Well, having roamed around the solar system (and the cosmos, but that’s a page for another day), and ducked a little into evolutionary anthropology, it looks like time to dip my toe into the waters of physical chemistry.
Or, rather, dip my toe into the physical chemistry of water.
For background, here’s a good start: http://www.ccl.net/cca/documents/dyoung/water/lp3.shtml
And, finding myself a bit short of time to compose my thoughts, here’s my take on a water molecule model, marked with pits, peaks, and passes, contours, ridges and valleys. It’s meant to represent a “free” water molecule, not connected to any other. Think of it as a unit of steam, let’s say.
The surface is what chemists call an isosurface, which, I suppose, means that from the electron’s point of view, it (the surface) is all at the same level; it has no contours, no peaks or pits If we conceive of “a hypothetical being of intelligence but [electronic] order of size” (a la Maxwell’s Demon) and two-dimensional extent (a la one of Abbott’s Flatlanders) and set her loose on the isosurface, equipped with a quantum altimeter, the instrument will give a constant reading, no matter where she travels on the isosurface.
I’m not a chemist, so I leave it an open question what readings she’d get on her quantum odometer, making various circumferential traverses around her world. However, from our point of view, there are shorter and longer straight paths of travel to return to the place of departure.
If we equip our Thomson’s Demon with a classical altimeter, she’d eventually be able to locate the critical points and paths, and level contours, that I’ve sketched on the model and transform to the constant-scale natural boundary maps.
I say “sort of” on the model because I goofed in an early step — I made the the hydrogen angle 120 degrees, roughly ten degrees more than it should be for regular water, and 15 degrees out of whack for heavy water. Thus the maps are halted at the sketch stage while I fabricate a better model. But at least you see generally what results when mapping molecules.
To me, the interesting speculation is the animation (think: “map able to change its outline”) that would result from knocking extra neutrons into the system (and then out again, of course). If I read the encyclopedia correctly, each extra neutron in the hydrogen atom cranks the angle closed by five degrees or so, and thus the isosurface would morph accordingly. This will change lengths along the critical paths, and, because the critical paths are mapped at constant scale, the map will follow suit, and reveal the precise extent and locations of these otherwise subtle changes in shape. Neat, huh?