Selection rules for collisional energy transfer in homonuclear diatomics. rotationally inelastic collisions

We have made a precise study of the circular polarisation of rotationally resolved features of laser-excited iodine. The J′ = 19, ν′ = 16 level of ³II⁺_ou was excited using circularly polarised dye-laser fluorescence and a quantitative data on polarisation features representing inelastic transfer of ΔJ′ = 30 was recorded. The experimental circular polarisation ratios were compared to those predicted by two totally conserving models, ΔM = 0 and Δθ = 0. The agreement between experimental points and the predictions based on the former lead to the formation of a new selection due on rotationally inelastic transfer namely, ΔM = 0.     

Relaxation of internal energy and collisional energy transfer

Using the exponential model for the collisional transition probability, it is shown that relaxation of average internal energy is a measure of bulk-average energy transfer ?ΔE?. This is a macroscopic property which is a complicated function of both time and initial excitation and is only distantly related to average energy transferred per collision ?ΔE?, a microscopic property.     

Measurements of collisional energy transfer in unimolecular processes

It is shown that the optimal means of tabulating collisional energy transfer parameters in gas-phase uni- and ter-molecular reactions is as the average downward energy transfer, rather than the total energy transferred or the collision efficiency.     

Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.     

Kinetically controlled selective ionization study on the efficient collisional energy transfer in the deactivation of highly vibrationally excited trans-stilbene

Direct measurements of the gas-phase collisional energy transfer parameters are reported for the deactivation of highly vibrationally excited trans-stilbene molecules, initially prepared with an average energy of about 40 000 cm(-1), in the bath gases argon, CO2, and n-heptane. The method of kinetically controlled selective ionization (KCSI) has been used. Complete experimental collisional transition probability density functions P(E',E) are determined, which are represented by a monoexponential form with a parametric exponent in the argument, P(E',E) proportional to exp[-{(E - E')/(C0 + C1E)}Y] (for downward collisions), well established from earlier KCSI studies. A comparison of the first moments of energy transfer rate constants, kE,1, or of resulting first moments of energy transfer, , for trans-stilbene with those for azulene and toluene clearly shows the considerably more efficient deactivation of trans-stilbene for all bath gases, presumably due to the much greater number of very low-frequency modes of trans-stilbene. However, on a relative scale this gain in deactivation rate of excited trans-stilbene is clearly collider dependent and decreases distinctly with the growing collision efficiency of the larger bath gas molecules.     

M-dependence of collisional transfer of rotational energy in methanol

An M-resolved microwave double resonance experiment on methanol is described. Relative signal intensities and M-selection rules in pure CH₃OH are consistent with a dipole—dipole collisional interaction, while those for CH₃OHHe and CH₃OHH₂ mixtures indicate more complex interactions.     

High temperature collisional energy transfer in highly vibrationally excited molecules: Isotope effects in tert-butyl chloride systems

The average downward collisional energy transfer (<ΔE_down>) is obtained for highly vibrationally excited tert-butyl chloride, both undeuterated and per-deuterated, with Kr, N₂, CO₂, and C₂H₄ bath gases, at ca. 760 K. Data are obtained using the technique of pressure-dependent very low-pressure pyrolysis. Reactant internal energies to which the data are sensitive are in the range 200–250 kJ mol^?1. For C₄H₉Cl, the <ΔE_down> values (cm^?1) are 255 (Kr), 265 (N₂), 440 (CO₂), and 585 (C₂H₄), and for C₄D₉Cl, 245 (N₂), 370 (CO₂), and 540 (C₂H₄). The uncertainties in these values are ca. 20% (40% for Kr); the uncertainties in the deuteration ratios are 10–15%. The value for Kr is in agreement with theoretical predictions of a biased random walk model for internal energy change in monatomic/substrate collisions. The effect of deuteration of <ΔE_down> is also in accord with that predicted by a modification of the theory. Extrapolated highpressure rate coefficients for the thermal decomposition of reactant are 10^13.6 exp(-187 kJ mol^?1/RT) s^?1 (C₄H₉Cl) and 10^14.2 exp(?196 kJ mol^?1/RT) s^?1 (C₄D₉Cl), in accord with other studies and the expected isotope effect.     

