I don't know about you, but this picture has just blown my mind. What we're looking at here is an actual image which shows electrons orbiting around a molecule. Whoa.
Let me explain just what exactly is going on here. Pictured above is a single molecule of pentacene, made up of five rings of carbon atoms and bordered all the way around by hydrogen atoms. It looks like this:
Of course, the above diagram is just a representation of where the nuclei of the atoms are. We can take an actual image of the pentacene molecule using what's called an atomic force microscope:
An atomic force microscope (AFM) isn't anything like an optical microscope that you simply look through to make small things appear bigger. Instead, it's more like a very very very very very small bit of charcoal that you can rub on tracing paper placed over a surface to view carved patterns that you wouldn't otherwise be able to see. The tip of an AFM (also called a probe) is so small that you need an electron microscope to even see it:
To operate, the tip of the AFM moves across a surface, and when it encounters an atom or a molecule, the tip bumps up a little bit as it passes over. This jiggles a laser beam, which records precisely how much the tip was deflected. By making a bunch of passes, the AFM can gradually build up a sort of topographic map of a surface. It's also possible to place a single atom on the very tip of the AFM's probe, and by watching how that atom interacts with the atoms that it passes over, you can tell what's underneath.
Now, measuring an atom and measuring an electron orbital are two entirely different things. You probably know that in an atom, you've got the nucleus (protons and usually neutrons) in the middle, with electrons whizzing around the outside. But when electrons are hanging out with an atom or a molecule, they don't behave like particles. Instead, they behave more like waves. You can still think of an electron around an atom as a particle if you like, but the tricky bit to wrap your head around is that rather than existing in one specific spot, the electron instead has a certain probability that it will exist in a number of specific spots all at once, as defined by its wave function. This is what an orbital is: a region of probability than an electron will exist in a certain area.
If you're dealing with lots of electrons around different atoms all at once (like in a molecule), these orbitals all bunch up against one another, since multiple electrons can't* share the same orbital. To measure these tiny changes in probabilities across all the electron orbitals of a molecule, researchers suck a single atom of carbon dioxide onto the tip of their AFM. Carbon dioxide atoms have a very distinctive pattern of electron orbitals of their own, and by watching how those orbitals interact with a molecule, the researchers were able to make a map of where there definitely weren't electrons, and that let them estimate where the actual electron orbitals were and generate an image, which I've reposted below since you've probably forgotten what it looks like by now:
The two different pictures are showing two separate sets of orbitals: the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) which illustrates the full range of the orbiting electrons. On the bottom are mathematical models of what the orbitals should look like, and the actual images are pretty darn close, which I bet makes quantum physicists all over the world breathe a big sigh of relief. And as for practical applications, data like these could help with the construction of molecular machines that rely on "designer" orbitals to function.
*They can if they have different spins, but it's helpful not to worry about that when you're just trying to picture it in your head