Energy transfer between polyatomic molecules II: Energy transfer quantities and probability density functions in benzene, toluene, p-xylene, and azulene collisions

Collisional energy transfer, CET, is of major importance in chemical, photochemical, and photophysical processes in the gas phase. In Paper I of this series (J. Phys. Chem. B 2005, 109, 8310) we have reported on the mechanism and quantities of CET between an excited benzene and cold benzene and Ar bath. In the present work, we report on CET between excited toluene, p-xylene, and azulene with cold benzene and Ar and on CET of excited benzene with cold toluene, p-xylene, and azulene. We compare our results with those of Paper I and report average vibrational, rotational, and translational energy quantities, , transferred in a single collision. We discuss the effect of internal rotation on CET and the identity of the gateway modes in CET and the relative role of vibrational, rotational, and translational energies in the CET process, all that as a function of temperature and excitation energy. Energy transfer probability density functions, P(E,E'), for the various systems are reported and the shape of the curves for various systems and initial conditions is discussed. The major findings for polyatomic-polyatomic collisions are: CET takes place mainly via vibration-to-vibration energy transfer assisted by overall rotations. Internal free rotors in the excited molecule hinder energy exchange while in the bath molecule they do not. Energy transfer at low temperatures and high temperatures is more efficient than that at intermediate temperatures. Low-frequency modes are the gateway modes for energy transfer. Vibrational temperatures affect energy transfer. The CET probability density function, P(E,E'), is convex at low temperatures and can be concave at high temperatures. A mechanism that explains the high values of and the convex shape of P(E,E') is that in addition to short impulsive collisions there are chattering collisions where energy is transferred in a sequence of short encounters during the lifetime of the collision complex. This also leads to the observed supercollision tail at the down wing of P(E,E'). Polyatomic-Ar collisions show mechanistic similarities to polyatomic-polyatomic collisions, but there are also many dissimilarities: internal rotations do not inhibit energy transfer, P(E,E') is concave at all temperatures, and there is no contribution of chattering collisions.     

Energy transfer between polyatomic molecules. 3. Energy transfer quantities and probability density functions in self-collisions of benzene, toluene, p-xylene and azulene

This paper is the third and last in a series of papers that deal with collisional energy transfer, CET, between aromatic polyatomic molecules. Paper 1 of this series (J. Phys. Chem. B 2005, 109, 8310) reports on the mechanism and quantities of CET between an excited benzene and cold benzene and Ar bath. Paper 2 in the series (J. Phys. Chem., in press) discusses CET between excited toluene, p-xylene and azulene with cold benzene and Ar and CET between excited benzene colliding with cold toluene, p-xylene and azulene. The present work reports on CET in self-collisions of benzene, toluene, p-xylene and azulene. Two modes of excitation are considered, identical excitation energies and identical vibrational temperatures for all four molecules. It compares the present results with those of papers 1 and 2 and reports new findings on average vibrational, rotational, and translational energy, , transferred in a single collision. CET takes place mainly via vibration to vibration energy transfer. The effect of internal rotors on CET is discussed and CET quantities are reported as a function of temperature and excitation energy. It is found that the temperature dependence of CET quantities is unexpected, resembling a parabolic function. The density of vibrational states is reported and its effect on CET is discussed. Energy transfer probability density functions, P(E,E'), for various collision pairs are reported and it is shown that the shape of the curves is convex at low temperatures and can be concave at high temperatures. There is a large supercollision tail at the down wing of P(E,E'). The mechanisms of CET are short, impulsive collisions and long-lived chattering collisions where energy is transferred in a sequence of short internal encounters during the lifetime of the collision complex. The collision complex lifetimes as a function of temperature are reported. It is shown that dynamical effects control CET. A comparison is made with experimental results and it is shown that good agreement is obtained.     

