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Mazur and Rubin then follow what happens to the initial wave packet in accord with Eq. (192),which is solved numerically by a finite-difference approximation of a high order of accuracy. By computing the probability of finding part of the packet at a final time t, in a region such that rais small and r, is large, they can thus determine the probability of reaction to a product state. , V(7,,r2)= 0. Also, although one could take different wave packets representing different velocities, Mazur and Rubin analytically prepare a special wave packet which represents a classical distribution of velocities.

Thus, the valence-bond method may be regarded as a special case of the molecular orbital (MO) approximation in a “linear combination of atomic orbitals” (LCAO) modification which omits ionic terms. It should be emphasized, however, that although we have “derived” valence bonds from molecular orbitals, this is not necessary and has been done merely to show the relationship between the two methods. We could just as easily have written ab initio the particular linear combination of atomic orbitals which excludes ionic terms.

1) reduces, after center-of-mass motion is removed, to (191) 54 HENRY AROESTE where m,,m,,and m3are the masses of atoms B, C, and A, respectively; rl is the distance between B and C; and 7, is the distance between A and C. Suppose now that we have a wave packet representing the initial state of the system, in which the average relative momentum between A and BC is Po). rr(dR)2]-) exp [-(R + iP(O)R/;ti] (194) - R(0))2/4(4R)2 In Eq. (194) (dR), is the root-mean-square deviation from the mean value R(0).