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Volume 86, Issue 6, 15 March 1987

Accurate localized and delocalized vibrational states of HCN/HNC
View Description Hide DescriptionResults of the first accurate quantum calculation of the delocalized, large amplitude motion vibrational (J=0) levels of HCN/HNC, lying above the isomerization barrier, are presented. The recently developed DVR‐DGB quantum method [Z. Bačić and J. C. Light, J. Chem. Phys. 8 5, 4594 (1986)] is employed in this work. A model, empirical surface by Murrell e t a l. is used. All modes are included; the energy level calculation does not involve any approximations. Over a hundred vibrational levels are calculated accurately for this model surface. A number of them lie above the isomerization barrier; some are extensively delocalized over both HCN and HNC minima. Analysis shows that for HCN/HNC the threshold for significant delocalization is determined by the height of the vibrationally adiabatic bending barrier. In addition, the nearest neighbor level spacing distribution is obtained and compared to that of LiCN/LiNC. Various computational aspects of the DVR‐DGB approach, which is applicable to any triatomic molecule, are also discussed. The method is very suitable for efficient, accurate treatment of floppy molecules and molecules which can isomerize. The DVR‐DGB (i.e., ray eigenvector) basis provides a rapidly convergent expansion for the delocalized (and localized) states. Consequently, a single diagonalization of the DVR‐ray eigenvector Hamiltonian matrix, whose size is modest relative to the number of accurately determined energy levels, yields the energies of both localized and delocalized states. Accurate evaluation of the two‐dimensional integrals in the potential matrix elements requires only 3–4 Gauss–Hermite quadrature points per dimension.

Fourier transform detection of laser‐induced fluorescence from the CCN free radical
View Description Hide DescriptionThe technique of high‐resolution Fourier transform spectroscopy has been used to detect the laser‐induced fluorescencespectrum of the CCN free radical. Emission from a single vibronic level in the Ã ^{2}Δ state to the X̃ ^{2}Π state yielded rotational constants for several vibronic levels of the ground state. From the analysis of the 0v _{2}1 levels the size of the Renner–Teller interaction was determined, yielding ε=0.410.

The potential energy barrier of the Na_{2} B ^{1}Π_{ u } state
View Description Hide DescriptionThe technique of modulated gain spectroscopy has provided detailed information about the shape of the Na_{2} B ^{1}Π_{ u } state potential barrier to dissociation. By measuring the rotation–vibration energies (to ±0.006 cm^{−} ^{1}) of all (v’=27–33) quasibound vibrational levels and the rotation‐dependent tunneling rates (as obtained from linewidthmeasurements) of the highest quasibound vibrational level, v’=33, we have been able to characterize this barrier. Our studies show that the barrier height is U(r _{max},J=0)=375.2±3.9 cm^{−} ^{1}, relative to the center of gravity of the Na(3s)+Na(3p) atomic limit, and the barrier maximum is located at r _{max}=6.85±0.02 Å.

Iterative maps with multiple fixed points for excitation of two level systems
View Description Hide DescriptionIterative schemes have been used in NMR to generate pulse sequences which excite spin systems over narrow or broad ranges of transition frequencies and radio frequency amplitudes. Mathematical methods employing iterative maps and related concepts from nonlinear dynamics have been applied in the analysis of these schemes. The effect of transforming a pulse sequence by an iterative procedure can be represented as an iterative map on a quantum statistical propagator space, with fixed points in this space corresponding to certain desired responses of the spin system. The stability of these points with respect to variations of parameters, such as amplitudes or energies, determines the bandwidth characteristics of the corresponding sequence; broadband behavior results from stable fixed points, and narrowband behavior from unstable fixed points. This paper examines schemes which produce maps with more than one stable fixed point. Such schemes are shown to generate sequences which exhibit bistable or selective, bandpass behavior. Spatially selective NMR, spin decoupling, n k‐quantum selective multiple‐quantum NMR,isotope selective zero‐field NMR, and optical information storage are some of the applications which can benefit from bandpass selective excitation sequences.

