Level‐to‐level vibrationally inelastic rate constants for Li2* –X (X=He, Ne, Ar, Xe) collisions

Direct observation of coherence transfer and rotational-to-vibrational energy exchange in optically centrifuged CO2 super-rotors

Optical centrifuges are laser-based molecular traps that can rotationally accelerate molecules to energies rivalling or exceeding molecular bond energies. Here we report time and frequency-resolved ultrafast coherent Raman measurements of optically centrifuged CO₂ at 380 Torr spun to energies beyond its bond dissociation energy of 5.5 eV (J_max = 364, E_rot = 6.14 eV, E_rot/k_B = 71, 200 K). The entire rotational ladder from J = 24 to J = 364 was resolved simultaneously which enabled a more accurate measurement of the centrifugal distortion constants for CO₂. Remarkably, coherence transfer was directly observed, and time-resolved, during the field-free relaxation of the trap as rotational energy flowed into bending-mode vibrational excitation. Vibrationally excited CO₂ (ν₂ > 3) was observed in the time-resolved spectra to populate after 3 mean collision times as a result of rotational-to-vibrational (R-V) energy transfer. Trajectory simulations show an optimal range of J for R-V energy transfer. Dephasing rates for molecules rotating up to 5.5 times during one collision were quantified. Very slow decays of the vibrational hot band rotational coherences suggest that they are sustained by coherence transfer and line mixing.

State-resolved rotational distributions and collision dynamics of CO molecules made in a tunable optical centrifuge

State-resolved distributions and collision dynamics of optically centrifuged CO molecules with orientated angular momentum are investigated by probing the CO J = 29-80 rotational levels using high-resolution transient IR absorption spectroscopy. An optical centrifuge with tunable bandwidth is used to control the extent of rotational excitation in the sample. The rotational distributions are inverted with a maximum population in J = 62. Rotational levels with J > 62 have populations that correlate with the intensity profile of the optical trap. The full bandwidth trap excites CO up to the J = 80 level, while J = 67 is the highest level observed in the reduced bandwidth trap. Polarization-sensitive transient spectroscopy shows that the initial orientational anisotropy is r = 0.8 for levels with J ≥ 55, while anisotropy values are near r = 0.4 for levels with J < 50. The rotational distribution for J > 50 is broadened slightly by collisions, consistent with small |ΔJ| propensity rules for rotational energy transfer. Doppler-broadened line profiles show that the J = 60-80 levels have translational temperatures near T_trans = 300 K and that these temperatures remain constant for as much as 24 gas kinetic collisions. Doppler linewidths for levels with J < 60 are broadened by non-resonant rotation-to-translation energy transfer. Kinetic analysis of transient signals shows that collisions with thermal bath molecules are the predominant relaxation pathway.

Rotational Energy Transfer in Highly Excited States of Lithium Dimer: Experiment and Modeling

We report level-resolved rate coefficients for collision-induced rotational energy transfer in the ⁷Li₂^*-Ne system, with ⁷Li₂^* in the highly electronically excited E(3)¹Σ_g⁺(v_i = 4, j_i = 31) and F(4)¹Σ_g⁺(v_i = 10, j_i = 31) states. The distributions of rate coefficients are strikingly different from those previously measured for the A(1)¹Σ_u⁺(v_i = 2-24, j_i = 30) state of the same molecule, falling off much more rapidly with increasing rotational quantum number change |Δj|. The reason for the difference was explored by means of an inverse Monte Carlo approach employing classical trajectories and a model potential, which was adjusted to give agreement with experiment. The modeling strongly suggests that the E and F state interaction potentials are much more nearly isotropic than that of the A state. The resulting dramatic reduction in rate coefficient, especially for large |Δj|, may be relevant in the relaxation of gases at high temperatures.

