  The propagation of high-energy electrons in crystals is in general a
complicated multiple scattering problem. However, along high-symmetry zone axes
the problem can be mapped to the time evolution of a two-dimensional (2D)
molecular system. Each projected atomic column can be approximated by the
potential of a 2D screened hydrogenic atom. When two columns are in close
proximity, their bound states overlap and form analogs to molecular orbitals.
For sub-angstrom electron beams, excitation of anti-symmetric orbitals can
result in the failure of the simple incoherent imaging approximation. As a
result, the standard resolution test and the one-to-one correspondence of
atomic positions of a crystal imaged along a zone-axis with closely spaced
projected columns ("dumbbells") can fail dramatically at finite and realistic
sample thicknesses. This is demonstrated experimentally in high angle annular
dark field scanning transmission electron microscope (HAADF STEM) images of
[211]-oriented Si showing an apparent inter-column spacing of 1.28(+-.09)
Angstroms, over 64% larger than the actual 0.78 Angstrom spacing. Furthermore,
the apparent spacing can be tuned with sample thickness and probe size to
produce a larger, smaller, or even the actual spacing under conditions when the
peaks of two adjacent Si columns should not even have been resolved given the
electron probe size.
