Trajectory studies

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

A Warshel. Dynamics of reactions m polar solvents. Semiclassical trajectory studies of electron-transfer and proton-transfer reactions. J Phys Chem 86 2218-2224, 1982. 

The analytical method of jet trajectory study developed by Shepelev allows the derivation of several other useful features and is worth describing. On the schematic of a nonisothermal jet supplied at some angle to the horizon (Fig. 7.25), 5 is the jet s axis, X is the horizontal axis, and Z is the vertical axis. The ordinate of the trajectory of this jet can be described as z = xtga a- Az, where Az is the jet s rise due to buoyancy forces. To evaluate Az, the elementary volume dW with a mass equal to dm dV on the jet s trajectory was considered. The buoyancy force influencing this volume can be described as dP — g(p -Pj). Vertical acceleration of the volume under the consideration is j — dP / dm — -p,)/ g T,-T / T. Vertical... 

Classical trajectory calculations, performed on the PES1 and PESl(Br) potential energy surfaces described above, have provided a detailed picture of the microscopic dynamics of the Cl- + CH3Clb and Cl" + CH3Br SN2 nucleophilic substitution reactions.6,8,35-38 In the sections below, different aspects of these trajectory studies and their relation to experimental results and statistical theories are reviewed. 

In the trajectory study of Cl-—CHjCl complex formation by Cl" + CH3C1 association, the number of complexes with a lifetime t, i.e. N(t), was evaluated for different Cl" + CH3C1 initial conditions.36,37 The resulting plots of N(t) are highly nonexponential and plots of N(t)/N(0) were fit with the biexponential function... 

The analytic potential energy surfaces, used for the Cl + CH3Clb and Cl + CHjBr trajectory studies described here, should be viewed as initial models. Future classical and quantum dynamical calculations of SN2 nucleophilic substitution should be performed on quantitative potential energy functions, derived from high-level ab initio calculations. By necessity, the quantum dynamical calculations will require reduced dimensionality models. However, by comparing the results of these reduced dimensionality classical and quantum dynamical calculations, the accuracy of the classical dynamics can be appraised. It will also be important to compare the classical and quantum reduced dimensionality and classical complete dimensionality dynamical calculations with experiment. 

Vande Linde, S. R. and Hase, W. L. Trajectory studies of SN2 nucleophilic substitution. I. Dynamics ofCT + CH3C1 reactive collisions, J.ChemJ hys., 93 (1990),... 

Hase and co-workers have recently carried out extensive trajectory studies of the dynamics of a number of 8 2 reactions, most notably the symmetric reaction between chloride ion and methyl chloride. Equation (5). Experimental results... 

Tabazadeh, A., O. B. Toon, and P. Hamill, Freezing Behavior of Stratospheric Sulfate Aerosols Inferred from Trajectory Studies, Geophys. Res. Lett., 22, 1725-1728 (1995). 

The trajectory studies in Ref. (78) were initiated by running a single-state trajectory on the Si surface of Cr(CO)6. Dissociation of a CO ligand was observed within 90 fs, and this ligand was noted to leave in a rotationally excited fashion, consistent with the measured rotational temperature observed in the similar W(CO)6 (103). Although the ejection of the ligand was the dominant nuclear motion, a subtle initialization of the in-plane symmetric L-M-L bending was also observed. 

There have been several studies of the iodine-atom recombination reaction which have used numerical techniques, normally based on the Langevin equation. Bunker and Jacobson [534] made a Monte Carlo trajectory study to two iodine atoms in a cubical box of dimension 1.6 nm containing 26 carbon tetrachloride molecules (approximated as spheres). The iodine atom and carbon tetrachloride molecules interact with a Lennard—Jones potential and the iodine atoms can recombine on a Morse potential energy surface. The trajectives were followed for several picoseconds. When the atoms were formed about 0.5—0.7 nm apart initially, they took only a few picoseconds to migrate together and react. They noted that the motion of both iodine atoms never had time to develop a characteristic diffusive form before reaction occurred. The dominance of the cage effect over such short times was considerable. 

The classical trajectory simulations of Rydberg molecular states carried out by Levine ( Separation of Time Scales in the Dynamics of High Molecular Rydberg States, this volume) remind me of the related question asked yesterday by Prof. Woste (see Berry et a]., Size-Dependent Ultrafast Relaxation Phenomena in Metal Clusters, this volume). Here I wish to add that similar classical trajectory studies of ionic model clusters of the type A B have been carried out by... 

F.J. Aoiz, L. Banares, V.J. Herrero, V.S. Rabanos, K. Stark, H-J. Werner, The F+HD DF(HF)+H(D) reaction revisited Quasiclassical trajectory study on an ab initio potential energy surface and comparison with molecular beam experiments, J. Chem. Phys. 102 (1995) 9248. 

Amatatsu, Y., Morokuma, K., and Yabushita, S. (1991). Ab initio potential energy surfaces and trajectory studies of A-band photodissociation dynamics CH3I —> CH3 + I and CH3 +1, J. Chem. Phys. 94, 4858-4876. 

Goursaud, S., Sizun, M., and Fiquet-Fayard, F. (1976). Energy partitioning and isotope effects in the fragmentation of triatomic negative ions Monte Carlo Scheme for a classical trajectory study, J. Chem. Phys. 65, 5453-5461. 

Guo, H. and Murrell, J.N. (1988a). A classical trajectory study of the A-state photodissociation of the water molecule, J. Chem. Soc., Faraday Trans. 2 84, 949-959. 

Nonella, M., Huber, J.R., Untch, A., and Schinke, R. (1989). Photodissociation of CH3ONO in the first absorption band A three-dimensional classical trajectory study, J. Chem. Phys. 91, 194-204. 

Schatz, G.C. (1983). Quasiclassical trajectory studies of state to state collisions energy transfer in polyatomic molecules, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin). 

Classical trajectory studies of the association reactions M+ + H20 and M+ + D20 with M = Li, Na, K (Hase et al. 1992 Hase and Feng 1981 Swamy and Hase 1982,1984), Li+(H20) + H20 (Swamy and Hase 1984), Li+ + (CH3)20 (Swamy and Hase 1984 Vande Linde and Hase 1988), and Cl- + CH3C1 (Vande Linde and Hase 1990a,b) are particularly relevant to cluster dynamics. In these studies, the occurrence of multiple inner turning points in the time dependence of the association radial coordinate was taken as the criterion for complex formation. A critical issue (Herbst 1982) is whether the collisions transfer enough energy from translation to internal motions to result in association. Comparison of association probabilities from various studies leads to the conclusion that softer and/or floppier ions and molecules that have low frequency vibrations typically recombine the most efficiently. Thus, it has been found that Li+ + (CH3)20 association is more likely than Li+ + H20 association, and similarly H20 association with Li(H20)+ is more likely than with the bare cation Li+. The authors found a nonmonotonic dependence of association probability on the assumed HaO bend frequency and also a dependence on the impact parameter, the rotational temperature, and the orientation of the H20 dipole during the collision. 

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