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Volume 85, Issue 7, 01 October 1986

Infrared rotational transitions in CH_{2} X̃ ^{3} B _{1} observed by diode laser absorption
View Description Hide DescriptionFive rotational transitions involving K _{ a }=4←3 in the ground vibronic state of the methylene radical have been detected by diode laserabsorption spectroscopy in the infrared at wavelengths around 25 μm. The radical was formed in a mild glow discharge in a dilute mixture of ketene in helium that was pumped continuously through the absorption cell, and the methylene absorption lines were detected using a Zeeman modulation technique. The solenoid used to generate the required oscillating magnetic field was powered by a simpler and less expensive electrical circuit than has previously been described for this type of spectroscopy.

The ν_{2} fundamental band of triplet CH_{2}
View Description Hide DescriptionThe ν_{2} (bending) fundamental band of CH_{2} in its X̃ ^{3} B _{1}ground electronic state has been studied using tunable diode laser spectroscopy and also the LMR (laser magnetic resonance) technique in the 800–911 cm^{−} ^{1} and 1030–1173 cm^{−} ^{1} regions. For the diode laser study, a multiple‐traversal absorption cell was used with Zeeman modulation, and the CH_{2} radicals were produced by a mild discharge in a flowing mixture of ketene (∼0.3 Torr) and helium (∼2 Torr). Under these conditions, the apparent lifetime of CH_{2} following cutoff of the discharge was about 1 ms. A total of 53 new transitions with rotational quantum numbers up to N=10, K ^{‘} _{ a } =3, and K _{ a } =2 were observed to add to the 11 transitions previously measured in this band. A combined analysis of the present data and all the previous pure rotational and ν_{2} band results on CH_{2} has yielded an improved set of molecular parameters, including the first determination of centrifugal distortion effects for the dominant spin–spin interaction parameter, D. The present data have also been used in a comprehensive new analysis of triplet methylene rotation–vibration energies using the nonrigid bender Hamiltonian by Bunker e t a l. in an accompanying paper.

The potential surface of X̃ ^{3} B _{1} methylene (CH_{2}) and the singlet–triplet splitting
View Description Hide DescriptionThe data in the two immediately preceding papers, when combined with the extant microwave, infrared, and photodetachmentspectroscopic data, provide 152 rotation and rotation‐bending energy level separations in X̃ ^{3} B _{1} methylene (involving ^{1} ^{2}CH_{2}, ^{1} ^{3}CH_{2}, and CD_{2}). In the present paper we fit all this data using the two nonrigid bender Hamiltonians NRB1 and NRB2. The more refined model (NRB2) leads to the following results for triplet methylene: r _{ e }=1.0766±0.0014 Å, α_{ e }=134.037°±0.045°, and the barrier height to linearity=1931±30 cm^{−} ^{1} (the uncertainties are three times the standard errors). Rotation‐bending energy levels for CH_{2}, CD_{2}, and CHD are calculated for v _{2}≤4 and N≤6. The determination of the rotation‐bending energy levels in CH_{2} leads to an improved determination of the singlet–triplet splitting T _{0}(ã^{1} A _{1}) in methylene as 3156±5 cm^{−} ^{1} (9.023±0.014 kcal/mol, 0.3913±0.0006 eV). Although the rotation‐bending energy levels are accurately predicted it is not possible to predict the stretching frequencies of CH_{2} very accurately, since the data to hand are not very sensitive to the stretching force field.

Long‐lived high energy vibrational levels in benzene vapor
View Description Hide DescriptionSingle vibronic level fluorescence spectra from the 6^{1}1^{2} level in ^{1} B _{2u } benzene and benzene‐d _{6} in a free jet expansion include sharp transitions to S_{0} levels identified as high normal mode overtones of the C–C ring breathing mode up to 10 000 cm^{−} ^{1}. For these levels, and for the reported method of state preparation, the upper bound for the rate of intramolecular vibrational redistribution is k _{IVR} <10^{1} ^{2} s^{−} ^{1}. This rate is several times smaller than for C–H or C–D stretch local mode levels of similar energy when they are prepared via overtone absorption from the ground state.

