Individual Rotational States Research Articles

Measurements of rotational energy transfer and quenching in OHA 2 ? +,?? = 0 at elevated temperature

Total rotational energy transfer rates have been measured at 1330 K for specific rotational levels in the OHA2σ+,υ′ = 0 state in collisions with H2O. Rotational levels ranging fromN′ = 0 to 15 were studied. Measurements were performed in the post-flame region of a stoichiometric H2/O2/He flame operating at 25 mbar. Quenching rates following excitation of individual upper rotational states were also measured. The RET and quenching rates both exhibit monotonic decreases with increasing rotational quantum number.

Dissociation dynamics of H2O(D2O) following photoexcitation at the Lyman-α wavelength (121.6 nm)

The technique of H(D) atom photofragment translation spectroscopy has been used to investigate the collision free photodissociation of jet cooled H2O(D2O) molecules following excitation to their B̃(1A1) excited state at 121.6 nm. The resolution of the total kinetic energy release spectrum obtained with this technique, allows assignment of the eigenvalues for the individual rotational quantum states and an estimation of the respective quantum state population distributions for the nascent OH(X 2Π) and OH(A 2Σ+) photofragments (and their deuterated analogs). This provides us the first experimental observations of high angular momentum states of OD(X). Analysis of the quantum state population distribution show both the ground (X 2Π) and electronically excited (A 2Σ+) OH(OD) fragments to be formed with little vibrational excitation but with highly inverted rotational distributions. Spectral simulation enables estimation of relative branching ratios for these two dissociation channels, and for the three-body fragmentation yielding ground state atoms. The observed energy disposal has been rationalized by considering the motion of a wavepacket launched on the B̃ state surface at a geometry corresponding to the ground state equilibrium configuration. Electronically excited OH(OD) fragments result from that fraction of the photoexcited molecules that dissociate on the B̃ state surface; their rotational excitation results from the marked angular anisotropy of the B̃ state surface. Ground state OH(OD) fragments can arise as a result of radiationless transfer to the lower Ã(1B1) or X̃(1A1) surfaces. The wavepacket calculations show that B̃■X̃ transfer via the conical intersection linking these two surfaces leads to the most highly rotationally excited OH(OD) fragments. These calculations also show that the contribution made by B̃■Ã radiationless transfer to the overall rotational distribution in the ground state OH(OD) fragments scales with the amount of a-axis rotational excitation in the photoexcited molecules: The detailed form of the OH(OD) product state population distribution is thus predicted to be temperature dependent.

Hyperfine quantum beats in C 2N 2

Molecular quantum beats are observed in the isotropic fluorescence decay following laser excitation of individual rotational states of C 2N 2 via the vibronically allowed 4 1 0 Ã( 1Σ − u)←X̃( 1Σ + g) transition near 219 nm. Strong quantum beats occur with selective excitation, by both P- and R-branch transitions, of over a dozen rotational states. Observations of hyperfine quantum beats following excitation of the N′ = 12 rotational level yield estimates of spin—orbit coupling matrix elements, Born-Oppenheimer state separations, and magnetic and quadrupolar hyperfine coupling constants. Observations of Zeeman splitting establish that the three hyperfine levels of N′ = 12 are coupled to those of a single triplet state.

Bond breaking without barriers: Photofragmentation of ketene at the singlet threshold

Ketene (CH2CO) in a supersonic free jet was photodissociated by a tunable pulsed laser in the frequency range just above the threshold for production of singlet methylene, CH2 (ã 1A1). CH2 was detected by laser-induced fluorescence (LIF). The appearance threshold and yield curve of individual 1CH2 rotational states were obtained by scanning the photolysis laser frequency with a fixed LIF probe laser frequency. The dissociation occurs on the ground electronic state potential energy surface. The threshold for CH2CO→1CH2+CO is found to be 30 116.2±0.4 cm−1. By varying the delay between the photolysis and probe pulses, a lower bound of 7×107 s−1 was set for the dissociation rate on the triplet surface at the singlet energy threshold. The yield curves, or photofragment excitation (PHOFEX) spectra, exhibit sharp steps spaced by the CO rotational term values. The experimental data provide a rigorous test of theoretical models of photofragment dynamics. The data clearly show that nuclear spin is conserved through the photodissociation. PHOFEX curves calculated from phase space theory (PST) are in excellent agreement with the experiment and show that there is no barrier along the reaction coordinate. The singlet/triplet branching ratio as a function of photolysis laser frequency is inferred from PST fits to the PHOFEX data. Comparisons with the statistical adiabatic channel model (SACM) are also presented. The data show that the only dynamical constraints on product state rotational energy distributions are conservation of energy, angular momentum, and nuclear spin.

