Classical calculations of energy disposal

The accuracy of trajectory calculations have been examined by comparing the results of exact quantum and quasi-classical calculations [143], The most difficult problem lies in the selection of a method for quantising the continuous classical product energy distributions. There is no formal justification for such a procedure, but it enables comparison with experimental vibrational and rotational distributions. No single method appears to be suitable for all systems. 

Most studies have been restricted to three-atom systems, but there are examples of calculations involving larger numbers of atoms. The reviews of Connor [143] and of Walker and Light [153] detail the reactions that have been studied by classical methods. 

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A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

The energetics of isomer prediction using molecular mechanics is discussed in detail in Chapter 7. One of the results of such a study is the structure of each of the isomers.The archetypal studies in this field relate to the complexes [Co(dien)2]3+ (dien = 3-azapentane-l,5-diamine see Chapter 7). Other important studies include those on macrocyclic ligands (see also Chapter 8). Tetraaza macrocyclic ligands, for example, can adopt a series of configurational isomers, and these have been the subject of numerous molecular mechanics calculations. Consider an equatorially coordinated tetraaza macrocylce. Each of the amine groups can coordinate with the amine proton or substituent disposed above or below the coordination plane. How many isomers result depends on the symmetry of the macrocycle. For example, in the classic case of cyclam (cyclam - 14-ane-N4 = 1,4,8,11-tetraazacyclotetradecane) there are five isomers[12] and these are shown schematically in Fig. 6.3. It is not always possible to prepare or separate all of these isomers and, therefore, in many cases only a minority have been structurally characterized. Thus, the energy-minimized structures represent the best available three-dimensional representations of the other isomers. 

Quantum mechanical and classical calculations have been performed [245] for H + Cl2 on a recently optimised extended LEPS surface [204]. The quantum mechanical results were transformed to three dimensions by the information theoretic procedure and are in good agreement with the distributions determined in the chemiluminescence experiments. However, three-dimensional trajectory calculations on the surface consistently underestimate (FR) at thermal energies and it is concluded that the LEPS surface which was optimised using one-dimensional calculations does not possess the angular dependence of the true three-dimensional surface. This appears to result from the lack of flexibility of the LEPS form. Trajectory studies [196] for H + Cl2 on another LEPS surface find a similar disposal of the enhanced reagent energy as was found for H + F2. The effect of vibrational excitation of the Cl2 on the detailed form of the product vibrational and rotational state distributions was described in Sect. 2.3. 

Many semi-classical and quantum mechanical calculations have been performed on the F + H2 reaction, mainly being restricted to one dimension [520, 521, 602]. The prediction of features due to quantum-mechanical interferences (resonances) dominates many of the calculations. In one semi-classical study [522], it was predicted that the rate coefficient for the reaction F (2P1/2) + H2 is about an order of magnitude smaller than that for F(2P3/2) 4- H2, which lends support to the conclusion [508] that the experimental studies relate solely to the reaction of ground state fluorine atoms. Information theory has been applied to many aspects of the reaction including the rotational energy disposal and branching ratios for F + HD [523, 524] and has been used for transformation of one-dimensional quantum results to three dimensions [150]. Linear surprisal plots occur for F 4- H2(i> = 0), as noted before, but non-linear surprisal plots are noted in calculations for F + H2 (v < 2) [524],... 

The energy disposal and effective upper state lifetimes have been reproduced using classical trajectory calculations a quasi-diatomic assumption was made to determine the slope of the section through the upper potential energy surface along the N—a bond from the shape of the u.v. absorption profile. The only adjustable parameter was the assumption of a parallel transition in the quasi-diatomic molecule. In contrast, a statistical adiabatic channel model which assumed dissociation via unimolecular decomposition out of vibrationally and rotationally excited level in the ground electronic state (following internal con-... 

An assumed model potential surface and the energy disposal observations can be related via comparison of classical (or quasiclassical) trajectory results to the experimentally measured product state distributions. In the latter part of this review the energy disposal calculated from model potential surfaces designed to simulate a given, well-studied reaction is discussed and compared to the experimental distributions. The classical or quasiclassical trajectory calculations become much more difficult for cases having more than three or four atoms, and the use of approximate models, empirical analogies, and chemical intuition becomes necessary. For such situations the information theoretic analysis developed by Levine and Bernstein is particularly valuable and will be used in this review. 

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