Close-coupling approach

The close-coupling approach works readily and simply if the reaction is purely melastic . The method can also be made to work very simply for a single product arrangement (as in collinear reactions), by using a twisted coordinate system, most conveniently reaction path coordinates [37, 38 and 39] as shown in figure B3.4.3. 

Close-coupling approach to positron scattering from potassium. J. Phys. B At. Mol. Opt. Phys. 21 L611-L616. 

Abstract. Cross sections for electron transfer in collisions of atomic hydrogen with fully stripped carbon ions are studied for impact energies from 0.1 to 500 keV/u. A semi-classical close-coupling approach is used within the impact parameter approximation. To solve the time-dependent Schrodinger equation the electronic wave function is expanded on a two-center atomic state basis set. The projectile states are modified by translational factors to take into account the relative motion of the two centers. For the processes C6++H(1.s) —> C5+ (nlm) + H+, we present shell-selective electron transfer cross sections, based on computations performed with an expansion spanning all states ofC5+( =l-6) shells and the H(ls) state. 

In principle, Equation (3.5) represents an infinite set of coupled equations. In practice, however, we must truncate the expansion (3.4) at a maximal channel n which turns (3.5) into a finite set that can be numerically solved by several, specially developed algorithms (Thomas et al. 1981). The required basis size depends solely on the particular system. The convergence of the close-coupling approach must be tested for each system and for each total energy by variation of n until the desired cross sections do not change when additional channels are included. Expansion (3.4) should, in principle, include all open channels (k > 0) as well as some of the closed vibrational channels (k% < 0). Note, however, that because of energy conservation the latter cannot be populated asymptotically. 

Within the close-coupling approach each partial photodissociation wavefunction (R,r Ef,n) is represented by the expansion functions Xn (R >Ef,n) and the vibrational basis functions n(r) with n and n = 0,1,2,..., n. Here, n denotes the highest state considered in expansion (3.4). It is not necessarily identical with nmox, the highest state that can be populated for a given total energy. In order to simplify the subsequent notation we consider the total of the radial functions as the elements Xn n R i Ef) of a (n + 1) x (n + 1) matrix... 

In this section we will explain the essential mechanism of vibrational predissociation by virtue of a linear atom-diatom complex such as Ar H2. Figure 12.1 illustrates the corresponding Jacobi coordinates, t In particular, we consider the excitation from the vibrational ground state of H2 to the first excited state as illustrated in Figure 12.2. The close-coupling approach in the diabatic representation, summarized in Section 3.1, provides a convenient basis for the description of this elementary process. For simplicity of presentation we assume that the coupling between the van der Waals coordinate R and the vibrational coordinate r is so weak that it suffices to include only the two lowest vibrational states, n = 0 and n = 1, in expansion (3.4) for the total wavefunction,... 

McGuire, P. and Kouri, D.J. (1974). Quantum mechanical close coupling approach to molecular collisions, -conserving coupled states approximation, J. Chem. Phys. 60, 2488-2499. 

Molecular beam scattering experiments provide direct and detailed information about the repulsive part of the interaction potential between the colliding particles. With such scattering data available, detailed studies of the short and intermediate-range parts of the potential energy surfaces can readily be made, provided that accurate theoretical methods, e.g. quantum close-coupling approach, are used to describe the scattering phenomena. 

Tennyson J, Sutcliffe BT (1982) The ab initio calculation of the vibrational-rotational spectrum of triatomic systems in the close-coupling approach, with KCN and H2Ne as examples. J Chem Phys 77 4061 1072... 

Both close-coupling approaches (h q)erspherical or with absorbing potentials) and iterative/time-dependent absorbing-potential arrangement-decoupling approaches are readily extended to three-dimensional atom-molecule and molecule-molecule scattering. The wavefunction representation becomes more complicated and includes rotational matrices, but the essence and application of the method remains analogous [58. 65. 75. 76]. 

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