Nearly free internal rotation in Ar–CH_{3}Cl
View Description Hide DescriptionRotational spectra of Ar–CH_{3}Cl, for both Cl isotopes, have been observed, at 4 kHz resolution, using a pulsed nozzle Fourier transformmicrowave spectrometer. The observed spectra are consistent with a T‐shaped complex in which the methyl group is undergoing nearly free internal rotation. Analysis of the ground (A) internal rotor state spectrum for Ar–CH_{3} ^{3} ^{5}Cl using an asymmetrical top Hamiltonian produces the following spectroscopic constants (in MHz); A=13 633.020(14), B=1593.5683(79), C=1420.4572(52), Δ_{ J }=0.012 16(14), Δ_{ J K } =0.1381(48), δ_{ J } =0.000 96(17), H _{ J J K }=−0.000 58(25), e Q q _{ a a } =34.895(30), e Q q _{ b b } =−72.185(25), and e Q q _{ c c } =37.290(35). A combined analysis of the ground and excited (E) internal rotor states places an upper bound of 20 cm^{−} ^{1} on the threefold barrier to internal rotation. The Coriolis interactions in the E state also allow the determination of ‖e Q q _{ a b }‖ for Ar–CH_{3} ^{3} ^{5}Cl as 13.0(3) MHz. The symmetry axis of the CH_{3}Cl subunit is nearly perpendicular (∼82°) to the line joining the centers of mass of the two binding partners. The isotopic data indicate that the Cl end of the methyl chloride is tilted toward the argon. The distance between the centers of mass of the two subunits is 3.7826 Å for Ar–CH_{3} ^{3} ^{5}Cl and 3.7839 Å for Ar–CH_{3} ^{3} ^{7}Cl implying an Ar–Cl distance of 3.750 Å. Centrifugal distortion analysis yields a weak bond stretching force constant of 0.0157 mdyn/Å and stretching frequency of 34.6 cm^{−} ^{1} for Ar–CH_{3} ^{3} ^{5}Cl. The results from this investigation are related to previous lower resolution microwave studies on Ar–CH_{3}Cl.

Overtone and combination stretching vibrational bands of hydrogen peroxide, ethene, and propadiene
View Description Hide DescriptionSymmetry allowed Coriolis and H _{2} _{2} operators have been constructed for the OH stretching vibrational states of hydrogen peroxide and for the CH (CD) stretching vibrational states of ethene and propadiene. The behavior of the coefficients of these terms has been investigated at a special local mode limit with no kinetic or potential energy coupling between the bondoscillators and with special constraints on the molecular geometry and the atomic masses. It is found that the Coriolis coefficients disappear but that the H _{2} _{2} coefficients remain important at this limit. For the stretching vibrational overtones and combinations the effects of quartic anharmonic resonance terms, Darling–Dennison resonance terms, on effective Coriolis and H _{2} _{2} constants are investigated. Finally the effects of the tunneling motion of H_{2}O_{2} on the rotational energy level structure are discussed.

Manifestations of latent space group symmetry in the vibrational spectra of three alkali metal perchlorates
View Description Hide DescriptionThe vibrational spectra of crystalline MClO_{4} where M=K, Rb, and Cs are reinterpreted in terms of a vibrational unit cell (I m m a) which is one‐half the size of the crystallographic (P n m a). Single crystal Raman data on these species are reported.

The Ã ^{2}Π–X̃ ^{2}Σ^{+} transition of HC_{2} isolated in solid argon
View Description Hide DescriptionFourier transformabsorption spectra have been obtained between 700 and 7900 cm^{−} ^{1} at a resolution of 0.2 cm^{−} ^{1} for Ar:C_{2}H_{2} samples codeposited at 12 K with a beam of argon atoms that had been excited in a microwavedischarge. Detailed isotopic substitution studies have confirmed that the predominant product species is HC_{2}, which contributes not only the absorptions previously assigned to its two stretching fundamentals but also several weaker absorptions in the 2000–3600 cm^{−} ^{1}spectral region and a prominent, complicated pattern of absorptions between 3600 and 7800 cm^{−} ^{1}. The previous assignment of the 3611 cm^{−} ^{1} HC_{2} absorption as the CH‐stretching fundamental is reviewed, and the assignment of an absorption at 2104 cm^{−} ^{1} as ν_{2}+ν_{3} of ground‐state HC_{2} is discussed. The near infrared absorption band system has been assigned to the Ã ^{2}Π–X̃ ^{2}Σ^{+} transition of HC_{2}, extensively perturbed by interaction with high vibrational levels of the ground state. The position of the transition origin could not be definitively established. The previous assignment of gas‐phase absorptions of HC_{2} at 3786, 4012, and 4108 cm^{−} ^{1} to ground‐state combination bands has been confirmed, and carbon‐isotopic data have been obtained for these bands. Because all of the HC_{2} absorptions observed in an argon matrix must originate in the X̃(000) state and because the observed matrix shifts are relatively small, these studies may provide a map to facilitate more detailed gas‐phase studies.

