Atomic reaction systems

Thus, the critical measure of the applicability of a method to polyatomic reaction dynamics is the scaling of its computational cost with respect to the number of basis functions or degrees of freedom. Since the standard time-independent scattering methods solve boundary-value problems, they scale as with the number of basis functions N, and are thus difficult to extend to large systems. Until a few years ago, the reduced-dimensionality approach (RDA) [32, 33] provided the only means for treating the four-atom reactive scattering problem in which a four-atom reaction system is reduced to an effective atom-diatom system through the elimi-... 

The second term is the diabatic electronic potential matrix of a tetra-atomic reaction system. The kinetic energy operator of the system is given by ... 

In this chapter we present the time-dependent quantum wave packet approaches that can be used to compute rate constants for both nonadiabatic and adiabatic chemical reactions. The emphasis is placed on our recently developed time-dependent quantum wave packet methods for dealing with nonadiabatic processes in tri-atomic and tetra-atomic reaction systems. Quantum wave packet studies and rate constants computations of nonadiabatic reaction processes have been dynamically achieved by implementing nuclear wave packet propagation on multiple electronic states, in combination with the coupled diabatic PESs constructed from ab initio calculations. To this end, newly developed propagators are incorporated into the solution of the time-dependent Schrodinger equation in matrix formulism. Applications of the nonadiabatic time-dependent wave packet approaches and the adiabatic ones to the rate constant computations of the nonadiabatic tri-atomic F (P3/2, P1/2) + D2 (v = 0,... 

The most widely studied F atom reaction system is that of F plus ethylene, which was initially studied for the purpose of using ethylene as a scavenger in CF4 systems, and more recently wifc interest in the excited fluoroethyl radical intermediate. Studies using widely different sample preparation procedures and irradiation conditions are mutually consistent, ( , jj) and have demonstrated that the kinetics of the F atom reactions under study are independent of their irradiation history. 

The present pure calculations illustrate the significance of non-Boltzmann rate coefficients for hot atom reaction systems, bxnce i (t) is a strongly varying function, Eq. 22 cannot be approximated by a first order linear differential rate expression. The mean hot atom reactive lifetime is given by Eq. 26. 

There is one special class of reaction systems in which a simplification occurs. If collisional energy redistribution of some reactant occurs by collisions with an excess of heat bath atoms or molecules that are considered kinetically structureless, and if fiirthennore the reaction is either unimolecular or occurs again with a reaction partner M having an excess concentration, dien one will have generalized first-order kinetics for populations Pj of the energy levels of the reactant, i.e. with... 

Atoms and free radicals are highly reactive intermediates in the reaction mechanism and therefore play active roles. They are highly reactive because of their incomplete electron shells and are often able to react with stable molecules at ordinary temperatures. They produce new atoms and radicals that result in other reactions. As a consequence of their high reactivity, atoms and free radicals are present in reaction systems only at very low concentrations. They are often involved in reactions known as chain reactions. The reaction mechanisms involving the conversion of reactants to products can be a sequence of elementary steps. The intermediate steps disappear and only stable product molecules remain once these sequences are completed. These types of reactions are refeiTcd to as open sequence reactions because an active center is not reproduced in any other step of the sequence. There are no closed reaction cycles where a product of one elementary reaction is fed back to react with another species. Reversible reactions of the type A -i- B C -i- D are known as open sequence mechanisms. The chain reactions are classified as a closed sequence in which an active center is reproduced so that a cyclic reaction pattern is set up. In chain reaction mechanisms, one of the reaction intermediates is regenerated during one step of the reaction. This is then fed back to an earlier stage to react with other species so that a closed loop or... 

Enamines have a three-atom tt system and are thus in principle capable of reaction with an electrophile on nitrogen or on carbon as shown by the mesomeric forms (1) and (2),... 

This reaction system illustrates that metal-atom reactions can proceed in unexpected directions, in this case, the oxidation of CO to CO2. 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

Accurate quantum reaction theory has been achieved for the simplest possible chemical reaction system atom-diatom reactions A + BC — AB + C, AC + B.3 5 In particular, for three decades, rigorous and detailed quantum calculations in three-dimensions have been carried out for the... 

Similar to the diatom-diatom reaction, the initial wavefunction is chosen as the direct product of a localized translational wavepacket for R and a specific (JMe) state for the atom-triatom system with a specific rovibrational eigenstate (z/o, Lo,Bo) f°r the triatom ABC ... 

In general three position variables will be needed to specify the potential energy of the reaction system. These may be the X-Y, Y-Z, and X-Z internuclear distances or two internuclear distances and the included angle. Even in this relatively simple case, four dimensions would be required for generation of the potential energy surface. However, if we restrict our attention to linear configurations of these atoms, it is possible... 

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