Rotational sudden approximation

As opposed to the adiabatic limit, we assume in the sudden approximation that the internal motion is slow compared to the external (i.e., translational) motion. Most familiar is the rotational sudden approximation which is frequently exploited in energy transfer studies in full collisions (Pack 1974 Secrest 1975 Parker and Pack 1978 Kouri 1979 Gianturco 1979 ch.4). Its application to photodissociation is straightforward and will be outlined below for the model discussed in Section 3.2. 

Within the rotational sudden approximation we assume that the interaction time is much smaller than the rotational period of the fragment molecule so that the diatom BC does not appreciably rotate from its original position while the two fragments separate. In terms of energies, this requires the rotational energy, Erot, to be much smaller than the total available energy. If that is true, the operator for the rotational motion of BC, hrot, can be neglected in (3.16). The partial differential equation thus becomes an ordinary differential equation,... 

Further simplifications upon CS involve approximations to the rotational motions. Here there are two schools of thought as to how best to do this. One school argues that since the rotational periods are usually slow compared to vibrational periods, it makes sense to use the rotational sudden approximation wherein the atom-diatom orientation angle is fixed for motion in the reagent and product arrangement channels >The other school argues that since rotational motion correlates into bend motion along the reaction path, and the bend is only weakly coupled by curvature to reaction path motions, while at the same time the bend frequency is comparable to the other perpendicular modes near the reaction bottleneck, it is more... 

A futther simplification in effort in this treatment is obtained by invoking a rotational sudden approximation to eliminate coupling between different rotational states. This reduces the effort required for a 3D calculation to that for a set of collinear ones, and thus it widens the possible domain of practical calculations to... 

One very effective approach for partitioning the molecular Hamiltonian so as to simplify vibration-rotation interaction effects involves the use of classical rotational sudden approximations. These are primarily applicable to high-velocity collisions, and they have been applied quite effectively to the Li" + CO2 system.In... 

Quasiclassical trajectory calculations are performed using a number of different fits to the ah initio 0( P) + H2O ground state potential energy surface. We perform full three-dimensional calculations, and we also use a classical rotational sudden approximation. The use of several fits allows the effect of variations in the potential surface on the computed cross sections to be investigated. In all cases the water molecule is initially in its ground vibrational state. 

Figure B3.4.14. The infmite-order-sudden approximation for A+ BC AB + C. In this approximation, the BC molecule does not rotate until reaction occurs.

Goldflam R., Green S., Kouri D. J. Infinite order sudden approximation for rotational energy transfer in gaseous mixtures, J. Chem. Phys. 67, 4149-61, (1977). 

The sudden approximation is easy to implement. One solves the onedimensional Schrodinger equation (3.43) for several fixed orientation angles 7, evaluates the 7-dependent amplitudes (3.47), and determines the partial photodissociation amplitudes (3.46) by integration over 7. Because of the spherical harmonic Yjo(x, 0) on the right-hand side of (3.46), the integrand oscillates rapidly as a function of 7 if the rotational... 

Atabek, O., Beswick, J.A., and Delgado-Barrio, G. (1985). A test of the rotational infinite order sudden approximation in molecular fragmentation, J. Chem. Phys. 83, 2954-58. 

Korsch, H.J. and Schinke, R. (1980). A uniform semiclassical sudden approximation for rotationally inelastic scattering, J. Chem. Phys. 73, 1222-1232. 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Exploiting a four-dimensional rotation group analysis, the transformation between harmonic expansions in the two coordinates systems was given explicitly [32], as well as the most general representation in terms of Jacobi functions [2], In practice, however, the two representations are in one form or another those being used in all applications and specifically in recent treatments of the elementary chemical reactions as a three-body problem [11,33-36]. For example, Eqs. (29)-(31) and Eqs. (47)-(49) permitted to establish [37] the explicit connection between coordinates for entrance and exit channels to be used in sudden approximation treatments of chemical reactions [38],... 

The relevance of optical potentials to direct molecular reactions was considered by Micha (1969). Numerical results were presented for real and imaginary parts of the optical potential for H + H2, in an adiabatic approximation that included vibrational and rotational motion of H2. Distortion, adiabatic and sudden approximations to optical potentials, and their validity, have recently been described (Micha, 1974). This work also presents procedures for calculating upper and lower bounds to the second term of f P, in certain ranges of energies. The various approaches are developed in detail for atom-diatom collisions. 

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