Collisional relaxation of the three vibrationally excited difluorobenzene isomers by collisions with CO2: effect of donor vibrational mode

Relaxation of highly vibrationally excited 1,2-, 1,3-, and 1,4-difluorobenzne (DFB) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot DFB (E' approximately 41,000 cm(-1)) was prepared by 248 nm excimer laser excitation followed by rapid radiationless relaxation to the ground electronic state. Collisions between hot DFB isomers and CO2 result in large amounts of rotational and translational energy transfer from the hot donors to the bath. The CO2 nascent rotational population distribution of the high-J (J = 58-80) tail of the 00(0)0 state was probed at short times following the excimer laser pulse to measure rate constants and probabilities for collisions populating these states. The amount of translational energy gained by CO2 during collisions was determined using Doppler spectroscopy to measure the width of the absorption line for each transition. The energy transfer probability distribution function, P(E,E'), for the large DeltaE tail was obtained by resorting the state-indexed energy transfer probabilities as a function of DeltaE. P(E,E') was fit to a biexponential function to determine the average energy transferred in a single DFB/CO2 collision and fit parameters describing the shape of P(E,E'). P(E,E') fit parameters for DFB/CO2 and the previously studied C6F6/CO2 system are compared to various donor molecular properties. A model based on Fermi's Golden Rule indicates that the shape of P(E,E') is primarily determined by the low-frequency out-of-plane donor vibrational modes. A fractional mode population analysis is performed, which suggests that for energy transfer from DFB and C6F6 to CO2 the two key donor vibrational modes from which energy leaks out of the donor into the bath are nu11 and nu16. These "gateway" modes are some of the same modes determined to be the most efficient energy transfer modes by quantum scattering studies of benzene/He collisions.     

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.     

Quantum state-resolved energy redistribution in gas ensembles containing highly excited N2

A computational model is used to quantify the evolution of quantum state populations as highly vibrationally excited (14)N(2) ((14)N(2)?) equilibrates in various bath gases. Multicollision energy disposal follows general principles established in related single collision processes. Thus when state-to-state routes permit, maximum amounts of energy are deposited into partner species by direct vibration-to-vibration (V-V) exchange. When these pathways are absent, e.g., when Ar is the bath species, relaxation is very slow and multistaged. Conversely, in a bath of v = 0 (14)N(2) molecules, 16 vibrational quanta (Δv = ± 8) are resonantly exchanged from (v;j) = (8;10) with vibrational equilibration so rapid that rotation and translation still lag far behind after 1000 collisions. Near-resonant V-V exchange dominates the initial phase when (15)N(2) forms the bath gas and although some rotational warming occurs, vibrational modes remain decoupled from, and significantly hotter than, the low heat capacity modes. These forms of behavior seem likely to characterize excited and bath species that have closely similar vibration and rotation constants. More generic in nature is (14)N(2) in O(2) or in a mixture that closely resembles air. Here, asymmetric V-V exchange is a dominant early feature in ensemble evolution but energy differences in the key vibration and rotation quanta lead to V-V energy defects that are compensated for by the low energy modes. This results in much more rapid ensemble equilibration, generally within 400-500 collisions, when O(2) is present even as a minor constituent. Our results are in good general agreement with those obtained from experimental studies of N(2) plasmas both in terms of modal temperatures and initial (first collision cycle) cross-sections.     

Accounting for the dependence of P(E',E) on the maximum impact parameter in classical trajectory calculations: application to the H2O-H2O collisional relaxation

In this work we report a novel methodology that is able to predict how energy transfer transition probability density functions [P(E',E)] change with the maximum impact parameter (bmax) used in trajectory calculations (TC's). The method assumes that P(E',E) can be described by a sum of exponential functions and that all the trajectories with an initial impact parameter beyond a certain critical value will contribute only to the elastic peak [P(E',E) for E'=E]. This approach is applied to H2O-H2O collisions at different initial vibrational energies of the excited molecules and temperatures of bath gas. The results show that it is possible to reproduce with high accuracy the whole P(E',E) obtained from a given bmax, using the results of TC's performed at another bmax. The new methodology also leads us to propose a new criterion to choose the value of bmax.     

