Index of content:
Volume 91, Issue 7, 01 October 1989

On the apparent spectroscopic rigidity of floppy molecular systems
View Description Hide DescriptionThere has been a wealth of recent infrared experimental data on van der Waals and hydrogen bonded complexes obtained under cooled, supersonic jet conditions where only a small fraction of the total bound quantum states can be elucidated. This partial set of data can often be well fit to a traditional Watson Hamiltonian derived from a rigid rotor perspective with low order centrifugal distortion effects included. In this paper we show that even in extremely floppy molecular systems with wide amplitude vibrational motion, the quantum term values are very well fit by a rigid or semirigid rotor Hamiltonian over the limited range of energy states accessible in a cooled beam. We provide explicit examples of this behavior by full quantum solutions in two extremes of floppy motion: (1) a symmetric triatomic with a square well bending potential (‘‘hinge’’) and (2) a nearly free internal rotor (‘‘pinwheel’’). These results show that potentials with fundamentally different topologies can be consistent with same data, and indicate that even the limits of nearly rigid and floppy internal motion may be difficult to distinguish from a limited set of rovibrational eigenvalues.

On the laser‐wavelength dependence of plasmon surface polariton field‐enhanced Raman spectroscopy
View Description Hide DescriptionWe analyzeplasmonsurfacepolariton field‐enhanced Raman spectroscopic data for the CH stretching vibrational range (2800–3000 cm^{−} ^{1}) of cadmium arachidate multilayer assemblies, taken as a function of the exciting laser wavelength λ_{ L }. In addition to the well‐known λ^{−} ^{4} dependence of ordinary (photon) Raman scattering we find a variation of the intensity ratio of the methylene antisymmetric to symmetric stretching band (ν_{ a }=2885 cm^{−} ^{1} and ν_{ s }=2850 cm^{−} ^{1}, respectively) which can be attributed quantitatively to a specific surface plasmon field property: a longitudinal field component parallel to the propagation direction adds to the dominant perpendicular field with increasing relative strength for decreasing wavelength.

Highly excited rovibrational states using a discrete variable representation: The H^{+} _{3} molecular ion
View Description Hide DescriptionA formulation of the rovibrational problem in Jacobi coordinates is presented which employs a discrete variable representation for the angular internal coordinate. Rotational excitation is implemented via a two‐step procedure and symmetry (for A B _{2} systems) included using a computationally efficient method. Energies for the lowest 180 vibrational states of H^{+} _{3} are presented and their wavefunctionsanalyzed graphically. J=1←0 excitation energies are presented for the lowest 41 vibrational states. The significance of the regular states in the high‐energy regime of H^{+} _{3} is discussed.

The vibrational spectra of molecular ions isolated in solid neon. II. O^{+} _{4} and O^{−} _{4}
View Description Hide DescriptionWhen a relatively concentrated Ne:O_{2} sample is codeposited at ∼5 K with a beam of excited neon atoms, prominent infrared absorptions appear which are assigned to O^{+} _{4} and O^{−} _{4}. Absorptions of O_{3} and O^{−} _{3} are also present, and their product distributions in isotopic substitution experiments indicate that O‐atom production and reaction is a minor channel in this experimental system. Detailed isotopic substitution experiments require that both O^{+} _{4} and O^{−} _{4} possess two equivalent O_{2} units. Analysis of the isotopic shifts strongly favors a planar t r a n s configuration (C _{2h }) for both molecules. Several combination bands of O^{+} _{4} are observed, and give evidence regarding the position of ν_{1}(a _{ g }), which is infrared inactive, and regarding perturbations by combinations of low‐frequency fundamentals. The mechanism of photodestruction of the ions in this system is also considered.

Optical refractive and reflective properties of resonantly absorbing media
View Description Hide DescriptionExperiments on the reflection of polarized monochromatic laser light at the planar interface of resonantly absorbing medium and the air were made for a variety of situations, including Brewster’s angle in the spectral vicinity of the resonance wavelength. An ethanolic solution of Rhodamine B, an organic laser dye luminofor with a well defined resonance absorptionspectrum, was chosen as the absorbing medium. The tunable polarized output of a cw dye laser was used to provide the collimated monochromatic beam. To compare the experimental results with theory, the Fresnel reflectivity equations combined with the Kramers–Kronig relations were used to predict the reflectance in terms of the known absorption coefficient. The experimental results generally confirm the theoretical predictions.