Reinvestigation of the aluminum hydride (AlH^{+} and AlD^{+}) cation radicals by ESR in argon matrices at 4 K: Generation by reactive laser sputtering
View Description Hide DescriptionThe ESR spectra previously assigned to the AlH^{+} radical ion (X ^{2}Σ) [J. Chem. Phys. 7 1, 3991 (1979)] actually belong to the divalent neutral aluminum radical AlHOH whose charge distribution and electronic structure can be described as AlH^{+}OH^{−} with 90% of the unpaired electron on the AlH^{+} part of the molecule. Reactive laser sputtering and photoionization of AlH(g) were used to generate the AlH^{+} and AlD^{+} cation radicals, whose ESR spectra have been observed for the first time. A detailed analysis of the ESR results for argon matrices at 4 K reveal unusually large Alhyperfine interaction (hfi) with A _{iso} and A _{dip} values of 1586(2) and 49(1) MHz, respectively. The H hfi is essentially isotropic with A _{iso}=442(2) MHz. The observed nuclear hyperfineAtensors for Al and H show excellent agreement with a b i n i t i o CI theoretical calculations. The results for AlH^{+} are compared with the isoelectronic neutral radical MgH, and the similar AlF^{+} cation radical. The Al hfi is slightly larger in AlD^{+} relative to AlH^{+}. This interesting isotopic effect is qualitatively explained on the basis of electronic structure dependence on small changes in the bond distance for the two isotopic radicals.

High sensitivity, high‐resolution IR laser spectroscopy in slit supersonic jets: Application to N_{2}HF ν_{1} and ν_{5}+ν_{1}−ν_{5}
View Description Hide DescriptionA difference frequency IR spectrometer is combined with a slit supersonic expansion for high‐resolution (≤50 MHz FWHM) direct absorption investigations of jet‐cooled species. The 1.25 cm long nozzle provides a long path length and high densities suitable for synthesis and observation of van der Waals clusters, with a gradual spatial temperature gradient that permits experimental control of low frequency vibrational populations. Due to collisional quenching of velocity distributions, absorptionlinewidths are reduced and peak absorbance increased five‐ to sevenfold compared to pinhole expansions. Minimum detectable concentrations of HF containing complexes are 2×10^{9} molecules/cm^{3}/quantum state in a 2.5 cm path length. The combination of high sensitivity, sub‐Doppler resolution, long path lengths, and temperature control make direct absorption in slit nozzle expansions a powerful and general technique for high‐resolution study of jet‐cooled species. The spectometer is used to obtain the near‐infrared spectrum of N_{2}HF. The ν_{1} (HF stretch) fundamental is observed at 3918.2434(2) cm^{−} ^{1}, red shifted by 43.1795(2) cm^{−} ^{1} from the HF origin. In the warmer regions of the expansion close to the nozzle the ν_{5}+ν_{1}−ν_{5} Π←Π hot band is also observed, blue shifted by 2.7160(4) from the ν_{1} fundamental. Rotational analysis of these spectra reveals changes in vibrationally averaged molecular geometries upon excitation that are consistent with a near linear equilibrium geometry. The ν_{5} (N_{2} bend) frequency is estimated at 85±20 cm^{−} ^{1}, based on the relative intensities of the two bands and on an analysis of the l doubling. The linewidths of the N_{2}HF transitions show no increase over the HF monomer and are limited by instrumental resolution to 50 MHz FWHM; the lifetime of the upper level is therefore at least ≥3 ns.

Multiphoton spectroscopy of X–NO (X=Kr, Xe, CH_{4}) van der Waals molecules
View Description Hide DescriptionThe vibronic spectroscopy of the van der Waals species KrNO, XeNO, and CH_{4}NO has been investigated via mass‐resolved multiphoton ionization (MPI) spectroscopy. Spectra are presented for the two‐photon excited electronic transition of the various complexes associated with the C ^{2}Π (v=0) state of nitric oxide. Dissociation pathways are analyzed for XeNO, which appears at the Xe^{+} mass following MPI. Trends in bonding and spectroscopic constants are discussed.

