Molecular Imaging. Markus Rudin

thermodynamic ensemble and so it consists of an enormous number of microstates x^∗.”

      NOTE: At an “infinite” number of places on the intersection surface, there may be a microscopic reacting system x^∗ with the same nuclear configuration and the same energy of a microscopic products system x where the electron transfer reaction may happen.

      M: “The activated complex or the transition state is of 10²³–1 configurations, if the dimension of the space is 10²³, it’s a hyper-surface one dimension less than the entire phase space. That’s a transition state.”

      8.M: “The electron tunneling . . . that’s a different way of describing the overlap of electronic wave functions if they don’t overlap well, if you have a weak overlap of wave functions. An alternative description is that to go from one to the other you tunnel and there is a quantitative relation of the two, you can take the overlap of the wave functions, you can use semi-classical theory and get a tunneling probability out of it, so there is a whole theory associated with that.”

      NOTE: M. comments below on Pauling’s description of the oscillation back and forth between two configurations in relation with the configuration of the system at the TS and that immediately after the electron transfer:

      M: “That description is OK for a static system, but your system isn’t static, so you don’t have that kind of oscillation. If you calculate that way the probability of going from one to the other, you get that right ballpark, but conceptually that theory is not right because the nuclei are moving, so you don’t have that oscillation back and forth, you would have it if the nuclei were static and if you were exactly at the crossing point of those crossing energy curves, but that’s not what you have, so you get a result that is on the right ballpark, but it’s more conceptual than actually describing the process as it occurs when you take into account the combined electron-nuclear motion. But if you had a static picture . . . that gives you sort of the frequency of tunneling. One would use that way if one tried to be moderately modern. You don’t do that way because you don’t have static nuclei, nevertheless you get some result out of it, which is right ballpark, but you have to take into account that [in the case of Pauling’s treatment] you are dealing with static nuclei which don’t exist. This is a question almost of beauty of theory, I mean not that the theory which is unbeautiful gives you answers wrong by any magnitude, it’s just that’s not really the most complete picture. Pauling gives you a picture of what it would be statically and in a ballpark, but the system doesn’t oscillate back and forth, so physically that part isn’t right [for ET] but the oscillation is related to the probability of tunneling. You won’t use that equilibrium description, that wouldn’t be a good quantum mechanical description, you wouldn’t say you have a static system and that there is an equilibrium with the other electronic structure . . . there is no equilibrium there, you would treat the transition. Once you reach the TS you have one electronic configuration and then there is a certain probability that you form the other at the same nuclear configuration, but there is not a back and forth going. Look at how LZ treats it. You go through identical nuclear configurations and you solve the Schrödinger equation that is appropriate for that whole process. In other words, you don’t sit still at the intersection region, it’s quite un-dynamical, it’s quite un-quantum-mechanical. In Pauling’s case the interaction is large and you don’t start with one configuration and go over to the other in his description.”

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