Dicke narrowing of the polarized Stokes–Raman Q branch of the v=0→1 transition of D_{2} in He
View Description Hide DescriptionA b i n i t i o calculations were carried out for several Stokes–Raman Q branch line shapes of the v=0→1 transition of D_{2} in helium in the low pressure regime where Dicke narrowing is observed. Five different approximations were studied: a generalization of Hess’s method, which is based on the equivalent of a Bhatnagar–Gross–Krook model of the Waldmann–Snider kinetic equation; two high pressure asymptotes of Hess’s method; a moment method of the Chapman–Cowling type due to Corey and McCourt; and a collision kernel method that has found extensive use lately in rarefied gas dynamics and other highly nonequilibrium states. Using generalized cross sections incorporating S‐matrices calculated in the close coupled approximation with an a b i n i t i opotential energy surface, most of the methods agreed moderately well with the most recent line width determinations at most densities. Of the five methods, the generalized Hess and collision kernel methods agreed best with experiment over the whole range. At the lowest densities where the collision kernel method might be expected to have convergence problems none were observed, and at high densities the a b i n i t i o generalized Hess method may not be flexible enough.

Resonant two‐photon ionization‐photoelectron spectroscopy of Cu_{2}: Autoionization dynamics and Cu^{+} _{2} vibronic states
View Description Hide DescriptionResonant two‐photon ionization of gas phase Cu_{2} in a cold molecular beam in conjunction with time‐of‐flight photoelectron spectroscopy provides new vibronic state spectroscopic information for the dimer cation Cu^{+} _{2}. One color ionization via the 0–0, 1–0, and 2a–0 bands of Smalley’s System V neutral Cu_{2} resonant states (J←X transition) accesses Cu^{+} _{2} states in the range 0–1.4 eV. The electron kinetic energy measurements slightly refine the first adiabatic ionization energy of Cu_{2} to I_{1}(Cu_{2})=7.899±0.007 eV. We observe two electronic states of Cu^{+} _{2} which we assign as X ^{2}Σ^{+} _{ g } and an excited ^{2}Π spin–orbit pair of sublevels with origins at T _{0}(^{2}Π_{3} _{/} _{2})=1.143±0.002 eV and T _{0}(^{2}Π_{1} _{/} _{2})=1.256±0.002 eV. The absence of spin–orbit splitting identifies the ground state^{2}Σ symmetry; the spin–orbit splitting of 898±8 cm^{−} ^{1} identifies the excited states as ^{2}Π. Within X ^{2}Σ^{+} _{ g } we observe a remarkably long vibrational progression, perhaps extending from v=0–80. The vibrational intervals determine the constants ω_{ e }=188±4 cm^{−} ^{1} and ω_{ e } x _{ e }=0.75±0.09 cm^{−} ^{1}. The ^{2}Π vibrational intervals determine ω_{ e }=244±6 cm^{−} ^{1}. The adiabatic bond dissociation energy of ground stateCu^{+} _{2} is D _{0}(Cu^{+}–Cu)=1.84±0.08 eV. The intensity pattern of the X ^{2}Σ^{+} _{ g } vibrational bands exhibits multiple peaks whose positions and amplitudes are sensitive to the resonant J state vibrational level. For 0–0 excitation, we observe reproducible band intensity alternation. We present preliminary mass spectral and photoelectron data indicating that the cause of the highly non‐Franck–Condon band intensities is excitation of long lived, dissociative autoionization states which undergo extensive nuclear motion on the time scale of electron ejection. We propose an autoionization mechanism that includes a description of the Cu_{2} J state and explains the observed phenomena invoking only one electron transition.

Pressure tuning of Fermi resonance in crystal CO_{2}
View Description Hide DescriptionA solid state theory on pressure tuning of Fermi resonance in crystals is presented and applied to the CO_{2} case. The theory relies on consideration of delocalized ω_{2}+ω_{2} two‐phonon states anharmonically coupled to ω_{1} and it is developed along the formalism of the Green function technique. This gives a straightforward method to split bound states (or biphonons) out of the continuum. Explicit expressions for their energy separation and intensity are obtained. Calculations are performed on the pressure dependence of the main parameters governing the Fermi resonance and discussed in terms of the crystal approach. In contrast with the more limited molecular treatment, W is seen to decrease with pressure. The effect is specifically related to the spread of the two‐phonon continuum over a finite energy interval. Other quantities, for instance the intensity ratio between bound states, do not suffer such a big discrepancy between the two models. Limits of applicability of our approach are also sketched.