Rotationally inelastic collisions of excited NaK and NaCs molecules with noble gas and alkali atom perturbers

We report measurements of rate coefficients at T ≈ 600 K for rotationally inelastic collisions of NaK molecules in the 2(A)¹Σ⁺ electronic state with helium, argon, and potassium atom perturbers. Several initial rotational levels J between 14 and 44 were investigated. Collisions involving molecules in low-lying vibrational levels (v = 0, 1, and 2) of the 2(A)¹Σ⁺ state were studied using Fourier-transform spectroscopy. Collisions involving molecules in a higher vibrational level, v = 16, were studied using pump/probe, optical-optical double resonance spectroscopy. In addition, polarization spectroscopy measurements were carried out to study the transfer of orientation in these collisions. Many, but not all, of the measurements were carried out in the "single-collision regime" where more than one collision is unlikely to occur within the lifetime of the excited molecule. The analysis of the experimental data, which is described in detail, includes an estimate of effects of multiple collisions on the reported rate coefficients. The most significant result of these experiments is the observation of a strong propensity for ΔJ = even transitions in collisions involving either helium or argon atoms; the propensity is much stronger for helium than for argon. For the initial rotational levels studied experimentally, almost all initial orientation is preserved in collisions of NaK 2(A)¹Σ⁺ molecules with helium. Roughly between 1/3 and 2/3 of the orientation is preserved in collisions with argon, and almost all orientation is destroyed in collisions with potassium atoms. Complementary measurements on rotationally inelastic collisions of NaCs 2(A)¹Σ⁺ with argon do not show a ΔJ = even propensity. The experimental results are compared with new theoretical calculations of collisions of NaK 2(A)¹Σ⁺ with helium and argon. The calculations are in good agreement with the absolute magnitudes of the experimentally determined rate coefficients and accurately reproduce the very strong propensity for ΔJ = even transitions in helium collisions and the less strong propensity for ΔJ = even transitions in argon collisions. The calculations also show that collisions with helium are less likely to destroy orientation than collisions with argon, in agreement with the experimental results.

Quantum state-resolved, bulk gas energetics: Comparison of theory and experiment

Until very recently, the computational model of state-to-state energy transfer in large gas mixtures, introduced by the author and co-workers, has had little experimental data with which to assess the accuracy of its predictions. In a novel experiment, Alghazi et al. [Chem. Phys. 448, 76 (2015)] followed the equilibration of highly vibrationally excited CsH(D) in baths of H2(D2) with simultaneous time- and quantum state-resolution. Modal temperatures of vibration, rotation, and translation for CsH(D) were obtained and presented as a function of pump-probe delay time. Here the data from this study are used as a test of the accuracy of the computational method, and in addition, the consequent changes in bath gas modal temperatures, not obtainable in the experiment, are predicted. Despite large discrepancies between initial CsH(D) vibrational states in the experiment and those available using the computational model, the quality of agreement is sufficient to conclude that the model's predictions constitute at least a very good representation of the overall equilibration that, for some measurements, is very accurate.

State-to-state, multi-collision, energy transfer in H-H2 gas ensembles

We use our recently developed computational model of energy flow in gas ensembles to study translation-to-internal energy conversion in an ensemble consisting of H2(0; 0) in a bath of H atoms. This mixture is found in plasmas of industrial importance and also in interstellar clouds. The storage of energy of relative motion as rovibrational energy of H2 represents a potential mechanism for cooling translation. This may have relevance in astrophysical contexts such as the post-recombination epoch of the early universe when hydrogenic species dominated and cooling was a precondition for the formation of structured objects. We find that conversion of translational motion to H2 vibration and rotation is fast and, in our closed system, is complete within around 100 cycles of ensemble collisions. Large amounts of energy become stored as H2 vibration and a tentative mechanism for this unequal energy distribution is suggested. The "structured dis-equilibrium" we observe is found to persist through many collision cycles. In contrast to the rapidity of excitation, the relaxation of H2(6; 10) in H is very slow and not complete after 10(5) collision cycles. The quasi-equilibrium modal temperatures of translation, rotation, and vibration are found to scale linearly with collision energy but at different rates. This may be useful in estimating the partitioning of energy within a given H + H2 ensemble.

