Ground-state wave function reaction

Figure 8. (a) Pulse sequence resulting from optimization of the control field to generate H in the same reaction as studied in Fig. 6. (6) The Husimi transform of the pulse sequence shown in (a). (c) Time dependence of the norms of the ground-state and excited-state populations as a result of application of the pulse sequence shown in (a). Absolute value of the ground-state wave function at 1500 au (37.5 fs) propagated under the pulse sequence shown in (a), shown superposed on a contour diagram of the ground-state potential energy surface. (From D. J. Tannor and Y. Jin, in Mode Selective Chemistry, B. Pullman, J. Jortner, and R. D. Levine, Eds. Kluwer, Dordrecht, 1991.)...

We can immediately draw important conclusions about molecular stability from Figure 2.2, and the identification of It] with the HOMO-LUMO energy gap. Soft molecules will be less stable than similar hard molecules. They will dissociate or isomerize more readily. In the perturbation theory of such reactions, change occurs by mixing in excited-state wave functions with the ground-state wave function. If Q is the reaction coordinate,... 

A collection of nuclei will have a ground state wave function with a certciin number of nodal surfaces of various kinds, a and n. As the nuclei are rearranged to correspond to a chemical reaction, these nodal surfaces will be distorted and deformed. However, except for certain limiting cases, their number and kind will not change. In other words the wave function maintains its topological identity. This is the more generalized equivalent of conservation of orbital symmetry. 

We may object that our conclusions seem quite naive. Indeed, there is something to worry about. We have assumed that, independent of the reaction stage, the ground-state wave function represents a single Slater determinant I o, whereas we should use a configuration interaction expansion. In such an expansion, besides the dominant contribution of I o, double excitations would be the most important (p. 653), whieh in our simple approximation of the three (p orbitals means a leading role for 2d and i sd-... 

And what about the end of the reaction We have calculated that C2 (DA) = > 0 and (DA) = i > 0. This means that at the end of the reaction, the coefficient corresponding to the DA structure will be certainly smaller than (DA) = 0.25, the value obtained for the single determinant approximation for the ground-state wave function. 

What, therefore, represents the ground-state wave function at the end of the reaction ... 

Now, let us ask what is the contribution of each of these structures in Fo, 2d, and in the three stages of the reaction. This question is especially important for I o> because this Slater determinant is dominant for the ground-state wave function. The corresponding contributions in 2d and 1 3 are less important because these configurations enter the ground-state Cl wave function multiplied by the tiny coefficients k. We have already calculated these contributions for the DA structure. The contributions of all the structures are given in Table 14.2 (with the largest contributions in bold). 

Table 14.4. Expansion coefficients Co(i) at the acceptor-donor structures in the ground-state wave function at various stages of the 8 2 substitution reaction of ethylene reactant (R), intermediate (I), and product (P). The most important contributions are in bold. ...

What therefore represents the ground-state wave function at the end of the reaction lb answer this question let us consider first all possible occupations of the three energy levels (corresponding to n, x, X ) four electrons. As before we assume for the orbital energy levels < s <. The number of such singlet-type... 

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