Conversations with Henry

Henry:  Did you see that business in the news about negative absolute temperatures?

Me:  You mean this?

Henry:  Yeah, that.  Good thing you know how to manipulate the Internet. I never got the hang of it. You know what that news reminded me of?

Me: No, what Henry?

Henry:  The inverted Marcus region.

Me: Remind me what the inverted Marcus region is.

[Henry moves to the white board, grumbling that people no longer use chalk & blackboards. He sketched three related figures, and then explained them in words]:

Henry: Rudy Marcus laid out three different scenarios for the reaction coordinate of a simple "downhill" reaction using intersecting parabolas to represent reactant and product. Parabolas have a long history in physics (think of pendulums, and they "track" the potential energy in molecules). In the first, notice that the "initial state" reactant parabola is slightly higher in energy than the "final state" product parabola; where they cross represents a moderately uphill barrier given by the distance, ΔG^‡.

In the second (middle) scheme, the initial state (left) parabola is higher in energy while the final state parabola stays the same—follow?  He got there by translating the left hand reactant parabola straight upwards and their intersection slides "down." The barrier to the more downhill reaction is now zero. See that?

Me: Yes!

Henry:  Here is where Marcus was an absolute genius:  if you keep on going as in the third scheme, the initial state parabola gets higher still—this is now a very downhill reaction—but notice that the barrier, ΔG^‡, goes back up because the intersect climbs up the other side!  This is the so-called "Marcus Inverted Region" and is utterly counter intuitive that a more downhill state should require more energy to reach. Boy, he really shook things up with that one!

Me: Fine, but how does that translate to the real world?

Henry: What?  Didn't you read my other stuff?

Me: Here's what I think...I've been saying all along that uphill effort requires more energy than downhill effort, for example here.  But suppose that we have something really severe like the Fiscal Cliff.  Suppose that the fall is so downhill that we will actually face a higher hurdle to get down there than if it weren't so precipitous.

Henry: Hair-brained economics!