Energy Transfer Probability Density Functions Research Articles

Energy transfer of highly vibrationally excited 2-methylnaphthalene: Methylation effects

The methylation effects in the energy transfer between Kr atoms and highly vibrationally excited 2-methylnaphthalene in the triplet state were investigated using crossed-beam/time-sliced velocity-map ion imaging at a translational collision energy of approximately 520 cm(-1). Comparison of the energy transfer between naphthalene and 2-methylnaphthalene shows that the difference in total collisional cross section and the difference in energy transfer probability density functions are small. The ratio of the total cross sections is sigma(naphthalene): sigma(methylnaphthalene)=1.08+/-0.05:1. The energy transfer probability density function shows that naphthalene has a little larger probability at small T-->VR energy transfer, DeltaE(u)<300 cm(-1), and 2-methylnaphthalene has a little larger probability at large V-->T energy transfer, -800 cm(-1)<DeltaE(d)<-100 cm(-1). However, these differences are close to our experimental uncertainty. No significant difference in the probability of very large energy transfer, such as supercollisions defined arbitrarily as DeltaE(d)<-1500 cm(-1), was observed. The possible methylation effects due to the subsequent successive collisions were discussed.

Differential cross-sections and energy transfer quantities in azulene/argon collisions

Computational results on collisional energy transfer between excited and cold azulene and Ar are reported under initial conditions similar to those of crossed molecular beam experiments (Liu, Hsu, Lyu and Ni, J. Chem. Phys. 125 204309 (2006)). The in-plane scattering cross-section is asymmetric with a preference for positive angles. The out-of-plane scattering angle is symmetric in both positive and negative angles with a strong forward scattering peak. In both T → V/R dominates over V → R/T. The double differential cross-section shows a high probability for forward, then sideways and finally, backward scattering. The latter shows relatively high probability for supercollisions. Average energy transfer quantities and collisional energy transfer probability density functions, P(E,E′), are presented and results for Ar and Kr as colliders are compared. At low initial relative translational energies the up-collision branch of P(E,E′) shows a peak. This peak, which is absent at higher relative translational energies, is due to the formation of a collision complex. Special attention is paid to the role of rotational energy in the energy transfer process. Changing the rotational temperature from 0.5 K to 2000 K changes the percentage of up and down collisions as well as the values of the average energy transferred quantities. The effect of the translational energy on energy transfer is discussed. There is broad agreement between experiment and computation.

Collisional energy transfer in polyatomic molecules in the gas phase

AbstractThis paper is an attempt to present an overall view of energy transfer between excited polyatomic molecules and polyatomic and monatomic bath, based on results obtained by classical trajectory calculations. It is not a general review of the subject but a summary based on work done by us in the last few years. We report average energies transferred in a collision and collisional energy transfer probability density functions for various collision partners as a function of various system parameters: temperature, vibrational and rotational energies of the hot and cold molecule, and relative translational energies. Various mechanisms for energy transfer are proposed, their dependence on the system parameters is explored, and the relevance of empirical numerical models to computational results is discussed.

Energy transfer of highly vibrationally excited naphthalene. I. Translational collision energy dependence

Energy transfer between highly vibrationally excited naphthalene and Kr atom in a series of translational collision energies (108-847 cm(-1)) was studied separately using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. Highly vibrationally excited naphthalene in the triplet state (vibrational energy: 16,194 cm(-1); electronic energy: 21,400 cm(-1)) was formed via the rapid intersystem crossing of naphthalene initially excited to the S(2) state by 266 nm photons. The collisional energy transfer probability density functions were measured directly from the scattering results of highly vibrationally excited naphthalene. At low collision energies a short-lived naphthalene-Kr complex was observed, resulting in small amounts of translational to vibrational-rotational (T-->VR) energy transfer. The complex formation probability decreases as the collision energy increases. T-->VR energy transfer was found to be quite efficient at all collision energies. In some instances, nearly all of the translational energy is transferred to vibrational-rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy. The translational energy gained from vibrational energy extend to large energy transfer (up to 3000 cm(-1)) as the collision energy increases to 847 cm(-1). Substantial amounts of large V-->T energy transfer were observed in the forward and backward directions at large collision energies.

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.