Energy transfer between azulene and krypton: comparison between experiment and computation

Trajectory calculations of collisional energy transfer between excited azulene and Kr are reported, and the results are compared with recent crossed molecular beam experiments by Liu et al. [J. Chem. Phys. 123, 131102 (2005); 124, 054302 (2006)]. Average energy transfer quantities are reported and compared with results obtained before for azulene-Ar collisions. A collisional energy transfer probability density function P(E,E'), calculated at identical initial conditions as experiments, shows a peak at the up-collision branch of P(E,E') at low initial relative translational energy. This peak is absent at higher relative translational energies. There is a supercollision tail at the down-collision side of the probability distribution. Various intermolecular potentials are used and compared. There is broad agreement between experiment and computation, but there are some differences as well.     

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.     

Mode-specific energy absorption by solvent molecules during CO2 vibrational cooling

Non-equilibrium molecular dynamics (NEMD) simulations of energy transfer from vibrationally excited CO(2) to CCl(4) and CH(2)Cl(2) solvent molecules are performed to identify the efficiency of different energy pathways into the solvent bath. Studying in detail the work performed by the vibrationally excited solute on the different solvent degrees of freedom, it is shown that vibration-to-vibration (V-V) processes are strongly dominant and controlled by those accepting modes which are close in frequency to the CO(2) bend and symmetric stretch vibration.     

Energy transfer of highly vibrationally excited naphthalene: collisions with CHF3, CF4, and Kr

Energy transfer of highly vibrationally excited naphthalene in the triplet state in collisions with CHF(3), CF(4), and Kr was studied using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. Highly vibrationally excited naphthalene (2.0 eV vibrational energy) was formed via the rapid intersystem crossing of naphthalene initially excited to the S(2) state by 266 nm photons. The shapes of the collisional energy-transfer probability density functions were measured directly from the scattering results of highly vibrationally excited naphthalene. In comparison to Kr atoms, the energy transfer in collisions between CHF(3) and naphthalene shows more forward scatterings, larger cross section for vibrational to translational (V → T) energy transfer, smaller cross section for translational to vibrational and rotational (T → VR) energy transfer, and more energy transferred from vibration to translation, especially in the range -ΔE(d) = -100 to -800 cm(-1). On the other hand, the difference of energy transfer properties between collisional partners Kr and CF(4) is small. The enhancement of the V → T energy transfer in collisions with CHF(3) is attributed to the large attractive interaction between naphthalene and CHF(3) (1-3 kcal/mol).     

Rotationally resolved IR-diode laser studies of ground-state CO2 excited by collisions with vibrationally excited pyridine

Relaxation of highly vibrationally excited pyridine (C5NH5) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot pyridine (E' = 40,660 cm(-1)) was prepared by 248 nm excimer laser excitation followed by rapid radiationless relaxation to the ground electronic state. Pyridine then collides with CO2, populating the high rotational CO2 states with large amounts of translational energy. The CO2 nascent rotational population distribution of the high-J (J = 58-80) tail of the 00(0)0 state was probed at short times following the excimer laser pulse to measure rate constants and probabilities for collisions populating these CO2 rotational states. Doppler spectroscopy was used to measure the CO2 recoil velocity distribution for J = 58-80 of the 00(0)0 state. The energy-transfer distribution function, P(E,E'), from E' - E approximately 1300-7000 cm(-1) was obtained by re-sorting the state-indexed energy-transfer probabilities as a function of DeltaE. P(E,E') is fit to an exponential or biexponential function to determine the average energy transferred in a single collision between pyridine and CO2. Also obtained are fit parameters that can be compared to previously studied systems (pyrazine, C6F6, methylpyrazine, and pyrimidine/CO2). Although the rotational and translational temperatures that describe pyridine/CO2 energy transfer are similar to previous systems, the energy-transfer probabilities are much smaller. P(E,E') fit parameters for pyridine/CO2 and the four previously studied systems are compared to various donor molecular properties. Finally, P(E,E') is analyzed in the context of two models, one indicating that P(E,E') shape is primarily determined by the low-frequency out-of-plane donor vibrational modes, and the other that indicates that P(E,E') shape can be determined from how the donor molecule final density of states changes with DeltaE.     