Multiple‐quantum dynamics in NMR: A directed walk through Liouville space
View Description Hide DescriptionAn approach to spin dynamics in systems with many degrees of freedom, based on a recognition of the constraints common to all large systems, is developed and used to study the excitation of multiple‐quantum coherence under a nonsecular dipolar Hamiltonian. The exact equation of motion is replaced by a set of coupled rate equations whose exponential solutions reflect the severe damping expected when many closely spaced frequency components are superposed. In this model the evolution of multiple‐quantum coherence under any bilinear Hamiltonian is treated as a succession of discrete hops in Liouville space, with each hop taking the system from a K‐spin/n‐quantum mode to a K’‐spin/n’‐quantum mode. In particular, for a pure double‐quantum Hamiltonian the selection rules are ΔK=±1 and Δn=±2. The rate for each move depends on the number of Liouville states at the origin and destination, and on the total number of spins present. All rates are scaled uniformly by a factor dependent on the properties of the material, such as the dipolar linewidth, but otherwise the behavior predicted is universal for all sufficiently complicated systems. Results derived by this generic approach are compared to existing multiple‐quantum data obtained from solids and liquid crystals.

Time‐resolved spectroscopic measurements on microscopic solvation dynamics
View Description Hide DescriptionThis paper reinvestigates the use of transient fluorescence spectroscopy of polar aromatics in solution as a method to determine microscopic solvation dynamics. It is shown that the compounds previously employed as polar fluorescent probes tend to fall into three photophysical classes depending upon: (i) whether the photon induced change in μ occurs simultaneously with photon absorption (ii) whether solvent motion subsequent to photon absorption is required to induce the change in μ; or (iii) whether two excited‐state isomers with different μ’s are present simultaneously. The consequence of the different classes on microscopic solvation dynamicmeasurements is discussed with a molecular example for each class: (i) 4‐aminophthalimide, (ii) 4‐(9‐anthryl)‐N, N‐dimethylaniline, and (iii) bianthryl, respectively. In addition, we introduce a new transient fluorescence procedure for the determination of solvation dynamics that has advantages over the traditional transient Stokes‐shift method. Finally, for the first time, extensive measurements on the solvation dynamics of a polar aprotic solvent have been made. The observed dynamics of the solvent (glycerol triacetate) are highly nonexponential; this has important implications for chemical reactions in similar solvents. Interestingly, the experimentally observed microscopic dynamics are in qualitative agreement with predictions of the dielectric continuum model.

Spectroscopic studies of cryogenic fluids: Benzene in propane
View Description Hide DescriptionEnergy shifts and bandwidths for the ^{1} B _{2u }↔^{1} A _{1g }optical absorption and emission transitions of benzene dissolved in propane are presented as a function of pressure, temperature, and density. Both absorption and emission spectra exhibit shifts to lower energy as a function of density, whereas no shifts are observed if density is kept constant and temperature and pressure are varied simultaneously. Density is thus the fundamental microscopic parameter for energy shifts of optical transitions. The emission half‐width is a linear function of both temperature and pressure but the absorption half‐width is dependent only upon pressure. These results are interpreted qualitatively in terms of changes occurring in the intermolecular potentials of the ground and excited states. Both changes in shape of and separation between the ground and excited state potentials are considered as a function of density. Classical dielectric (Onsager–Böttcher), microscopic dielectric (Wertheim) and microscopic quantum statistical mechanical (Schweizer–Chandler) theories of solvent effects on solute electronic spectra are compared with the experimental results. Calculations suggest limited applicability of dielectric theories but good agreement between experiment and microscopic theory. The results demonstrate the usefulness of cryogenic solutions for high pressure, low temperature spectroscopic studies of liquids.

Brillouin scattering on noncrystalline ZnCl_{2}
View Description Hide DescriptionMeasurements of Brillouin scattering spectra from liquid and glassy (300–600 °C, 25–130 °C) ZnCl_{2} are reported. High resolution Fabry–Perot spectroscopy has been used, and temperature as well as momentum transfer have been varied so as to go completely across the condition (Brillouin frequency)⋅(characteristic relaxation time)=1, where very non‐Lorentzian spectral shapes are observed. They are fully described by viscoelastic theory, i.e., a Mori‐form including fourth moment, two sound velocities, and relaxation times. Connection with current ideas on glass‐forming liquids is made.

Molecular beam photoelectron spectroscopy: The C_{2}D_{4} ^{+}(X̃ ^{2} B _{3}) ground state
View Description Hide DescriptionThe He i (584 Å) photoelectron spectrum of C_{2}D^{+} _{4} in its ground electronic state has been measured, using a supersonic molecular beam. The combination of rotational cooling and improved resolution permits new vibrational fine structure to be observed and assigned. In particular, the ν_{3} value is accurately determined. A systematic increase in the ν_{4} torsional frequency with increasing excitation of the ν_{2} C=C stretching vibration is observed, indicating significant coupling between these modes.

