Classical 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. 

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... 

A. Warshel. Dynamics of reactions in polar-solvents - semi-classical trajectory studies of electron-transfer and proton-transfer reactions. J. Phys. Chem., 86(12) 2218-2224, 1982. 

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. 

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. 

In conclusion, it is worth reflecting on a classical trajectory study of neutral ethane [335] in which it was found that there were dynamical restrictions to intramolecular energy transfer among C—H motions and between these and C—C motions. It was pointed out [335] that this non-ergodicity might not produce results observable at present levels of experimental resolution. This is probably the situation in mass spectrometry. QET is a respected theory in mass spectrometry because, proceeding from clearly stated assumptions, it is mathematically tractable and is able to explain the currently available experimental data. 

Extensive use has been made of classical trajectory methods to investigate various forms of the potential-energy surface for the reaction F + H2. Muckerman [518] has recently presented a very thorough review of potential-energy surfaces and classical trajectory studies for F + H2. The calculations all correctly predict vibrational population inversion, the value of and backward scattering of the products. Most calculations overestimate (FR) and those giving the lowest values of (Fr > use a potential-energy surface that unrealistically has wells in the entrance and exit valleys [519]. 

Initiated by the pioneering work of Bunker [323,324] classical trajectory simulations have been extensively used to study the decomposition of energized molecules. In a unimolecular classical trajectory study, the motions of atoms for an ensemble of molecules are simulated by solving their classical equations of motion, usually in the form of Hamilton s equations, i.e.,... 

Skouteris, D., Werner, H.-J., Aoiz, F. J., Banares, L., Castillo, J. F., Menendez, M., Balucani, N., Cartechini, L. and Casavecchia, P. (2001) Experimental and theoretical differential cross sections for the reactions Cl + H2/D2, J. Chem. Phys. 114, 10662-72 Aoiz, F. J., Banares, L., Castillo, J., Menendez, M., Skouteris, D. and Werner, H.-J. (2001) A quantum mechanical and quasi-classical trajectory study of the Cl + H2 reaction and its isotopic variants Dependence of the integral cross section on the collision energy and reagent rotation, J. Chem. Phys. 115, 2074-81. 

Quantum mechanical and quasi-classical trajectory study of the C( D) + H2 reaction dynamics, J. Chern. Phy.s. 118, 565-568. 

Johnson, B.R. and Winter, N.W. (1977) Classical trajectory study of effect of vibrational energy on reaction of molecular hydrogen with atomic oxygen. J. Chem. Phys 66, 4116-4120. 

Beam studies have until recently been largely confined to systems in which the dynamics are governed by a single potential surface. The use of classical trajectory studies and adiabatic correlation diagrams in predicting the reaction path are both implicitly founded on the Born-Oppenheimer approximation which allows us to deal with only one electronic state during... 

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