Energy transfer of highly vibrationally excited naphthalene. III. Rotational effects

The rotational effects in the energy transfer between Kr atoms and highly vibrationally excited naphthalene in the triplet state were investigated using crossed-beam/time-sliced velocity map ion imaging at various translational collision energies. As the initial rotational temperature changes from less than 10 to approximately 350 K, the ratio of vibrational to translational (V-->T) energy transfer cross section to translational to vibrational/rotational (T-->VR) energy transfer cross section increases, but the probability of forming a complex during the collisions decreases. Significant increases in the large V-->T energy transfer probabilities, termed supercollisions, at high initial rotational temperature were observed.     

Quasiclassical Trajectory Study of Collisional Energy Transfer between Highly Excited C6F6 and N2 ,O2 and Ground State C6F6

Quasiclassical trajectory calculation (QCT) is used frequently for studying collisional energy transfer between highly vibrationally excited molecules and bath gases. In this paper, the QCT of the energy transfer between highly vibrationally excited C6F6 and N2 ,O2 and ground state C6F6 were performed. The results indicate that highly vibrationally excited C6F6 transferred vibrational energy to vibrational distribution of N2, O2 and ground state C6F6, so they are V-V energy transfer. Especially it is mainly V-V resonance energy transfer between excited C6F6 andground state C6F6, excited C6F6 transfers more vibrational energy to ground state C6F6 than to N2 and O2. The values of QCT, - (ΔEvib) of excited C6F6 are smaller than those of experiments.     

Statistical theory of collisional energy transfer in molecular collisions. trans-stilbene deactivation by argon, carbon dioxide, and n-heptane

Recent advances in experimental techniques have made it possible to measure the full conditional probability density P(E, E') of the energy transfer between two colliding molecules in the gas phase, one of which is highly energized and the other in thermal equilibrium at a given temperature. Data have now become available for trans-stilbene deactivation by the three bath gas molecules Ar, CO2, and n-heptane (C7H16). The initial energies of trans-stilbene are set to 10 000, 20 000, 30 000, and 40 000 cm (-1). The results show that exceptionally large amounts of energy are transferred in each collision. By application of our partially ergodic collision theory (PECT), we find that the energy transfer efficiency betaE ranges from a rather normal value of 0.15 for n-heptane at the highest excitation energy to 0.93-nearly in the ergodic collision limit-for the argon bath gas at high excitation energy. Generally, the PECT produces a good fit of the data except for the nearly elastic peak in the case of n-heptane, where PECT produces a rounded and downshifted peak in contrast to a sharply defined elastic maximum of the monoexponential functional fit produced from the original experimental data obtained by kinetically controlled selective ionization in the work of the group of Luther in G?ttingen. This problem is analyzed and found to be related partly to the lack of treatment of glancing collisions in the theory with a remaining uncertainty due to the weak dependence of energy transfer efficiency on nearly elastic collisions. A summary of the present state of understanding shows that collisional activation and deactivation of reactant molecules is more efficient and more statistical than has been previously realized.     

Collisional energy transfer with statistical energy exchange: an analytical solution in the statistical limit

Collisional energy transfer between highly vibrationally excited molecules and bath gas is considered with a statistical kernel, describing energy exchange in complex-forming collisions. Knowledge of the bilinear formula for the Laguerre polynomials offers a means for determining eigenvalues and eigenfunctions of the kernel. An exact solution to master equation for the conditional probability is given as an expansion in terms of these eigenfunctions. The bulk averages of internal energy moments and energy transfer moments are calculated analytically.     