Pressure dependence of zero‐field splittings in organic triplets. I. Aromatics
View Description Hide DescriptionOptically detected magnetic resonance experiments have been conducted at pressure up to 45 kbar for p‐dichlorobenzene (DCB), s‐tetrachlorobenzene (TCB) and quinoxaline (Q). The pressure dependence of their zero‐field splitting parameters and, for DCB, the quadrupolar splitting are reported. For all three systems the D value decreases moderately with increasing pressure. The slope for TCB is approximately twice that for DCB. These results are interpreted in terms of pressure dependence of the mesomeric effect and the inductive effect of the substituents on the aromatic triplet state. For Q, the influence of pressure on spin‐orbit interaction is also suggested.

Vibrational assignments and intensity considerations of the fluorescence excitation spectra of jet‐cooled S _{1} t r a n s‐stilbene and its three isotopic analogues
View Description Hide DescriptionVibrational mode assignments of S _{1} t r a n s‐stilbene (tSB) in a jet, particularly those for fundamental vibrational levels above the isomerization barrier, are reported with three partially isotope‐substituted analogues (C_{6} H_{5} –^{1} ^{3}CH=^{1} ^{3}CH–C_{6} H_{5} , C_{6} H_{5} –CD=CD–C_{6} H_{5} , and C_{6} D_{5} –CH=CH–C_{6} D_{5} ). Vibrational levels are assigned on the basis of the frequency shifts due to isotopic substitution. The established mode assignments then enable us to discuss the individual band intensities in the fluorescence excitation spectra which bear mode specific information on the isomerization dynamics in isolated tSB molecules. Upon deuteration, the intensities of several CH deformation modes increase drastically as their frequencies become lower than the isomerization barrier. Intensities of several fundamental bands are found much smaller than those of nearby combination bands, contrary to what is expected from ordinary absorption spectra in condensed phases. The intensity ratio of the 7^{1} (C=C stretch) to the 0^{0} band is semiquantitatively studied with reference to a molecular‐orbital calculation, the resonance Raman intensity, and the absorption intensity in a low‐temperature crystal. The unusually low fluorescence excitation intensities are ascribable to large isomerization rates specific to certain kinds of fundamental vibrational levels.

Torsional damping and solvent friction in liquid n‐butane: Experimental estimates from Raman spectroscopy
View Description Hide DescriptionThe isotropic Raman linewidths of the in‐phase CCC bending modes of liquid n‐butane are analyzed in terms of dephasing by torsional oscillations. A simple, effective Hamiltonian is developed to calculate the coupling between this bending mode and the torsion. For the g a u c h e conformer the coupling is linear in the torsional coordinate and quite strong, but for the t r a n s conformer the coupling is weak. This coupling is used to relate the linewidths of the bending modes to the torsional dynamics, which are modeled by a damped, harmonic oscillator. The damping constant and a related torsional correlation time are then extracted from the experimental linewidths. The resulting correlation times are compared with those calculated assuming either hydrodynamic or collisional (Enskog) friction on the torsional coordinate. Both theoretical models give values that lie below the experimental upper bound, but the Enskog friction compares somewhat better with our best experimental estimates of the torsional damping.

Bath‐induced vibronic coherence transfer effects on femtosecond time‐resolved resonant light scattering spectra from molecules
View Description Hide DescriptionEffects of vibronic coherence transfer induced by the heat bath on ultrafast time‐resolved resonant light scattering (RLS) spectra are theoretically investigated within the master equation approach. The vibronic coherence initially created by a coherent optical excitation transfers to other vibronic coherent states due to inelastic interactions between the vibronic system concerned (the relevant system) and the heat bath. The vibronic coherence transfer results in the quantum beats in the time‐resolved RLS spectra. The bath‐induced vibronic transition operator is derived in the double space representation of the density matrix theory. Model calculations of the femtosecond (fs) time‐resolved RLS spectra are performed to demonstrate the effects of the bath‐induced vibronic coherence transfer.

Jet‐resolved vibronic structure in the higher excited states of N_{2}O: Ultraviolet three‐photon absorption spectroscopy from 80 000 to 90 000 cm^{−} ^{1}
View Description Hide DescriptionIonization‐detected ultraviolet multiphoton absorptionspectroscopy reveals Rydberg structure in the excited states of N_{2}O within 20 000 cm^{−} ^{1} of the first ionization threshold. This structure persists, with atomic‐like quantum defects and vibrational structure well matched with that of the ion, despite evidence for coupling of vibrationally excited Rydberg states with the underlying valence continuum. In the most completely resolved spectrum, which is assigned to the 3pσ ^{1}Π state, hot‐band, fundamental and overtone transitions involving the bending mode ν_{2}, indicate Renner–Teller and Herzberg–Teller coupling of electronic and vibrational angular momentum. Vibronic intensities and positions suggest that these couplings can be regarded as properties of the N_{2}O^{+} ion core, mirroring behavior manifested in the electronic emission spectrum of the ion. Window resonances are observed in the ionization‐detected absorptionspectrum above the four‐photon ionization threshold, which are assigned to vibrationally excited Rydberg states that couple to competing continuua in which predissociation dominates Δv=−1 vibrational autoionization.