Experimental and computational investigation of energy transfer between azulene and krypton

Experimental results of energy transfer in crossed molecular beams of excited and cold azulene and Kr are reported and compared with computations performed under identical initial conditions of rotational temperature of 0.5 K and 2.0 K and translational energies of 170, 410, and 780 cm −1. Energy transfer quantities are reported and collisional energy transfer probability density functions, P( E, E′), are given for experiment and computation. The results show that a collision complex is formed at low translational energies and that translation to rotation is a major energy transfer channel. There is good agreement between experiment and theory.

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, <DeltaE>, 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.

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, <DeltaE>, 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 <DeltaE(a)> 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. 1. Gateway Modes, Energy Transfer Quantities and Energy Transfer Probability Density Functions in Benzene−Benzene and Ar−Benzene Collisions

We report collisional energy transfer, CET, quantities for polyatomic-polyatomic collisions and use excited benzene collisions with cold benzene bath, B-B, as our sample system and compare our results with the CET of excited benzene with Ar bath. We find that the gateway mode for both systems is the out-of-plane modes and that in B-B CET, vibration to vibration, V-V, is the dominant channel. Rotations play a mechanistic role in the CET but the net rotational energy transfer is small compared to V-V. The shape of the down side of the energy transfer probability density function, P(E,E'), is convex for B-B collisions and it becomes less so as the temperature increases. In Ar-B collisions, P(E,E') is concave and it becomes less so as the temperature decreases. We report average vibrational, rotational, and translational energy transferred, <DeltaE>, as function of temperature for various initial conditions.

Endohedral formation, energy transfer, and dissociation in collisions between Li+ and C60

Quasiclassical trajectory calculations were performed on Li+ ion collisions with a C60 molecule. The probabilities of endohedral formation and escape from the cage are reported. It is found that endohedral formation depends on the relative translational energy and it is independent of the internal energy. The average energy transferred per collision of a Li+ with a fullerene molecule is reported and its dependence on the relative translational energy is given. The collisional energy transfer probability density function, P(E′,E), is calculated for two translational energies and the results are used to calculate the degree of dissociation of the fullerene molecule following a collision with Li+. Details of the intramolecular vibrational energy redistribution, IVR, are reported. It is found that following an exciting collision, energy relaxes by moving from one moiety to another within the molecule. Initial partial relaxation can be as fast as ∼67 fs but total redistribution of energy takes ∼1.5 ps.

Intermolecular energy transfer probabilities from trajectory calculations: A new approach

A new method to calculate intermolecular energy transfer probability density function P(E′,E) from trajectory calculations is proposed. The method distinguishes between effective trajectories that contribute to P(E′,E) and those with very large impact parameter which do not. The P(E′,E) thus found obeys conservation of probability and detailed balance and is independent of the impact parameter. The method is demonstrated for benzene–Ar collisions at various temperatures and internal energies. With this method it is possible to combine ab initio inter and intramolecular potentials with trajectory calculations, obtain P(E′,E) and use that in master equation calculations to obtain rate coefficients and populations distributions without resorting to any a priori assumptions and energy transfer models. In addition, the effects of internal energy, temperature and rotations on the average energy transferred are discussed. Global potentials in center-of-mass and minimal distance coordinates which are obtained by averaging 20 000 and 50 000 trajectories are reported. It is shown that Lennard-Jones or ab initio pairwise potentials yield a Buckingham-type global potentials.

Measurement of rotational energy transfer rates for HD (v=1) in collisions with thermal HD

We report state-to-state rotational energy transfer rates for HD excited to the first excited vibrational level of the ground electronic state. Stimulated Raman scattering is used to produce the rotationally selected, vibrationally excited HD. Subsequent collisional energy transfer from the prepared state, upon collision with a thermal distribution of HD, is monitored by multiphoton ionization through the E,F electronic state. The data are analyzed by solving the rate equations coupling the lowest six rotational states of the first excited vibrational level. In this manner, both the absolute rate constants and the shape of the energy transfer probability density function are determined. The best fit of the data to trial probability density functions indicates that the HD–HD collisions preserve the magnetic sublevel, mj. The total rotational energy transfer rate out of a particular rotational level is compared to high resolution Raman linewidth measurements in order to determine the degree to which the rotational energy transfer rate contributes to the linewidth.