Scattering of NO from Ag(111): a model system for probing gas-surface inelastic collision dynamics

The suitability of the NO molecule for laser detection and the relatively inert nature of the Ag(111) surface have resulted in extensive studies of the state-to-state inelastic scattering dynamics of this system. This work is critically reviewed, beginning with experiments by McClelland et al and by Kleyn et al, who reported the rotational distributions of the scattered molecules, the latter group making the first observation of rotational rainbows in gas-surface scattering. More recently, velocity distributions have been determined for individual rotational states of molecules scattered into specific directions, allowing a full accounting of the disposal of initial kinetic energy and momentum of molecules incident on the surface. These results, combined with trajectory studies using simple and realistic potentials have led to a detailed understanding of the dynamics of rotational excitation and of energy transfer to photons.

State-resolved investigation of the dynamics of scattering and formation of NO at Ge surfaces

A combination of resonantly enhanced two-photon ionization and time-of-flight (REMPI-TOF) spectroscopy was applied to determine the translational energy distributions of NO molecules in individual rotational states coming off clean or oxidized Ge surfaces, either as a consequence of scattering of a NO molecular beam or of formation in the surface reaction NO 2 + Ge → NO + GeO. The incident supersonic molecular beam exhibited a narrow translational energy distribution with E kin,i > being variable between 0.1 and 0.8 eV and was rotationally cold so that the scattering experiments represent a good approximation to true state selectivity. The two channels of trapping/desorption and direct-inelastic scattering can be clearly resolved from each other in the TOF spectra if the incident kinetic energy is greater than 700 meV. The thermal desorption channel exhibits Boltzmann distributions for translation and rotation, with E trans,f > independent of E rot . At a surface temperature of T s - 550 K the translational energy of the desorbing particles amounts only to about 80% of T s . This effect of “translational cooling in desorption” supplements previous observations in the same system of a similar effect, “rotational cooling”. In direct-inelastic scattering the rotational state population exhibits a pronounced “rotational rainbow” effect. Those molecules which are rotationally excited in the collision transfer less of their kinetic energy to the solid. Semi-quantitative description of this effect is achieved by application of a simple classical model of non-spherical molecules bouncing off a surface. NO molecules formed in the exothermic decomposition of NO 2 differ to some extent with respect to their rotational and translational energy distributions from thermally desorbing particles, but there is no indication that a substantial fraction of the large excess energy ( ~ 2 eV) is carried away into the gas phase which is instead transferred to the heat bath of the solid.

On the applicability of the molecular-mechanical force field (MM2) scheme to the gauche oxygen effect characteristic of glycol ethers such as 1,2-dimethoxyethane, 1,2-dimethoxypropane and 1,2-dimethoxy-2-methylpropane

MM2 calculations have been carried out for a series of glycol ethers such as 1,2-dimethoxyethane (DME), 1,2-dimethoxypropane (DME) and 1,2-dimethoxy-2-methylpropane (DMMP). For DME, in accordance with the results of Baldwin [11], the observed energy of the gauche state ( E σ = −0.5 kcal mol −1) for the OCCO bond is found to be approximately reproduced by the calculation when the dipole—dipole interaction term is suppressed by adopting a relatively large dielectric constant (ϵ eff = 7.5). With the same value of ϵ eff, the gauche energy of DMMP is calculated to be Eψ = —0.9 kcal mol −1, which is at variance with the observed value of 0.5 kcal mol −1. In DMP, the two gauche forms around the OCCO bond are non-equivalent, and the stability of the conformers varies in the order g α &>; t &>; g ß. These experimental observations were not produced by the calculation. The MM2 program failed, in the state of the art, to provide an adequate explanation for the gauche oxygen effect observed in the aboved-mentioned glycol ethers as well as in there polymer analogs. It is pointed out that inclusion of an empirical correction term in the torsional potential for the individual rotational states offers a simple amendment which serves for practical purposes.

Time evolution of individual rotational states after pulsed Doppler-free two-photon excitation: Influence of perturbations in S1 benzene

Single rovibronic level excitation has been demonstrated for a molecule representing the statistical limit of a nonradiative electronic relaxation process. Resolution of the complex 1410 two-photon band of benzene was possible after elimination of the Doppler broadening in a Doppler-free two-photon absorption process with narrow bandwidth pulsed laser light and allowed for selective excitation of individual rotational states. Fluorescence decay measurements of these states under low pressure conditions display a pure exponential behavior and reveal that the nonradiative rate is independent of the rotational quantum numbers J, K for an electronic nonradiative relaxation process in the statistical limit. The decrease in lifetime found for perturbed states is attributed to the mixing with a background state containing quanta of an accepting mode.