High orbital angular momentum states in H_{2} and D_{2}. II. The 6h–5g and 6g–5f transitions
View Description Hide DescriptionA group of lines accompanying the first line of the Pfund series of the H atom has been observed by Fourier transforminfrared spectrometry. The lines are due to transitions in molecular hydrogen of a nonpenetrating Rydberg electron possessing a high‐orbital angular momentum, which is coupled only loosely to the vibrations and rotations of the H^{+} _{2} core. Lines belonging to the 6h–5g and 6g–5f (v=0–3) transitions of H_{2} have been identified. The identifications are based on a calculation of the spectrum from first principles by multichannel quantum defect theory. The interaction between the nonpenetrating electron and the core was evaluated in terms of the permanent and induced molecular moments of H^{+} _{2} as calculated by Bishop and collaborators. The analogous transitions in D_{2} have also been observed and assigned.

Statistical fluctuations of decay rates
View Description Hide DescriptionWe introduce a general Hamiltonian describing two coupled subsystems, each having a finite zero‐order decay probability. With use of simple statistical assumptions on the underlying states, we derive new probability distributions of individual decay rates. We analyze the cases of weak and intermediate to strong coupling, respectively. The resulting distributions often resemble a suitable χ^{2} distribution, but do not belong to that class of functions. An interpretation of decay rates in terms of a χ^{2} model thus may lead to wrong conclusions. As a concrete realization, we study a Hamiltonian describing the non‐Born–Oppenheimer coupling of two electronic states via the nuclear motion. The model is applied to the calculation of absorption‐type spectra of NO_{2} and C_{2}H^{+} _{4}. We investigate statistical properties of energy levels, line intensities, and decay rates. For NO_{2}, we find from all statistics a completely irregular behavior, consistent with random matrix predictions and demonstrating the strong mixing of zero‐order states due to the nonadiabatic coupling. For C_{2}H^{+} _{4}, all statistics exhibit characteristic deviations from the irregular limit that can be given a consistent interpretation.

Observation of collisionally transferred spikes in NH_{3} by infrared–infrared double resonance
View Description Hide DescriptionThe shapes of spectral lines obtained by a series of four‐level infrared–infrared double‐resonance experiments in ^{1} ^{5}NH_{3} have been used to obtain information about the collisional transfer of energy in this molecule. In these experiments a CO_{2} laser has been used to pump a near‐resonant vibration–rotation transition in the ν_{2} band while an infrared microwave sideband laser system scans a vibration–rotation transition in the 2ν_{2}←ν_{2} band. When the k quantum numbers in the pump and probe are such that Δk=3n, where n is a positive or negative integer, the probe transition is a superposition of a Gaussian part and a transferred spike. When Δk≠3n, only the Gaussian part is observed. The widths of the transferred spike for ‖Δk‖=3 and 6 transitions, which have been observed for the first time in this work, are substantially greater than the width of the spike observed for Δk=0 transitions. Theoretical expressions are given for the line shape of the transferred spike and for the ratio of the intensities of the two components of the double resonance. The line shapes have been used to estimate the root‐mean‐square change in velocity upon collision for Δk=0 and ‖Δk‖=3 transitions. The results of three‐level double resonance measurements in which a ν_{2} fundamental transition is pumped while a 2ν_{2}←ν_{2} transition is probed are also reported. The widths of the three‐level double resonance for copropagating and counterpropagating beams are significantly different and the results of simulations to reproduce the line shapes and their implications for collisional energy transfer are discussed.