Hyperfine structure of the BaI X ^{2}Σ^{+} and C ^{2}Π states
View Description Hide DescriptionOptical‐microwave double resonance measurements were carried out to find the hyperfine structure constants of the v=0 level of the BaI X ^{2}Σ^{+} state. These were combined with sub‐Doppler optical measurements of the BaI C ^{2}Π–X ^{2}Σ^{+}(0,0) band in order to derive the hyperfine structure constants of the excited state. We have determined the following molecular constants (in MHz) where the numbers in parentheses represent one standard deviation in a least squares fit: for the BaI X ^{2}Σ^{+} state, γ‘=75.8501(33), b‘=93.117(19), c‘=52.170(54), and e Q q‘=−33.62(12), and for the BaI C ^{2}Π state, a’=263(53), b’+c’=−430(212), d’=−66.7(1.4), and e Q q’=−214(11). The Fermi contact interaction and the electric quadrupole coupling constants for both the BaI X and C states appear to arise from the distortion of closed‐shell I^{−} orbitals by the field of the Ba^{+} ion. In the BaI X state, the charge distribution on the Ba^{+} center is directed away from I^{−} while in the C state toward I^{−}.

Simple interpretation of dephasing in absorption and resonance Raman theory
View Description Hide DescriptionIt is shown that the effects of ‘‘pure dephasing’’ in vibronic absorption and resonance Raman scattering may be simply derived by beginning with the Fermi Golden Rule. The medium introduces electronic dephasing by modulating the electronic energy gap of the molecule. In both absorption and Raman scattering the cross section depends upon a medium correlation function φ(t) whose form is identical to one that appears in vibrational relaxation theory. Explicit equations for the resonance Raman cross section are derived for an exponential medium correlation function. Also, φ(t) is derived for medium models which consist of a collection of classical and quantum mechanical oscillators.

Laser spectroscopy, rotational assignment, and perturbation analysis of the A ^{1}Σ^{+} _{ u }– X ^{1}Σ^{+} _{ g } Ca_{2} red system
View Description Hide DescriptionWe measured the Ca_{2} red system using filtered laser excitation to simplify the spectrum. The transition is assigned A ^{1}Σ^{+} _{ u } −X ^{1}Σ^{+} _{ g }, where X is the previously studied van der Waals ground state and A correlates adiabatically to ^{1} S+^{1} Dcalcium atoms. The A state suffers many homogeneous and heterogeneous perturbations, which are assigned to interactions with components of c ^{3}Π_{ u }. Following deperturbation of the band spectra, we find that the A state dissociation energy,D ^{’} _{ e } is 8694±2 cm^{−} ^{1}, with a vibrational frequency, ω_{ e }, of 126.73±0.11 cm^{−} ^{1}, and an equilibrium internuclear separation, R _{ e }, of 3.63 Å. The analysis shows c ^{3}Π_{ u }, which correlates to ^{1} S+^{3} P atoms, is bound by at least 1170 cm^{−} ^{1}, with ω_{ e }≥67.7 cm^{−} ^{1} and R _{ e }≤4.25 Å. The assignment of the previously analyzed green system of Ca_{2} is revised to B ^{1}Σ^{+} _{ u }– X ^{1}Σ^{+} _{ g }, where B correlates adiabatically to ^{1} S+^{1} P atoms. The new assignment gives B a dissociation energy of 5783 cm^{−} ^{1}, and resolves some confusion about the origin of the Ca_{2} red and green systems.

