The Solid State Failure Of The Born–Oppenheimer Approximation - A Major Theory Glitch Or A Minor Setback?

   H-atom impacting crystal surface of Germanium to test theory

Let's be forthright, the Born–Oppenheimer approximation is mystifying to those not into computational chemistry or solid-state physics.  Basically it arose from a 1927 paper to explain the gap in mass and time scale between certain atomic nuclei. It has profoundly influenced how chemical physicists think about atoms and molecules to this day.   Thus it has been shocking to learn that Kerstin Krüger of Georg-August University in Göttingen, Germany; her Ph.D. adviser, Oliver Bünermann; and their colleagues a group of researchers at Georg-August University in Gottingen, Germany, recently found at least some interactions - between atoms and solid surfaces-  don't adhere to the theory.  

Specifically, the Gottingen team fired hydrogen atoms at the surface of Germanium (Ge) 111, and found that a large fraction of the atoms were losing a significant portion of their energy.  (See top graphic). Close examination of the collected data showed the H-atoms were impacting the Ge surface hard enough to excite them from the valence band to the conduction band.  However, under the theory behind the Born–Oppenheimer approximation that's not supposed to occur. The electrons are supposed to be able to get out of the way so no such transition happens.  

So toss out the decades -old approximation?  Not on your life.  If not for that approximation the discipline of computational chemistry might never have gotten off the ground.   Instead, to simulate the dynamics of a molecule, researchers would have to solve all the multi-particle time independent Schrodinger equations, i.e.

Where the 'i' subscript denotes each contribution from a multi-particle atom.  Note that the dynamics of all the nuclei and electrons would have to be computed simultaneously.  So no, we can't just chuck the approximation.  What we need is to account for the divergence in this particular experiment. 

To that end, it helps to know Bünermann and colleagues developed a specialized machine for firing H atoms at solid surfaces. With it, they generated H atoms by splitting molecules of hydrogen iodide, forming the atoms into a beam with a specified kinetic energy, and measured the post-collision speed and direction of the scattered atoms.  The results are shown in the figure below (Phys. Today, June, p. 27 ):

The first of the peaks was quantitatively reproduced by the molecular dynamics simulations of Bünermann's collaborators at the University of New Mexico.(Yingqi Wang and her thesis adviser Hua Guo).  That peak is fully consistent with the Born–Oppenheimer approximation.  The problem is the appearance of the 2nd peak which is not reproduced in the simulations at all.  

The researchers were stumped.  They were unable to find a theory to quantitatively account for their observations, but they suspected that strong coupling between the H atoms and substrate electrons may be involved. They’ve repeated the experiment under various conditions—different semiconductors, different crystal surfaces, different H-atom isotopes and kinetic energies, different temperatures—and they obtained roughly the same effect each time. 

What gives?  How could the impacting atoms lose so much initial energy? A clue may be embedded in the diagram below (Phys. Today, p. 27 )  

This has to do with why the energies separate into two peaks.  Hence, because of the computational reconstruction  - which alters distribution of surface atoms - one found the Ge atoms at the surface were not all chemically equivalent.  About half of the atoms with an initial energy of 0.99 eV emerged in the high energy transfer channel. But for an initial energy 6.17 eV the portion jumped to more than 90 %.  It stood to reason that increasing the incoming atoms kinetic energy would speed up the effect.  

If atoms could so easily excite electrons in semiconductors, it shouldn’t take many collisions to generate a detectable electric current.  This has now become a working temporary hypothesis while other semiconductor surfaces are examined in similar experimental modalities.

 Lastly, it's important to point out that the primary team's Ge(111) surface was chosen because it was easier for the adjunct team (Wang and Guo) to handle in their simulations. This is obviously all the more reason to solve the energy disparity issue.  What is needed is a more or less universal method that isn't affected by choice of semiconductor surface.

See Also:

K. Krüger et al., Nat. Chem., 2022, doi:10.1038/s41557-022-01085-x.)