Dissociation on ground-state potential-energy surfaces

Two new techniques allowing for the resolved spectral study of dissociation on ground-state potential-energy surfaces are presented. First, Stark level-crossing spectra of highly vibrationally excited ground-state formaldehyde (S*0) characterize the initial rovibrational wavefunctions of dissociative formaldehyde states. Individual S*0 D2CO states are resolved near the barrier to dissociation but broaden and overlap at higher energies. Neighbouring resolvable states possess enough individual vibrational character to vary by over one order of magnitude in lifetime. A potential barrier height of 78.0–81.1 kcal mol–1 has been determined for H2CO → H2+ CO dissociation. Second, photofragment excitation (PHOFEX) spectra probe the production of correlated fragment states from ketene photodissociation. Molecular-beam PHOFEX spectra show that ketene possesses no observable rotational structure and only weak vibrational structure. The PHOFEX spectrum of an individual rotational state of the lowest vibronic state of singlet methylene gives the energetic threshold for formation of that state along with ground-state CO. The threshold for the combination with each successive CO(v″= 0, J″) channel is clearly resolved. A statistical calculation reproduces the main features of the PHOFEX spectra. Analysis of the PHOFEX spectra gives a H2CCO →1CH2+ CO dissociation threshold of 30 102 ± 15 cm–1. Finally, the effect of a potential barrier in the dissociation coordinate on statistical vs. dynamical control of dissociation is discussed.

Vibrational overtone predissociation spectroscopy of hydrogen peroxide

Vibrational overtone predissociation spectroscopy, which detects the products of a unimolecular reaction initiated by overtone vibration excitation as a function of wavelength, is an informative means of studying highly vibrationally excited molecules. The spectrum, obtained by varying the excitation laser wavelength while keeping the probe laser tuned to interrogate a single product state, mirrors the overtone vibration absorption spectrum of those molecules that decompose into the detected quantum state. Using this technique to detect individual rotational states of the OH fragments from hydrogen peroxide excited in the regions of the third to the fifth OH stretching overtone (4νOH, 5νOH, 6νOH) reveals coarse and fine vibrational structure in the spectrum. A vibration-torsion model, in which the high frequency OH stretching vibration and the low frequency torsional vibration are separated adiabatically, recovers the observed transition wave numbers and intensities and predicts previously unobserved transitions. Because the measurements probe individual product quantum states, the excitation spectrum also depends on the partitioning of the products among their states. This appears as a variation in the intensity of different transitions with the product state that is probed, and a statistical model of the unimolecular decomposition in combination with the vibration-torsion model of the absorption spectrum explains the dependence of the overtone vibrational predissociation spectra on the probed rotational state of the OH product.

Rotational energy transfer in HF(v=2): Energy corrected sudden approximation scaling relations applied to double resonance measurements

Applying scaling relations based on the energy corrected sudden (ECS) approximation to a large set of laser double resonance measurements of HF self-relaxation allows the time evolution of individual rotational states from J′=2 to 6 to be described by only a few fitting parameters and permits extraction of state-to-state energy transfer rate constants. Obtaining a qualitatively correct description of the data requires inclusion of a significant (∼25%) multiple rotational quantum pathway (‖ΔJ‖≥2). The ECS approximation based scaling relation seems to provide a better description of the rotational energy transfer for high rotational levels (J′=5 and 6) than do relations based solely on energy defect. Comparing the double resonance results to those of linewidth analysis shows differences that may arise from the sensitivity of the measurements to different aspects of the energy transfer dynamics. Extrapolating the rate constants obtained by fitting the double resonance data on low rotational levels (J′≤6) yields good agreement with recent independent measurements on J′=11 to 14 in HF(v=0).