Radiative decay and radiationless relaxation of NH/ND(a ^{1}Δ) isolated in rare gas matrices
View Description Hide DescriptionLifetimes of matrix‐isolated NH/ND(a ^{1}Δ) radicals have been measured as function of temperature and rare gas host. The metastable species were generated directly by i n s i t uphotolysis of hydrazoic or isocyanic acid, or by pulsed excitation of the b ^{1}Σ^{+} state with a dye laser, which subsequently decays to the a state on a μs time scale. Rotation of NH/ND in the electronic ground state is perturbed or inhibited by the second photofragment in the photolysis systems. The lifetimes of NH(a ^{1}Δ) in Ne, Ar, and Kr show little temperature dependence. This is consistent with a radiationless contribution to the overall relaxation in which the energy gap to the next lower vibrational level of the ground state is accepted by guest rotation and/or other local modes. The strong temperature dependent decay of ND(a ^{1}Δ) in Ar and Kr is due to endothermic near resonant relaxation to the sixth vibrational level of the ground state, with an activation energy in the order of the energy gap, and a frequency factor of 20±5 s^{−} ^{1}. The relaxation mechanism of NH/ND(a ^{1}Δ) in solid Xe is of a different nature, the data being consistent with a temperature dependent external heavy atom effect. A lower limit of 1.9 s has been deduced for the radiative lifetime of the (a ^{1}Δ) state i n v a c u o, in reasonable agreement with a recent a b i n i t i o calculation.

Zeeman, hyperfine, and magnetic dipolar effects on the EPR spectrum of a cubic copper tetramer
View Description Hide DescriptionThe Zeeman interaction for an isolated multiplet of a cubic Cu^{2} ^{+} tetramer, characterized by the total spin quantum number S, is shown to be essentially isotropic, with g=(g _{∥}+2g _{⊥})/3, where g _{∥} and g _{⊥} are single Cu^{2} ^{+} ion components. Matrix elements are given for the off‐diagonal part of the Zeeman interaction within the three S=1 multiplets. The hyperfine structure for each isotope in a [100] direction is shown to be a 13 line structure. The intracluster magnetic dipole–dipole (MDD) interaction has nonzero matrix elements within the three S=1 multiplets, which are degenerate for an isotropic exchange interaction with equal coupling constants. With the MDD interaction treated as a perturbation of the Zeeman interaction, it is found that the single line at g=2.10, expected on the basis of the Zeeman interaction alone, is split into four lines separated from the former line by ±h _{0} and ±2h _{0}, where h _{0}≂480 G. The MDD coupling constant, calculated assuming point dipoles, is an order of magnitude too small to explain the zero‐field splitting of the S=2 multiplet measured by EPR in Cu_{4}OCl_{6}(TPPO)_{4}.

Fourier transform photoelectron spectroscopy: The correlation function and the harmonic oscillator approximation
View Description Hide DescriptionThe correlation function describes the time development of the wave packet placed by photoabsorption or photoionization onto the potential surface of an upper electronic state. The function can be obtained as a Fourier transform of the electronic band, and gives information about the features of the final state. The analytical expressions for the correlation function within the harmonic oscillator approximation are presented. Because of some unique properties of the correlation function, the expressions can be used to obtain accurate geometric details of the final state from experimental data. The approach is tested on some photoelectron spectra of diatomics and compared to known data. The method yields the equilibrium internuclear distance with an accuracy of ±0.0025 Å, and resolves the sign uncertainty present in the conventional harmonic Franck–Condon analysis. The comparison of the experimental data with the predictions of the harmonic model gives a deeper insight into the behavior of a wave packet in an anharmonic potential.

Free jet infrared absorption spectroscopy of the ν_{3} band of TeF_{6}
View Description Hide DescriptionThe ν_{3} band of TeF_{6} is studied at a low rotational and vibrational temperature using a tunable diode laser. The vibration–rotation lines are measured in the 752 to 759 cm^{−} ^{1} range with a Doppler‐limited resolution. Five spectroscopic constants, ν_{3}, B _{3}, Bζ_{3}, α_{2} _{2} _{0}, and α_{2} _{2} _{4}, are determined for the four major isotopic species, ^{1} ^{3} ^{0}TeF_{6}, ^{1} ^{2} ^{8}TeF_{6}, ^{1} ^{2} ^{6}TeF_{6}, and ^{1} ^{2} ^{5}TeF_{6}. Only the Q‐branch peaks are measured for ^{1} ^{2} ^{4}TeF_{6} and ^{1} ^{2} ^{2}TeF_{6}. Harmonic force constants for the F _{1u } block and two anharmonic force constants, f _{ r r r } and F _{3} _{3} _{5}, are calculated for SeF_{6}, TeF_{6}, and WF_{6} from the spectroscopic constants determined by free jet measurements. Isotopic dependence of B _{0}−B _{3}, α_{2} _{2} _{0}, and α_{2} _{2} _{4} are calculated for these molecules and compared with experimental values. Similarity in structure of the ν_{3} Q‐branch of hexafluorides is discussed on the basis of frequency correlation between ω_{1} and ω_{2}.