High-temperature collisional energy transfer in highly vibrationally excited molecules II: Isotope effects in isopropyl bromide systems

Values for 〈ΔE_down〉, the average downward energy transferred from the reactant to the bath gas upon collision, have been obtained for highly vibrationally excited undeuterated and per-deuterated isopropyl bromide with the bath gases Ne, Xe, C₂H₄, and C₂D₄, at ca. 870 K. The technique of pressure-dependent very low-pressure pyrolysis (VLPP) was used to obtain the data. For C₃H₇Br, the 〈ΔE_down〉 values (cm^?1) are 490 (Ne), 540 (Xe), 820 (C₂H₄), and 740 (C₂D₄), and for C₃D₇Br, 440 (Ne), 570 (Xe), 730 (C₂H₄), and 810 (C₂D₄). The uncertainties in these values are ca. ±10%. The 〈ΔE_down〉 values for the inert bath gases Ne and Xe show excellent agreement with the theoretical predictions of the semi-empirical biased random walk model for monatomic/substrate collisional energy exchange [J. Chem. Phys., 80 , 5501 (1984)]. The relative effects of deuteration of the reactant molecule on 〈ΔE_down〉 also compare favorably with the predictions of this theoretical model. Extrapolated high-pressure rate coefficients (s^?1) for the thermal decomposition of reactant are 10^13.6±0.3 exp(?200 ± 8 kJ mol^?1/RT) for C₃H₇Br and 10^13.9±0.3 exp(?207 ± 8 kJ mol^±1/RT) for C₃D₇Br, which are consistent with previous studies and the expected isotope effect.     

Isotopically selective collisional vibrational energy transfer in CF3H

The authors investigate here the mechanism of collisionally enhanced isotopic selectivity observed in infrared multiple photon dissociation (IRMPD) of vibrationally preexcited CF3H by Boyarkin et al. [J. Chem. Phys. 118, 93 (2003)]. For both the carbon-12 and carbon-13 isotopic species they measure the dependence of the IRMPD yield on the time delay between the preexcitation and the dissociation pulses at different dissociation frequencies as well as its dependence on the initial isotopic composition of the sample. The results reveal that the collisional increase in isotopic selectivity originates not only from that of IRMPD itself but also from the isotopic selectivity of vibrational energy transfer, with the latter making the major contribution under their experimental conditions. They suggest that the observed isotopic selectivity in collisional energy transfer arises from the difference in overlap between the absorption spectra of the nu5 mode in the 12CF3H acceptor molecule with emission spectra of the same mode in the two isotopically different donors. Understanding the origin of this collisional effect has important implications for optimization of laser isotope separation processes.     

High temperature collisional energy transfer in highly vibrationally excited molecules. III: Isotope effects in tert-butyl bromide systems

Changes in the magnitude of 〈ΔE_down〉, the average downward collisional energy transferred between a highly vibrationally excited reactant molecule and an inert bath gas, upon perdeuteration of the substrate are reported for tert-butyl bromide dilute in Ar, Kr, N₂, and CO₂. The technique of pressure-dependent very low-pressure pyrolysis (VLPP) was used to obtain the absolute values of 〈ΔE_down〉, which are for C₄H₉Br, 230 (Ar), 285 (Kr), 270 (N₂), and 365 (CO₂) while for C₄D₉Br, 200 (Ar), 250 (Kr), 220 (N₂), and 335 (CO₂), all in cm^?1 at ca. 720 K. The estimated uncertainties in these values are ca. ± 10%. These observed 〈ΔE_down〉, values and trends found with results from this series of isotope studies, are compared with current theoretical models. Extrapolated high-pressure temperature-dependent rate coefficients (s^?1) for the thermal decomposition of reactant are 10^13.8±0.3 exp(?175 ± 8 kJ mol^?1/RT) for C₄H₉Br and 10^14.3±0.3 exp(?183 ± 8 kJ mol^?1/RT) for C₄D₉Br. These results are in accord with other studies and the expected isotope effect.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.     