Dissociative excitation of water by metastable argon

The reaction Ar( 2P 2,0) + H 2O → Ar + H + OH(A 2Σ +)was studied in crossed molecular beams by observing the luminescence from OH(A 2Σ +). No significant dependence of the spectrum on collision energy was found over the 22–52 meV region. Spectral simulation was used to obtain the OH(A) vibrational distribution and rotational temperature, assuming a Boltzmann rotational distribution. Since predissociation is known to strongly affect the rovibrational distribution, the individual rotational state lifetimes were included in the simulation program and were used to obtain the average vibrational state lifetimes. Excellent agreement with experiment was obtained for vibrational population ratios N 0/ N 1/ N 2 of 1.00/ 0.40/0.013 and a rotational temperature of 4000 K. Correction for the different average vibrational lifetimes gave formation rate ratios P 0/ P 1/ P 2 of 1.00/0.49/0.25. The differences between these results and those from flowing afterglow studies on the same system are discussed. Three reaction mechanisms are considered, and the vibrational prior distributions are calculated from a simple density-of-states model. Only fair agreement with experiment is obtained. The best agreement for the mechanisms giving OH(A) in two 2-body dissociation steps is obtained by assuming 1.0 eV of internal energy remains in the second step. The OH(A) vibrational population distribution of the present work is similar to that found in the photolysis of H 2O at 122 nm, where there is 1.10 eV of excess internal energy.

Radiative lifetimes of OH(A 2Σ) and Einstein coefficients for the A-X system of OH and OD

Radiative lifetimes of individual rotational states of OH( A 2Σ) were observed using a delayed coincidence technique. The values obtained were scaled to a theoretical functional form to give τ rad( A 2Σ, v = 0, N = 1, J = 3 2 = 686 ± 14 ns. Einstein A and B coefficients for the A- X system of OH and OD were computed, using numerical integrals of a transition moment of the form Re( r) = 3.75 × 10 -30 (1-0.75 r) C … m and vibrational wavefunctions obtained from numerical solutions of the radial Schrödinger equations (including centrifugal terms) for RKR potentials for the two electronic states. Matrix elements in Hund's case b were transformed to intermediate coupling for the X state to yield proper oscillator strengths for computation of the Einstein coefficients. Tables of the A and B coefficients for the 0-0 vibrational transitions are included. Extended tables are available on microfiche or microfilm from the authors.

Beam maser rotational relaxation measurements on OCS

Rotational relaxation cross section measurements were made for J = 0, 1 and 2 rotational states of OCS using a beam maser spectrometer. Individual rotational states were selected using electrostatic fields and cross sections for scattering and relaxation of these states by polar and non-polar scattering gasses were obtained. The angular resolution was carefully controlled so that cross sections can be compared for the different rotational states. An analysis of dipolar contributions to scattering cross sections in terms of relaxation matrix elements is presented and this is consistent with some of the observed differences in pure-states cross sections.

Rotational relaxation of molecular nitrogen in a freely expanding jet

In connection with the assumption about the possibility of producing a gasdynamic laser at rotational transitions of diatomic molecules (1, 2] and a gasdynamic condense-laser by using the phenomenon of condensation to produce the population inversion [3–5], a quantitative description of the kinetics of the rotational relaxation of the simplest diatomic molecules is necessary. In contrast to the traditional approach in gasdynamics and the theory of transport processes, when one parameter (the rotational relaxation time) is used in the description of rotational relaxation, a substantially more detailed description at the population level of the individual rotational states is required in solving spectroscopy and laser physics problems. This paper is devoted to a theoretical and experimental investigation of the rotational relaxation of nitrogen in a free, low density jet under conditions when a substantial nonequilibrium holds in the rotational level populations. On the basis of representations developed earlier [1, 6], a model is constructed for a relaxing gas which yields the magnitude of the population of individual rotational levels. The selection of a molecular nitrogen free jet as a subject for investigation is explained by the fact that the gasdynamics of such a flow has been studied well [7]. Moreover, at this time diagnostic methods have been developed to determine the molecule concentrations at many (k≤20) rotational levels [8]; hence, a jet is a good object on which a detailed comparison between theory and experiment can be made, as is done in this paper. Separation of the translational and rotational relaxation processes is allowed in the theoretical description of the flow with relaxation studied in this paper on the basis of the fact that the buildup of a Maxwell molecule velocity distribution because of elastic collisions occurs more rapidly than the redistribution of molecules at the rotational levels because of inelastic collisions. Such an approach is apparently valid for molecular hydrogen with a large value of the rotational quantum [9]. A model with separation of the processes is hypothetical for nitrogen molecules whose rotational constant is ≈ 1/20 that for hydrogen, and is confirmed in this paper by comparing computations with experiment. It is hence assumed that rotational relaxation proceeds in an N2 molecule stream with a known temperature, density, and velocity distribution obtained from measurements.