Comparison of experiment and theory for the resonance Raman spectrum of I_{2} in solution. I. The Raman excitation profile of I_{2} in n‐hexane
View Description Hide DescriptionThe absolute Raman excitation profiles (REPs) of the fundamental and first two overtones of I_{2} dissolved in n‐hexane were determined with excitation frequencies from 15 000 to 22 000 cm^{−} ^{1}. Calculations for both the absorptionspectrum and the REPs were performed and the results compared to the experimental results. Good agreement was found using gas phase potentials for the A, B, and B‘ states and a ground state potential modified to reproduce the observed anharmonicity of the I_{2} vibrations in n‐hexane. The homogeneous linewidth in the excited electronic states is Γ=15–20 cm^{−} ^{1} (HWHM), which corresponds to a T _{2} of ≊0.3 ps. The spectra have an inhomogeneous component of 400 cm^{−} ^{1} (HWHM). Separate calculations demonstrate the effects of the excited electronic states individually and demonstrate the importance of the interference terms in the REP. Calculations also demonstrate the sensitivity of the depolarization ratio to the contributions of the various excited electronic states. The index of refraction corrections required in solution are close to those expected.

The scattering matrix for randomly oriented particles
View Description Hide DescriptionAn efficient numerical method is derived for evaluation of the scatteringproperties of randomly distributed particles described by the coupled dipole approximation. An exact analytic average for these properties is also derived. All elements of the scattering matrix for a collection of randomly oriented particles can be obtained by either method. The results are applicable to model calculations of the scattering matrix for realistic particles. The analytic average also allows qualitative interpretation of the dependence of the matrix elements on dipolar interactions.

Dipolar SASS NMR spectroscopy: Separation of heteronuclear dipolar powder patterns in rotating solids
View Description Hide DescriptionTwo‐dimensional sample‐spinning NMR techniques for separately obtaining heteronuclear dipolar powder patterns of chemically distinct nuclei are proposed, which involve switching the spinning axis on and off the magic angle. Procedures for the computation of dipolar spectra obtained by this method are described, and various features of such spectra are discussed using simulated spectra. Practical applications of this method are demonstrated with ^{1} ^{3}C spectra of calcium formate, β‐quinol‐methanol clathrate, and urea‐t r a n s‐4‐octene clathrate, providing information on the absolute sign and magnitude of the indirect dipolar couplings, ^{1} ^{3}C–^{1}H distances, and dynamics of trapped molecules in clathrates.

Band broadening of CH_{2} vibrations in the Raman spectra of polymethylene chains
View Description Hide DescriptionThe isotropic and anisotropiclinewidths of methylene vibrations in a homologous series of alkanes of increasing chain length have been measured in the liquid state as a function of temperature. The bandwidths of the CH_{2} symmetric stretching modes, which are in Fermi resonance with overtones of the CH_{2} bending vibrations, are temperature insensitive over a 200 K interval; this is best explained in terms of a vibrational dephasing mechanism (inhomogeneous broadening) for these modes. In contrast, for the bending and antisymmetric stretching vibrations, significant band broadening occurs over this same temperature interval. In addition, for these modes, both the absolute value of the bandwidth and the relative rate of increase of the bandwidth with increasing temperature, decrease with increasing chain length. These observations are consistent with a reorientational broadening mechanism as the principal bandwidth contribution for these vibrations. Hindered end‐over‐end rotation of the molecules, which contributes to the band broadening for very low molecular weight alkanes, rapidly becomes too slow to be observable on the time scale of the Raman experiment for the higher molecular weight alkanes and polyethylene. For longer chain lengths, torsional backbone motions coupled to the high frequency antisymmetric stretching modes can account for the breadth of the bands.