Theory of collisional energy transfer - bromine in low-density inert gases

Classical binary collision trajectory calculations have been carried out to study the energy transfer efficiency between the internal degrees of freedom of highly energized bromine (Br₂) and the translation degrees of freedom of an inert gas (He, Ne, Ar, Kr, Xe) in the low-density limit. The dependence on species (mass, strength of attraction), temperature of the gas (T = 160, 300, and 1500 K) and internal energy of the bromine (14, 28, 43 kcal/mole; E_d = 45.5 kcal/mole) is considered. Global statistical theories overestimate the average energy transferred per collision by an order of magnitude or more. A simple impulsive collision theory is developed and found to account for the magnitudes (typically within a factor of 2–3) and the gross-trends to reasonable accuracy.     

A Modified statistical theory of collisional energy transfer in thermal reactions

A fully statistical kernel describing the probability of energy transfer in collisions between polyatomic reactant (A) and heat bath (M) molecules in a thermal system is developed, proceeding through the formation of an intermediate collision complex (AM) whose internal degrees of freedom are assumed to exchange energy. After pointing out that this kernel does not give a quantitatively useful answer, the kernel is modified by introducing the concept that the collision complex lifetime is due to orbiting collisions, and that the (AM) lifetime must equal collision duration. This puts two constraints on the internal degrees of freedom of (AM): (1) those that correlate with relative translation and intrinsic rotation of separated A and M (= transitional modes) can contain only an amount of energy not exceeding E_*, which is the maximum energy for which orbiting can occur; (2) those that correlate with internal degrees of freedom of M must have a density of states such that, subject to constraint (1), the lifetime of (AM) is equal to collision duration. It turns out, quite unambiguously, that the appropriate density of states is equivalent to just one oscillator of M participating in energy exchange. Calculations of average amount of energy transferred (Δ E>) in the system CH₃NC + M show good quantitative agreement with experiment for both polar and non-polar M. The modified theory does not give any appreciable dependence of Δ E> on the size of M because collision duration is assumed to depend only on the long-range part of the potential.     

A phase-corrected coupled-states approximation for inelastic scattering

A simple phase correction is derived for the coupled-states (CS) approximation based on WKB phase shifts for the electric part of the potential. The resulting phase-corrected CS (PCCS) scattering matrix agrees well in both phase and magnitude with the exact one. The PCCS approximation should then give accurate m-state information for any quantization axis.     

Semiclassical time-correlation function approach to collisional energy transfer into many-atom systems

Cross sections for energy transfer into many-body systems can be expressed in terms of time-correlation functions (TCFS ) of transition operators. A semiclassical version is presented by treating internal motions as quantized and relative motions as classical. The time evolution of internal motions can be calculated in the Heisenberg picture and avoids expansions in target states. The decoupling of fast and slow internal motions is treated and applied to vibrational–rotational decoupling in polyatomic molecules. Results are presented for Li⁺-CO₂ collisions.     

70 years of Landau-Teller theory for collisional energy transfer. Semiclassical three-dimensional generalizations of the classical collinear model

This article, in historical retrospective, describes the development of the celebrated Landau-Teller (LT) model of 1936 for vibrational-translational energy exchange in collisions of an atom with a diatomic molecule. We discuss semiclassical generalizations of the classical LT model and generalizations of the collinear LT model to account for the effects of rotation of the diatom on the vibrational relaxation rate. The former is based on the recovery of the Landau semiclassical exponent from the classical LT encounter time, and the latter on the definition of a 1-D driving mode within the manifold of the translational and rotational degrees of freedom of the colliding partners. The utility of generalized LT models is illustrated by three case studies that exemplify weak and strong effects of the rotation as well as the efficiencies of different driving modes in the vibrational relaxation of highly asymmetric diatoms.     

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems

This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)] by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.     

Vibrational-translational energy transfer from highly excited anharmonic oscillators

Model trajectory calculations reveal a simple power law behavior for anharmonic oscillator energy transfer for all bound vibrational levels.     

Supercollisions and energy transfer of highly vibrationally excited molecules

Collisional energy-transfer probability distribution functions of highly vibrationally excited molecules and the existence of supercollisions remain as the outstanding questions in the field of intermolecular energy transfer. In this investigation, collisional interactions between ground state Kr atoms and highly vibrationally excited azulene molecules (4.66 eV internal energy) were examined at a collision energy of 410 cm-1 using a crossed molecular beam apparatus and time-sliced ion imaging techniques. A large amount of energy transfer (1000-5000 cm-1) in the backward direction was observed. We report the experimental measurement for the shape of the energy-transfer probability distribution function along with a direct observation of supercollisions.