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The examples discussed in the preceding chapters concentrated on three or at most four atom systems. The problem of how the theory may practically be extended to larger systems is discussed. The first approach considered is an approximate one, involving ignoring or approximating the vibrational motion of some of the chemical bonds that are not broken during the reaction. The next approach discussed, the Multi-Configuration Time-Dependent Hartree method (MCTDH), is a more general one which can systematically be improved until an exact solution is obtained. Finally, a method for directly computing rate constants without first calculating S matrices, based on the so-called “flux–flux auto-correlation method”, is described.

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