A variable energy photoelectron study of the valence levels and I 4d core levels of CF_{3}I
View Description Hide DescriptionUsing monochromatized synchrotron radiation, gas phase photoelectron spectra of CF_{3}I have been obtained between 21 and 100 eV photon energies. Experimental valence band branching ratios have been compared with theoretical branching ratios from MS‐Xα calculations. The generally good agreement between experiment and theory confirms the orbital assignment: 4e<4a _{1}<1a _{2}∼3e<2e<3a _{1}<1e∼2a _{1} <1a _{1}, in order of increasing binding energy. In contrast to CF_{4}, MS‐Xα calculations predict two shape resonances for CF_{3}I at 15.2 eV (e channel) and 17.2 eV (a _{1} channel). Experimentally, weak shape resonances are observed on e orbitals at ∼14 eV kinetic energy. The cross sections are very useful for correlating orbitals in CF_{3}I with those of CF_{4}. For example, the cross sections suggest that the 3e orbital in CF_{3}I correlates with the 1t _{1} orbital rather than the 4t _{2} orbital in CF_{4}. After the onset of the I 4d level at ∼57 eV, intershell coupling becomes important in enhancing valence band levels having high I 5p character such as the 4e orbital. The I 4d branching ratio from 66 to 110 eV is similar to the Xe 4d branching ratio in atomic Xe, indicating atomic‐like behavior for the I 4d subshell.

Studies of the reaction of O^{+} _{2} with deuterated methanes
View Description Hide DescriptionIn the gas phase O^{+} _{2} reacts with methane at 300 K to produce a hydrogen atom and the CH_{3}O^{+} _{2} ion. The structure of this ion has recently been determined to be H_{2}COOH^{+}, methylene hydroperoxide ion. The reaction rate coefficients and product distributions have now been measured at 300 K for the CH_{ n }D_{4−n }isotopes. The reaction shows both inter‐ and intramolecular isotope effects, e.g., CH_{2}D_{2} reacts more slowly than methane and more rapidly than CD_{4}, but loses hydrogen or deuterium with equal probability. The ion readily transfers HO^{+} to alkenes, CS_{2}, and many other neutral molecules. The reaction with CS_{2} has been used to investigate the isotopic distribution within mixed isotope product ions. In addition, the reaction rate coefficients for both CH_{4} and CD_{4} have been measured as functions of temperature between 20 and 500 K; in both cases a clear minimum is observed in the reaction rate coefficient near room temperature. A mechanism for the reaction is proposed which allows us to model the temperature dependence of the reaction rate coefficient over the entire range for which there are data.

State‐resolved study of collisional energy transfer between A ^{2}Π v=7 and X ^{2}Σ^{+} v=11 rotational levels of CN
View Description Hide DescriptionCollisional transfer from the A ^{2}Π state of CN has been studied with initial and final state resolution by an optical–optical double resonance technique. Specific rotational levels in the v=7 vibrational manifold of the A state of CN in a flow of several Torr of argon are prepared by pulsed laser excitation in the A–X (7,2) band. After a short time delay, a second laser probes the populations of quantum levels in this vibrational manifold and in the nearly isoenergetic v=11 manifold of the X ^{2}Σ^{+} state by fluorescence excitation in the overlapped B–A (8,7) and B–X (8,11) bands. The interelectronic A→X transfer rate is found to be comparable to that for purely rotational collisional transitions within the A state for all incident levels studied, regardless of whether or not they possess significant X state character, because of isolated molecule non‐Born–Oppenheimer mixing. Reflecting the near homonuclear character of the CN–Ar interaction potentials, the final X state populations exhibited a significant even–odd alternation as a function of the final rotational angular momentum quantum number. These populations could be adequately fit by the sudden scaling relationship for Π→Σ cross sections derived by Alexander and Corey [J. Chem. Phys. 8 4, 100 (1986)].

