple approach for quantum‐state‐resolved measurement of the full three‐dimensional recoil velocity distribution of the products from photodissociation or photoinitiated chemical reaction. The method uses pulsed lasers to determine two components of the recoil velocity vector, by spatial displacement of a probe laser beam relative to a photolysislaser beam, so we call this method POSTS, for position sensitive translational spectroscopy. The third component of the velocity vector is obtained from Doppler selection, ion time‐of‐flight mass spectrometry, spatial masking of a detector, or use of a one‐dimensional array detector. POSTS requires only a single probe laser, and it is not essential that this laser have a narrow frequency bandwidth. Its TOFmeasurements can be made with very high resolution on a spatial scale as small as 0.1 cm. POSTS will work with all atomic and molecular species having any magnitude of recoil velocity, and with most pulsed‐laser detection techniques. We demonstrate the capabilities of the POSTS method by velocity measurements on the H atoms from photodissociation of HI, and HCl molecules from the vibrational predissociation of (HCl)_{2}. In the latter case the high resolution capabilities of POSTS allow a determination of the bond dissociation energy of the HCl dimer to an accuracy of ±1 cm^{−1} from TOFmeasurements on a spatial scale of only 0.1 cm.

New time‐dependent methods in quantum scattering
View Description Hide DescriptionThe present paper developed two kinds of new time‐dependent methods in quantum scattering calculation. One method is to combine a split‐operator method with a differential method to achieve better convergent property than a pure differential method and better adaptive property in a multidimensional case than the pure split‐operator method. Another method is to adopt a desired time‐dependent variational principle to achieve variational correction in numerical calculations, which can improve the result from direct numerical evaluation with little additional consumed time.

Numerical methods with a high order of accuracy applied in the quantum system
View Description Hide DescriptionTwo kinds of numerical methods with a high order of accuracy are developed in this paper. In the general classical Hamiltonian system, it was claimed that no explicit n‐step symplectic difference method with the nth order of accuracy can be achieved if n is larger than 4. We show that there is no such constraint in the quantum system. We also exploit to investigate the high order Newton–Cotes differential methods in the quantum system. For the first time, we work out the generalized derivation of explicit symplectic difference methods with any finite order of accuracy in the quantum system. We point out that different coefficients in the same multistep symplectic method will lead to quite different results. The choices of coefficients and order of accuracy for the best efficiency in multistep symplectic methods and Newton–Cotes differential methods are studied. The connections between explicit symplectic difference structure, Newton–Cotes differential schemes, and other methods are presented. Numerical tests on the model system have also been carried out. The comparison shows that the explicit symplectic difference methods and the Newton–Cotes differential methods are both accurate and efficient.

Induced oscillations in an electron transfer reaction in the presence of a bichromatic electromagnetic field
View Description Hide DescriptionThe effect of a bi‐(multi‐)chromatic electromagnetic field on electron transfer dynamics in a polar solvent is examined. Whereas the electron population dynamics is characterized by simple exponential decay in the presence of a monochromatic field, a bichromatic field gives rise to large induced coherent oscillations in electronic density between the reactant and product states. This oscillation is driven indefinitely by the applied field despite the strongly dissipative environment. The dependence of the dynamics on the reaction heat and the laser field properties is explored using an analytical expression derived within the noninteracting blip approximation. The oscillations depend on the field properties: both cosinelike and more complicated behavior can be obtained. For a trichromatic driving force, aperiodic (chaotic) oscillations are found. Ideal conditions and possibly appropriate chemical systems for the experimental verification of this phenomenon are discussed.

Nearside–farside analysis of differential cross sections: Diffraction and rainbow scattering in atom–atom and atom–molecule rotationally inelastic sudden collisions
View Description Hide DescriptionNearside–farside (NF) theory, as used to understand nuclear heavy‐ion differential cross sections, is applied for the first time to the angular scattering of atom–atom and atom–diatom collisions. A NF decomposition of the partial wave series (PWS) for the scattering amplitude has the following advantages: (a) it is exact, (b) it uses PW scattering matrix elements (quantum or semiclassical) as calculated by standard computer programs, (c) it is easily incorporated into existing computer programs which calculate angular distributions, (d) semiclassical techniques, such as stationary phase or saddle point integration, are not invoked for the PWS, although the semiclassical picture is still evident. A disadvantage of a NF decomposition is that it is not unique. The Fuller and Hatchell NF decompositions are used to analyze the angular scattering of four collision systems whose PWS involve Legendre polynomials: (a) atom–atom He+Ne elastic diffraction scattering, (b) atom–atom H^{+}+Ar elastic rainbow scattering, (c) atom rigid‐rotator Ne+D_{2}(j=0) →Ne+D_{2}(j) diffraction scattering under sudden conditions so that the infinite‐order‐sudden (IOS) approximation is valid, (d) atom rigid‐rotator He+N_{2}(j=0)→He+N_{2}(j) rotational rainbow IOS scattering. The utility of these two NF decompositions is assessed by comparison with results from the semiclassical complex angular momentum (CAM) representation of the scattering amplitude. This is chosen because it allows an unambiguous separation of the scattering amplitude into nearside and farside subamplitudes under semiclassical conditions. The Fuller NF decomposition, unlike the Hatchell NF decomposition, provides a physically clear explanation of the angular scattering, which always agrees with the semiclassical CAM interpretation (except for scattering angles ≊180°). The Fuller NF decomposition is therefore recommended for applications to atomic and molecular collisions. The NF theory for the decomposition of Legendre polynomials is generalized to scattering amplitudes whose PWS involve associated Legendre functions or reduced rotation matrix elements.

Theoretical study of the excitation spectra of five‐membered ring compounds: Cyclopentadiene, furan, and pyrrole
View Description Hide DescriptionMultireference perturbation theory with complete active space self‐consistent field (CASSCF) reference functions was applied to the study of the valence and Rydbergexcited states in the range of 5–8 eV of five‐membered ring compounds, cyclopentadiene, furan, and pyrrole. The spectra of these molecules have been studied extensively for many years but characterization is far from complete. The present approach can describe all kinds of excited states with the same accuracy. The calculated transition energies are in good agreement with corresponding experimental data. We were able to predict the valence and Rydbergexcited states with an accuracy of 0.27 eV or better except for the B^{+} _{2} of pyrrole. The valence excited states of five‐membered ring compounds were interpreted in terms of the covalent minus states and ionic plus states of the alternate symmetry. The unobserved 1A _{1}→A ^{−} _{1} transition with very weak intensity, which is hidden under the strong 1A _{1}→B ^{+} _{2} transition, is also discussed. Overall, the present theory supports the assignments recently made by Serrano‐Andres et al. based on the CASSCF plus second‐order perturbation results. However, there remain some discrepancies in the assignment of the spectrum of pyrrole.

Excited and ionized states of free base porphin studied by the symmetry adapted cluster‐configuration interaction (SAC‐CI) method
View Description Hide DescriptionThe SAC(symmetry adapted cluster)/SAC‐CI method is applied to the calculations of the ground, excited, and ionized states of the free base porphin. The electronic spectrum of porphin is well reproduced and new assignments for the B (Soret), N, L, and M bands are proposed. The present result shows that the four‐orbital model is strongly perturbed for the B and N bands by the excitations from the lower 4b _{1u } MO and that the σ electron correlations are important for the description of the excited states. The absorption peaks in the ionizationspectrum are assigned and the reorganization effect is found to be large especially for the n and σ electron ionizations.