Atom-diatom reactions

The reaction of an atom with a diatomic molecule is the prototype of a chemical reaction. As the dynamics of a number of atom-diatom reactions are being understood in detail, attention is now being turned to the study of the dynamics of reactions involving larger molecules. The reaction of Cl atoms with small aliphatic hydrocarbons is an example of the type of polyatomic reactions which are now being studied [M, 72, 73]. 

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... 

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

We mention, in addition, that complete and highly accurate ab initio11 theoretical solutions for a number of simple atom-diatom reactions like H + HD —> H2 + D have been obtained. Recently, the quantum dynamics of the four-atom reaction H2 + OH —> H20 + H and its reverse has also been reported [9,10], The general features of these results at the level of k(T) will typically agree fairly well with the quasi-classical approach, provided the temperature is sufficiently high so that quantum mechanical tunneling is negligible. 

We shall discuss some examples of reactions of excited van der Waals complexes. Up to now, only a few examples of a atom-diatom reactions have been studied—the atom being Hg, Ca, or Xe, and the diatom being H2 and halogen-containing molecules. These examples show clearly the new features in the reaction dynamics, such as orbital specificity, selectivity in the products, products state distribution, and observation of the intermediate states. 

Under the high density after the impact, several O2 and N2 molecules can interact simultaneously. While the high density conditions prevail, many reactions can occur through different mechanisms the four-center N2 + O2 —> 2NO reaction and the Zeldovich - type atom-diatom reactions, O -t- N2 —> NO + N and N -t- O2 — NO -t- O, just as in the case of a cluster containing a single N2/O2 pair, and also by a new mechanism, a multicenter one, where more than four atoms interact simultaneously. A snapshot of a multiatom configuration is shown in Fig. 20. 

The development of theory for reliable calculations of chemical dynamics has two components the construction of accurate, ab initio, multidimensional potential energy surfaces (PESs) and the performance of reactive scattering calculations, either by time-independent (TI) or time-dependent (TD) methods, on these surfaces. Accurate TI quantum methods for describing atom-diatom reactions, in particular for the benchmark H + H2 reaction, have been achieved since 1975.[1,2,3] Many exact and approximate theories have been tested with the H + H2 reaction.[4,5]... 

Resonance energies. In Table I, the resonance energies for three collinear atom-diatom reactions are compiled. These include three resonances each for the H + FH and D + FD reactions and the lowest-energy resonance for H + H2 on the PK2 surface. All energies are relative to the minimum of the asymptotic reactant well. 

Table I. Resonance Energies (kcal/mol) for Three Collinear Atom-Diatom Reactions... 

Resonances in three-dimensional atom-diatom reactions... 

For three-dimensional atom-diatom reactions with collinear minimum-energy-paths, the adiabatic potential curve is given by... 

We present in this subsection the TD treatment for calculating initial state-specific total reaction probabilities for the atom-diatom reaction, H + 02 - HO + O. This is a particularly important combustion reaction (86) and it presents a real challenge to theoretical calculations because the PES has a deep well of more than 2.3 eV which supports many bound states and narrow resonances. Much progress has been made in the past few years by Neuhauser et al. in TD calculation of atom-diatom reactive scattering... 

We will also find it useful to present densities that result from taking the energy derivative of sums of other subsets of the state-to-state reaction probabilities. Parity-specific densities can be obtained from the derivative of the sum of Pnn having the same parity P = (—l)7 (When 7 = 0, = /, and so P = +1.) Furthermore, for atom-diatom reactions of the form A + H2 - AH -I- H, we can define a spatial permutation symmetry S, which equals +1 for para hydrogen and —1 for ortho hydrogen. Symmetry-specific densities are obtained by summing those Pnn- with the same spatial permutation symmetry. Densities for a specific set (7, P, S) are denoted p,/ s when these are summed over P and S, the above densities p are obtained. 

The cross section and rate constant expressions for an A + reaction, where both reactants are polyatomics, are the same as those above for an atom + diatom reaction, except for polyatomics there are more vibrational and rotational quantum numbers to consider. If the polyatomics are symmetric tops with rotational quantum numbers J and K, the state specific cross section becomes a, (urel, vA, JA, KA, vB, JB, KB), where vA represents the vibrational quantum numbers for A. If the polyatomic reactants have Boltzmann distributions of vibrational-rotational energies, the reactive cross section becomes a function of viel and T = TA = TB [i.e., ffr(vTCl T)] and is determined by summing over the quantum numbers as is done in Eq. 

During the past few years we have observed an intensive development of many-channel approaches to the collision problem. In particular, the coupled-channels method is based on an expansion of the total wave fmiction in internal states of reactants and products and a numerical solution of the coupled-channels equations.This method was applied in the usual way to the atom-diatom reaction A + BC by MOR-TENSBN and GUCWA /86/, MILLER /102/, WOLKEN and KARPLUS /103/, and EL-KOWITZ and WYATT /101b/. Operator techniques based on the Lippmann-Schwinger equation (46.II) or on the transition operator (38 II) has also been used, for instance, by BAER and KIJORI /104/ The effective Hamiltonian approach( opacity and optical-potential models) and the statistical approach (phase space models, transition state models, information theory) provide other relatively simple ways for a solution of the collision problem in the framework of the many-channel method /89/<. 

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