Entrance and exit channels

Figure 14.8 The overall structure of the CotA laccase from Bacillus subtilis showing the entrance and exit channels for dioxygen and water, above and below the trinuclear cluster, respectively. (From Bento et al., 2006. With kind permission of Springer Science and Business Media.)...

Figure 3.16 The PES for the F+HCl reaction in the entrance and exit channels as a function of the Jacobi coordinates [R, y).

In Figure 3.16, we show the potential contours in the entrance and exit channels. In these plots, the diatomic distance is held fixed at the equilibrium bond length and the PES is plotted against Jacobi distance and angle (R, 0). A vdW well of depth 2.5 kcal/mol is observed in the entrance channel with a bent configuration. In the exit channel, a collinear vdW well of depth 2.0 kcal/mol is found. Variational calculations of the vibrational states reveal that several bound states exist in these wells [128]. More pertinent to the present discussion, the vdW wells can also lead to the existence of resonance states in both the entrance and exit channels. 

Although most resonances in the F+HCl system are clearly of the reagent type or product type, there are some mixed" cases. Because the resonance manifold is dense, degeneracies can occur between zero-order reagent-type or product-type states. Thus, the resonance wavefunctions for these states are linear combinations of entrance and exit channel expressions. 

If we consider the potential energy as a function of the Jacobi coordinates X and X2 and draw the energy contours in the X1-X2 plane, then the entrance and exit valleys will asymptotically be at an angle to one another and in the mass-weighted skewed angle coordinate system parallel to its axes. So the idea with this coordinate system is that it allows us to directly determine the atomic distances as they develop in time and that it shows us the asymptotic directions of the entrance and exit channels. 

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],... 

Consider then an adiabatic well in the hyperspherical coordinate system. Classically, the motion of the periodic orbit at the well would be an oscillation from a point on the inner equipotential curve in the reactant channel to a point on the same equipotential curve in the product channel. This is qualitatively the motion of what are termed "resonant periodic orbits" (RPO s). For example the RPO s of the IHI system are given in Fig. 5. Thus, finding adiabatic wells in the radial coordinate system corresponds to finding RPO s and quantizing their action. Note that in Fig. 5 we have also plotted all the periodic orbit dividing surfaces (PODS) of the system, except for the symmetric stretch. By definition, a PODS is a periodic orbit that starts and ends on different equi-potentials. Thus the symmetric stretch PODS would be an adiabatic well for an adiabatic surface in reaction path coordinates. However, the PODS in the entrance and exit channels shown in Fig. 5 may be considered as adiabatic barrieres in either the radial or reaction path coordinate systems. Here, the barrier in radial coordinates, has quantally a tunneling path between the entrance and exit channels. 

Figure 16. Reaction coordinate trajectory outlining the entrance and exit channels of the hydrolysis. reaction.

G. C. Lynch, P. Halvick, M. Zhao, D. G. Truhlar, C.-H. Yu, D. J. Kouri, and D. W. Schwenke, Converged three-dimensional quantum mechanical reaction probabilities for the F + H2 reaction on a potential energy surface with realistic entrance and exit channels and comparisons to results for three other surfaces, J. Chem. Phys. 94 7150 (1991). 

Connections between harmonics are important for providing orthogonal transformations between basis set expansions pertaining to different Jacobi parametrizations. They were first introduced by Raynal and Revai. Their use, especially for nonorthogonal treatments where it may be convenient to expand over different basis sets for entrance and exit channels, is still to be exploited. The extension to more than three particles is the goed of current investigations. 

There are four energy parameters in T 0) (i) the potential energy difference between the entrance and exit channels, U(—oo) (ii) the height of the potential barrier,... 

Besides the barrier height, the widths of the entrance and exit channels also count. 

Fig. 14.27. Electron transfer in the reaction DA -> D+A , as well as the relation of the Marcus parabolas to the concepts of the conical intersection, diabatic and adiabatic states, entrance and exit channels and the reaction barrier. Panel (a) shows two diabatic surfaces as functions of the and 2 variables that describe the deviation from the comical intersection point (within the...

Coriolis coupling (p. 906 and 912) critical points (p. 888) cross section (p. 901) curvature coupling (p. 906 and 914) cycloaddition reaction (p. 944) democratic coordinates (p. 898) diabatic and adiabatic states (p. 949) donating mode (p. 914) early and late reaction barriers (p. 895) electrophilic attack (p. 938) entrance and exit channels (p. 895) exo- and endothermic reactions (p. 909) femtosecond spectroscopy (p. 889) Franck-Condon factors (p. 962) intrinsic reaction coordinate (IRC) (p. 902) inverse Marcus region (p. 954) mass-weighted coordinates (p. 903)... 

C.AB) systems respectively and kyj and ky are the wavenumbers of the Initial and final collision systems respectively. To avoid a cumbersome notation, the entrance and exit channels will be labelled by... 

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