Molecular Imaging. Markus Rudin

      Q: My ideas are much more clear now.

      M: So are mine.

      Q: Through these discussions things become more clear. M: Yes, and that’s the beauty of discussions.

      7.M. “If you are thinking of each pair X^∗ and X as occupying some section of the 10²³–1 dimensional hypersurface that constitutes the [whole] TS and if you are assigning to each pair, to each member of the pair a free energy, then the one that has the minimum free energy, that would be the TS [considered in the paper]. You don’t have to consider the full thing, you can consider just an important part of it. In other words, it is wise to consider the subset of the hypersurface which is associated with the minimum free energy. The different parts of the hypersurface correspond to different thermodynamic systems and you pick the one that has the minimum free energy. . . you think of that 10²³–1 dimensional hypersurface effectively broken into different systems. . . each polarization function being specific of each system.”

      8.M: “The 1956 theory neglects interactions of other pairs of reactants on this particular pair, it neglects the effects of other reactants, it focuses only on this pair. . . it treats the different pairs as independent of each other. A later paper treats the effects of other ions, of the ionic atmosphere, on the particular pair.”

      9.M. used the variational condition δP_udV = 0 to demonstrate that P_u = α_uE. He did so because he wanted to be sure that there were no other constraints that would give the earlier standard equilibrium result P_u = α_uE, that is, he wanted to be sure that if he didn’t impose other conditions he would get the usual expected result.

      10.M. points out that when one considers the condition F^∗ = F, that means that one is at the intersection of the potential energy surfaces and one should consider that F^∗ is a function of P_u and that F^∗ equals F as function of P_u and that when one considers δF one means δF obtained by varying δP_u. It is from the condition F^∗ = F that δF^∗ − δF = 0 follows. If one plots the free energies of reactants and products as functions of P_u, one has δF^∗ = 0 at the bottom of the reactants free energy well, δF = 0 at the bottom of the free energy well of the products with different values of P_u corresponding to those two minima. One has δF^∗ − δF = 0 at the TS at the same common value of P_u.

      11.M. comments on the mistake that was made by the authors in Ref. [27] in the calculation of tunneling probability:

      M: “They calculated the probability of tunneling, but that’s tunneling of the electron, what they should have done is multiply that tunneling by the number of times the electron is hitting that tunneling barrier, in this classical picture you have sort of classical frequency, but that’s 10¹³ per second, so [overlooking that] they made a big error.”

       References

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