Temperature dependence of OH(8;6) equilibration in an air-like gas ensemble

We present a quantum state-resolved computational investigation of the equilibration of rovibrationally excited OH, present as the minor component in an air-like mixture of N(2) and O(2), over the temperature range 100-1200 K. Generic features of the equilibration that are present over the entire range are identified, and the increase in speed of the principal energy exchange mechanism as the temperature increases is quantified. The data demonstrate that partitioning of excess energy and angular momentum among the modes of the three different molecules is independent of the magnitude of excess energy and of its form. The rotational temperature of OH is found to vary widely over the equilibration process, varying with number of collision cycles and with initial temperature. However, at equilibration, the rotational temperature of OH is invariably the lowest of all modes of all three species present in the ensemble. This suggests that rotational temperatures of OH obtained from rotational state populations are unlikely to provide a reliable guide to other modal temperatures in ensembles of the kind we consider.

Collisional transfer of population and orientation in NaK

Collisional satellite lines with |ΔJ| ≤ 58 have been identified in recent polarization spectroscopy V-type optical-optical double resonance (OODR) excitation spectra of the Rb(2) molecule [H. Salami et al., Phys. Rev. A 80, 022515 (2009)]. Observation of these satellite lines clearly requires a transfer of population from the rotational level directly excited by the pump laser to a neighboring level in a collision of the molecule with an atomic perturber. However to be observed in polarization spectroscopy, the collision must also partially preserve the angular momentum orientation, which is at least somewhat surprising given the extremely large values of ΔJ that were observed. In the present work, we used the two-step OODR fluorescence and polarization spectroscopy techniques to obtain quantitative information on the transfer of population and orientation in rotationally inelastic collisions of the NaK molecules prepared in the 2(A)(1)Σ(+)(v' = 16, J' = 30) rovibrational level with argon and potassium perturbers. A rate equation model was used to study the intensities of these satellite lines as a function of argon pressure and heat pipe oven temperature, in order to separate the collisional effects of argon and potassium atoms. Using a fit of this rate equation model to the data, we found that collisions of NaK molecules with potassium atoms are more likely to transfer population and destroy orientation than collisions with argon atoms. Collisions with argon atoms show a strong propensity for population transfer with ΔJ = even. Conversely, collisions with potassium atoms do not show this ΔJ = even propensity, but do show a propensity for ΔJ = positive compared to ΔJ = negative, for this particular initial state. The density matrix equations of motion have also been solved numerically in order to test the approximations used in the rate equation model and to calculate fluorescence and polarization spectroscopy line shapes. In addition, we have measured rate coefficients for broadening of NaK 3(1)Π ← 2(A)(1)Σ(+)spectral lines due to collisions with argon and potassium atoms. Additional broadening, due to velocity changes occurring in rotationally inelastic collisions, has also been observed.

Equilibration of vibrationally excited OH in atomic and diatomic bath gases

In this work, a computational model of state-to-state energy flow in gas ensembles is used to investigate collisional relaxation of excited OH, present as a minor species in various bath gases. Rovibrational quantum state populations are computed for each component species in ensembles consisting of 8000 molecules undergoing cycles of binary collisions. Results are presented as quantum state populations and as (approximate) modal temperatures for each species after each collision cycle. Equilibration of OH is slow with Ar as the partner but much faster when N(2) and/or O(2) forms the bath gas. This accelerated thermalization is shown to be the result of near-resonant vibration-vibration transfer, with vibrational de-excitation in OH matched in energy by excitation in bath molecules. Successive near-resonant events result in an energy cascade. Such processes are highly dependent on molecule pair and on initial OH vibrational state. OH rotational temperatures initially increase, but at equilibration, they are lower than those of other modes. Possible reasons for this observation in molecules such as OH are suggested. There are indications of an order of precedent in the equilibration process, with vibrations taking priority over rotations, and potential explanations for this phenomenon are discussed.