Temperature dependence of association of diatomic ions in diatomic gases
View Description Hide DescriptionThe temperature dependence of experimental rate coefficients for association of diatomic ions in diatomic gases is compared to model calculations in which the stabilization of the initially formed unstable association complex is assumed to occur by formation of a ‘‘super complex.’’ It is shown that acceptable agreement between the model and experimental data on four sample reactions can be obtained with a minimum of plausible assumptions. The agreement indicates that earlier theoretical models may provide an accurate description of the formation and destruction of the association complex, but failed to reproduce the experimental data, because the temperature dependence of the stabilization step was inadequately treated.

A state‐to‐state study of the electron transfer reactions Ar^{+}(^{2} P _{3/2,1/2})+N_{2}(X̃,v=0)→Ar(^{1} S _{0}) +N^{+} _{2}(X̃,v’)
View Description Hide DescriptionThe vibrational state distributions of N^{+} _{2}(X̃,v’) ions resulting from the reactions, Ar^{+}(^{2} P _{3} _{/} _{2})+N_{2}(X̃,v=0)→Ar(^{1} S _{0}) +N^{+} _{2}(X̃,v’) [reaction (1)] and Ar^{+}(^{2} P _{1} _{/} _{2})+N_{2}(X̃,v=0)→Ar(^{1} S _{0}) +N^{+} _{2}(X̃,v’) [reaction (2)], over the center‐of‐mass collisional energy (E _{c.m.}) range of 0.25–41.2 eV in a crossed ion–neutral beam experiment have been probed by the charge exchange method. The experimental results obtained for reaction (1) are in accord with the predictions of the semiclassical multistate calculation of Spalburg and Gislason that N^{+} _{2} ions are formed predominantly (≳85%) in the v’=1 state and that the production of N^{+} _{2}(X̃,v’=0) becomes more important as E _{c.m.} is increased. The experiment also supports the theoretical results for reaction (2) at E _{c.m.}=1.2 and 4.1 eV showing that ≳80% of N^{+} _{2} product ions are in the v’=2 state. However, the calculation is found to either over‐estimate the populations for N^{+} _{2}(v’<2) or underestimate the populations for N^{+} _{2}(v’>2) resulting from reaction (2) at E _{c.m.}=10.3
and 41.2 eV. Absolute spin‐orbit‐state‐selected total cross sections for reactions (1) and (2), σ_{3} _{/} _{2} and σ_{1} _{/} _{2}, respectively, at the E _{c.m.} range of 0.25–115.3 eV have also been measured using a tandem photoionization mass spectrometer which is equipped with a radio frequency (RF) octopole ion guide reaction gas cell. The measured values for σ_{3} _{/} _{2} at E _{c.m.}=4.1, 10.3, and 41.2 eV and σ_{1} _{/} _{2} at 41.2 eV are in reasonable agreement with the theoretical cross sections. However, the experimental values for σ_{3} _{/} _{2} at 1.2 eV and σ_{1} _{/} _{2} at 1.2, 4.1, and 10.3 eV are approximately a factor of 2 higher than the theoretical predictions. A model analysis, which takes into account possible collision‐induced spin‐orbit mixings of the reactant Ar^{+} states in the RF octopole gas cell, shows that the values for σ_{1} _{/} _{2}/σ_{3} _{/} _{2} and σ_{1} _{/} _{2} determined using the ion beam–RF octopole gas cell arrangement can be strongly susceptible to gas cell pressure effects whereas the experimental values for σ_{3} _{/} _{2} are reliable. The values for σ_{1} _{/} _{2} deduced by multiplying the values for σ_{3} _{/} _{2} and the ratios σ_{1} _{/} _{2}/σ_{3} _{/} _{2} determined in the crossed ion–neutral beam experiment are in agreement with the theoretical cross sections. Both σ_{3} _{/} _{2} and σ_{1} _{/} _{2} are found to increase as E _{c.m.} is increased from 41.2 eV. This observation is interpreted as due to the formation of N^{+} _{2} in the Ã ^{2}Π_{ u } state at high E _{c.m.} . Combining the measured vibrational state distributions of product N^{+} _{2}(X̃,v’) ions and the absolute state‐selected total cross sections, absolute state‐to‐state total cross sections for reactions (1) and (2) at selected E _{c.m.} are determined.