Observation of collisionally transferred spikes in ^{1} ^{3}CH_{3}F by infrared–infrared double resonance
View Description Hide DescriptionThe method of infrared–infrared double resonance has been used to record the line shapes of a number of transitions in the 2ν_{3}←ν_{3} band of ^{1} ^{3}CH_{3}F by means of an infrared microwave sideband laser spectrometer while the ^{ Q } R(4,3) transition in the ν_{3} band was being pumped by constant‐frequency radiation from a CO_{2} laser operating on the 9P(32) transition. A double modulation technique was used to eliminate single‐resonance effects. The double‐resonance line shapes for a series of transitions whose lower state is the (J,3) level in the v _{3}=1 vibrational state show a transferred spike whose width is narrow for J values near 5, but slowly increases as J increases. The transferred spike is superimposed on a component of the line shape that is Gaussian with the expected Doppler width. Evidence for a transferred spike still remains for J=22. By contrast, for K≠3, there is only a Gaussian component for any J, except for J≊5, K=6, for which some evidence for a transferred spike can be seen. If the dominant selection rule for collisionally induced transitions is ΔJ=0,±1, then observation of a transferred spike for J=22 indicates some retention of velocity after as many as 17 collisions. The transferred spikes have been analyzed by a line shape function based on the Keilson–Storer collision kernel and the results have been used to estimate the root‐mean‐square value of the change in velocity upon collision.

High resolution spectroscopic detection of acetylene–vinylidene isomerization by spectral cross correlation
View Description Hide DescriptionInformation about the unimolecular acetylene (HC 3/4 CH)↔vinylidene (H_{2}C=C:) isomerization on the S _{0} energy surface has been extracted from vibrationally unassigned high resolution stimulated emission pumping (SEP) spectra of acetylene. The combination of a new pattern recognition scheme, spectral cross correlation (SCC) with complete nuclear permutation‐inversion (CNPI) group theory is shown to be a powerful new technique for characterizing bond rearrangement in highly vibrationally excited normally rigid polyatomic molecules. SCC detects isomerization ‘‘resonances’’ which destroy an approximate vibrational symmetry (e.g., the number of c i s‐bending quanta). The energies (relative to the zero point level of the stablest isomer) and widths of such resonances provide information about the ‘‘energies’’ of isomer rovibrational levels and the isomer‐level‐specific isomerization rate. Vinylidene isomerization resonances may be distinguished from ordinary acetylene Fermi or Coriolis perturbations by a unique rotational symmetry dependence due to the correlation between acetylene [D _{∞h }(M)] and vinylidene [C _{2v }(M)] levels in the CNPI group G_{8}. An SCC map of the HCCH S _{0} 15 000–15 900 cm^{−} ^{1} energy region above the zero point level was obtained by comparing SEP spectra recorded via S _{1}(Ã ^{1} A _{ u })3^{3} and 2^{1}6^{2} K _{ a }=1 intermediate levels. The predicted rotational symmetry dependence of the SCC was found between 15 410–15 640 cm^{−} ^{1}, but the vinylidene resonance line shape was obscured by Franck–Condon interference effects from well known perturbations between the 3^{3} and 2^{1}6^{2} SEP intermediate levels. It was therefore not yet possible to determine the height of the isomerization barrier (or even whether a barrier exists) but an upper bound for the vinylidene zero point level of 15 525 cm^{−} ^{1} was inferred from the SCC data.

Energy‐dependent vibrational frame transformation for electron–molecule scattering with simplified models
View Description Hide DescriptionA recent extension of the vibrational frame transformation method to allow for energy dependence of its parameters is explored through applications to model systems. Assuming the Born–Oppenheimer approximation when the incident electron moves inside the target, this method accounts for the energy dependence of body‐frame scatteringinformation by defining potential curves of the electron–molecule compound which depend on an eigenphase parameter. Escape of the scattered electron to large distances is treated by quantum defect methods. Calculations for some simple models show many realistic aspects encountered in electron–molecule scattering.

Unstable periodic orbits, recurrences, and diffuse vibrational structures in the photodissociation of water near 128 nm
View Description Hide DescriptionThe photodissociation of H_{2}O in the second absorption band (X̃→B̃) is investigated in a completely time‐dependent approach. The Schrödinger equation is solved by a time‐dependent close‐coupling method expanding the two‐dimensional wave packet in terms of free rotor states. The vibrational degree of freedom of the OH fragment is fixed and only motion on the B̃‐state potential‐energy surface is considered. The calculated absorptionspectrum exhibits a long progression of diffuse structures, ΔE∼0.1 eV, in very good agreement with the experimental spectrum. The structure is readily explained in terms of a recurrence of the autocorrelation function after about 40 fs. The recurrence, in turn, is attributed to special indirect trajectories which on the average perform one oscillation within the deep potential well before they dissociate into products H+OH. These trajections are ‘‘guided’’ by so‐called unstable periodic orbits which persist to energies high above the H+OH(^{2} Σ) threshold. The existence of unstable periodic orbits leading to a recurrence of the autocorrelation function gives, for the first time, a consistent explanation of the diffuse structure in the absorptionspectrum of H_{2} O in the second band.