Quantum-resolved dynamics of excited states. Part 2.—Stable levels of the B3Π(0+) state of BrF

The stable, lower vibrational levels (v′⩽ 6) of the excited B3Π(0+) state of 79BrF have been investigated. Laser induced fluorescence has been used to identify individual vibrational and rotational states, as well as to determine their zero-pressure lifetimes τ0 involving the B3Π(0+)–X1Σ+ transition.As a result of this and other work, the vibrational and rotational energies of all accessible states in the B3Π(0+) manifold of 79BrF are known, and a detailed knowledge of the variation of τ0 with v′ and J′ has been obtained. For levels v′⩽ 6, all states are essentially unperturbed, with non-collisional lifetimes τ0 in the range (26.8 ± 2.1) to (40.6 ± 6.9)µs.

A Discussion on photoelectron spectroscopy - Angular distributions and intensity in molecular photoelectron spectroscopy I. General theory for diatomic molecules

A theory of the angular distribution of photoelectrons ejected with a given energy from diatomic molecules is presented. The differential cross-section OO is of the form a = ^ [l+ /JP ,(co»® )] where O Total is the total cross-section, B an anisotropy parameter and O the angle between the polarization vector of the incident light and the direction of the photoelectron. Expressions for O total and B in terms of internal transition dipole moments are obtained for transitions between individual rotational states of the molecule and ion, for either of Hund’s cases (a) or (b) . The formulae have been developed for central-field bases for the eigenstates of the electron before and after ionization. When rotational structure in the photoelectron spectrum is unresolved the angular distribution is independent of the choice of Hund’s case

Measurement of the Lifetime of theAΠ1State of CO by Level-Crossing Spectroscopy

The lifetime of the $v=2$ level of the $A^{1}\ensuremath{\Pi}$ state of CO has been measured by molecular level-crossing spectroscopy. Unlike previous experiments with molecules in which the Hanle effect has been analyzed for individual rotational states, the present results are obtained from analysis of the composite level-crossing signal from all of the rotational states which are excited by the entire $A\ensuremath{\rightarrow}X(2, 0)$ resonance band. Our experimental result is $\ensuremath{\tau}(v=2)=9.0\ifmmode\pm\else\textpm\fi{}1.0$ nsec in good agreement with Hesser's value of 10.5 \ifmmode\pm\else\textpm\fi{} 1.0 nsec obtained from phase-shift experiments.

Metastability of Rotationally Hot Dihelium at 77° K

WE report here the detection by kinetic absorption spectroscopy of He2 (a3Σu+(σ=0)) produced in the gas phase at 77° K with an intense microwave pulse discharge. Although vibrationally cold, at this temperature the molecules exhibit an extremely non-equilibrium distribution in the high rotational states, which show only a minor degree of relaxation during their lifetime of 10−4 sec with total helium pressures up to 100 mm. The observations appear to constitute a unique example, as yet, in which the absorption spectrum of a rotationally hot molecule yields relative reaction rates into individual rotational states. It is suggested that the observed rotational distributions of He2 (a3Σu+) may reveal the states of He2+ (X2Σu+) from which it is formed.

THE HYDROGEN–CHLORINE SYSTEM IN THE MM PRESSURE RANGE II. THE VIBRATIONAL GROUND STATE STUDIED BY SELF-ABSORPTION

Studies of energy distribution among reaction products, through the agency of infrared chemiluminescence, have previously only yielded information concerning the distribution among vibrationally excited states. In the work described here it was shown that self-absorption of the infrared emission could be used as a measure both of the relative and the absolute amount of product present in the vibrational ground state, ν = 0. Two independent methods were used to measure the extent of self-absorption. The first method relied on measurements of an apparent deviation from Boltzmann-type rotational intensity distribution within the ν(1–0) and ν(2–1) bands. The second method depended on measurements of an apparent deviation of the relative intensity of corresponding H35Cl and H37Cl isotopic lines from the natural abundance ratio. (It was shown, at the same time, that the isotopic reactions H + 35Cl2 → H35Cl + 35Cl and H + 37Cl2 → H37Cl + 37Cl have the same rate constant, within ±10%). A third method of measuring the extent of self-absorption, which depends on the detection of an anomaly in the relative intensity of P- and R-branch emission lines is discussed.The self-absorption method was applied to the study of the hydrogen–chlorine system in the 1–2 mm Hg pressure range (see also Part I). Mean partial pressures of HClν=0 ~ 10−2 mm Hg were measured in individual rotational states to an accuracy of ca. ±10%, using an optical path length of 20 cm. The rotational distribution in ν = 0 corresponded to a temperature of 1150 ± 150 °K (the uncertainty in this figure encompasses two independent methods of estimating the self-absorption), as compared with 1300 ± 100 °K for all vibrationally excited states (Part I).