Three-dimensional sliced fluorescence imaging in bulbs

To study dynamic behaviors of molecular photodissociation processes and photoinitiated inelastic and reactive collisions in a bulb environment, a three-dimensional sliced fluorescence imaging method has been developed. This experimental method combines the sliced fluorescence imaging techniques and a double resonance spectroscopic detection scheme to acquire the central slice of state-selected Newton spheres of scattering products. To illustrate the essence and simplicity of the present method, experimental images of state-selected CN photofragments from the ICN photodissociation are presented. For other chemically significant product species with a single fluorescent excited state, an infrared-optical double resonance detection scheme warrants the present technique a general method in the study of dynamic processes in bulbs.

Nearly resonant multidimensional systems under a transient perturbative interaction

We analyze the response of a classical system with N>or=2 internal degrees of freedom satisfying R<or=(N-1) approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise N-R adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.

Absolute level-resolved reactive and inelastic rate constants in Li+Li2*

We have used nuclear parity-changing collisions to obtain absolute level-to-level rate constants for reactive scattering in a triatomic system with identical nuclei. We have determined rate constants for the system (7)Li(2) (*)(A (1)Sigma(u) (+))(v(i)=2,j(i)=19)+(7)Li-->(7)Li+(7)Li(2) (*)(A (1)Sigma(u) (+))(v(f),j(f)), from laser-induced fluorescence spectra of lithium vapor in a heat pipe oven. Parity-preserving collisions yielded measurements of absolute rotationally and vibrationally inelastic rate constants as well. We compare the reactive rate constants with statistical prior distributions and the inelastic results with previously measured results on the Ne+(7)Li(2) (*) system.

Quasiresonance: switching internal energy transfer on and off

Quasiresonance involves a slow "external" switching on and off of an interaction between internal degrees of freedom described by action-angle variables having approximate resonances. The resonances or near-resonances spawn slow coordinates that fail to be adiabatic, but the remaining coordinates may be fast enough to have conserved actions. The interaction either can be imposed externally as a time dependent coupling or can arise autonomously due to interactions with other degrees of freedom. A resonance transformation into slow and fast angles reveals the action corresponding to the fast angle is adiabatic and conserved to very high accuracy. This paper extends our work on quasiresonance to new systems and regimes, including the He-H2 system, collisions with a periodic lattice, perturbative interactions, and discussion of quasiresonance in higher dimensional systems.

Exit Routes from the Transition State: Angular Momentum Constraints on the Formation of Products

We have analyzed experimental data from a number of exothermic processes in which molecules in well-defined initial states are deactivated by inelastic, dissociative, or reactive collisions. Further, we analyze deactivation processes that do not occur in molecules despite their containing high levels of excitation. Significant common elements are found among these forms of deactivation. The initial step consists of transition to a product state involving minimum rotation state change (Delta j) consistent with energy conservation. Frequently, this process is near-energy-resonant. More critically, it may frequently require substantial angular momentum (AM) change. Analysis of experimental data indicates that constraints act upon on the formation of products in processes that involve release of excess energy. These constraints are associated with the magnitude of AM that must be generated for the initial transition to occur and this AM "load" increases with the amount of energy to be released. In general, the probability of generating rotational AM falls rapidly as Delta j increases, and this effectively limits the size of energy gap that may be bridged by a given reactant pair and at some point the constraint is sufficient to constitute a barrier that prevents the process from taking place. The choice of reactant species strongly affects the probability of each process that increases (i) when molecules efficiently interconvert momentum and (ii) when many product states are available in the critical near-resonant region. These factors increase the proportion of initial trajectories that possess the energy and momentum necessary to open a "product" channel. Evidence is presented showing that AM load-reduction strategies lead to marked enhancement of rates of collision-induced processes, suggesting that reduction of constraints in the exit channels from the transition state may constitute a previously unrecognized form of catalysis.