I'm not saying it can never happen. It is theoretically possible to see atoms moving (And in fact using different technology, it has been done), but using electron microscopy to see the atoms moving will be very difficult and I don't think it will happen for many years. When you start talking about watching atoms move though you have to keep in mind that they are vibrating at petahertz (1015 times per second), and so our eyes wouldn't be able to see it anyways. We would have to artificially slow down what we were looking at to actually see anything. Now atomic displacement (As I was originally mentioning) is easy to detect, that is where we detect some permanent shift in the atom's position within a crystal lattice. But actual atomic motion (Or thermal motion) becomes much harder to display in a meaningful manner.
For first time, individual atoms seen keeping away from each other or bunching up as pairs
If you bottle up a gas and try to image its atoms using today's most powerful microscopes, you will see little more than a shadowy blur. Atoms zip around at lightning speeds and are difficult to pin down at ambient temperatures. If, however, these atoms are plunged to ultracold temperatures, they slow to a crawl, and scientists can start to study how they can form exotic states of matter, such as superfluids, superconductors, and quantum magnets. Ref. Source 5o.
Scientists set traps for atoms with single-particle precision
Researchers report a new method to use lasers as optical "Tweezers" to pick individual atoms out from a cloud and hold them in place. As the atoms are "Trapped," the scientists use a camera to create images of the atoms and their locations. Based on these images, they then manipulate the angle of the laser beams, to move individual atoms into any number of different configurations. Ref. Source 7c.
World's smallest magnifying glass makes it possible to see chemical bonds between atoms
For centuries, scientists believed that light, like all waves, couldn't be focused down smaller than its wavelength, just under a millionth of a meter. Now, researchers have created the world's smallest magnifying glass, which focuses light a billion times more tightly, down to the scale of single atoms. Ref. Source 2m.
Researchers create artificial materials atom-by-atom
Researchers have manufactured artificial materials with engineered electronic properties. By moving individual atoms under their microscope, the scientists were able to create atomic lattices with a predetermined electrical response. The possibility to precisely arrange the atoms on a sample bring 'designer quantum materials' one step closer to reality. By arranging atoms in a lattice, it becomes possible to engineer the electronic properties of the material through the atomic structure. Ref. Source 6b.
Scientists watch a molecule protect itself from radiation damage
When DNA is hit with ultraviolet light, it can lose excess energy from radiation by ejecting the core of a hydrogen atom — a single proton — to keep other chemical bonds in the system from breaking. To gain insight into this process, researchers used X-ray laser pulses from the Linac Coherent Light Source (LCLS) at the Department of Energy’s SLAC National Accelerator Laboratory to investigate how energy from light transforms a relatively simple molecule, 2-thiopyridone. Ref. Source 9r.
Computers create recipe for two new magnetic materials
Material scientists have predicted and built two new magnetic materials, atom-by-atom, using high-throughput computational models. The success marks a new era for the large-scale design of new magnetic materials at unprecedented speed. Ref. Source 5y.