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.     

PECT model analysis and predictions of experimental collisional energy transfer probabilities P(E',E) and moments <DeltaE> for azulene and biphenylene

Experimental collisional energy transfer data from kinetically controlled selective ionization (KCSI) and ultraviolet absorption (UVA) experiments are analyzed in the framework of the partially ergodic collision theory (PECT). Collisions of azulene and biphenylene with different colliders are investigated as case studies. The downward wings of the P(E',E) energy transfer distributions obtained from the PECT model are fitted to the recently introduced "variable-shape"-exponential 3-parameter functional form of P(E',E) obtained from KCSI experiments, P(E',E) proportional, variant exp[-{(E - E')/(C(0) + C(1)E)}(Y)]. The PECT model is able to reproduce the characteristic dependence of the KCSI "shape parameter" Y on the choice of collider, the energy dependent width of the KCSI P(E',E) distributions, described by alpha(E) = C(0) + C(1)E, and the temperature dependence of the UVA data above room temperature. The statistical approach of PECT obviously captures the essence of large molecule energy transfer at chemically significant energies without the need of knowing specific features of the detailed collision dynamics. It therefore shows promise for predicting the shape of P(E',E) in master equation kernels for larger molecules.     

Energy transfer of highly vibrationally excited phenanthrene and diphenylacetylene

The energy transfer between Kr atoms and highly vibrationally excited, rotationally cold phenanthrene and diphenylacetylene in the triplet state was investigated using crossed-beam/time-of-flight mass spectrometer/time-sliced velocity map ion imaging techniques. Compared to the energy transfer between naphthalene and Kr, energy transfer between phenanthrene and Kr shows a larger cross-section for vibrational to translational (V → T) energy transfer, a smaller cross-section for translational to vibrational and rotational (T → VR) energy transfer, and more energy transferred from vibration to translation. These differences are further enlarged in the comparison between naphthalene and diphenylacetylene. In addition, less complex formation and significant increases in the large V → T energy transfer probabilities, termed supercollisions in diphenylacetylene and Kr collisions were observed. The differences in the energy transfer between these highly vibrationally excited molecules are attributed to the low-frequency vibrational modes, especially those vibrations with rotation-like wide-angle motions.     

The He-LiH potential energy surface revisited. II. Rovibrational energy transfer on a three-dimensional surface

We use our rigid rotor He-LiH potential energy surface [B. K. Taylor and R. J. Hinde, J. Phys. Chem. 111, 973 (1999)] as a starting point to develop a three-dimensional potential surface that describes the interaction between He and a rotating and vibrating LiH molecule. We use a fully quantum treatment of the collision dynamics on the current potential surface to compute rovibrational state-to-state cross sections. We compute excitation and relaxation vibrational rate constants as a function of temperature by integrating these cross sections over a Maxwell-Boltzmann translational energy distribution and summing over Boltzmann-weighted initial rotational levels. The rate constants for vibrational excitation of LiH are very small for temperatures below 300 K. Rate constants for vibrational relaxation of excited LiH molecules, however, are several orders of magnitude larger and show very little temperature dependence, suggesting that the collisions that result in vibrational relaxation are governed by long-range attractive interactions.     

Vibrational energy transfer in hydrogen liquid and its isotopes

The transfer of vibrational energy (V-V) from H₂ to isotopic impurities (HD or D₂) has been studied in the liquid state, between 15 and 30 K. The subsequent relaxation (V-T) of the excited impurity by the H₂ liquid host has also been measured and contrasted with the vibrational relaxation behaviour of pure H₂ and D₂ liquids. The isothermal density dependence of both V-V and V-T transfer has been investigated in the fluid state at 30 K. High density relaxation rates are also compared to our data in the pure gases and to other available gas phase results. Measurements in the solid, near the triple point temperature, are equally reported for each process studied.