High pressure isotropic bandwidths and frequency shifts of the C–H and C–O modes of liquid methanol
View Description Hide DescriptionThe Raman bands of the C–H ν_{3} and C–O ν_{8} stretching modes of liquid methanol have been measured at temperatures ranging from 273 to 363 K and pressures from 10 bar to 4 kbar. The effects of density and temperature on the isotropic linewidth, peak frequency of the isotropic band, ν_{0} (ISO), and the difference δν between anisotropic ν_{0}(VH) and ν_{0}(ISO) band frequencies are reported and discussed qualitatively in terms of available theoreticalmodels. It appears that repulsive interactions are responsible for the observed C–H line changes, and the Schweizer–Chandler (SC) model is used to evaluate frequency shift and bandwidth of the ν_{3} C–H mode after the effect of Fermi resonance coupling to the 2ν_{4} overtone was removed. In particular, the anomalous temperature and density dependence of the Raman band of the C–O stretching mode is noted and compared to the relatively typical behavior observed for the Raman line shape of the C–H mode.

Floquet–Liouville supermatrix approach. II. Intensity‐dependent generalized nonlinear optical susceptibilities
View Description Hide DescriptionWe present a practical n o n p e r t u r b a t i v e method for e x a c t treatment of i n t e n s i t y‐d e p e n d e n t generalized nonlinear optical susceptibilities χ(ω) in intense polychromatic fields, valid for arbitrary laser intensities, detunings, and relaxation. By means of the many‐mode Floquet theory, the time‐dependent Liouville equation can be transformed into an equivalent t i m e‐i n d e p e n d e n t infinite‐dimensional Floquet–Liouville supermatrix (FLSM) eigenvalue problem. It is then shown that the nonlinear optical susceptibilities χ(ω) can be completely determined simply from the supereigenvalues and eigenfunctions of the Floquet–Liouvillian L̂_{ F }. In addition to this exact FLSM approach, we have also presented higher‐order perturbative results, based on the extension of the Salwen’s nearly degenerate perturbation theory, appropriate for somewhat weaker fields and near‐resonant multiphoton processes, but beyond the conventional perturbative or rotating wave approximation (RWA). In the case of two‐level systems, for example, the implementation of Salwen’s method in the time‐independent L̂_{ F } allows the reduction of the infinite‐dimensional FLSM into a 4×4 dimensional effective Hamiltonian, from which essential a n a l y t i c a l formulas for intensity‐dependent χ(ω) can be obtained. These methods are applied to a detailed study of intensity‐dependent spectralline shapes (such as hole burning and extra resonance peaks at the line center, and the effects of saturation, detuning, and radiative and collisional damping, etc.) and subharmonic structures in nonlinear multiple wave mixings χ[(m+1)ω_{1}−mω_{2}] for two‐level systems in intense linearly polarized bichromatic fields.

Interpretation of the Auger electron spectra of nitrous oxide
View Description Hide DescriptionThe nitrogen and oxygen Auger spectra associated with the nitrous oxide molecule have been calculated using a semiempirical model analogous to that used previously to explain atomic Auger spectra. The role of the central and terminal nitrogen atoms is elucidated. Good agreement with the experimental spectrum is obtained especially for the outer valence region.

Diode laser probing of vibrational product state distributions in metal–molecule collisions: Hg(6 ^{3} P _{1})–CO_{2}(m n ^{ l } p)
View Description Hide DescriptionDiode laser probing has been used to follow the time dependent changes in the populations of low lying vibrational states of CO_{2} produced via quenching of Hg(6 ^{3} P _{1}) initially excited by a pulse from a doubled dye laser. The conversion of mercury electronic energy into CO_{2} vibrational energy is quite efficient and mode specific. The ratio of the number of bending mode quanta to the number of asymmetric stretch quanta produced by the quenching process is 40±12. The rate of filling of both the bending and asymmetric stretch levels is identical and corresponds to 80 CO_{2}/CO_{2} gas kinetic collisions. This data, taken in conjunction with the known quenching rate of Hg(6 ^{3} P _{1}) by CO_{2} (four gas kinetic collisions) suggests that the quenching process produces a metastable state of CO_{2} which is either a bent electronic triplet or a highly excited vibrational level of the ground electronic state.